%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRA173-1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 06:34:23 PM UTC 2026
% Result : Unsatisfiable 0.64s 0.83s
% Output : Proof 0.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRA173-1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.15/0.32 % Computer : n016.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 01:04:53 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.64/0.83 % SZS status Unsatisfiable
% 0.64/0.83 % SZS output start Proof
% 0.64/0.83 tff(r_type, type, (
% 0.64/0.83 r: ( $i * $i ) > $o)).
% 0.64/0.83 tff(s_type, type, (
% 0.64/0.83 s: $i > $i)).
% 0.64/0.83 tff(z_type, type, (
% 0.64/0.83 z: $i)).
% 0.64/0.83 tff(b_type, type, (
% 0.64/0.83 b: ( $i * $i ) > $o)).
% 0.64/0.83 tff(inj_0_type, type, (
% 0.64/0.83 inj_0: $i > $i)).
% 0.64/0.83 tff(1,plain,
% 0.64/0.83 ((s(s(z)) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(z)))))) = s(s(z)))),
% 0.64/0.83 inference(commutativity,[status(thm)],[])).
% 0.64/0.83 tff(2,plain,
% 0.64/0.83 ((s(s(s(s(s(s(z)))))) = s(s(z))) <=> (s(s(z)) = s(s(s(s(s(s(z)))))))),
% 0.64/0.83 inference(symmetry,[status(thm)],[1])).
% 0.64/0.83 tff(3,plain,
% 0.64/0.83 ((~(s(s(s(s(s(s(z)))))) = s(s(z)))) <=> (~(s(s(z)) = s(s(s(s(s(s(z))))))))),
% 0.64/0.83 inference(monotonicity,[status(thm)],[2])).
% 0.64/0.83 tff(4,plain,
% 0.64/0.83 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0) <=> ![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 0.64/0.83 inference(rewrite,[status(thm)],[])).
% 0.64/0.83 tff(5,plain,
% 0.64/0.83 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y)) <=> ![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 0.64/0.83 inference(rewrite,[status(thm)],[])).
% 0.64/0.83 tff(6,plain,
% 0.64/0.83 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y)) <=> ![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 0.64/0.83 inference(rewrite,[status(thm)],[])).
% 0.64/0.83 tff(7,axiom,(![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','sinj')).
% 0.64/0.83 tff(8,plain,
% 0.64/0.83 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 0.64/0.83 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.64/0.83 tff(9,plain,(
% 0.64/0.83 ![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 0.64/0.83 inference(skolemize,[status(sab)],[8])).
% 0.64/0.83 tff(10,plain,
% 0.64/0.83 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 0.64/0.83 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.64/0.83 tff(11,plain,
% 0.64/0.83 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 0.64/0.83 inference(modus_ponens,[status(thm)],[10, 4])).
% 0.64/0.83 tff(12,plain,
% 0.64/0.83 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(z)) = z)),
% 0.64/0.83 inference(quant_inst,[status(thm)],[])).
% 0.64/0.83 tff(13,plain,
% 0.64/0.83 (inj_0(s(z)) = z),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[12, 11])).
% 0.64/0.83 tff(14,plain,
% 0.64/0.83 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(z))) = s(z))),
% 0.64/0.83 inference(quant_inst,[status(thm)],[])).
% 0.64/0.83 tff(15,plain,
% 0.64/0.83 (inj_0(s(s(z))) = s(z)),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[14, 11])).
% 0.64/0.83 tff(16,assumption,(s(s(s(s(s(s(z)))))) = s(s(z))), introduced(assumption)).
% 0.64/0.83 tff(17,plain,
% 0.64/0.83 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(s(z)))),
% 0.64/0.83 inference(monotonicity,[status(thm)],[16])).
% 0.64/0.83 tff(18,plain,
% 0.64/0.83 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z))))))),
% 0.64/0.83 inference(quant_inst,[status(thm)],[])).
% 0.64/0.83 tff(19,plain,
% 0.64/0.83 (inj_0(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[18, 11])).
% 0.64/0.83 tff(20,plain,
% 0.64/0.83 (s(s(s(s(s(z))))) = inj_0(s(s(s(s(s(s(z)))))))),
% 0.64/0.83 inference(symmetry,[status(thm)],[19])).
% 0.64/0.83 tff(21,plain,
% 0.64/0.83 (s(s(s(s(s(z))))) = s(z)),
% 0.64/0.83 inference(transitivity,[status(thm)],[20, 17, 15])).
% 0.64/0.83 tff(22,plain,
% 0.64/0.83 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(z))),
% 0.64/0.83 inference(monotonicity,[status(thm)],[21])).
% 0.64/0.83 tff(23,plain,
% 0.64/0.83 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(z)))))) = s(s(s(s(z)))))),
% 0.64/0.83 inference(quant_inst,[status(thm)],[])).
% 0.64/0.83 tff(24,plain,
% 0.64/0.83 (inj_0(s(s(s(s(s(z)))))) = s(s(s(s(z))))),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[23, 11])).
% 0.64/0.83 tff(25,plain,
% 0.64/0.83 (s(s(s(s(z)))) = inj_0(s(s(s(s(s(z))))))),
% 0.64/0.83 inference(symmetry,[status(thm)],[24])).
% 0.64/0.83 tff(26,plain,
% 0.64/0.83 (s(s(s(s(z)))) = z),
% 0.64/0.83 inference(transitivity,[status(thm)],[25, 22, 13])).
% 0.64/0.83 tff(27,plain,
% 0.64/0.83 (^[X: $i] : refl((~(s(X) = z)) <=> (~(s(X) = z)))),
% 0.64/0.83 inference(bind,[status(th)],[])).
% 0.64/0.83 tff(28,plain,
% 0.64/0.83 (![X: $i] : (~(s(X) = z)) <=> ![X: $i] : (~(s(X) = z))),
% 0.64/0.83 inference(quant_intro,[status(thm)],[27])).
% 0.64/0.83 tff(29,plain,
% 0.64/0.83 (![X: $i] : (~(s(X) = z)) <=> ![X: $i] : (~(s(X) = z))),
% 0.64/0.83 inference(rewrite,[status(thm)],[])).
% 0.64/0.83 tff(30,axiom,(![X: $i] : (~(s(X) = z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','snz')).
% 0.64/0.83 tff(31,plain,
% 0.64/0.83 (![X: $i] : (~(s(X) = z))),
% 0.64/0.83 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.64/0.83 tff(32,plain,(
% 0.64/0.83 ![X: $i] : (~(s(X) = z))),
% 0.64/0.83 inference(skolemize,[status(sab)],[31])).
% 0.64/0.83 tff(33,plain,
% 0.64/0.83 (![X: $i] : (~(s(X) = z))),
% 0.64/0.83 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.64/0.83 tff(34,plain,
% 0.64/0.83 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(z)))) = z))),
% 0.64/0.83 inference(quant_inst,[status(thm)],[])).
% 0.64/0.83 tff(35,plain,
% 0.64/0.83 (~(s(s(s(s(z)))) = z)),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[34, 33])).
% 0.64/0.83 tff(36,plain,
% 0.64/0.83 ($false),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[35, 26])).
% 0.64/0.83 tff(37,plain,(~(s(s(s(s(s(s(z)))))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.83 tff(38,plain,
% 0.64/0.83 (~(s(s(z)) = s(s(s(s(s(s(z)))))))),
% 0.64/0.83 inference(modus_ponens,[status(thm)],[37, 3])).
% 0.64/0.83 tff(39,assumption,(r(s(s(z)), s(z))), introduced(assumption)).
% 0.64/0.83 tff(40,assumption,(r(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 0.64/0.83 tff(41,assumption,(r(s(s(z)), s(s(s(s(z)))))), introduced(assumption)).
% 0.64/0.83 tff(42,assumption,(r(z, s(s(s(z))))), introduced(assumption)).
% 0.64/0.83 tff(43,assumption,(r(z, s(s(s(s(z)))))), introduced(assumption)).
% 0.64/0.83 tff(44,plain,
% 0.64/0.83 (^[X0: $i, X2: $i, X1: $i] : refl(((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))) <=> ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))))),
% 0.64/0.83 inference(bind,[status(th)],[])).
% 0.64/0.83 tff(45,plain,
% 0.64/0.83 (![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))) <=> ![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 0.64/0.83 inference(quant_intro,[status(thm)],[44])).
% 0.64/0.83 tff(46,plain,
% 0.64/0.83 (![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))) <=> ![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 0.64/0.83 inference(rewrite,[status(thm)],[])).
% 0.64/0.83 tff(47,plain,
% 0.64/0.83 (^[X0: $i, X2: $i, X1: $i] : rewrite((((~r(X0, X1)) | (~r(X0, X2))) | (~r(X1, X2))) <=> ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))))),
% 0.64/0.83 inference(bind,[status(th)],[])).
% 0.64/0.83 tff(48,plain,
% 0.64/0.83 (![X0: $i, X2: $i, X1: $i] : (((~r(X0, X1)) | (~r(X0, X2))) | (~r(X1, X2))) <=> ![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 0.64/0.83 inference(quant_intro,[status(thm)],[47])).
% 0.64/0.83 tff(49,axiom,(![X0: $i, X2: $i, X1: $i] : (((~r(X0, X1)) | (~r(X0, X2))) | (~r(X1, X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axr')).
% 0.64/0.83 tff(50,plain,
% 0.64/0.83 (![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 0.64/0.83 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.64/0.83 tff(51,plain,
% 0.64/0.83 (![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 0.64/0.83 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.64/0.83 tff(52,plain,(
% 0.64/0.83 ![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 0.64/0.83 inference(skolemize,[status(sab)],[51])).
% 0.64/0.83 tff(53,plain,
% 0.64/0.83 (![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 0.64/0.83 inference(modus_ponens,[status(thm)],[52, 45])).
% 0.64/0.83 tff(54,plain,
% 0.64/0.83 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))),
% 0.64/0.83 inference(rewrite,[status(thm)],[])).
% 0.64/0.83 tff(55,plain,
% 0.64/0.83 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(z)))))))),
% 0.64/0.83 inference(quant_inst,[status(thm)],[])).
% 0.64/0.83 tff(56,plain,
% 0.64/0.83 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(z))))))),
% 0.64/0.83 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.64/0.83 tff(57,plain,
% 0.64/0.83 ($false),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[56, 53, 40, 43, 42])).
% 0.64/0.83 tff(58,plain,((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.83 tff(59,plain,
% 0.64/0.83 (~r(z, s(s(s(s(z)))))),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[58, 42, 40])).
% 0.64/0.83 tff(60,plain,
% 0.64/0.83 ((z = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = z)),
% 0.64/0.83 inference(commutativity,[status(thm)],[])).
% 0.64/0.83 tff(61,plain,
% 0.64/0.83 ((s(s(s(s(z)))) = z) <=> (z = s(s(s(s(z)))))),
% 0.64/0.83 inference(symmetry,[status(thm)],[60])).
% 0.64/0.83 tff(62,plain,
% 0.64/0.83 ((~(s(s(s(s(z)))) = z)) <=> (~(z = s(s(s(s(z))))))),
% 0.64/0.83 inference(monotonicity,[status(thm)],[61])).
% 0.64/0.83 tff(63,plain,
% 0.64/0.83 (~(z = s(s(s(s(z)))))),
% 0.64/0.83 inference(modus_ponens,[status(thm)],[35, 62])).
% 0.64/0.83 tff(64,plain,
% 0.64/0.83 (^[Y: $i, X: $i] : refl(((X = Y) | b(X, Y) | r(X, Y)) <=> ((X = Y) | b(X, Y) | r(X, Y)))),
% 0.64/0.83 inference(bind,[status(th)],[])).
% 0.64/0.83 tff(65,plain,
% 0.64/0.83 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.64/0.83 inference(quant_intro,[status(thm)],[64])).
% 0.64/0.83 tff(66,plain,
% 0.64/0.83 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.64/0.83 inference(rewrite,[status(thm)],[])).
% 0.64/0.83 tff(67,plain,
% 0.64/0.83 (^[Y: $i, X: $i] : rewrite((((X = Y) | r(X, Y)) | b(X, Y)) <=> ((X = Y) | b(X, Y) | r(X, Y)))),
% 0.64/0.83 inference(bind,[status(th)],[])).
% 0.64/0.83 tff(68,plain,
% 0.64/0.83 (![Y: $i, X: $i] : (((X = Y) | r(X, Y)) | b(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.64/0.83 inference(quant_intro,[status(thm)],[67])).
% 0.64/0.83 tff(69,axiom,(![Y: $i, X: $i] : (((X = Y) | r(X, Y)) | b(X, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rb')).
% 0.64/0.83 tff(70,plain,
% 0.64/0.83 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.64/0.83 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.64/0.83 tff(71,plain,
% 0.64/0.83 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.64/0.83 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.64/0.83 tff(72,plain,(
% 0.64/0.83 ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.64/0.83 inference(skolemize,[status(sab)],[71])).
% 0.64/0.83 tff(73,plain,
% 0.64/0.83 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.64/0.83 inference(modus_ponens,[status(thm)],[72, 65])).
% 0.64/0.83 tff(74,plain,
% 0.64/0.83 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(z))))) | b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(z))))) | b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z))))))),
% 0.64/0.83 inference(rewrite,[status(thm)],[])).
% 0.64/0.83 tff(75,plain,
% 0.64/0.83 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(z))))) | b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z))))))),
% 0.64/0.83 inference(quant_inst,[status(thm)],[])).
% 0.64/0.83 tff(76,plain,
% 0.64/0.83 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(z))))) | b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z)))))),
% 0.64/0.83 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.64/0.83 tff(77,plain,
% 0.64/0.83 ((z = s(s(s(s(z))))) | b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z)))))),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[76, 73])).
% 0.64/0.83 tff(78,plain,
% 0.64/0.83 (b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z)))))),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[77, 63])).
% 0.64/0.83 tff(79,plain,
% 0.64/0.83 (b(z, s(s(s(s(z)))))),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[78, 59])).
% 0.64/0.83 tff(80,assumption,(r(s(s(s(s(z)))), z)), introduced(assumption)).
% 0.64/0.83 tff(81,plain,
% 0.64/0.83 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 0.64/0.83 inference(rewrite,[status(thm)],[])).
% 0.64/0.83 tff(82,plain,
% 0.64/0.83 (((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 0.64/0.83 inference(rewrite,[status(thm)],[])).
% 0.64/0.83 tff(83,plain,
% 0.64/0.83 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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)))), z))))),
% 0.64/0.83 inference(monotonicity,[status(thm)],[82])).
% 0.64/0.83 tff(84,plain,
% 0.64/0.83 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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)))), z)))),
% 0.64/0.83 inference(transitivity,[status(thm)],[83, 81])).
% 0.64/0.83 tff(85,plain,
% 0.64/0.83 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 0.64/0.83 inference(quant_inst,[status(thm)],[])).
% 0.64/0.83 tff(86,plain,
% 0.64/0.83 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z))),
% 0.64/0.83 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.64/0.83 tff(87,plain,
% 0.64/0.83 ($false),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[86, 53, 40, 80, 42])).
% 0.64/0.83 tff(88,plain,((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.83 tff(89,plain,
% 0.64/0.83 (~r(z, s(s(s(z))))),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[88, 80, 40])).
% 0.64/0.83 tff(90,assumption,(z = s(s(s(z)))), introduced(assumption)).
% 0.64/0.83 tff(91,plain,
% 0.64/0.83 (s(s(s(z))) = z),
% 0.64/0.83 inference(symmetry,[status(thm)],[90])).
% 0.64/0.83 tff(92,plain,
% 0.64/0.83 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(z))) = z))),
% 0.64/0.83 inference(quant_inst,[status(thm)],[])).
% 0.64/0.83 tff(93,plain,
% 0.64/0.83 (~(s(s(s(z))) = z)),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[92, 33])).
% 0.64/0.83 tff(94,plain,
% 0.64/0.83 ($false),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[93, 91])).
% 0.64/0.83 tff(95,plain,(~(z = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.83 tff(96,assumption,(~b(z, s(s(s(z))))), introduced(assumption)).
% 0.64/0.83 tff(97,assumption,(~r(z, s(s(s(z))))), introduced(assumption)).
% 0.64/0.83 tff(98,plain,
% 0.64/0.83 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z)))))),
% 0.64/0.83 inference(rewrite,[status(thm)],[])).
% 0.64/0.83 tff(99,plain,
% 0.64/0.83 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z)))))),
% 0.64/0.83 inference(quant_inst,[status(thm)],[])).
% 0.64/0.83 tff(100,plain,
% 0.64/0.83 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z))))),
% 0.64/0.83 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.64/0.83 tff(101,plain,
% 0.64/0.83 ($false),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[100, 73, 97, 96, 95])).
% 0.64/0.83 tff(102,plain,(r(z, s(s(s(z)))) | b(z, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.83 tff(103,plain,
% 0.64/0.83 (b(z, s(s(s(z))))),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[102, 89])).
% 0.64/0.83 tff(104,assumption,(r(s(s(s(z))), z)), introduced(assumption)).
% 0.64/0.83 tff(105,plain,
% 0.64/0.83 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 0.64/0.83 inference(rewrite,[status(thm)],[])).
% 0.64/0.83 tff(106,plain,
% 0.64/0.83 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 0.64/0.83 inference(quant_inst,[status(thm)],[])).
% 0.64/0.83 tff(107,plain,
% 0.64/0.83 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 0.64/0.83 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.64/0.83 tff(108,plain,
% 0.64/0.83 ($false),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[107, 53, 40, 104, 80])).
% 0.64/0.83 tff(109,plain,((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.83 tff(110,plain,
% 0.64/0.83 (~r(s(s(s(z))), z)),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[109, 80, 40])).
% 0.64/0.83 tff(111,assumption,(~b(s(s(s(z))), z)), introduced(assumption)).
% 0.64/0.83 tff(112,assumption,(~r(s(s(s(z))), z)), introduced(assumption)).
% 0.64/0.83 tff(113,plain,
% 0.64/0.83 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = z) | b(s(s(s(z))), z) | r(s(s(s(z))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = z) | b(s(s(s(z))), z) | r(s(s(s(z))), z))),
% 0.64/0.83 inference(rewrite,[status(thm)],[])).
% 0.64/0.83 tff(114,plain,
% 0.64/0.83 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = z) | b(s(s(s(z))), z) | r(s(s(s(z))), z))),
% 0.64/0.83 inference(quant_inst,[status(thm)],[])).
% 0.64/0.83 tff(115,plain,
% 0.64/0.83 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = z) | b(s(s(s(z))), z) | r(s(s(s(z))), z)),
% 0.64/0.83 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.64/0.83 tff(116,plain,
% 0.64/0.83 ($false),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[115, 73, 93, 112, 111])).
% 0.64/0.83 tff(117,plain,(b(s(s(s(z))), z) | r(s(s(s(z))), z)), inference(lemma,lemma(discharge,[]))).
% 0.64/0.83 tff(118,plain,
% 0.64/0.83 (b(s(s(s(z))), z)),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[117, 110])).
% 0.64/0.83 tff(119,assumption,(r(s(s(z)), s(s(s(z))))), introduced(assumption)).
% 0.64/0.83 tff(120,plain,
% 0.64/0.83 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 0.64/0.83 inference(rewrite,[status(thm)],[])).
% 0.64/0.83 tff(121,plain,
% 0.64/0.83 (((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 0.64/0.83 inference(rewrite,[status(thm)],[])).
% 0.64/0.83 tff(122,plain,
% 0.64/0.83 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 0.64/0.83 inference(monotonicity,[status(thm)],[121])).
% 0.64/0.83 tff(123,plain,
% 0.64/0.83 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 0.64/0.83 inference(transitivity,[status(thm)],[122, 120])).
% 0.64/0.83 tff(124,plain,
% 0.64/0.83 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 0.64/0.83 inference(quant_inst,[status(thm)],[])).
% 0.64/0.83 tff(125,plain,
% 0.64/0.83 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 0.64/0.83 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.64/0.83 tff(126,plain,
% 0.64/0.83 ($false),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[125, 53, 40, 119, 41])).
% 0.64/0.83 tff(127,plain,((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.83 tff(128,plain,
% 0.64/0.83 (~r(s(s(z)), s(s(s(z))))),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[127, 41, 40])).
% 0.64/0.83 tff(129,assumption,(s(s(z)) = s(s(s(z)))), introduced(assumption)).
% 0.64/0.83 tff(130,plain,
% 0.64/0.83 (inj_0(s(s(z))) = inj_0(s(s(s(z))))),
% 0.64/0.83 inference(monotonicity,[status(thm)],[129])).
% 0.64/0.83 tff(131,plain,
% 0.64/0.83 (inj_0(s(s(s(z)))) = inj_0(s(s(z)))),
% 0.64/0.83 inference(symmetry,[status(thm)],[130])).
% 0.64/0.83 tff(132,plain,
% 0.64/0.83 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(z)))) = s(s(z)))),
% 0.64/0.83 inference(quant_inst,[status(thm)],[])).
% 0.64/0.83 tff(133,plain,
% 0.64/0.83 (inj_0(s(s(s(z)))) = s(s(z))),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[132, 11])).
% 0.64/0.83 tff(134,plain,
% 0.64/0.83 (s(s(z)) = inj_0(s(s(s(z))))),
% 0.64/0.83 inference(symmetry,[status(thm)],[133])).
% 0.64/0.83 tff(135,plain,
% 0.64/0.83 (s(s(s(z))) = s(s(z))),
% 0.64/0.83 inference(symmetry,[status(thm)],[129])).
% 0.64/0.83 tff(136,plain,
% 0.64/0.83 (s(s(s(z))) = s(z)),
% 0.64/0.83 inference(transitivity,[status(thm)],[135, 134, 131, 15])).
% 0.64/0.83 tff(137,assumption,(s(s(s(z))) = s(z)), introduced(assumption)).
% 0.64/0.83 tff(138,plain,
% 0.64/0.83 (inj_0(s(s(s(z)))) = inj_0(s(z))),
% 0.64/0.83 inference(monotonicity,[status(thm)],[137])).
% 0.64/0.83 tff(139,plain,
% 0.64/0.83 (s(s(z)) = z),
% 0.64/0.83 inference(transitivity,[status(thm)],[134, 138, 13])).
% 0.64/0.83 tff(140,plain,
% 0.64/0.84 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(z)) = z))),
% 0.64/0.84 inference(quant_inst,[status(thm)],[])).
% 0.64/0.84 tff(141,plain,
% 0.64/0.84 (~(s(s(z)) = z)),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[140, 33])).
% 0.64/0.84 tff(142,plain,
% 0.64/0.84 ($false),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[141, 139])).
% 0.64/0.84 tff(143,plain,(~(s(s(s(z))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.84 tff(144,plain,
% 0.64/0.84 ($false),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[143, 136])).
% 0.64/0.84 tff(145,plain,(~(s(s(z)) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.84 tff(146,plain,
% 0.64/0.84 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z)))))),
% 0.64/0.84 inference(rewrite,[status(thm)],[])).
% 0.64/0.84 tff(147,plain,
% 0.64/0.84 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z)))))),
% 0.64/0.84 inference(quant_inst,[status(thm)],[])).
% 0.64/0.84 tff(148,plain,
% 0.64/0.84 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z))))),
% 0.64/0.84 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.64/0.84 tff(149,plain,
% 0.64/0.84 ((s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z))))),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[148, 73])).
% 0.64/0.84 tff(150,plain,
% 0.64/0.84 (b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z))))),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[149, 145])).
% 0.64/0.84 tff(151,plain,
% 0.64/0.84 (b(s(s(z)), s(s(s(z))))),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[150, 128])).
% 0.64/0.84 tff(152,assumption,(r(s(s(z)), z)), introduced(assumption)).
% 0.64/0.84 tff(153,plain,
% 0.64/0.84 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 0.64/0.84 inference(rewrite,[status(thm)],[])).
% 0.64/0.84 tff(154,plain,
% 0.64/0.84 (((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 0.64/0.84 inference(rewrite,[status(thm)],[])).
% 0.64/0.84 tff(155,plain,
% 0.64/0.84 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))))),
% 0.64/0.84 inference(monotonicity,[status(thm)],[154])).
% 0.64/0.84 tff(156,plain,
% 0.64/0.84 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 0.64/0.84 inference(transitivity,[status(thm)],[155, 153])).
% 0.64/0.84 tff(157,plain,
% 0.64/0.84 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 0.64/0.84 inference(quant_inst,[status(thm)],[])).
% 0.64/0.84 tff(158,plain,
% 0.64/0.84 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))),
% 0.64/0.84 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.64/0.84 tff(159,plain,
% 0.64/0.84 ($false),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[158, 53, 152, 80, 41])).
% 0.64/0.84 tff(160,plain,((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.84 tff(161,plain,
% 0.64/0.84 (~r(s(s(z)), z)),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[160, 41, 80])).
% 0.64/0.84 tff(162,plain,
% 0.64/0.84 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = z) | b(s(s(z)), z) | r(s(s(z)), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = z) | b(s(s(z)), z) | r(s(s(z)), z))),
% 0.64/0.84 inference(rewrite,[status(thm)],[])).
% 0.64/0.84 tff(163,plain,
% 0.64/0.84 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = z) | b(s(s(z)), z) | r(s(s(z)), z))),
% 0.64/0.84 inference(quant_inst,[status(thm)],[])).
% 0.64/0.84 tff(164,plain,
% 0.64/0.84 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = z) | b(s(s(z)), z) | r(s(s(z)), z)),
% 0.64/0.84 inference(modus_ponens,[status(thm)],[163, 162])).
% 0.64/0.84 tff(165,plain,
% 0.64/0.84 (b(s(s(z)), z) | r(s(s(z)), z)),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[164, 73, 141])).
% 0.64/0.84 tff(166,plain,
% 0.64/0.84 (b(s(s(z)), z)),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[165, 161])).
% 0.64/0.84 tff(167,assumption,(b(z, s(s(s(z))))), introduced(assumption)).
% 0.64/0.84 tff(168,assumption,(b(s(s(s(z))), z)), introduced(assumption)).
% 0.64/0.84 tff(169,assumption,(b(s(s(z)), s(s(s(z))))), introduced(assumption)).
% 0.64/0.84 tff(170,assumption,(b(s(s(z)), z)), introduced(assumption)).
% 0.64/0.84 tff(171,plain,
% 0.64/0.84 (^[X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : refl(((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) <=> ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))))),
% 0.64/0.84 inference(bind,[status(th)],[])).
% 0.64/0.84 tff(172,plain,
% 0.64/0.84 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) <=> ![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 0.64/0.84 inference(quant_intro,[status(thm)],[171])).
% 0.64/0.84 tff(173,plain,
% 0.64/0.84 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) <=> ![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 0.64/0.84 inference(rewrite,[status(thm)],[])).
% 0.64/0.84 tff(174,plain,
% 0.64/0.84 (^[X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) <=> ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))), (((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) <=> (((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X2, X3))))), rewrite((((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X2, X3))) <=> ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))), (((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) <=> ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))))), ((((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) | (~b(X0, X4))) <=> (((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X0, X4))))), rewrite((((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X0, X4))) <=> ((~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))), ((((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) | (~b(X0, X4))) <=> ((~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))))), (((((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) | (~b(X0, X4))) | (~b(X1, X4))) <=> (((~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X1, X4))))), rewrite((((~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X1, X4))) <=> ((~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))), (((((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) | (~b(X0, X4))) | (~b(X1, X4))) <=> ((~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))))), ((((((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) | (~b(X0, X4))) | (~b(X1, X4))) | (~b(X3, X4))) <=> (((~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X3, X4))))), rewrite((((~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X3, X4))) <=> ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))), ((((((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) | (~b(X0, X4))) | (~b(X1, X4))) | (~b(X3, X4))) <=> ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))))),
% 0.64/0.84 inference(bind,[status(th)],[])).
% 0.64/0.84 tff(175,plain,
% 0.64/0.84 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : (((((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) | (~b(X0, X4))) | (~b(X1, X4))) | (~b(X3, X4))) <=> ![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 0.64/0.84 inference(quant_intro,[status(thm)],[174])).
% 0.64/0.84 tff(176,axiom,(![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : (((((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) | (~b(X0, X4))) | (~b(X1, X4))) | (~b(X3, X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axb')).
% 0.64/0.84 tff(177,plain,
% 0.64/0.84 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 0.64/0.84 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.64/0.84 tff(178,plain,
% 0.64/0.84 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 0.64/0.84 inference(modus_ponens,[status(thm)],[177, 173])).
% 0.64/0.84 tff(179,plain,(
% 0.64/0.84 ![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 0.64/0.84 inference(skolemize,[status(sab)],[178])).
% 0.64/0.84 tff(180,plain,
% 0.64/0.84 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 0.64/0.84 inference(modus_ponens,[status(thm)],[179, 172])).
% 0.64/0.84 tff(181,plain,
% 0.64/0.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)))),
% 0.64/0.84 inference(rewrite,[status(thm)],[])).
% 0.64/0.84 tff(182,plain,
% 0.64/0.84 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)))),
% 0.64/0.84 inference(rewrite,[status(thm)],[])).
% 0.64/0.84 tff(183,plain,
% 0.64/0.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z))))),
% 0.64/0.84 inference(monotonicity,[status(thm)],[182])).
% 0.64/0.84 tff(184,plain,
% 0.64/0.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)))),
% 0.64/0.84 inference(transitivity,[status(thm)],[183, 181])).
% 0.64/0.84 tff(185,plain,
% 0.64/0.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 0.64/0.84 inference(quant_inst,[status(thm)],[])).
% 0.64/0.84 tff(186,plain,
% 0.64/0.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z))),
% 0.64/0.84 inference(modus_ponens,[status(thm)],[185, 184])).
% 0.64/0.84 tff(187,plain,
% 0.64/0.84 ($false),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[186, 180, 170, 169, 168, 167])).
% 0.64/0.84 tff(188,plain,((~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.84 tff(189,plain,
% 0.64/0.84 ($false),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[188, 166, 151, 118, 103])).
% 0.64/0.84 tff(190,plain,((~r(s(s(z)), s(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,[]))).
% 0.64/0.84 tff(191,plain,
% 0.64/0.84 (~r(s(s(z)), s(s(s(s(z)))))),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[190, 80, 40])).
% 0.64/0.84 tff(192,assumption,(s(s(z)) = s(s(s(s(z))))), introduced(assumption)).
% 0.64/0.84 tff(193,plain,
% 0.64/0.84 (s(s(s(s(z)))) = s(s(z))),
% 0.64/0.84 inference(symmetry,[status(thm)],[192])).
% 0.64/0.84 tff(194,assumption,(s(s(s(s(z)))) = s(s(z))), introduced(assumption)).
% 0.64/0.84 tff(195,plain,
% 0.64/0.84 (s(s(z)) = s(s(s(s(z))))),
% 0.64/0.84 inference(symmetry,[status(thm)],[194])).
% 0.64/0.84 tff(196,plain,
% 0.64/0.84 (inj_0(s(s(z))) = inj_0(s(s(s(s(z)))))),
% 0.64/0.84 inference(monotonicity,[status(thm)],[195])).
% 0.64/0.84 tff(197,plain,
% 0.64/0.84 (inj_0(s(s(s(s(z))))) = inj_0(s(s(z)))),
% 0.64/0.84 inference(symmetry,[status(thm)],[196])).
% 0.64/0.84 tff(198,plain,
% 0.64/0.84 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(z))))) = s(s(s(z))))),
% 0.64/0.84 inference(quant_inst,[status(thm)],[])).
% 0.64/0.84 tff(199,plain,
% 0.64/0.84 (inj_0(s(s(s(s(z))))) = s(s(s(z)))),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[198, 11])).
% 0.64/0.84 tff(200,plain,
% 0.64/0.84 (s(s(s(z))) = inj_0(s(s(s(s(z)))))),
% 0.64/0.84 inference(symmetry,[status(thm)],[199])).
% 0.64/0.84 tff(201,plain,
% 0.64/0.84 (s(s(s(z))) = s(z)),
% 0.64/0.84 inference(transitivity,[status(thm)],[200, 197, 15])).
% 0.64/0.84 tff(202,plain,
% 0.64/0.84 ($false),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[143, 201])).
% 0.64/0.84 tff(203,plain,(~(s(s(s(s(z)))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.84 tff(204,plain,
% 0.64/0.84 ($false),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[203, 193])).
% 0.64/0.84 tff(205,plain,(~(s(s(z)) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.84 tff(206,assumption,(~b(s(s(z)), s(s(s(s(z)))))), introduced(assumption)).
% 0.64/0.84 tff(207,assumption,(~r(s(s(z)), s(s(s(s(z)))))), introduced(assumption)).
% 0.64/0.84 tff(208,plain,
% 0.64/0.84 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z))))))),
% 0.64/0.84 inference(rewrite,[status(thm)],[])).
% 0.64/0.84 tff(209,plain,
% 0.64/0.84 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z))))))),
% 0.64/0.84 inference(quant_inst,[status(thm)],[])).
% 0.64/0.84 tff(210,plain,
% 0.64/0.84 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z)))))),
% 0.64/0.84 inference(modus_ponens,[status(thm)],[209, 208])).
% 0.64/0.84 tff(211,plain,
% 0.64/0.84 ($false),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[210, 73, 207, 206, 205])).
% 0.64/0.84 tff(212,plain,(r(s(s(z)), s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.84 tff(213,plain,
% 0.64/0.84 (b(s(s(z)), s(s(s(s(z)))))),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[212, 191])).
% 0.64/0.84 tff(214,plain,
% 0.64/0.84 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 0.64/0.84 inference(rewrite,[status(thm)],[])).
% 0.64/0.84 tff(215,plain,
% 0.64/0.84 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 0.64/0.84 inference(quant_inst,[status(thm)],[])).
% 0.64/0.84 tff(216,plain,
% 0.64/0.84 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z))))),
% 0.64/0.84 inference(modus_ponens,[status(thm)],[215, 214])).
% 0.64/0.84 tff(217,plain,
% 0.64/0.84 (~r(s(s(s(s(z)))), s(s(z)))),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[216, 53, 152, 80])).
% 0.64/0.84 tff(218,plain,
% 0.64/0.84 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z))))),
% 0.64/0.84 inference(rewrite,[status(thm)],[])).
% 0.64/0.84 tff(219,plain,
% 0.64/0.84 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z))))),
% 0.64/0.84 inference(quant_inst,[status(thm)],[])).
% 0.64/0.84 tff(220,plain,
% 0.64/0.84 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z)))),
% 0.64/0.84 inference(modus_ponens,[status(thm)],[219, 218])).
% 0.64/0.84 tff(221,plain,
% 0.64/0.84 (b(s(s(s(s(z)))), s(s(z)))),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[220, 73, 203, 217])).
% 0.64/0.84 tff(222,assumption,(b(s(s(s(s(z)))), s(s(z)))), introduced(assumption)).
% 0.64/0.84 tff(223,assumption,(b(s(s(z)), s(s(s(s(z)))))), introduced(assumption)).
% 0.64/0.84 tff(224,assumption,(b(s(z), s(s(s(s(z)))))), introduced(assumption)).
% 0.64/0.84 tff(225,assumption,(b(s(s(z)), s(z))), introduced(assumption)).
% 0.64/0.84 tff(226,plain,
% 0.64/0.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 0.64/0.84 inference(rewrite,[status(thm)],[])).
% 0.64/0.84 tff(227,plain,
% 0.64/0.84 (((~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(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z)))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 0.64/0.84 inference(rewrite,[status(thm)],[])).
% 0.64/0.84 tff(228,plain,
% 0.64/0.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))))),
% 0.64/0.84 inference(monotonicity,[status(thm)],[227])).
% 0.64/0.84 tff(229,plain,
% 0.64/0.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 0.64/0.84 inference(transitivity,[status(thm)],[228, 226])).
% 0.64/0.84 tff(230,plain,
% 0.64/0.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))))),
% 0.64/0.84 inference(quant_inst,[status(thm)],[])).
% 0.64/0.84 tff(231,plain,
% 0.64/0.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))),
% 0.64/0.84 inference(modus_ponens,[status(thm)],[230, 229])).
% 0.64/0.84 tff(232,plain,
% 0.64/0.84 ($false),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[231, 180, 225, 224, 222, 223])).
% 0.64/0.84 tff(233,plain,((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.84 tff(234,plain,
% 0.64/0.84 (~b(s(s(z)), s(z))),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[233, 224, 223, 222])).
% 0.64/0.84 tff(235,assumption,(~r(s(s(z)), s(z))), introduced(assumption)).
% 0.64/0.84 tff(236,assumption,(~b(s(s(z)), s(z))), introduced(assumption)).
% 0.64/0.84 tff(237,plain,
% 0.64/0.84 ((s(s(z)) = s(z)) <=> (s(z) = s(s(z)))),
% 0.64/0.84 inference(commutativity,[status(thm)],[])).
% 0.64/0.84 tff(238,plain,
% 0.64/0.84 ((s(z) = s(s(z))) <=> (s(s(z)) = s(z))),
% 0.64/0.84 inference(symmetry,[status(thm)],[237])).
% 0.64/0.84 tff(239,plain,
% 0.64/0.84 ((~(s(z) = s(s(z)))) <=> (~(s(s(z)) = s(z)))),
% 0.64/0.84 inference(monotonicity,[status(thm)],[238])).
% 0.64/0.84 tff(240,assumption,(s(z) = s(s(z))), introduced(assumption)).
% 0.64/0.84 tff(241,plain,
% 0.64/0.84 (inj_0(s(z)) = inj_0(s(s(z)))),
% 0.64/0.84 inference(monotonicity,[status(thm)],[240])).
% 0.64/0.84 tff(242,plain,
% 0.64/0.84 (inj_0(s(s(z))) = inj_0(s(z))),
% 0.64/0.84 inference(symmetry,[status(thm)],[241])).
% 0.64/0.84 tff(243,plain,
% 0.64/0.84 (s(z) = inj_0(s(s(z)))),
% 0.64/0.84 inference(symmetry,[status(thm)],[15])).
% 0.64/0.84 tff(244,plain,
% 0.64/0.84 (s(s(z)) = s(z)),
% 0.64/0.84 inference(symmetry,[status(thm)],[240])).
% 0.64/0.84 tff(245,plain,
% 0.64/0.84 (s(s(z)) = z),
% 0.64/0.84 inference(transitivity,[status(thm)],[244, 243, 242, 13])).
% 0.64/0.84 tff(246,plain,
% 0.64/0.84 ($false),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[141, 245])).
% 0.64/0.84 tff(247,plain,(~(s(z) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.84 tff(248,plain,
% 0.64/0.84 (~(s(s(z)) = s(z))),
% 0.64/0.84 inference(modus_ponens,[status(thm)],[247, 239])).
% 0.64/0.84 tff(249,plain,
% 0.64/0.84 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z)))),
% 0.64/0.84 inference(rewrite,[status(thm)],[])).
% 0.64/0.84 tff(250,plain,
% 0.64/0.84 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z)))),
% 0.64/0.84 inference(quant_inst,[status(thm)],[])).
% 0.64/0.84 tff(251,plain,
% 0.64/0.84 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z))),
% 0.64/0.84 inference(modus_ponens,[status(thm)],[250, 249])).
% 0.64/0.84 tff(252,plain,
% 0.64/0.84 ($false),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[251, 73, 248, 236, 235])).
% 0.64/0.84 tff(253,plain,(r(s(s(z)), s(z)) | b(s(s(z)), s(z))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.84 tff(254,plain,
% 0.64/0.84 (r(s(s(z)), s(z))),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[253, 234])).
% 0.64/0.84 tff(255,assumption,(r(s(z), z)), introduced(assumption)).
% 0.64/0.84 tff(256,plain,
% 0.64/0.84 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))),
% 0.64/0.84 inference(rewrite,[status(thm)],[])).
% 0.64/0.84 tff(257,plain,
% 0.64/0.84 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))),
% 0.64/0.84 inference(quant_inst,[status(thm)],[])).
% 0.64/0.84 tff(258,plain,
% 0.64/0.84 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z)))),
% 0.64/0.84 inference(modus_ponens,[status(thm)],[257, 256])).
% 0.64/0.84 tff(259,plain,
% 0.64/0.84 ($false),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[258, 53, 152, 255, 39])).
% 0.64/0.84 tff(260,plain,((~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.84 tff(261,plain,
% 0.64/0.84 (~r(s(z), z)),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[260, 254, 152])).
% 0.64/0.84 tff(262,plain,
% 0.64/0.84 ((~![X: $i] : (~(s(X) = z))) | (~(s(z) = z))),
% 0.64/0.84 inference(quant_inst,[status(thm)],[])).
% 0.64/0.84 tff(263,plain,
% 0.64/0.84 (~(s(z) = z)),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[262, 33])).
% 0.64/0.84 tff(264,plain,
% 0.64/0.84 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = z) | b(s(z), z) | r(s(z), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = z) | b(s(z), z) | r(s(z), z))),
% 0.64/0.84 inference(rewrite,[status(thm)],[])).
% 0.64/0.84 tff(265,plain,
% 0.64/0.84 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = z) | b(s(z), z) | r(s(z), z))),
% 0.64/0.84 inference(quant_inst,[status(thm)],[])).
% 0.64/0.84 tff(266,plain,
% 0.64/0.84 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = z) | b(s(z), z) | r(s(z), z)),
% 0.64/0.84 inference(modus_ponens,[status(thm)],[265, 264])).
% 0.64/0.84 tff(267,plain,
% 0.64/0.84 (b(s(z), z) | r(s(z), z)),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[266, 73, 263])).
% 0.64/0.84 tff(268,plain,
% 0.64/0.84 (b(s(z), z)),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[267, 261])).
% 0.64/0.84 tff(269,assumption,(r(z, s(z))), introduced(assumption)).
% 0.64/0.84 tff(270,plain,
% 0.64/0.84 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), z)))),
% 0.64/0.84 inference(rewrite,[status(thm)],[])).
% 0.64/0.84 tff(271,plain,
% 0.64/0.84 (((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z))) <=> ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), z)))),
% 0.64/0.84 inference(rewrite,[status(thm)],[])).
% 0.64/0.84 tff(272,plain,
% 0.64/0.84 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), z))))),
% 0.64/0.84 inference(monotonicity,[status(thm)],[271])).
% 0.64/0.84 tff(273,plain,
% 0.64/0.84 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), z)))),
% 0.64/0.84 inference(transitivity,[status(thm)],[272, 270])).
% 0.64/0.84 tff(274,plain,
% 0.64/0.84 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))),
% 0.64/0.84 inference(quant_inst,[status(thm)],[])).
% 0.64/0.84 tff(275,plain,
% 0.64/0.84 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), z))),
% 0.64/0.84 inference(modus_ponens,[status(thm)],[274, 273])).
% 0.64/0.84 tff(276,plain,
% 0.64/0.84 ($false),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[275, 53, 269, 152, 39])).
% 0.64/0.84 tff(277,plain,((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.84 tff(278,plain,
% 0.64/0.84 (~r(z, s(z))),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[277, 254, 152])).
% 0.64/0.84 tff(279,plain,
% 0.64/0.84 ((z = s(z)) <=> (s(z) = z)),
% 0.64/0.84 inference(commutativity,[status(thm)],[])).
% 0.64/0.84 tff(280,plain,
% 0.64/0.84 ((s(z) = z) <=> (z = s(z))),
% 0.64/0.84 inference(symmetry,[status(thm)],[279])).
% 0.64/0.84 tff(281,plain,
% 0.64/0.84 ((~(s(z) = z)) <=> (~(z = s(z)))),
% 0.64/0.84 inference(monotonicity,[status(thm)],[280])).
% 0.64/0.84 tff(282,plain,
% 0.64/0.84 (~(z = s(z))),
% 0.64/0.84 inference(modus_ponens,[status(thm)],[263, 281])).
% 0.64/0.84 tff(283,plain,
% 0.64/0.84 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(z)) | b(z, s(z)) | r(z, s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(z)) | b(z, s(z)) | r(z, s(z)))),
% 0.64/0.84 inference(rewrite,[status(thm)],[])).
% 0.64/0.84 tff(284,plain,
% 0.64/0.84 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(z)) | b(z, s(z)) | r(z, s(z)))),
% 0.64/0.84 inference(quant_inst,[status(thm)],[])).
% 0.64/0.85 tff(285,plain,
% 0.64/0.85 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(z)) | b(z, s(z)) | r(z, s(z))),
% 0.64/0.85 inference(modus_ponens,[status(thm)],[284, 283])).
% 0.64/0.85 tff(286,plain,
% 0.64/0.85 ((z = s(z)) | b(z, s(z)) | r(z, s(z))),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[285, 73])).
% 0.64/0.85 tff(287,plain,
% 0.64/0.85 (b(z, s(z)) | r(z, s(z))),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[286, 282])).
% 0.64/0.85 tff(288,plain,
% 0.64/0.85 (b(z, s(z))),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[287, 278])).
% 0.64/0.85 tff(289,assumption,(b(s(s(s(z))), s(z))), introduced(assumption)).
% 0.64/0.85 tff(290,assumption,(b(s(z), z)), introduced(assumption)).
% 0.64/0.85 tff(291,assumption,(b(z, s(z))), introduced(assumption)).
% 0.64/0.85 tff(292,plain,
% 0.64/0.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(293,plain,
% 0.64/0.85 (((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z)))))) <=> ((~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(294,plain,
% 0.64/0.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z)))))),
% 0.64/0.85 inference(monotonicity,[status(thm)],[293])).
% 0.64/0.85 tff(295,plain,
% 0.64/0.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))))),
% 0.64/0.85 inference(transitivity,[status(thm)],[294, 292])).
% 0.64/0.85 tff(296,plain,
% 0.64/0.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))),
% 0.64/0.85 inference(quant_inst,[status(thm)],[])).
% 0.64/0.85 tff(297,plain,
% 0.64/0.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z)))),
% 0.64/0.85 inference(modus_ponens,[status(thm)],[296, 295])).
% 0.64/0.85 tff(298,plain,
% 0.64/0.85 ($false),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[297, 180, 291, 290, 289, 167])).
% 0.64/0.85 tff(299,plain,((~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,[]))).
% 0.64/0.85 tff(300,plain,
% 0.64/0.85 (~b(s(s(s(z))), s(z))),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[299, 288, 167, 268])).
% 0.64/0.85 tff(301,assumption,(~r(s(s(s(z))), s(z))), introduced(assumption)).
% 0.64/0.85 tff(302,assumption,(~b(s(s(s(z))), s(z))), introduced(assumption)).
% 0.64/0.85 tff(303,plain,
% 0.64/0.85 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z)))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(304,plain,
% 0.64/0.85 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z)))),
% 0.64/0.85 inference(quant_inst,[status(thm)],[])).
% 0.64/0.85 tff(305,plain,
% 0.64/0.85 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z))),
% 0.64/0.85 inference(modus_ponens,[status(thm)],[304, 303])).
% 0.64/0.85 tff(306,plain,
% 0.64/0.85 ($false),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[305, 73, 302, 143, 301])).
% 0.64/0.85 tff(307,plain,(r(s(s(s(z))), s(z)) | b(s(s(s(z))), s(z))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.85 tff(308,plain,
% 0.64/0.85 (r(s(s(s(z))), s(z))),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[307, 300])).
% 0.64/0.85 tff(309,assumption,(r(s(s(s(z))), s(z))), introduced(assumption)).
% 0.64/0.85 tff(310,plain,
% 0.64/0.85 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(311,plain,
% 0.64/0.85 (((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(312,plain,
% 0.64/0.85 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z)))))))),
% 0.64/0.85 inference(monotonicity,[status(thm)],[311])).
% 0.64/0.85 tff(313,plain,
% 0.64/0.85 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 0.64/0.85 inference(transitivity,[status(thm)],[312, 310])).
% 0.64/0.85 tff(314,plain,
% 0.64/0.85 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 0.64/0.85 inference(quant_inst,[status(thm)],[])).
% 0.64/0.85 tff(315,plain,
% 0.64/0.85 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z)))))),
% 0.64/0.85 inference(modus_ponens,[status(thm)],[314, 313])).
% 0.64/0.85 tff(316,plain,
% 0.64/0.85 ($false),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[315, 53, 39, 119, 309])).
% 0.64/0.85 tff(317,plain,((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.85 tff(318,plain,
% 0.64/0.85 (~r(s(s(z)), s(s(s(z))))),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[317, 308, 254])).
% 0.64/0.85 tff(319,plain,
% 0.64/0.85 (b(s(s(z)), s(s(s(z))))),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[150, 318])).
% 0.64/0.85 tff(320,assumption,(s(s(s(z))) = s(s(z))), introduced(assumption)).
% 0.64/0.85 tff(321,plain,
% 0.64/0.85 (s(s(z)) = s(s(s(z)))),
% 0.64/0.85 inference(symmetry,[status(thm)],[320])).
% 0.64/0.85 tff(322,plain,
% 0.64/0.85 ($false),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[145, 321])).
% 0.64/0.85 tff(323,plain,(~(s(s(s(z))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.85 tff(324,plain,
% 0.64/0.85 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(325,plain,
% 0.64/0.85 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 0.64/0.85 inference(quant_inst,[status(thm)],[])).
% 0.64/0.85 tff(326,plain,
% 0.64/0.85 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z))))),
% 0.64/0.85 inference(modus_ponens,[status(thm)],[325, 324])).
% 0.64/0.85 tff(327,plain,
% 0.64/0.85 (~r(s(s(s(z))), s(s(z)))),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[326, 53, 254, 308])).
% 0.64/0.85 tff(328,plain,
% 0.64/0.85 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z))))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(329,plain,
% 0.64/0.85 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z))))),
% 0.64/0.85 inference(quant_inst,[status(thm)],[])).
% 0.64/0.85 tff(330,plain,
% 0.64/0.85 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z)))),
% 0.64/0.85 inference(modus_ponens,[status(thm)],[329, 328])).
% 0.64/0.85 tff(331,plain,
% 0.64/0.85 (b(s(s(s(z))), s(s(z)))),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[330, 73, 327, 323])).
% 0.64/0.85 tff(332,plain,
% 0.64/0.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(333,plain,
% 0.64/0.85 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(334,plain,
% 0.64/0.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))))),
% 0.64/0.85 inference(monotonicity,[status(thm)],[333])).
% 0.64/0.85 tff(335,plain,
% 0.64/0.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 0.64/0.85 inference(transitivity,[status(thm)],[334, 332])).
% 0.64/0.85 tff(336,plain,
% 0.64/0.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))),
% 0.64/0.85 inference(quant_inst,[status(thm)],[])).
% 0.64/0.85 tff(337,plain,
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% 0.64/0.85 inference(modus_ponens,[status(thm)],[336, 335])).
% 0.64/0.85 tff(338,plain,
% 0.64/0.85 (~b(s(z), s(s(z)))),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[337, 180, 224, 222, 223])).
% 0.64/0.85 tff(339,plain,
% 0.64/0.85 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z))))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(340,plain,
% 0.64/0.85 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z))))),
% 0.64/0.85 inference(quant_inst,[status(thm)],[])).
% 0.64/0.85 tff(341,plain,
% 0.64/0.85 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z)))),
% 0.64/0.85 inference(modus_ponens,[status(thm)],[340, 339])).
% 0.64/0.85 tff(342,plain,
% 0.64/0.85 (r(s(z), s(s(z)))),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[341, 73, 247, 338])).
% 0.64/0.85 tff(343,plain,
% 0.64/0.85 ((s(s(s(s(z)))) = s(z)) <=> (s(z) = s(s(s(s(z)))))),
% 0.64/0.85 inference(commutativity,[status(thm)],[])).
% 0.64/0.85 tff(344,plain,
% 0.64/0.85 ((s(z) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(z))),
% 0.64/0.85 inference(symmetry,[status(thm)],[343])).
% 0.64/0.85 tff(345,plain,
% 0.64/0.85 ((~(s(z) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(z)))),
% 0.64/0.85 inference(monotonicity,[status(thm)],[344])).
% 0.64/0.85 tff(346,assumption,(s(z) = s(s(s(s(z))))), introduced(assumption)).
% 0.64/0.85 tff(347,plain,
% 0.64/0.85 (inj_0(s(z)) = inj_0(s(s(s(s(z)))))),
% 0.64/0.85 inference(monotonicity,[status(thm)],[346])).
% 0.64/0.85 tff(348,plain,
% 0.64/0.85 (inj_0(s(s(s(s(z))))) = inj_0(s(z))),
% 0.64/0.85 inference(symmetry,[status(thm)],[347])).
% 0.64/0.85 tff(349,plain,
% 0.64/0.85 (s(s(s(z))) = z),
% 0.64/0.85 inference(transitivity,[status(thm)],[200, 348, 13])).
% 0.64/0.85 tff(350,plain,
% 0.64/0.85 ($false),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[93, 349])).
% 0.64/0.85 tff(351,plain,(~(s(z) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.85 tff(352,plain,
% 0.64/0.85 (~(s(s(s(s(z)))) = s(z))),
% 0.64/0.85 inference(modus_ponens,[status(thm)],[351, 345])).
% 0.64/0.85 tff(353,assumption,(b(s(z), s(s(s(z))))), introduced(assumption)).
% 0.64/0.85 tff(354,plain,
% 0.64/0.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(355,plain,
% 0.64/0.85 (((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z)))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(356,plain,
% 0.64/0.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z)))))))),
% 0.64/0.85 inference(monotonicity,[status(thm)],[355])).
% 0.64/0.85 tff(357,plain,
% 0.64/0.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))))),
% 0.64/0.85 inference(transitivity,[status(thm)],[356, 354])).
% 0.64/0.85 tff(358,plain,
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% 0.64/0.85 inference(quant_inst,[status(thm)],[])).
% 0.64/0.85 tff(359,plain,
% 0.64/0.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z)))))),
% 0.64/0.85 inference(modus_ponens,[status(thm)],[358, 357])).
% 0.64/0.85 tff(360,plain,
% 0.64/0.85 ($false),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[359, 180, 291, 353, 168, 167])).
% 0.64/0.85 tff(361,plain,((~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.85 tff(362,plain,
% 0.64/0.85 (~b(s(z), s(s(s(z))))),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[361, 288, 167, 168])).
% 0.64/0.85 tff(363,assumption,(s(z) = s(s(s(z)))), introduced(assumption)).
% 0.64/0.85 tff(364,plain,
% 0.64/0.85 (s(s(s(z))) = s(z)),
% 0.64/0.85 inference(symmetry,[status(thm)],[363])).
% 0.64/0.85 tff(365,plain,
% 0.64/0.85 ($false),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[143, 364])).
% 0.64/0.85 tff(366,plain,(~(s(z) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.85 tff(367,assumption,(~r(s(z), s(s(s(z))))), introduced(assumption)).
% 0.64/0.85 tff(368,assumption,(~b(s(z), s(s(s(z))))), introduced(assumption)).
% 0.64/0.85 tff(369,plain,
% 0.64/0.85 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z)))))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(370,plain,
% 0.64/0.85 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z)))))),
% 0.64/0.85 inference(quant_inst,[status(thm)],[])).
% 0.64/0.85 tff(371,plain,
% 0.64/0.85 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z))))),
% 0.64/0.85 inference(modus_ponens,[status(thm)],[370, 369])).
% 0.64/0.85 tff(372,plain,
% 0.64/0.85 ($false),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[371, 73, 368, 367, 366])).
% 0.64/0.85 tff(373,plain,(r(s(z), s(s(s(z)))) | b(s(z), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.85 tff(374,plain,
% 0.64/0.85 (r(s(z), s(s(s(z))))),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[373, 362])).
% 0.64/0.85 tff(375,plain,
% 0.64/0.85 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(376,plain,
% 0.64/0.85 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))),
% 0.64/0.85 inference(quant_inst,[status(thm)],[])).
% 0.64/0.85 tff(377,plain,
% 0.64/0.85 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z)))),
% 0.64/0.85 inference(modus_ponens,[status(thm)],[376, 375])).
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% 0.64/0.85 inference(unit_resolution,[status(thm)],[377, 53, 40, 374])).
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% 0.64/0.85 inference(rewrite,[status(thm)],[])).
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% 0.64/0.85 inference(quant_inst,[status(thm)],[])).
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% 0.64/0.85 inference(modus_ponens,[status(thm)],[380, 379])).
% 0.64/0.85 tff(382,plain,
% 0.64/0.85 ((s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z))),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[381, 73, 378])).
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% 0.64/0.85 (b(s(s(s(s(z)))), s(z))),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[382, 352])).
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% 0.64/0.85 tff(385,assumption,(s(s(s(s(s(s(z)))))) = s(s(s(s(z))))), introduced(assumption)).
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% 0.64/0.85 inference(monotonicity,[status(thm)],[385])).
% 0.64/0.85 tff(387,plain,
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% 0.64/0.85 inference(symmetry,[status(thm)],[386])).
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% 0.64/0.85 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(s(z))))))),
% 0.64/0.85 inference(monotonicity,[status(thm)],[388])).
% 0.64/0.85 tff(390,plain,
% 0.64/0.85 (s(s(z)) = s(s(s(s(z))))),
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% 0.64/0.85 (inj_0(s(s(z))) = inj_0(s(s(s(s(z)))))),
% 0.64/0.85 inference(monotonicity,[status(thm)],[390])).
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% 0.64/0.85 inference(symmetry,[status(thm)],[391])).
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% 0.64/0.85 inference(unit_resolution,[status(thm)],[143, 393])).
% 0.64/0.85 tff(395,plain,(~(s(s(s(s(s(s(z)))))) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.85 tff(396,plain,
% 0.64/0.85 (((~![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))))))),
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% 0.64/0.85 inference(modus_ponens,[status(thm)],[397, 396])).
% 0.64/0.85 tff(399,plain,
% 0.64/0.85 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[398, 73, 395, 384])).
% 0.64/0.85 tff(400,assumption,(b(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 0.64/0.85 tff(401,plain,
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% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(402,plain,
% 0.64/0.85 (((~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(z)))), 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(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)))))), s(s(s(s(z)))))))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(403,plain,
% 0.64/0.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(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(z)))))) | (~b(s(s(s(s(s(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 0.64/0.86 inference(monotonicity,[status(thm)],[402])).
% 0.64/0.86 tff(404,plain,
% 0.64/0.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(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(z)))))) | (~b(s(s(s(s(s(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 0.64/0.86 inference(transitivity,[status(thm)],[403, 401])).
% 0.64/0.86 tff(405,plain,
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% 0.64/0.86 inference(quant_inst,[status(thm)],[])).
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% 0.64/0.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 0.64/0.86 inference(modus_ponens,[status(thm)],[405, 404])).
% 0.64/0.86 tff(407,plain,
% 0.64/0.86 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[406, 180, 224, 400, 399])).
% 0.64/0.86 tff(408,assumption,(b(s(s(s(z))), s(s(z)))), introduced(assumption)).
% 0.64/0.86 tff(409,assumption,(b(s(s(s(s(s(s(z)))))), s(s(z)))), introduced(assumption)).
% 0.64/0.86 tff(410,plain,
% 0.64/0.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 0.64/0.86 inference(rewrite,[status(thm)],[])).
% 0.64/0.86 tff(411,plain,
% 0.64/0.86 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 0.64/0.86 inference(rewrite,[status(thm)],[])).
% 0.64/0.86 tff(412,plain,
% 0.64/0.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(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(s(s(s(z)))))), 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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))))),
% 0.64/0.86 inference(monotonicity,[status(thm)],[411])).
% 0.64/0.86 tff(413,plain,
% 0.64/0.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(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(s(s(s(z)))))), 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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 0.64/0.86 inference(transitivity,[status(thm)],[412, 410])).
% 0.64/0.86 tff(414,plain,
% 0.64/0.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(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(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 0.64/0.86 inference(quant_inst,[status(thm)],[])).
% 0.64/0.86 tff(415,plain,
% 0.64/0.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))),
% 0.64/0.86 inference(modus_ponens,[status(thm)],[414, 413])).
% 0.64/0.86 tff(416,plain,
% 0.64/0.86 ($false),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[415, 180, 169, 408, 222, 409, 399])).
% 0.64/0.86 tff(417,plain,((~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.86 tff(418,plain,
% 0.64/0.86 (~b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[417, 384, 408, 222, 169])).
% 0.64/0.86 tff(419,plain,
% 0.64/0.86 (((~![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))))),
% 0.64/0.86 inference(rewrite,[status(thm)],[])).
% 0.64/0.86 tff(420,plain,
% 0.64/0.86 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(s(z))) | b(s(s(s(s(s(s(z)))))), s(s(z))) | r(s(s(s(s(s(s(z)))))), s(s(z))))),
% 0.64/0.86 inference(quant_inst,[status(thm)],[])).
% 0.64/0.86 tff(421,plain,
% 0.64/0.86 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(s(z))) | b(s(s(s(s(s(s(z)))))), s(s(z))) | r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.64/0.86 inference(modus_ponens,[status(thm)],[420, 419])).
% 0.64/0.86 tff(422,plain,
% 0.64/0.86 (r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[421, 73, 37, 418])).
% 0.64/0.86 tff(423,assumption,(r(s(z), s(s(z)))), introduced(assumption)).
% 0.64/0.86 tff(424,plain,
% 0.64/0.86 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 0.64/0.86 inference(rewrite,[status(thm)],[])).
% 0.64/0.86 tff(425,plain,
% 0.64/0.86 (((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(z)))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 0.64/0.86 inference(rewrite,[status(thm)],[])).
% 0.64/0.86 tff(426,plain,
% 0.64/0.86 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(z))))))),
% 0.64/0.86 inference(monotonicity,[status(thm)],[425])).
% 0.64/0.86 tff(427,plain,
% 0.64/0.86 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 0.64/0.86 inference(transitivity,[status(thm)],[426, 424])).
% 0.64/0.86 tff(428,plain,
% 0.64/0.86 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 0.64/0.86 inference(quant_inst,[status(thm)],[])).
% 0.64/0.86 tff(429,plain,
% 0.64/0.86 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(z))))),
% 0.64/0.86 inference(modus_ponens,[status(thm)],[428, 427])).
% 0.64/0.86 tff(430,plain,
% 0.64/0.86 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[429, 53, 423, 422])).
% 0.64/0.86 tff(431,assumption,(s(s(s(s(s(s(z)))))) = s(z)), introduced(assumption)).
% 0.64/0.86 tff(432,plain,
% 0.64/0.86 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(z))),
% 0.64/0.86 inference(monotonicity,[status(thm)],[431])).
% 0.64/0.86 tff(433,plain,
% 0.64/0.86 (s(s(s(s(s(z))))) = z),
% 0.64/0.86 inference(transitivity,[status(thm)],[20, 432, 13])).
% 0.64/0.86 tff(434,plain,
% 0.64/0.86 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(z))))) = z))),
% 0.64/0.86 inference(quant_inst,[status(thm)],[])).
% 0.64/0.86 tff(435,plain,
% 0.64/0.86 (~(s(s(s(s(s(z))))) = z)),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[434, 33])).
% 0.64/0.86 tff(436,plain,
% 0.64/0.86 ($false),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[435, 433])).
% 0.64/0.86 tff(437,plain,(~(s(s(s(s(s(s(z)))))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.86 tff(438,plain,
% 0.64/0.86 (((~![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)))),
% 0.64/0.86 inference(rewrite,[status(thm)],[])).
% 0.64/0.86 tff(439,plain,
% 0.64/0.86 ((~![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)))),
% 0.64/0.86 inference(quant_inst,[status(thm)],[])).
% 0.64/0.86 tff(440,plain,
% 0.64/0.86 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(z)) | b(s(s(s(s(s(s(z)))))), s(z)) | r(s(s(s(s(s(s(z)))))), s(z))),
% 0.64/0.86 inference(modus_ponens,[status(thm)],[439, 438])).
% 0.64/0.86 tff(441,plain,
% 0.64/0.86 ($false),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[440, 73, 437, 430, 407])).
% 0.64/0.86 tff(442,plain,(r(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(z)))), s(z))) | (~r(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.86 tff(443,plain,
% 0.64/0.86 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[442, 224, 383, 342, 331, 222, 319])).
% 0.64/0.86 tff(444,plain,
% 0.64/0.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), 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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 0.64/0.86 inference(rewrite,[status(thm)],[])).
% 0.64/0.86 tff(445,plain,
% 0.64/0.86 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(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(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 0.64/0.86 inference(rewrite,[status(thm)],[])).
% 0.64/0.86 tff(446,plain,
% 0.64/0.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(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(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))))),
% 0.64/0.86 inference(monotonicity,[status(thm)],[445])).
% 0.64/0.86 tff(447,plain,
% 0.64/0.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(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(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 0.64/0.86 inference(transitivity,[status(thm)],[446, 444])).
% 0.64/0.86 tff(448,plain,
% 0.64/0.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(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(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 0.64/0.86 inference(quant_inst,[status(thm)],[])).
% 0.64/0.86 tff(449,plain,
% 0.64/0.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))),
% 0.64/0.86 inference(modus_ponens,[status(thm)],[448, 447])).
% 0.64/0.86 tff(450,plain,
% 0.64/0.86 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[449, 180, 319, 331, 222])).
% 0.64/0.86 tff(451,assumption,(s(s(s(s(z)))) = s(s(s(z)))), introduced(assumption)).
% 0.64/0.86 tff(452,plain,
% 0.64/0.86 (s(s(s(z))) = s(s(s(s(z))))),
% 0.64/0.86 inference(symmetry,[status(thm)],[451])).
% 0.64/0.86 tff(453,plain,
% 0.64/0.86 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(z)))))),
% 0.64/0.86 inference(monotonicity,[status(thm)],[452])).
% 0.64/0.86 tff(454,plain,
% 0.64/0.86 (s(s(z)) = s(s(s(z)))),
% 0.64/0.86 inference(transitivity,[status(thm)],[134, 453, 199])).
% 0.64/0.86 tff(455,plain,
% 0.64/0.86 ($false),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[145, 454])).
% 0.64/0.86 tff(456,plain,(~(s(s(s(s(z)))) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.86 tff(457,plain,
% 0.64/0.86 ((s(s(s(z))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(z))))),
% 0.64/0.86 inference(commutativity,[status(thm)],[])).
% 0.64/0.86 tff(458,assumption,(s(s(s(z))) = s(s(s(s(z))))), introduced(assumption)).
% 0.64/0.86 tff(459,plain,
% 0.64/0.86 (s(s(s(s(z)))) = s(s(s(z)))),
% 0.64/0.86 inference(modus_ponens,[status(thm)],[458, 457])).
% 0.64/0.86 tff(460,assumption,(~(s(s(s(s(z)))) = s(s(s(z))))), introduced(assumption)).
% 0.64/0.86 tff(461,plain,
% 0.64/0.86 ($false),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[460, 459])).
% 0.64/0.86 tff(462,plain,((~(s(s(s(z))) = s(s(s(s(z)))))) | (s(s(s(s(z)))) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.86 tff(463,plain,
% 0.64/0.86 (~(s(s(s(z))) = s(s(s(s(z)))))),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[462, 456])).
% 0.64/0.86 tff(464,plain,
% 0.64/0.86 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z))))))),
% 0.64/0.86 inference(rewrite,[status(thm)],[])).
% 0.64/0.86 tff(465,plain,
% 0.64/0.86 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z))))))),
% 0.64/0.86 inference(quant_inst,[status(thm)],[])).
% 0.64/0.86 tff(466,plain,
% 0.64/0.86 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z)))))),
% 0.64/0.86 inference(modus_ponens,[status(thm)],[465, 464])).
% 0.64/0.86 tff(467,plain,
% 0.64/0.86 ((s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z)))))),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[466, 73])).
% 0.64/0.86 tff(468,plain,
% 0.64/0.86 (b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z)))))),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[467, 463])).
% 0.64/0.86 tff(469,plain,
% 0.64/0.86 (r(s(s(s(z))), s(s(s(s(z)))))),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[468, 450])).
% 0.64/0.86 tff(470,plain,
% 0.64/0.86 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 0.64/0.86 inference(rewrite,[status(thm)],[])).
% 0.64/0.86 tff(471,plain,
% 0.64/0.86 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 0.64/0.86 inference(quant_inst,[status(thm)],[])).
% 0.64/0.86 tff(472,plain,
% 0.64/0.86 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 0.64/0.86 inference(modus_ponens,[status(thm)],[471, 470])).
% 0.64/0.86 tff(473,plain,
% 0.64/0.86 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[472, 53, 469, 443])).
% 0.64/0.86 tff(474,assumption,(s(s(s(s(s(s(z)))))) = s(s(s(z)))), introduced(assumption)).
% 0.64/0.86 tff(475,plain,
% 0.64/0.86 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(s(s(z))))),
% 0.64/0.86 inference(monotonicity,[status(thm)],[474])).
% 0.64/0.86 tff(476,plain,
% 0.64/0.86 (s(s(s(s(s(z))))) = s(s(z))),
% 0.64/0.86 inference(transitivity,[status(thm)],[20, 475, 133])).
% 0.64/0.86 tff(477,assumption,(s(s(s(s(s(z))))) = s(s(z))), introduced(assumption)).
% 0.64/0.86 tff(478,plain,
% 0.64/0.86 (s(s(z)) = s(s(s(s(s(z)))))),
% 0.64/0.86 inference(symmetry,[status(thm)],[477])).
% 0.64/0.86 tff(479,plain,
% 0.64/0.86 (inj_0(s(s(z))) = inj_0(s(s(s(s(s(z))))))),
% 0.64/0.86 inference(monotonicity,[status(thm)],[478])).
% 0.64/0.86 tff(480,plain,
% 0.64/0.86 (s(z) = s(s(s(s(z))))),
% 0.64/0.86 inference(transitivity,[status(thm)],[243, 479, 24])).
% 0.64/0.86 tff(481,plain,
% 0.64/0.86 ($false),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[351, 480])).
% 0.64/0.86 tff(482,plain,(~(s(s(s(s(s(z))))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.86 tff(483,plain,
% 0.64/0.86 ($false),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[482, 476])).
% 0.64/0.86 tff(484,plain,(~(s(s(s(s(s(s(z)))))) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.86 tff(485,plain,
% 0.64/0.86 (((~![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)))))),
% 0.64/0.86 inference(rewrite,[status(thm)],[])).
% 0.64/0.86 tff(486,plain,
% 0.64/0.86 ((~![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)))))),
% 0.64/0.86 inference(quant_inst,[status(thm)],[])).
% 0.64/0.86 tff(487,plain,
% 0.64/0.86 ((~![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))))),
% 0.64/0.86 inference(modus_ponens,[status(thm)],[486, 485])).
% 0.64/0.86 tff(488,plain,
% 0.64/0.86 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[487, 73, 484, 473])).
% 0.64/0.87 tff(489,plain,
% 0.64/0.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 0.64/0.87 inference(rewrite,[status(thm)],[])).
% 0.64/0.87 tff(490,plain,
% 0.64/0.87 (((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 0.64/0.87 inference(rewrite,[status(thm)],[])).
% 0.64/0.87 tff(491,plain,
% 0.64/0.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z)))))),
% 0.64/0.87 inference(monotonicity,[status(thm)],[490])).
% 0.64/0.87 tff(492,plain,
% 0.64/0.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))))),
% 0.64/0.87 inference(transitivity,[status(thm)],[491, 489])).
% 0.64/0.87 tff(493,plain,
% 0.64/0.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))),
% 0.64/0.87 inference(quant_inst,[status(thm)],[])).
% 0.64/0.87 tff(494,plain,
% 0.64/0.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z)))),
% 0.64/0.87 inference(modus_ponens,[status(thm)],[493, 492])).
% 0.64/0.87 tff(495,plain,
% 0.64/0.87 (~b(z, s(s(s(s(z)))))),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[494, 180, 288, 268, 383])).
% 0.64/0.87 tff(496,plain,
% 0.64/0.87 (r(z, s(s(s(s(z)))))),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[78, 495])).
% 0.64/0.87 tff(497,plain,
% 0.64/0.87 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, 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(z)))))))),
% 0.64/0.87 inference(rewrite,[status(thm)],[])).
% 0.64/0.87 tff(498,plain,
% 0.64/0.87 (((~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))) <=> ((~r(z, 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(z)))))))),
% 0.64/0.87 inference(rewrite,[status(thm)],[])).
% 0.64/0.87 tff(499,plain,
% 0.64/0.87 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 0.64/0.87 inference(monotonicity,[status(thm)],[498])).
% 0.64/0.87 tff(500,plain,
% 0.64/0.87 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 0.64/0.87 inference(transitivity,[status(thm)],[499, 497])).
% 0.64/0.87 tff(501,plain,
% 0.64/0.87 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), z)))),
% 0.64/0.87 inference(quant_inst,[status(thm)],[])).
% 0.64/0.87 tff(502,plain,
% 0.64/0.87 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 0.64/0.87 inference(modus_ponens,[status(thm)],[501, 500])).
% 0.64/0.87 tff(503,plain,
% 0.64/0.87 (~r(s(s(s(s(s(s(z)))))), z)),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[502, 53, 496, 443])).
% 0.64/0.87 tff(504,plain,
% 0.64/0.87 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(s(z)))))) = z))),
% 0.64/0.87 inference(quant_inst,[status(thm)],[])).
% 0.64/0.87 tff(505,plain,
% 0.64/0.87 (~(s(s(s(s(s(s(z)))))) = z)),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[504, 33])).
% 0.64/0.87 tff(506,plain,
% 0.64/0.87 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = z) | b(s(s(s(s(s(s(z)))))), z) | r(s(s(s(s(s(s(z)))))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = z) | b(s(s(s(s(s(s(z)))))), z) | r(s(s(s(s(s(s(z)))))), z))),
% 0.64/0.87 inference(rewrite,[status(thm)],[])).
% 0.64/0.87 tff(507,plain,
% 0.64/0.87 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = z) | b(s(s(s(s(s(s(z)))))), z) | r(s(s(s(s(s(s(z)))))), z))),
% 0.64/0.87 inference(quant_inst,[status(thm)],[])).
% 0.64/0.87 tff(508,plain,
% 0.64/0.87 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = z) | b(s(s(s(s(s(s(z)))))), z) | r(s(s(s(s(s(s(z)))))), z)),
% 0.64/0.87 inference(modus_ponens,[status(thm)],[507, 506])).
% 0.64/0.87 tff(509,plain,
% 0.64/0.87 (b(s(s(s(s(s(s(z)))))), z) | r(s(s(s(s(s(s(z)))))), z)),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[508, 73, 505])).
% 0.64/0.87 tff(510,plain,
% 0.64/0.87 (b(s(s(s(s(s(s(z)))))), z)),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[509, 503])).
% 0.64/0.87 tff(511,plain,
% 0.64/0.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 0.64/0.87 inference(rewrite,[status(thm)],[])).
% 0.64/0.87 tff(512,plain,
% 0.64/0.87 (((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(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)))))) <=> ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 0.64/0.87 inference(rewrite,[status(thm)],[])).
% 0.64/0.87 tff(513,plain,
% 0.64/0.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z))))),
% 0.64/0.87 inference(monotonicity,[status(thm)],[512])).
% 0.64/0.87 tff(514,plain,
% 0.64/0.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 0.64/0.87 inference(transitivity,[status(thm)],[513, 511])).
% 0.64/0.87 tff(515,plain,
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% 0.64/0.87 inference(quant_inst,[status(thm)],[])).
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% 0.64/0.87 inference(modus_ponens,[status(thm)],[515, 514])).
% 0.64/0.87 tff(517,plain,
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% 0.64/0.87 inference(unit_resolution,[status(thm)],[516, 180, 288, 268, 510, 168, 488])).
% 0.64/0.87 tff(518,plain,((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.87 tff(519,plain,
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% 0.64/0.87 inference(unit_resolution,[status(thm)],[518, 221, 118, 40, 103, 152, 213])).
% 0.64/0.87 tff(520,plain,
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% 0.64/0.87 inference(rewrite,[status(thm)],[])).
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% 0.64/0.87 inference(quant_inst,[status(thm)],[])).
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% 0.64/0.87 inference(modus_ponens,[status(thm)],[521, 520])).
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% 0.64/0.87 inference(unit_resolution,[status(thm)],[522, 73, 351])).
% 0.64/0.87 tff(524,plain,
% 0.64/0.87 (r(s(z), s(s(s(s(z)))))),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[523, 519])).
% 0.64/0.87 tff(525,assumption,(r(s(z), s(s(s(z))))), introduced(assumption)).
% 0.64/0.87 tff(526,assumption,(r(s(z), s(s(s(s(z)))))), introduced(assumption)).
% 0.64/0.87 tff(527,plain,
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% 0.64/0.87 inference(rewrite,[status(thm)],[])).
% 0.64/0.87 tff(528,plain,
% 0.64/0.87 (((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 0.64/0.87 inference(rewrite,[status(thm)],[])).
% 0.64/0.87 tff(529,plain,
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% 0.64/0.87 inference(monotonicity,[status(thm)],[528])).
% 0.64/0.87 tff(530,plain,
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% 0.64/0.87 inference(transitivity,[status(thm)],[529, 527])).
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% 0.64/0.87 inference(quant_inst,[status(thm)],[])).
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% 0.64/0.87 inference(modus_ponens,[status(thm)],[531, 530])).
% 0.64/0.87 tff(533,plain,
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% 0.64/0.87 inference(unit_resolution,[status(thm)],[532, 53, 40, 526, 525])).
% 0.64/0.87 tff(534,plain,((~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)))))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.87 tff(535,plain,
% 0.64/0.87 (~r(s(z), s(s(s(z))))),
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% 0.64/0.87 inference(unit_resolution,[status(thm)],[373, 535])).
% 0.64/0.87 tff(537,plain,
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% 0.64/0.87 inference(unit_resolution,[status(thm)],[361, 536, 103, 118])).
% 0.64/0.87 tff(538,plain,
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% 0.64/0.87 inference(unit_resolution,[status(thm)],[287, 537])).
% 0.64/0.87 tff(539,assumption,(b(s(s(s(z))), s(s(s(s(z)))))), introduced(assumption)).
% 0.64/0.87 tff(540,assumption,(b(z, s(s(s(s(z)))))), introduced(assumption)).
% 0.64/0.87 tff(541,plain,
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% 0.64/0.87 inference(rewrite,[status(thm)],[])).
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% 0.64/0.87 inference(rewrite,[status(thm)],[])).
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% 0.64/0.87 inference(monotonicity,[status(thm)],[542])).
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% 0.64/0.87 inference(transitivity,[status(thm)],[543, 541])).
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% 0.64/0.87 inference(quant_inst,[status(thm)],[])).
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% 0.64/0.87 inference(modus_ponens,[status(thm)],[545, 544])).
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% 0.64/0.87 inference(unit_resolution,[status(thm)],[546, 180, 539, 540, 167, 222, 223])).
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% 0.64/0.87 tff(549,plain,
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% 0.64/0.87 inference(unit_resolution,[status(thm)],[548, 539, 167, 222, 223])).
% 0.64/0.87 tff(550,plain,
% 0.64/0.87 (r(z, s(s(s(s(z)))))),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[78, 549])).
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% 0.64/0.87 inference(rewrite,[status(thm)],[])).
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% 0.64/0.87 (((~r(s(z), s(s(s(s(z)))))) | (~r(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)))))))),
% 0.64/0.87 inference(rewrite,[status(thm)],[])).
% 0.64/0.87 tff(553,plain,
% 0.64/0.87 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))))),
% 0.64/0.87 inference(monotonicity,[status(thm)],[552])).
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% 0.64/0.87 inference(transitivity,[status(thm)],[553, 551])).
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% 0.64/0.87 inference(quant_inst,[status(thm)],[])).
% 0.64/0.87 tff(556,plain,
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% 0.64/0.87 inference(unit_resolution,[status(thm)],[556, 53, 269, 43, 526])).
% 0.64/0.87 tff(558,plain,((~r(z, s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.87 tff(559,plain,
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% 0.64/0.87 inference(unit_resolution,[status(thm)],[558, 550, 269])).
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% 0.64/0.87 (b(s(z), s(s(s(s(z)))))),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[523, 559])).
% 0.64/0.87 tff(561,plain,
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% 0.64/0.87 inference(rewrite,[status(thm)],[])).
% 0.64/0.87 tff(562,plain,
% 0.64/0.87 (((~b(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(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(s(s(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(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 0.64/0.87 inference(rewrite,[status(thm)],[])).
% 0.64/0.87 tff(563,plain,
% 0.64/0.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(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(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))))),
% 0.64/0.87 inference(monotonicity,[status(thm)],[562])).
% 0.64/0.87 tff(564,plain,
% 0.64/0.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(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(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 0.64/0.87 inference(transitivity,[status(thm)],[563, 561])).
% 0.64/0.87 tff(565,plain,
% 0.64/0.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(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(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))),
% 0.64/0.87 inference(quant_inst,[status(thm)],[])).
% 0.64/0.87 tff(566,plain,
% 0.64/0.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))),
% 0.64/0.87 inference(modus_ponens,[status(thm)],[565, 564])).
% 0.64/0.87 tff(567,plain,
% 0.64/0.87 ($false),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[566, 180, 560, 353, 539, 222, 223])).
% 0.64/0.87 tff(568,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(z))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.87 tff(569,plain,
% 0.64/0.87 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[568, 538, 103, 213, 221, 536])).
% 0.64/0.87 tff(570,plain,
% 0.64/0.87 (r(s(s(s(z))), s(s(s(s(z)))))),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[468, 569])).
% 0.64/0.87 tff(571,assumption,(r(s(s(s(z))), s(s(s(s(z)))))), introduced(assumption)).
% 0.64/0.87 tff(572,plain,
% 0.64/0.87 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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)))))))),
% 0.64/0.87 inference(rewrite,[status(thm)],[])).
% 0.64/0.87 tff(573,plain,
% 0.64/0.87 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 0.64/0.88 inference(rewrite,[status(thm)],[])).
% 0.64/0.88 tff(574,plain,
% 0.64/0.88 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 0.64/0.88 inference(monotonicity,[status(thm)],[573])).
% 0.64/0.88 tff(575,plain,
% 0.64/0.88 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 0.64/0.88 inference(transitivity,[status(thm)],[574, 572])).
% 0.64/0.88 tff(576,plain,
% 0.64/0.88 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))),
% 0.64/0.88 inference(quant_inst,[status(thm)],[])).
% 0.64/0.88 tff(577,plain,
% 0.64/0.88 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 0.64/0.88 inference(modus_ponens,[status(thm)],[576, 575])).
% 0.64/0.88 tff(578,plain,
% 0.64/0.88 ($false),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[577, 53, 571, 526, 309])).
% 0.64/0.88 tff(579,plain,((~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)))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.88 tff(580,plain,
% 0.64/0.88 (~r(s(s(s(z))), s(z))),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[579, 570, 524])).
% 0.64/0.88 tff(581,plain,
% 0.64/0.88 (b(s(s(s(z))), s(z))),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[307, 580])).
% 0.64/0.88 tff(582,plain,
% 0.64/0.88 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 0.64/0.88 inference(rewrite,[status(thm)],[])).
% 0.64/0.88 tff(583,plain,
% 0.64/0.88 (((~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 0.64/0.88 inference(rewrite,[status(thm)],[])).
% 0.64/0.88 tff(584,plain,
% 0.64/0.88 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))))),
% 0.64/0.88 inference(monotonicity,[status(thm)],[583])).
% 0.64/0.88 tff(585,plain,
% 0.64/0.88 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 0.64/0.88 inference(transitivity,[status(thm)],[584, 582])).
% 0.64/0.88 tff(586,plain,
% 0.64/0.88 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 0.64/0.88 inference(quant_inst,[status(thm)],[])).
% 0.64/0.88 tff(587,plain,
% 0.64/0.88 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))),
% 0.64/0.88 inference(modus_ponens,[status(thm)],[586, 585])).
% 0.64/0.88 tff(588,plain,
% 0.64/0.88 ($false),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[587, 53, 255, 80, 526])).
% 0.64/0.88 tff(589,plain,((~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.88 tff(590,plain,
% 0.64/0.88 (~r(s(z), z)),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[589, 524, 80])).
% 0.64/0.88 tff(591,plain,
% 0.64/0.88 (b(s(z), z)),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[267, 590])).
% 0.64/0.88 tff(592,plain,
% 0.64/0.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 0.64/0.88 inference(rewrite,[status(thm)],[])).
% 0.64/0.88 tff(593,plain,
% 0.64/0.88 (((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 0.64/0.88 inference(rewrite,[status(thm)],[])).
% 0.64/0.88 tff(594,plain,
% 0.64/0.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z)))))),
% 0.64/0.88 inference(monotonicity,[status(thm)],[593])).
% 0.64/0.88 tff(595,plain,
% 0.64/0.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 0.64/0.88 inference(transitivity,[status(thm)],[594, 592])).
% 0.64/0.88 tff(596,plain,
% 0.64/0.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 0.64/0.88 inference(quant_inst,[status(thm)],[])).
% 0.64/0.88 tff(597,plain,
% 0.64/0.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 0.64/0.88 inference(modus_ponens,[status(thm)],[596, 595])).
% 0.64/0.88 tff(598,plain,
% 0.64/0.88 ($false),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[597, 180, 591, 581, 118, 103])).
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% 0.64/0.88 tff(600,plain,
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% 0.64/0.88 tff(603,plain,
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% 0.64/0.88 inference(rewrite,[status(thm)],[])).
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% 0.64/0.88 inference(quant_inst,[status(thm)],[])).
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% 0.64/0.88 inference(modus_ponens,[status(thm)],[605, 604])).
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% 0.64/0.88 tff(608,plain,
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% 0.64/0.88 tff(609,plain,
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% 0.64/0.88 inference(rewrite,[status(thm)],[])).
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% 0.64/0.88 inference(rewrite,[status(thm)],[])).
% 0.64/0.88 tff(611,plain,
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% 0.64/0.88 inference(monotonicity,[status(thm)],[610])).
% 0.64/0.88 tff(612,plain,
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% 0.64/0.88 inference(transitivity,[status(thm)],[611, 609])).
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% 0.64/0.88 inference(quant_inst,[status(thm)],[])).
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% 0.64/0.88 inference(modus_ponens,[status(thm)],[613, 612])).
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% 0.64/0.88 tff(616,plain,((~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.88 tff(617,plain,
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% 0.64/0.88 inference(unit_resolution,[status(thm)],[78, 617])).
% 0.64/0.88 tff(619,plain,
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% 0.64/0.88 inference(unit_resolution,[status(thm)],[534, 526, 40])).
% 0.64/0.88 tff(620,plain,
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% 0.64/0.88 inference(unit_resolution,[status(thm)],[373, 619])).
% 0.64/0.88 tff(621,plain,
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% 0.64/0.88 inference(unit_resolution,[status(thm)],[558, 526, 43])).
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% 0.64/0.88 inference(unit_resolution,[status(thm)],[287, 621])).
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% 0.64/0.88 tff(624,plain,((~r(s(z), s(s(s(s(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,[]))).
% 0.64/0.88 tff(625,plain,
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% 0.64/0.88 tff(626,plain,
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% 0.64/0.88 inference(rewrite,[status(thm)],[])).
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% 0.64/0.88 inference(monotonicity,[status(thm)],[630])).
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% 0.64/0.88 inference(transitivity,[status(thm)],[631, 629])).
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% 0.64/0.88 tff(637,plain,
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% 0.64/0.88 inference(unit_resolution,[status(thm)],[636, 628, 603])).
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% 0.64/0.88 inference(unit_resolution,[status(thm)],[317, 628, 603])).
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% 0.64/0.88 inference(rewrite,[status(thm)],[])).
% 0.64/0.88 tff(642,plain,
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% 0.64/0.88 inference(monotonicity,[status(thm)],[642])).
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% 0.64/0.88 inference(transitivity,[status(thm)],[643, 641])).
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% 0.64/0.88 inference(quant_inst,[status(thm)],[])).
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% 0.64/0.88 inference(modus_ponens,[status(thm)],[645, 644])).
% 0.64/0.88 tff(647,plain,
% 0.64/0.88 (~b(s(z), z)),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[646, 180, 638, 640, 103])).
% 0.64/0.88 tff(648,plain,
% 0.64/0.88 (r(s(z), z)),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[267, 647])).
% 0.64/0.88 tff(649,plain,
% 0.64/0.88 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 0.64/0.88 inference(rewrite,[status(thm)],[])).
% 0.64/0.88 tff(650,plain,
% 0.64/0.88 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 0.64/0.88 inference(quant_inst,[status(thm)],[])).
% 0.64/0.88 tff(651,plain,
% 0.64/0.88 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z)))),
% 0.64/0.88 inference(modus_ponens,[status(thm)],[650, 649])).
% 0.64/0.88 tff(652,plain,
% 0.64/0.88 (~r(s(s(s(s(z)))), s(z))),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[651, 53, 648, 80])).
% 0.64/0.88 tff(653,plain,
% 0.64/0.88 ((s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z))),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[381, 73, 652])).
% 0.64/0.88 tff(654,plain,
% 0.64/0.88 (b(s(s(s(s(z)))), s(z))),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[653, 352])).
% 0.64/0.88 tff(655,assumption,(b(s(s(s(s(s(s(z)))))), s(z))), introduced(assumption)).
% 0.64/0.88 tff(656,plain,
% 0.64/0.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 0.64/0.88 inference(rewrite,[status(thm)],[])).
% 0.64/0.88 tff(657,plain,
% 0.64/0.88 (((~b(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(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(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(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 0.64/0.88 inference(rewrite,[status(thm)],[])).
% 0.64/0.88 tff(658,plain,
% 0.64/0.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), 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(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 0.64/0.88 inference(monotonicity,[status(thm)],[657])).
% 0.64/0.88 tff(659,plain,
% 0.64/0.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), 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(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 0.64/0.88 inference(transitivity,[status(thm)],[658, 656])).
% 0.64/0.88 tff(660,plain,
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% 0.64/0.88 inference(quant_inst,[status(thm)],[])).
% 0.64/0.88 tff(661,plain,
% 0.64/0.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 0.64/0.88 inference(modus_ponens,[status(thm)],[660, 659])).
% 0.64/0.88 tff(662,plain,
% 0.64/0.88 ($false),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[661, 180, 353, 289, 400, 655, 399])).
% 0.64/0.88 tff(663,plain,((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.88 tff(664,plain,
% 0.64/0.88 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[663, 384, 289, 400, 353])).
% 0.64/0.88 tff(665,plain,
% 0.64/0.88 (r(s(s(s(s(s(s(z)))))), s(z))),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[440, 73, 437, 664])).
% 0.64/0.88 tff(666,plain,
% 0.64/0.88 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 0.64/0.88 inference(rewrite,[status(thm)],[])).
% 0.64/0.88 tff(667,plain,
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% 0.64/0.88 inference(quant_inst,[status(thm)],[])).
% 0.64/0.88 tff(668,plain,
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% 0.64/0.89 inference(modus_ponens,[status(thm)],[667, 666])).
% 0.64/0.89 tff(669,plain,
% 0.64/0.89 (~r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[668, 53, 39, 665])).
% 0.64/0.89 tff(670,plain,
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% 0.64/0.89 inference(rewrite,[status(thm)],[])).
% 0.64/0.89 tff(671,plain,
% 0.64/0.89 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(s(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(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 0.64/0.89 inference(rewrite,[status(thm)],[])).
% 0.64/0.89 tff(672,plain,
% 0.64/0.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), 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: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))))),
% 0.64/0.89 inference(monotonicity,[status(thm)],[671])).
% 0.64/0.89 tff(673,plain,
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% 0.64/0.89 inference(transitivity,[status(thm)],[672, 670])).
% 0.64/0.89 tff(674,plain,
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% 0.64/0.89 inference(quant_inst,[status(thm)],[])).
% 0.64/0.89 tff(675,plain,
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% 0.64/0.89 inference(modus_ponens,[status(thm)],[674, 673])).
% 0.64/0.89 tff(676,plain,
% 0.64/0.89 (~b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[675, 180, 224, 400, 223, 399])).
% 0.64/0.89 tff(677,plain,
% 0.64/0.89 ($false),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[421, 73, 37, 676, 669])).
% 0.64/0.89 tff(678,plain,(r(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(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.89 tff(679,plain,
% 0.64/0.89 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[678, 626, 654, 213, 628, 640, 638])).
% 0.64/0.89 tff(680,plain,
% 0.64/0.89 (~b(z, s(z))),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[361, 638, 103, 118])).
% 0.64/0.89 tff(681,plain,
% 0.64/0.89 (r(z, s(z))),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[287, 680])).
% 0.64/0.89 tff(682,plain,
% 0.64/0.89 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[568, 681, 103, 213, 608, 638])).
% 0.64/0.89 tff(683,plain,
% 0.64/0.89 (r(s(s(s(z))), s(s(s(s(z)))))),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[468, 682])).
% 0.64/0.89 tff(684,plain,
% 0.64/0.89 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[472, 53, 683, 679])).
% 0.64/0.89 tff(685,plain,
% 0.64/0.89 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[487, 73, 484, 684])).
% 0.64/0.89 tff(686,plain,
% 0.64/0.89 (~r(s(s(s(s(s(s(z)))))), z)),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[502, 53, 618, 679])).
% 0.64/0.89 tff(687,plain,
% 0.64/0.89 (b(s(s(s(s(s(s(z)))))), z)),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[509, 686])).
% 0.64/0.89 tff(688,assumption,(r(z, s(s(z)))), introduced(assumption)).
% 0.64/0.89 tff(689,plain,
% 0.64/0.89 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))))),
% 0.64/0.89 inference(rewrite,[status(thm)],[])).
% 0.64/0.89 tff(690,plain,
% 0.64/0.89 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))))),
% 0.64/0.89 inference(quant_inst,[status(thm)],[])).
% 0.64/0.89 tff(691,plain,
% 0.64/0.89 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z))))),
% 0.64/0.89 inference(modus_ponens,[status(thm)],[690, 689])).
% 0.64/0.89 tff(692,plain,
% 0.64/0.89 ($false),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[691, 53, 269, 688, 39])).
% 0.64/0.89 tff(693,plain,((~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.89 tff(694,plain,
% 0.64/0.89 (~r(z, s(s(z)))),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[693, 681, 628])).
% 0.64/0.89 tff(695,plain,
% 0.64/0.89 ((z = s(s(z))) <=> (s(s(z)) = z)),
% 0.64/0.89 inference(commutativity,[status(thm)],[])).
% 0.64/0.89 tff(696,plain,
% 0.64/0.89 ((s(s(z)) = z) <=> (z = s(s(z)))),
% 0.64/0.89 inference(symmetry,[status(thm)],[695])).
% 0.64/0.89 tff(697,plain,
% 0.64/0.89 ((~(s(s(z)) = z)) <=> (~(z = s(s(z))))),
% 0.64/0.89 inference(monotonicity,[status(thm)],[696])).
% 0.64/0.89 tff(698,plain,
% 0.64/0.89 (~(z = s(s(z)))),
% 0.64/0.89 inference(modus_ponens,[status(thm)],[141, 697])).
% 0.64/0.89 tff(699,plain,
% 0.64/0.89 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(z))) | b(z, s(s(z))) | r(z, s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(z))) | b(z, s(s(z))) | r(z, s(s(z))))),
% 0.64/0.89 inference(rewrite,[status(thm)],[])).
% 0.64/0.89 tff(700,plain,
% 0.64/0.89 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(z))) | b(z, s(s(z))) | r(z, s(s(z))))),
% 0.64/0.89 inference(quant_inst,[status(thm)],[])).
% 0.64/0.89 tff(701,plain,
% 0.64/0.89 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(z))) | b(z, s(s(z))) | r(z, s(s(z)))),
% 0.64/0.89 inference(modus_ponens,[status(thm)],[700, 699])).
% 0.64/0.89 tff(702,plain,
% 0.64/0.89 ((z = s(s(z))) | b(z, s(s(z))) | r(z, s(s(z)))),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[701, 73])).
% 0.64/0.89 tff(703,plain,
% 0.64/0.89 (b(z, s(s(z))) | r(z, s(s(z)))),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[702, 698])).
% 0.64/0.89 tff(704,plain,
% 0.64/0.89 (b(z, s(s(z)))),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[703, 694])).
% 0.64/0.89 tff(705,plain,
% 0.64/0.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, 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)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, 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)))))), z)))),
% 0.64/0.89 inference(rewrite,[status(thm)],[])).
% 0.64/0.89 tff(706,plain,
% 0.64/0.89 (((~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(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)))))) <=> ((~b(s(s(s(z))), z)) | (~b(z, 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)))))), z)))),
% 0.64/0.89 inference(rewrite,[status(thm)],[])).
% 0.64/0.89 tff(707,plain,
% 0.64/0.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, 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)))))), z))))),
% 0.64/0.89 inference(monotonicity,[status(thm)],[706])).
% 0.64/0.89 tff(708,plain,
% 0.64/0.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, 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)))))), z)))),
% 0.64/0.89 inference(transitivity,[status(thm)],[707, 705])).
% 0.64/0.89 tff(709,plain,
% 0.64/0.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(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))))))),
% 0.64/0.89 inference(quant_inst,[status(thm)],[])).
% 0.64/0.89 tff(710,plain,
% 0.64/0.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z))),
% 0.64/0.89 inference(modus_ponens,[status(thm)],[709, 708])).
% 0.64/0.89 tff(711,plain,
% 0.64/0.89 ($false),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[710, 180, 601, 704, 687, 118, 685])).
% 0.64/0.89 tff(712,plain,((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.89 tff(713,plain,
% 0.64/0.89 (~r(s(s(s(s(z)))), z)),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[712, 40])).
% 0.64/0.89 tff(714,plain,
% 0.64/0.89 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = z) | b(s(s(s(s(z)))), z) | r(s(s(s(s(z)))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = z) | b(s(s(s(s(z)))), z) | r(s(s(s(s(z)))), z))),
% 0.64/0.89 inference(rewrite,[status(thm)],[])).
% 0.64/0.89 tff(715,plain,
% 0.64/0.89 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = z) | b(s(s(s(s(z)))), z) | r(s(s(s(s(z)))), z))),
% 0.64/0.89 inference(quant_inst,[status(thm)],[])).
% 0.64/0.89 tff(716,plain,
% 0.64/0.89 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = z) | b(s(s(s(s(z)))), z) | r(s(s(s(s(z)))), z)),
% 0.64/0.89 inference(modus_ponens,[status(thm)],[715, 714])).
% 0.64/0.89 tff(717,plain,
% 0.64/0.89 (b(s(s(s(s(z)))), z) | r(s(s(s(s(z)))), z)),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[716, 73, 35])).
% 0.64/0.89 tff(718,plain,
% 0.64/0.89 (b(s(s(s(s(z)))), z)),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[717, 713])).
% 0.64/0.89 tff(719,assumption,(b(s(s(s(s(z)))), z)), introduced(assumption)).
% 0.64/0.89 tff(720,plain,
% 0.64/0.89 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 0.64/0.89 inference(rewrite,[status(thm)],[])).
% 0.64/0.89 tff(721,plain,
% 0.64/0.89 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z)))) <=> ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 0.64/0.89 inference(rewrite,[status(thm)],[])).
% 0.64/0.89 tff(722,plain,
% 0.64/0.89 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 0.64/0.89 inference(monotonicity,[status(thm)],[721])).
% 0.64/0.89 tff(723,plain,
% 0.64/0.89 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 0.64/0.89 inference(transitivity,[status(thm)],[722, 720])).
% 0.64/0.89 tff(724,plain,
% 0.64/0.89 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))))),
% 0.64/0.89 inference(quant_inst,[status(thm)],[])).
% 0.64/0.89 tff(725,plain,
% 0.64/0.89 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 0.64/0.89 inference(modus_ponens,[status(thm)],[724, 723])).
% 0.64/0.89 tff(726,plain,
% 0.64/0.89 ($false),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[725, 53, 39, 526, 41])).
% 0.64/0.89 tff(727,plain,((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.89 tff(728,plain,
% 0.64/0.89 (~r(s(z), s(s(s(s(z)))))),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[727, 41, 39])).
% 0.64/0.89 tff(729,plain,
% 0.64/0.89 (b(s(z), s(s(s(s(z)))))),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[523, 728])).
% 0.64/0.89 tff(730,plain,
% 0.64/0.89 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 0.64/0.89 inference(rewrite,[status(thm)],[])).
% 0.64/0.89 tff(731,plain,
% 0.64/0.89 (((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z))) <=> ((~r(s(s(z)), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 0.64/0.89 inference(rewrite,[status(thm)],[])).
% 0.64/0.89 tff(732,plain,
% 0.64/0.89 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 0.64/0.89 inference(monotonicity,[status(thm)],[731])).
% 0.64/0.89 tff(733,plain,
% 0.64/0.89 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 0.64/0.89 inference(transitivity,[status(thm)],[732, 730])).
% 0.64/0.89 tff(734,plain,
% 0.64/0.89 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z)))),
% 0.64/0.89 inference(quant_inst,[status(thm)],[])).
% 0.64/0.89 tff(735,plain,
% 0.64/0.89 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 0.64/0.89 inference(modus_ponens,[status(thm)],[734, 733])).
% 0.64/0.89 tff(736,plain,
% 0.64/0.89 ($false),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[735, 53, 152, 43, 41])).
% 0.64/0.89 tff(737,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.89 tff(738,plain,
% 0.64/0.89 (~r(z, s(s(s(s(z)))))),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[737, 41, 152])).
% 0.64/0.89 tff(739,plain,
% 0.64/0.89 (b(z, s(s(s(s(z)))))),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[78, 738])).
% 0.64/0.89 tff(740,plain,
% 0.64/0.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 0.64/0.89 inference(rewrite,[status(thm)],[])).
% 0.64/0.89 tff(741,plain,
% 0.64/0.89 (((~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z)))) <=> ((~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 0.64/0.89 inference(rewrite,[status(thm)],[])).
% 0.64/0.89 tff(742,plain,
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% 0.64/0.89 inference(monotonicity,[status(thm)],[741])).
% 0.64/0.89 tff(743,plain,
% 0.64/0.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 0.64/0.89 inference(transitivity,[status(thm)],[742, 740])).
% 0.64/0.89 tff(744,plain,
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% 0.64/0.89 inference(quant_inst,[status(thm)],[])).
% 0.64/0.89 tff(745,plain,
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% 0.64/0.89 inference(modus_ponens,[status(thm)],[744, 743])).
% 0.64/0.89 tff(746,plain,
% 0.64/0.89 ($false),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[745, 180, 291, 224, 719, 540])).
% 0.64/0.89 tff(747,plain,((~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.89 tff(748,plain,
% 0.64/0.89 ($false),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[747, 739, 729, 291, 719])).
% 0.64/0.89 tff(749,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.90 tff(750,plain,
% 0.64/0.90 (~r(s(s(z)), s(z))),
% 0.64/0.90 inference(unit_resolution,[status(thm)],[749, 291, 718, 41, 152])).
% 0.64/0.90 tff(751,assumption,(b(z, s(s(z)))), introduced(assumption)).
% 0.64/0.90 tff(752,assumption,(b(s(z), s(s(z)))), introduced(assumption)).
% 0.64/0.90 tff(753,plain,
% 0.64/0.90 (b(s(s(z)), s(z))),
% 0.64/0.90 inference(unit_resolution,[status(thm)],[251, 73, 248, 235])).
% 0.64/0.90 tff(754,plain,
% 0.64/0.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))))),
% 0.64/0.90 inference(rewrite,[status(thm)],[])).
% 0.64/0.90 tff(755,plain,
% 0.64/0.90 (((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))))),
% 0.64/0.90 inference(rewrite,[status(thm)],[])).
% 0.64/0.90 tff(756,plain,
% 0.64/0.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z)))))),
% 0.64/0.90 inference(monotonicity,[status(thm)],[755])).
% 0.64/0.90 tff(757,plain,
% 0.64/0.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))))),
% 0.64/0.90 inference(transitivity,[status(thm)],[756, 754])).
% 0.64/0.90 tff(758,plain,
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% 0.64/0.90 inference(quant_inst,[status(thm)],[])).
% 0.64/0.90 tff(759,plain,
% 0.64/0.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z)))),
% 0.64/0.90 inference(modus_ponens,[status(thm)],[758, 757])).
% 0.64/0.90 tff(760,plain,
% 0.64/0.90 ($false),
% 0.64/0.90 inference(unit_resolution,[status(thm)],[759, 180, 291, 751, 753, 752])).
% 0.64/0.90 tff(761,plain,((~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | r(s(s(z)), s(z))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.90 tff(762,plain,
% 0.64/0.90 (~b(s(z), s(s(z)))),
% 0.64/0.90 inference(unit_resolution,[status(thm)],[761, 291, 751, 235])).
% 0.64/0.90 tff(763,plain,
% 0.64/0.90 (r(s(z), s(s(z)))),
% 0.64/0.90 inference(unit_resolution,[status(thm)],[341, 73, 247, 762])).
% 0.64/0.90 tff(764,plain,
% 0.64/0.90 (b(s(s(z)), s(z))),
% 0.64/0.90 inference(unit_resolution,[status(thm)],[253, 235])).
% 0.64/0.90 tff(765,plain,
% 0.64/0.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))))),
% 0.74/0.90 inference(rewrite,[status(thm)],[])).
% 0.74/0.90 tff(766,plain,
% 0.74/0.90 (((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z))))) <=> ((~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))))),
% 0.74/0.90 inference(rewrite,[status(thm)],[])).
% 0.74/0.90 tff(767,plain,
% 0.74/0.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z)))))),
% 0.74/0.90 inference(monotonicity,[status(thm)],[766])).
% 0.74/0.90 tff(768,plain,
% 0.74/0.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))))),
% 0.74/0.90 inference(transitivity,[status(thm)],[767, 765])).
% 0.74/0.90 tff(769,plain,
% 0.74/0.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))),
% 0.74/0.90 inference(quant_inst,[status(thm)],[])).
% 0.74/0.90 tff(770,plain,
% 0.74/0.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z)))),
% 0.74/0.90 inference(modus_ponens,[status(thm)],[769, 768])).
% 0.74/0.90 tff(771,plain,
% 0.74/0.90 ($false),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[770, 180, 291, 290, 751, 225])).
% 0.74/0.90 tff(772,plain,((~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.90 tff(773,plain,
% 0.74/0.90 (~b(s(z), z)),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[772, 291, 764, 751])).
% 0.74/0.90 tff(774,plain,
% 0.74/0.90 (r(s(z), z)),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[267, 773])).
% 0.74/0.90 tff(775,plain,
% 0.74/0.90 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), z)))),
% 0.74/0.90 inference(rewrite,[status(thm)],[])).
% 0.74/0.90 tff(776,plain,
% 0.74/0.90 (((~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), z)))),
% 0.74/0.90 inference(rewrite,[status(thm)],[])).
% 0.74/0.90 tff(777,plain,
% 0.74/0.90 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), z))))),
% 0.74/0.90 inference(monotonicity,[status(thm)],[776])).
% 0.74/0.90 tff(778,plain,
% 0.74/0.90 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), z)))),
% 0.74/0.90 inference(transitivity,[status(thm)],[777, 775])).
% 0.74/0.90 tff(779,plain,
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% 0.74/0.90 inference(quant_inst,[status(thm)],[])).
% 0.74/0.90 tff(780,plain,
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% 0.74/0.90 inference(modus_ponens,[status(thm)],[779, 778])).
% 0.74/0.90 tff(781,plain,
% 0.74/0.90 ($false),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[780, 53, 152, 774, 763])).
% 0.74/0.90 tff(782,plain,((~b(z, s(z))) | (~r(s(s(z)), z)) | (~b(z, s(s(z)))) | r(s(s(z)), s(z))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.90 tff(783,plain,
% 0.74/0.90 (~b(z, s(s(z)))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[782, 750, 152, 291])).
% 0.74/0.90 tff(784,plain,
% 0.74/0.90 (r(z, s(s(z)))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[703, 783])).
% 0.74/0.90 tff(785,assumption,(r(s(s(s(z))), s(s(z)))), introduced(assumption)).
% 0.74/0.90 tff(786,plain,
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% 0.74/0.90 inference(rewrite,[status(thm)],[])).
% 0.74/0.90 tff(787,plain,
% 0.74/0.90 (((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z)))))) <=> ((~r(z, s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 0.74/0.90 inference(rewrite,[status(thm)],[])).
% 0.74/0.90 tff(788,plain,
% 0.74/0.90 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z))))))),
% 0.74/0.90 inference(monotonicity,[status(thm)],[787])).
% 0.74/0.90 tff(789,plain,
% 0.74/0.90 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 0.74/0.90 inference(transitivity,[status(thm)],[788, 786])).
% 0.74/0.90 tff(790,plain,
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% 0.74/0.90 inference(quant_inst,[status(thm)],[])).
% 0.74/0.90 tff(791,plain,
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% 0.74/0.90 inference(modus_ponens,[status(thm)],[790, 789])).
% 0.74/0.90 tff(792,plain,
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% 0.74/0.90 inference(unit_resolution,[status(thm)],[791, 53, 688, 42, 785])).
% 0.74/0.90 tff(793,plain,((~r(z, s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.90 tff(794,plain,
% 0.74/0.90 (~r(s(s(s(z))), s(s(z)))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[793, 784, 42])).
% 0.74/0.90 tff(795,plain,
% 0.74/0.90 (b(s(s(s(z))), s(s(z)))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[330, 73, 794, 323])).
% 0.74/0.90 tff(796,plain,
% 0.74/0.90 (~b(s(z), s(s(s(s(z)))))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[747, 291, 718, 79])).
% 0.74/0.90 tff(797,plain,
% 0.74/0.90 (r(s(z), s(s(s(s(z)))))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[523, 796])).
% 0.74/0.90 tff(798,plain,
% 0.74/0.90 (~r(s(z), s(s(s(z))))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[534, 797, 40])).
% 0.74/0.90 tff(799,plain,
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% 0.74/0.90 inference(unit_resolution,[status(thm)],[373, 798])).
% 0.74/0.90 tff(800,plain,
% 0.74/0.90 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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)))))))),
% 0.74/0.90 inference(rewrite,[status(thm)],[])).
% 0.74/0.90 tff(801,plain,
% 0.74/0.90 (((~r(s(s(z)), s(s(s(s(z)))))) | (~r(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)))))))),
% 0.74/0.90 inference(rewrite,[status(thm)],[])).
% 0.74/0.90 tff(802,plain,
% 0.74/0.90 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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))))))))),
% 0.74/0.90 inference(monotonicity,[status(thm)],[801])).
% 0.74/0.90 tff(803,plain,
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% 0.74/0.90 inference(transitivity,[status(thm)],[802, 800])).
% 0.74/0.90 tff(804,plain,
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% 0.74/0.90 inference(quant_inst,[status(thm)],[])).
% 0.74/0.90 tff(805,plain,
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% 0.74/0.90 inference(modus_ponens,[status(thm)],[804, 803])).
% 0.74/0.90 tff(806,plain,
% 0.74/0.90 (~r(s(z), s(s(z)))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[805, 53, 797, 41])).
% 0.74/0.90 tff(807,plain,
% 0.74/0.90 (b(s(z), s(s(z)))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[341, 73, 247, 806])).
% 0.74/0.90 tff(808,plain,
% 0.74/0.90 (b(s(s(z)), s(z))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[253, 750])).
% 0.74/0.90 tff(809,plain,
% 0.74/0.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))))),
% 0.74/0.90 inference(rewrite,[status(thm)],[])).
% 0.74/0.90 tff(810,plain,
% 0.74/0.90 (((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))))),
% 0.74/0.90 inference(rewrite,[status(thm)],[])).
% 0.74/0.90 tff(811,plain,
% 0.74/0.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z)))))))),
% 0.74/0.90 inference(monotonicity,[status(thm)],[810])).
% 0.74/0.90 tff(812,plain,
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% 0.74/0.90 inference(transitivity,[status(thm)],[811, 809])).
% 0.74/0.90 tff(813,plain,
% 0.74/0.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))))),
% 0.74/0.90 inference(quant_inst,[status(thm)],[])).
% 0.74/0.90 tff(814,plain,
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% 0.74/0.90 inference(modus_ponens,[status(thm)],[813, 812])).
% 0.74/0.90 tff(815,plain,
% 0.74/0.90 ($false),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[814, 180, 808, 807, 799, 795])).
% 0.74/0.90 tff(816,plain,((~b(z, s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.90 tff(817,plain,
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% 0.74/0.90 inference(unit_resolution,[status(thm)],[816, 152, 42, 40, 41])).
% 0.74/0.90 tff(818,plain,
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% 0.74/0.90 inference(unit_resolution,[status(thm)],[287, 817])).
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% 0.74/0.90 inference(rewrite,[status(thm)],[])).
% 0.74/0.90 tff(822,plain,
% 0.74/0.90 (((~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 0.74/0.90 inference(rewrite,[status(thm)],[])).
% 0.74/0.90 tff(823,plain,
% 0.74/0.90 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z)))))))),
% 0.74/0.90 inference(monotonicity,[status(thm)],[822])).
% 0.74/0.90 tff(824,plain,
% 0.74/0.90 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 0.74/0.90 inference(transitivity,[status(thm)],[823, 821])).
% 0.74/0.90 tff(825,plain,
% 0.74/0.90 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(z))))),
% 0.74/0.90 inference(quant_inst,[status(thm)],[])).
% 0.74/0.90 tff(826,plain,
% 0.74/0.90 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z)))))),
% 0.74/0.90 inference(modus_ponens,[status(thm)],[825, 824])).
% 0.74/0.90 tff(827,plain,
% 0.74/0.90 ($false),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[826, 53, 269, 42, 525])).
% 0.74/0.90 tff(828,plain,((~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.90 tff(829,plain,
% 0.74/0.90 (~r(s(z), s(s(s(z))))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[828, 818, 42])).
% 0.74/0.90 tff(830,plain,
% 0.74/0.90 (b(s(z), s(s(s(z))))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[373, 829])).
% 0.74/0.90 tff(831,plain,
% 0.74/0.90 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))))),
% 0.74/0.90 inference(rewrite,[status(thm)],[])).
% 0.74/0.90 tff(832,plain,
% 0.74/0.90 (((~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z)))))) <=> ((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))))),
% 0.74/0.90 inference(rewrite,[status(thm)],[])).
% 0.74/0.90 tff(833,plain,
% 0.74/0.90 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z)))))))),
% 0.74/0.90 inference(monotonicity,[status(thm)],[832])).
% 0.74/0.90 tff(834,plain,
% 0.74/0.90 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))))),
% 0.74/0.91 inference(transitivity,[status(thm)],[833, 831])).
% 0.74/0.91 tff(835,plain,
% 0.74/0.91 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))))),
% 0.74/0.91 inference(quant_inst,[status(thm)],[])).
% 0.74/0.91 tff(836,plain,
% 0.74/0.91 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z)))))),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[835, 834])).
% 0.74/0.91 tff(837,plain,
% 0.74/0.91 ($false),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[836, 53, 269, 42, 309])).
% 0.74/0.91 tff(838,plain,((~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.91 tff(839,plain,
% 0.74/0.91 (~r(s(s(s(z))), s(z))),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[838, 818, 42])).
% 0.74/0.91 tff(840,plain,
% 0.74/0.91 (b(s(s(s(z))), s(z))),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[307, 839])).
% 0.74/0.91 tff(841,plain,
% 0.74/0.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(842,plain,
% 0.74/0.91 (((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(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(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(843,plain,
% 0.74/0.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(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))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[842])).
% 0.74/0.91 tff(844,plain,
% 0.74/0.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(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))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 0.74/0.91 inference(transitivity,[status(thm)],[843, 841])).
% 0.74/0.91 tff(845,plain,
% 0.74/0.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(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))))),
% 0.74/0.91 inference(quant_inst,[status(thm)],[])).
% 0.74/0.91 tff(846,plain,
% 0.74/0.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[845, 844])).
% 0.74/0.91 tff(847,plain,
% 0.74/0.91 ($false),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[846, 180, 225, 353, 289, 169])).
% 0.74/0.91 tff(848,plain,((~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.91 tff(849,plain,
% 0.74/0.91 ($false),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[848, 840, 830, 820, 151])).
% 0.74/0.91 tff(850,plain,((~r(s(s(z)), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.91 tff(851,plain,
% 0.74/0.91 (~r(s(s(z)), z)),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[850, 42, 40, 41])).
% 0.74/0.91 tff(852,plain,
% 0.74/0.91 (b(s(s(z)), z)),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[165, 851])).
% 0.74/0.91 tff(853,plain,
% 0.74/0.91 (~r(s(z), s(s(z)))),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[805, 53, 526, 41])).
% 0.74/0.91 tff(854,plain,
% 0.74/0.91 (b(s(z), s(s(z)))),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[341, 73, 247, 853])).
% 0.74/0.91 tff(855,plain,
% 0.74/0.91 (~r(s(s(z)), s(z))),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[727, 526, 41])).
% 0.74/0.91 tff(856,plain,
% 0.74/0.91 (b(s(s(z)), s(z))),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[253, 855])).
% 0.74/0.91 tff(857,plain,
% 0.74/0.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), z)))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(858,plain,
% 0.74/0.91 (((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), z)))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(859,plain,
% 0.74/0.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), z))))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[858])).
% 0.74/0.91 tff(860,plain,
% 0.74/0.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), z)))),
% 0.74/0.91 inference(transitivity,[status(thm)],[859, 857])).
% 0.74/0.91 tff(861,plain,
% 0.74/0.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 0.74/0.91 inference(quant_inst,[status(thm)],[])).
% 0.74/0.91 tff(862,plain,
% 0.74/0.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), z))),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[861, 860])).
% 0.74/0.91 tff(863,plain,
% 0.74/0.91 ($false),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[862, 180, 291, 170, 856, 854])).
% 0.74/0.91 tff(864,plain,((~b(z, s(z))) | (~b(s(s(z)), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.91 tff(865,plain,
% 0.74/0.91 (~b(z, s(z))),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[864, 526, 170, 41])).
% 0.74/0.91 tff(866,plain,
% 0.74/0.91 (r(z, s(z))),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[287, 865])).
% 0.74/0.91 tff(867,plain,
% 0.74/0.91 (~r(s(z), s(s(s(z))))),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[828, 269, 42])).
% 0.74/0.91 tff(868,plain,
% 0.74/0.91 (b(s(z), s(s(s(z))))),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[373, 867])).
% 0.74/0.91 tff(869,plain,
% 0.74/0.91 (~r(z, s(s(s(s(z)))))),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[558, 269, 526])).
% 0.74/0.91 tff(870,plain,
% 0.74/0.91 (b(z, s(s(s(s(z)))))),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[78, 869])).
% 0.74/0.91 tff(871,plain,
% 0.74/0.91 (~r(s(s(z)), z)),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[275, 53, 269, 39])).
% 0.74/0.91 tff(872,plain,
% 0.74/0.91 (b(s(s(z)), z)),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[165, 871])).
% 0.74/0.91 tff(873,assumption,(b(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 0.74/0.91 tff(874,plain,
% 0.74/0.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(875,plain,
% 0.74/0.91 (((~b(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(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(876,plain,
% 0.74/0.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[875])).
% 0.74/0.91 tff(877,plain,
% 0.74/0.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 0.74/0.91 inference(transitivity,[status(thm)],[876, 874])).
% 0.74/0.91 tff(878,plain,
% 0.74/0.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 0.74/0.91 inference(quant_inst,[status(thm)],[])).
% 0.74/0.91 tff(879,plain,
% 0.74/0.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[878, 877])).
% 0.74/0.91 tff(880,plain,
% 0.74/0.91 ($false),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[879, 180, 873, 353, 289, 169, 223])).
% 0.74/0.91 tff(881,plain,((~b(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(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.91 tff(882,plain,
% 0.74/0.91 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[881, 223, 289, 169, 353])).
% 0.74/0.91 tff(883,plain,
% 0.74/0.91 (((~![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)))))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(884,plain,
% 0.74/0.91 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z)))))),
% 0.74/0.91 inference(quant_inst,[status(thm)],[])).
% 0.74/0.91 tff(885,plain,
% 0.74/0.91 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z))))),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[884, 883])).
% 0.74/0.91 tff(886,plain,
% 0.74/0.91 ((s(s(s(s(z)))) = s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z))))),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[885, 73])).
% 0.74/0.91 tff(887,plain,
% 0.74/0.91 (b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z))))),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[886, 456])).
% 0.74/0.91 tff(888,plain,
% 0.74/0.91 (r(s(s(s(s(z)))), s(s(s(z))))),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[887, 882])).
% 0.74/0.91 tff(889,plain,
% 0.74/0.91 (~r(s(s(s(s(z)))), z)),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[86, 53, 888, 42])).
% 0.74/0.91 tff(890,plain,
% 0.74/0.91 (b(s(s(s(s(z)))), z)),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[717, 889])).
% 0.74/0.91 tff(891,plain,
% 0.74/0.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(892,plain,
% 0.74/0.91 (((~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(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z))) <=> ((~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(893,plain,
% 0.74/0.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[892])).
% 0.74/0.91 tff(894,plain,
% 0.74/0.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 0.74/0.91 inference(transitivity,[status(thm)],[893, 891])).
% 0.74/0.91 tff(895,plain,
% 0.74/0.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)))),
% 0.74/0.91 inference(quant_inst,[status(thm)],[])).
% 0.74/0.91 tff(896,plain,
% 0.74/0.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[895, 894])).
% 0.74/0.91 tff(897,plain,
% 0.74/0.91 ($false),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[896, 180, 170, 890, 540, 223])).
% 0.74/0.91 tff(898,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.91 tff(899,plain,
% 0.74/0.91 (~b(s(s(z)), s(s(s(s(z)))))),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[898, 872, 870, 42, 289, 169, 868])).
% 0.74/0.91 tff(900,plain,
% 0.74/0.91 (~r(s(s(z)), s(s(s(s(z)))))),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[727, 39, 526])).
% 0.74/0.91 tff(901,plain,
% 0.74/0.91 ($false),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[210, 73, 900, 899, 205])).
% 0.74/0.91 tff(902,plain,((~r(s(s(z)), s(z))) | (~r(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.91 tff(903,plain,
% 0.74/0.91 (~r(s(s(z)), s(z))),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[902, 169, 289, 42, 269, 526])).
% 0.74/0.91 tff(904,plain,
% 0.74/0.91 (b(s(s(z)), s(z))),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[253, 903])).
% 0.74/0.91 tff(905,plain,
% 0.74/0.91 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(906,plain,
% 0.74/0.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[905])).
% 0.74/0.91 tff(907,plain,
% 0.74/0.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 0.74/0.91 inference(transitivity,[status(thm)],[906, 841])).
% 0.74/0.91 tff(908,plain,
% 0.74/0.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))))),
% 0.74/0.91 inference(quant_inst,[status(thm)],[])).
% 0.74/0.91 tff(909,plain,
% 0.74/0.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[908, 907])).
% 0.74/0.92 tff(910,plain,
% 0.74/0.92 ($false),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[909, 180, 904, 868, 289, 169])).
% 0.74/0.92 tff(911,plain,((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.92 tff(912,plain,
% 0.74/0.92 (~b(s(s(s(z))), s(z))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[911, 866, 169, 42, 526])).
% 0.74/0.92 tff(913,plain,
% 0.74/0.92 (~r(s(s(s(z))), s(z))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[838, 866, 42])).
% 0.74/0.92 tff(914,plain,
% 0.74/0.92 ($false),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[307, 913, 912])).
% 0.74/0.92 tff(915,plain,((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.92 tff(916,plain,
% 0.74/0.92 (~r(s(z), s(s(s(s(z)))))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[915, 852, 151, 42, 41])).
% 0.74/0.92 tff(917,plain,
% 0.74/0.92 (b(s(z), s(s(s(s(z)))))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[523, 916])).
% 0.74/0.92 tff(918,plain,
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% 0.74/0.92 tff(921,plain,
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% 0.74/0.92 tff(922,assumption,(r(s(s(s(s(s(s(z)))))), s(z))), introduced(assumption)).
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% 0.74/0.92 tff(924,plain,
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% 0.74/0.92 inference(monotonicity,[status(thm)],[926])).
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% 0.74/0.92 inference(modus_ponens,[status(thm)],[929, 928])).
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% 0.74/0.92 tff(932,plain,
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% 0.74/0.92 inference(unit_resolution,[status(thm)],[509, 931])).
% 0.74/0.92 tff(933,plain,
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% 0.74/0.92 inference(unit_resolution,[status(thm)],[693, 39, 269])).
% 0.74/0.92 tff(934,plain,
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% 0.74/0.92 inference(unit_resolution,[status(thm)],[703, 933])).
% 0.74/0.92 tff(935,plain,
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% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(936,plain,
% 0.74/0.92 (((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(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(z, s(s(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)))))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(937,plain,
% 0.74/0.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(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)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[936])).
% 0.74/0.92 tff(938,plain,
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% 0.74/0.92 inference(transitivity,[status(thm)],[937, 935])).
% 0.74/0.92 tff(939,plain,
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% 0.74/0.92 inference(quant_inst,[status(thm)],[])).
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% 0.74/0.92 inference(modus_ponens,[status(thm)],[939, 938])).
% 0.74/0.92 tff(941,plain,
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% 0.74/0.92 inference(unit_resolution,[status(thm)],[940, 180, 170, 934, 932, 924])).
% 0.74/0.92 tff(942,plain,((~r(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), z)) | (~r(s(s(z)), s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.92 tff(943,plain,
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% 0.74/0.92 tff(944,assumption,(~r(s(s(s(s(s(s(z)))))), s(z))), introduced(assumption)).
% 0.74/0.92 tff(945,assumption,(~b(s(s(s(s(s(s(z)))))), s(z))), introduced(assumption)).
% 0.74/0.92 tff(946,plain,
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% 0.74/0.92 inference(unit_resolution,[status(thm)],[440, 73, 437, 945, 944])).
% 0.74/0.92 tff(947,plain,(r(s(s(s(s(s(s(z)))))), s(z)) | b(s(s(s(s(s(s(z)))))), s(z))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.92 tff(948,plain,
% 0.74/0.92 (b(s(s(s(s(s(s(z)))))), s(z))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[947, 943])).
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% 0.74/0.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(950,plain,
% 0.74/0.92 (((~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(z), 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(z)))))) <=> ((~b(s(s(s(z))), 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))))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(951,plain,
% 0.74/0.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z), 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(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[950])).
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% 0.74/0.92 inference(transitivity,[status(thm)],[951, 949])).
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% 0.74/0.92 inference(quant_inst,[status(thm)],[])).
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% 0.74/0.92 tff(955,plain,
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% 0.74/0.92 inference(unit_resolution,[status(thm)],[954, 180, 868, 919, 948])).
% 0.74/0.92 tff(956,plain,
% 0.74/0.92 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[487, 73, 484, 955])).
% 0.74/0.92 tff(957,plain,
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% 0.74/0.92 inference(unit_resolution,[status(thm)],[693, 921, 269])).
% 0.74/0.92 tff(958,plain,
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% 0.74/0.92 inference(unit_resolution,[status(thm)],[703, 957])).
% 0.74/0.92 tff(959,plain,
% 0.74/0.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(960,plain,
% 0.74/0.92 (((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(961,plain,
% 0.74/0.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z))))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[960])).
% 0.74/0.92 tff(962,plain,
% 0.74/0.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)))),
% 0.74/0.92 inference(transitivity,[status(thm)],[961, 959])).
% 0.74/0.92 tff(963,plain,
% 0.74/0.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 0.74/0.92 inference(quant_inst,[status(thm)],[])).
% 0.74/0.92 tff(964,plain,
% 0.74/0.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[963, 962])).
% 0.74/0.92 tff(965,plain,
% 0.74/0.92 (~b(s(s(s(s(z)))), s(s(z)))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[964, 180, 170, 958, 718])).
% 0.74/0.92 tff(966,plain,
% 0.74/0.92 (r(s(s(s(s(z)))), s(s(z)))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[220, 73, 203, 965])).
% 0.74/0.92 tff(967,plain,
% 0.74/0.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(968,plain,
% 0.74/0.92 (((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(969,plain,
% 0.74/0.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[968])).
% 0.74/0.92 tff(970,plain,
% 0.74/0.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 0.74/0.92 inference(transitivity,[status(thm)],[969, 967])).
% 0.74/0.92 tff(971,plain,
% 0.74/0.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))))),
% 0.74/0.92 inference(quant_inst,[status(thm)],[])).
% 0.74/0.92 tff(972,plain,
% 0.74/0.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[971, 970])).
% 0.74/0.92 tff(973,plain,
% 0.74/0.92 (~b(s(z), s(s(z)))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[972, 180, 868, 919, 169])).
% 0.74/0.92 tff(974,plain,
% 0.74/0.92 (r(s(z), s(s(z)))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[341, 73, 247, 973])).
% 0.74/0.92 tff(975,plain,
% 0.74/0.92 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(976,plain,
% 0.74/0.92 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))),
% 0.74/0.92 inference(quant_inst,[status(thm)],[])).
% 0.74/0.92 tff(977,plain,
% 0.74/0.92 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z)))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[976, 975])).
% 0.74/0.92 tff(978,plain,
% 0.74/0.92 (~r(s(s(s(s(z)))), s(z))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[977, 53, 974, 966])).
% 0.74/0.92 tff(979,plain,
% 0.74/0.92 ((s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[381, 73, 978])).
% 0.74/0.92 tff(980,plain,
% 0.74/0.92 (b(s(s(s(s(z)))), s(z))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[979, 352])).
% 0.74/0.92 tff(981,plain,
% 0.74/0.92 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[663, 948, 919, 980, 868])).
% 0.74/0.92 tff(982,plain,
% 0.74/0.92 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(983,plain,
% 0.74/0.92 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 0.74/0.92 inference(quant_inst,[status(thm)],[])).
% 0.74/0.92 tff(984,plain,
% 0.74/0.92 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[983, 982])).
% 0.74/0.92 tff(985,plain,
% 0.74/0.92 ($false),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[984, 53, 40, 981, 956])).
% 0.74/0.92 tff(986,plain,((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.92 tff(987,plain,
% 0.74/0.92 (~r(z, s(z))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[986, 852, 40, 151, 42])).
% 0.74/0.92 tff(988,plain,
% 0.74/0.92 (b(z, s(z))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[287, 987])).
% 0.74/0.92 tff(989,plain,
% 0.74/0.92 ($false),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[747, 988, 917, 718, 79])).
% 0.74/0.92 tff(990,plain,((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.92 tff(991,plain,
% 0.74/0.92 (~r(z, s(s(s(z))))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[990, 41, 40])).
% 0.74/0.92 tff(992,plain,
% 0.74/0.92 (b(z, s(s(s(z))))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[102, 991])).
% 0.74/0.92 tff(993,plain,
% 0.74/0.92 (~r(z, s(s(s(s(z)))))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[737, 152, 41])).
% 0.74/0.92 tff(994,plain,
% 0.74/0.92 (b(z, s(s(s(s(z)))))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[78, 993])).
% 0.74/0.92 tff(995,plain,
% 0.74/0.92 (~b(s(z), s(s(s(s(z)))))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[747, 994, 718, 291])).
% 0.74/0.92 tff(996,plain,
% 0.74/0.92 (r(s(z), s(s(s(s(z)))))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[523, 995])).
% 0.74/0.92 tff(997,plain,
% 0.74/0.92 (~r(s(s(z)), s(z))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[749, 152, 718, 41, 291])).
% 0.74/0.92 tff(998,plain,
% 0.74/0.92 (b(s(s(z)), s(z))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[253, 997])).
% 0.74/0.92 tff(999,plain,
% 0.74/0.92 (~r(s(z), s(s(s(z))))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[534, 996, 40])).
% 0.74/0.92 tff(1000,plain,
% 0.74/0.92 (b(s(z), s(s(s(z))))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[373, 999])).
% 0.74/0.92 tff(1001,plain,
% 0.74/0.92 (~b(s(s(s(z))), s(z))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[848, 1000, 998, 151])).
% 0.74/0.92 tff(1002,plain,
% 0.74/0.92 (r(s(s(s(z))), s(z))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[307, 1001])).
% 0.74/0.92 tff(1003,plain,
% 0.74/0.92 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[579, 1002, 996])).
% 0.74/0.92 tff(1004,plain,
% 0.74/0.92 (b(s(s(s(z))), s(s(s(s(z)))))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[468, 1003])).
% 0.74/0.92 tff(1005,plain,
% 0.74/0.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(1006,plain,
% 0.74/0.92 (((~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(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(1007,plain,
% 0.74/0.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z))))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[1006])).
% 0.74/0.92 tff(1008,plain,
% 0.74/0.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 0.74/0.93 inference(transitivity,[status(thm)],[1007, 1005])).
% 0.74/0.93 tff(1009,plain,
% 0.74/0.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))),
% 0.74/0.93 inference(quant_inst,[status(thm)],[])).
% 0.74/0.93 tff(1010,plain,
% 0.74/0.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z))),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[1009, 1008])).
% 0.74/0.93 tff(1011,plain,
% 0.74/0.93 ($false),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[1010, 180, 718, 1004, 994, 992])).
% 0.74/0.93 tff(1012,plain,((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(z))) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.93 tff(1013,plain,
% 0.74/0.93 (~r(s(s(z)), z)),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[1012, 291, 40, 41])).
% 0.74/0.93 tff(1014,plain,
% 0.74/0.93 (b(s(s(z)), z)),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[165, 1013])).
% 0.74/0.93 tff(1015,plain,
% 0.74/0.93 (~b(s(s(s(z))), z)),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[188, 1014, 151, 992])).
% 0.74/0.93 tff(1016,plain,
% 0.74/0.93 (r(s(s(s(z))), z)),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[117, 1015])).
% 0.74/0.93 tff(1017,plain,
% 0.74/0.93 (~r(s(z), s(s(s(s(z)))))),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[864, 1014, 291, 41])).
% 0.74/0.93 tff(1018,plain,
% 0.74/0.93 (b(s(z), s(s(s(s(z)))))),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[523, 1017])).
% 0.74/0.93 tff(1019,plain,
% 0.74/0.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(1020,plain,
% 0.74/0.93 (((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(1021,plain,
% 0.74/0.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z))))))))),
% 0.74/0.93 inference(monotonicity,[status(thm)],[1020])).
% 0.74/0.93 tff(1022,plain,
% 0.74/0.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 0.74/0.93 inference(transitivity,[status(thm)],[1021, 1019])).
% 0.74/0.93 tff(1023,plain,
% 0.74/0.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 0.74/0.93 inference(quant_inst,[status(thm)],[])).
% 0.74/0.93 tff(1024,plain,
% 0.74/0.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z))))))),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[1023, 1022])).
% 0.74/0.93 tff(1025,plain,
% 0.74/0.93 ($false),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[1024, 180, 291, 290, 224, 719])).
% 0.74/0.93 tff(1026,plain,((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.93 tff(1027,plain,
% 0.74/0.93 (~b(s(z), z)),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[1026, 1018, 718, 291])).
% 0.74/0.93 tff(1028,plain,
% 0.74/0.93 (r(s(z), z)),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[267, 1027])).
% 0.74/0.93 tff(1029,plain,
% 0.74/0.93 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(1030,plain,
% 0.74/0.93 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 0.74/0.93 inference(quant_inst,[status(thm)],[])).
% 0.74/0.93 tff(1031,plain,
% 0.74/0.93 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[1030, 1029])).
% 0.74/0.93 tff(1032,plain,
% 0.74/0.93 (~r(s(s(s(z))), s(z))),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[1031, 53, 1028, 1016])).
% 0.74/0.93 tff(1033,plain,
% 0.74/0.93 (b(s(s(s(z))), s(z))),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[307, 1032])).
% 0.74/0.93 tff(1034,plain,
% 0.74/0.93 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(1035,plain,
% 0.74/0.93 (((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(1036,plain,
% 0.74/0.93 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z)))))))),
% 0.74/0.93 inference(monotonicity,[status(thm)],[1035])).
% 0.74/0.93 tff(1037,plain,
% 0.74/0.93 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 0.74/0.93 inference(transitivity,[status(thm)],[1036, 1034])).
% 0.74/0.93 tff(1038,plain,
% 0.74/0.93 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))),
% 0.74/0.93 inference(quant_inst,[status(thm)],[])).
% 0.74/0.93 tff(1039,plain,
% 0.74/0.93 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z)))))),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[1038, 1037])).
% 0.74/0.93 tff(1040,plain,
% 0.74/0.93 (~r(s(z), s(s(s(z))))),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[1039, 53, 1028, 1016])).
% 0.74/0.93 tff(1041,plain,
% 0.74/0.93 (b(s(z), s(s(s(z))))),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[373, 1040])).
% 0.74/0.93 tff(1042,plain,
% 0.74/0.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(1043,plain,
% 0.74/0.93 (((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z)))) <=> ((~b(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(1044,plain,
% 0.74/0.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))))),
% 0.74/0.93 inference(monotonicity,[status(thm)],[1043])).
% 0.74/0.93 tff(1045,plain,
% 0.74/0.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 0.74/0.93 inference(transitivity,[status(thm)],[1044, 1042])).
% 0.74/0.93 tff(1046,plain,
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% 0.74/0.93 inference(quant_inst,[status(thm)],[])).
% 0.74/0.93 tff(1047,plain,
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% 0.74/0.93 inference(modus_ponens,[status(thm)],[1046, 1045])).
% 0.74/0.93 tff(1048,plain,
% 0.74/0.93 ($false),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[1047, 180, 291, 1041, 1033, 992])).
% 0.74/0.93 tff(1049,plain,((~b(z, s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.93 tff(1050,plain,
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% 0.74/0.93 inference(unit_resolution,[status(thm)],[1049, 41, 40])).
% 0.74/0.93 tff(1051,plain,
% 0.74/0.93 (r(z, s(z))),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[287, 1050])).
% 0.74/0.93 tff(1052,plain,
% 0.74/0.93 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(1053,plain,
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% 0.74/0.93 inference(quant_inst,[status(thm)],[])).
% 0.74/0.93 tff(1054,plain,
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% 0.74/0.93 inference(modus_ponens,[status(thm)],[1053, 1052])).
% 0.74/0.93 tff(1055,plain,
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% 0.74/0.93 inference(unit_resolution,[status(thm)],[1054, 53, 269, 104, 309])).
% 0.74/0.93 tff(1056,plain,((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.93 tff(1057,plain,
% 0.74/0.93 (~r(s(s(s(z))), z)),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[1056, 309, 1051])).
% 0.74/0.93 tff(1058,plain,
% 0.74/0.93 (b(s(s(s(z))), z)),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[117, 1057])).
% 0.74/0.93 tff(1059,plain,
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% 0.74/0.93 inference(unit_resolution,[status(thm)],[188, 1058, 151, 992])).
% 0.74/0.93 tff(1060,plain,
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% 0.74/0.93 inference(unit_resolution,[status(thm)],[165, 1059])).
% 0.74/0.93 tff(1061,plain,
% 0.74/0.93 (~r(z, s(s(s(s(z)))))),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[737, 1060, 41])).
% 0.74/0.93 tff(1062,plain,
% 0.74/0.93 (b(z, s(s(s(s(z)))))),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[78, 1061])).
% 0.74/0.93 tff(1063,plain,
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% 0.74/0.93 inference(unit_resolution,[status(thm)],[277, 152, 1051])).
% 0.74/0.93 tff(1064,plain,
% 0.74/0.93 (b(s(s(z)), s(z))),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[253, 1063])).
% 0.74/0.93 tff(1065,assumption,(b(s(s(s(s(s(s(z)))))), z)), introduced(assumption)).
% 0.74/0.93 tff(1066,plain,
% 0.74/0.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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)))))))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(1067,plain,
% 0.74/0.93 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(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(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(1068,plain,
% 0.74/0.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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))))))))),
% 0.74/0.93 inference(monotonicity,[status(thm)],[1067])).
% 0.74/0.93 tff(1069,plain,
% 0.74/0.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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)))))))),
% 0.74/0.93 inference(transitivity,[status(thm)],[1068, 1066])).
% 0.74/0.93 tff(1070,plain,
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% 0.74/0.93 inference(quant_inst,[status(thm)],[])).
% 0.74/0.93 tff(1071,plain,
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% 0.74/0.93 inference(modus_ponens,[status(thm)],[1070, 1069])).
% 0.74/0.93 tff(1072,plain,
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% 0.74/0.93 inference(unit_resolution,[status(thm)],[1071, 180, 719, 1065, 540, 399])).
% 0.74/0.93 tff(1073,plain,((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.93 tff(1074,plain,
% 0.74/0.93 (~b(s(s(s(s(s(s(z)))))), z)),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[1073, 384, 540, 719])).
% 0.74/0.93 tff(1075,plain,
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% 0.74/0.93 inference(unit_resolution,[status(thm)],[509, 1074])).
% 0.74/0.93 tff(1076,plain,
% 0.74/0.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(1077,plain,
% 0.74/0.93 (((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z))) <=> ((~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(1078,plain,
% 0.74/0.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z))))))))),
% 0.74/0.93 inference(monotonicity,[status(thm)],[1077])).
% 0.74/0.93 tff(1079,plain,
% 0.74/0.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 0.74/0.93 inference(transitivity,[status(thm)],[1078, 1076])).
% 0.74/0.93 tff(1080,plain,
% 0.74/0.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))),
% 0.74/0.93 inference(quant_inst,[status(thm)],[])).
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% 0.74/0.93 inference(modus_ponens,[status(thm)],[1080, 1079])).
% 0.74/0.93 tff(1082,plain,
% 0.74/0.93 (~b(s(z), z)),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[1081, 180, 224, 719, 540])).
% 0.74/0.93 tff(1083,plain,
% 0.74/0.93 (r(s(z), z)),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[267, 1082])).
% 0.74/0.93 tff(1084,plain,
% 0.74/0.93 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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))))),
% 0.74/0.94 inference(rewrite,[status(thm)],[])).
% 0.74/0.94 tff(1085,plain,
% 0.74/0.94 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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))))),
% 0.74/0.94 inference(quant_inst,[status(thm)],[])).
% 0.74/0.94 tff(1086,plain,
% 0.74/0.94 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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)))),
% 0.74/0.94 inference(modus_ponens,[status(thm)],[1085, 1084])).
% 0.74/0.94 tff(1087,plain,
% 0.74/0.94 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[1086, 53, 1083, 1075])).
% 0.74/0.94 tff(1088,plain,
% 0.74/0.94 (b(s(s(s(s(s(s(z)))))), s(z))),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[947, 1087])).
% 0.74/0.94 tff(1089,plain,
% 0.74/0.94 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 0.74/0.94 inference(rewrite,[status(thm)],[])).
% 0.74/0.94 tff(1090,plain,
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% 0.74/0.94 inference(quant_inst,[status(thm)],[])).
% 0.74/0.94 tff(1091,plain,
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% 0.74/0.94 inference(modus_ponens,[status(thm)],[1090, 1089])).
% 0.74/0.94 tff(1092,plain,
% 0.74/0.94 (~r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[1091, 53, 152, 1075])).
% 0.74/0.94 tff(1093,assumption,(~r(s(s(s(s(s(s(z)))))), s(s(z)))), introduced(assumption)).
% 0.74/0.94 tff(1094,assumption,(~b(s(s(s(s(s(s(z)))))), s(s(z)))), introduced(assumption)).
% 0.74/0.94 tff(1095,plain,
% 0.74/0.94 ($false),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[421, 73, 37, 1094, 1093])).
% 0.74/0.94 tff(1096,plain,(r(s(s(s(s(s(s(z)))))), s(s(z))) | b(s(s(s(s(s(s(z)))))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.94 tff(1097,plain,
% 0.74/0.94 (b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[1096, 1092])).
% 0.74/0.94 tff(1098,plain,
% 0.74/0.94 (~r(s(z), s(s(z)))),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[780, 53, 152, 1083])).
% 0.74/0.94 tff(1099,plain,
% 0.74/0.94 (b(s(z), s(s(z)))),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[341, 73, 247, 1098])).
% 0.74/0.94 tff(1100,plain,
% 0.74/0.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 0.74/0.94 inference(rewrite,[status(thm)],[])).
% 0.74/0.94 tff(1101,plain,
% 0.74/0.94 (((~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(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z)))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), 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(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 0.74/0.94 inference(rewrite,[status(thm)],[])).
% 0.74/0.94 tff(1102,plain,
% 0.74/0.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), 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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))))),
% 0.74/0.94 inference(monotonicity,[status(thm)],[1101])).
% 0.74/0.94 tff(1103,plain,
% 0.74/0.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), 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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 0.74/0.94 inference(transitivity,[status(thm)],[1102, 1100])).
% 0.74/0.94 tff(1104,plain,
% 0.74/0.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 0.74/0.94 inference(quant_inst,[status(thm)],[])).
% 0.74/0.94 tff(1105,plain,
% 0.74/0.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))),
% 0.74/0.94 inference(modus_ponens,[status(thm)],[1104, 1103])).
% 0.74/0.94 tff(1106,plain,
% 0.74/0.94 ($false),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[1105, 180, 225, 1099, 224, 1097, 1088, 399])).
% 0.74/0.94 tff(1107,plain,(r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.94 tff(1108,plain,
% 0.74/0.94 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[1107, 224, 1064, 152, 994, 718])).
% 0.74/0.94 tff(1109,plain,
% 0.74/0.94 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 0.74/0.94 inference(rewrite,[status(thm)],[])).
% 0.74/0.94 tff(1110,plain,
% 0.74/0.94 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 0.74/0.94 inference(quant_inst,[status(thm)],[])).
% 0.74/0.94 tff(1111,plain,
% 0.74/0.94 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z))))),
% 0.74/0.94 inference(modus_ponens,[status(thm)],[1110, 1109])).
% 0.74/0.94 tff(1112,plain,
% 0.74/0.94 (~r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[1111, 53, 1108, 41])).
% 0.74/0.94 tff(1113,plain,
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% 0.74/0.94 inference(unit_resolution,[status(thm)],[1096, 1112])).
% 0.74/0.94 tff(1114,plain,
% 0.74/0.94 (~b(s(z), z)),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[1081, 180, 224, 718, 994])).
% 0.74/0.94 tff(1115,plain,
% 0.74/0.94 (r(s(z), z)),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[267, 1114])).
% 0.74/0.94 tff(1116,plain,
% 0.74/0.94 (~r(s(z), s(s(z)))),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[780, 53, 152, 1115])).
% 0.74/0.94 tff(1117,plain,
% 0.74/0.94 (b(s(z), s(s(z)))),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[341, 73, 247, 1116])).
% 0.74/0.94 tff(1118,plain,
% 0.74/0.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 0.74/0.94 inference(rewrite,[status(thm)],[])).
% 0.74/0.94 tff(1119,plain,
% 0.74/0.94 (((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z)))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 0.74/0.94 inference(rewrite,[status(thm)],[])).
% 0.74/0.94 tff(1120,plain,
% 0.74/0.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))))),
% 0.74/0.94 inference(monotonicity,[status(thm)],[1119])).
% 0.74/0.94 tff(1121,plain,
% 0.74/0.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 0.74/0.94 inference(transitivity,[status(thm)],[1120, 1118])).
% 0.74/0.94 tff(1122,plain,
% 0.74/0.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 0.74/0.94 inference(quant_inst,[status(thm)],[])).
% 0.74/0.94 tff(1123,plain,
% 0.74/0.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))),
% 0.74/0.94 inference(modus_ponens,[status(thm)],[1122, 1121])).
% 0.74/0.94 tff(1124,plain,
% 0.74/0.94 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[1123, 180, 1064, 1117, 1113])).
% 0.74/0.94 tff(1125,plain,
% 0.74/0.94 (r(s(s(s(s(s(s(z)))))), s(z))),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[947, 1124])).
% 0.74/0.94 tff(1126,plain,
% 0.74/0.94 (~r(s(s(s(s(s(s(z)))))), z)),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[930, 53, 1051, 1125])).
% 0.74/0.94 tff(1127,plain,
% 0.74/0.94 (b(s(s(s(s(s(s(z)))))), z)),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[509, 1126])).
% 0.74/0.94 tff(1128,plain,
% 0.74/0.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 0.74/0.94 inference(rewrite,[status(thm)],[])).
% 0.74/0.94 tff(1129,plain,
% 0.74/0.94 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(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(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 0.74/0.94 inference(rewrite,[status(thm)],[])).
% 0.74/0.94 tff(1130,plain,
% 0.74/0.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z))))),
% 0.74/0.94 inference(monotonicity,[status(thm)],[1129])).
% 0.74/0.94 tff(1131,plain,
% 0.74/0.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 0.74/0.94 inference(transitivity,[status(thm)],[1130, 1128])).
% 0.74/0.94 tff(1132,plain,
% 0.74/0.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 0.74/0.94 inference(quant_inst,[status(thm)],[])).
% 0.74/0.94 tff(1133,plain,
% 0.74/0.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z))),
% 0.74/0.94 inference(modus_ponens,[status(thm)],[1132, 1131])).
% 0.74/0.94 tff(1134,plain,
% 0.74/0.94 (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[1133, 180, 718, 1127, 994])).
% 0.74/0.94 tff(1135,plain,
% 0.74/0.94 ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(z)))))) = s(s(s(s(z)))))),
% 0.74/0.94 inference(commutativity,[status(thm)],[])).
% 0.74/0.94 tff(1136,plain,
% 0.74/0.94 ((s(s(s(s(s(s(z)))))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(s(s(s(z)))))))),
% 0.74/0.94 inference(symmetry,[status(thm)],[1135])).
% 0.74/0.94 tff(1137,plain,
% 0.74/0.94 ((~(s(s(s(s(s(s(z)))))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(s(s(s(s(s(z))))))))),
% 0.74/0.94 inference(monotonicity,[status(thm)],[1136])).
% 0.74/0.94 tff(1138,plain,
% 0.74/0.94 (~(s(s(s(s(z)))) = s(s(s(s(s(s(z)))))))),
% 0.74/0.94 inference(modus_ponens,[status(thm)],[395, 1137])).
% 0.74/0.94 tff(1139,plain,
% 0.74/0.94 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 0.74/0.94 inference(rewrite,[status(thm)],[])).
% 0.74/0.94 tff(1140,plain,
% 0.74/0.94 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 0.74/0.94 inference(quant_inst,[status(thm)],[])).
% 0.74/0.94 tff(1141,plain,
% 0.74/0.94 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.74/0.94 inference(modus_ponens,[status(thm)],[1140, 1139])).
% 0.74/0.94 tff(1142,plain,
% 0.74/0.94 (r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[1141, 73, 1138, 1134])).
% 0.74/0.94 tff(1143,plain,
% 0.74/0.94 ((s(z) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(z)))))) = s(z))),
% 0.74/0.94 inference(commutativity,[status(thm)],[])).
% 0.74/0.94 tff(1144,plain,
% 0.74/0.94 ((s(s(s(s(s(s(z)))))) = s(z)) <=> (s(z) = s(s(s(s(s(s(z)))))))),
% 0.74/0.94 inference(symmetry,[status(thm)],[1143])).
% 0.74/0.94 tff(1145,plain,
% 0.74/0.94 ((~(s(s(s(s(s(s(z)))))) = s(z))) <=> (~(s(z) = s(s(s(s(s(s(z))))))))),
% 0.74/0.94 inference(monotonicity,[status(thm)],[1144])).
% 0.74/0.94 tff(1146,plain,
% 0.74/0.94 (~(s(z) = s(s(s(s(s(s(z)))))))),
% 0.74/0.94 inference(modus_ponens,[status(thm)],[437, 1145])).
% 0.74/0.94 tff(1147,plain,
% 0.74/0.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 0.74/0.94 inference(rewrite,[status(thm)],[])).
% 0.74/0.94 tff(1148,plain,
% 0.74/0.94 (((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(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(s(z)))))),
% 0.74/0.94 inference(rewrite,[status(thm)],[])).
% 0.74/0.94 tff(1149,plain,
% 0.74/0.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))))),
% 0.74/0.94 inference(monotonicity,[status(thm)],[1148])).
% 0.74/0.94 tff(1150,plain,
% 0.74/0.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 0.74/0.94 inference(transitivity,[status(thm)],[1149, 1147])).
% 0.74/0.94 tff(1151,plain,
% 0.74/0.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(z)))))))))),
% 0.74/0.94 inference(quant_inst,[status(thm)],[])).
% 0.74/0.94 tff(1152,plain,
% 0.74/0.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))),
% 0.74/0.94 inference(modus_ponens,[status(thm)],[1151, 1150])).
% 0.74/0.94 tff(1153,plain,
% 0.74/0.94 (~b(s(z), s(s(s(s(s(s(z)))))))),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[1152, 180, 1064, 1117, 1113])).
% 0.74/0.94 tff(1154,plain,
% 0.74/0.94 (((~![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))))))))),
% 0.74/0.94 inference(rewrite,[status(thm)],[])).
% 0.74/0.94 tff(1155,plain,
% 0.74/0.94 ((~![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))))))))),
% 0.74/0.94 inference(quant_inst,[status(thm)],[])).
% 0.74/0.94 tff(1156,plain,
% 0.74/0.94 ((~![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)))))))),
% 0.74/0.94 inference(modus_ponens,[status(thm)],[1155, 1154])).
% 0.74/0.94 tff(1157,plain,
% 0.74/0.94 ((s(z) = s(s(s(s(s(s(z))))))) | r(s(z), s(s(s(s(s(s(z)))))))),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[1156, 73, 1153])).
% 0.74/0.94 tff(1158,plain,
% 0.74/0.94 (r(s(z), s(s(s(s(s(s(z)))))))),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[1157, 1146])).
% 0.74/0.94 tff(1159,plain,
% 0.74/0.94 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), 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)))))))))),
% 0.74/0.94 inference(rewrite,[status(thm)],[])).
% 0.74/0.94 tff(1160,plain,
% 0.74/0.94 (((~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(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)))))))))),
% 0.74/0.94 inference(rewrite,[status(thm)],[])).
% 0.74/0.94 tff(1161,plain,
% 0.74/0.94 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(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))))))))))),
% 0.74/0.95 inference(monotonicity,[status(thm)],[1160])).
% 0.74/0.95 tff(1162,plain,
% 0.74/0.95 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(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)))))))))),
% 0.74/0.95 inference(transitivity,[status(thm)],[1161, 1159])).
% 0.74/0.95 tff(1163,plain,
% 0.74/0.95 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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(s(s(s(z)))), s(z))))),
% 0.74/0.95 inference(quant_inst,[status(thm)],[])).
% 0.74/0.95 tff(1164,plain,
% 0.74/0.95 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z))))))))),
% 0.74/0.95 inference(modus_ponens,[status(thm)],[1163, 1162])).
% 0.74/0.95 tff(1165,plain,
% 0.74/0.95 (~r(s(s(s(s(z)))), s(z))),
% 0.74/0.95 inference(unit_resolution,[status(thm)],[1164, 53, 1158, 1142])).
% 0.74/0.95 tff(1166,plain,
% 0.74/0.95 ((s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z))),
% 0.74/0.95 inference(unit_resolution,[status(thm)],[381, 73, 1165])).
% 0.74/0.95 tff(1167,plain,
% 0.74/0.95 (b(s(s(s(s(z)))), s(z))),
% 0.74/0.95 inference(unit_resolution,[status(thm)],[1166, 352])).
% 0.74/0.95 tff(1168,plain,
% 0.74/0.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), 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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 0.74/0.95 inference(rewrite,[status(thm)],[])).
% 0.74/0.95 tff(1169,plain,
% 0.74/0.95 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 0.74/0.95 inference(rewrite,[status(thm)],[])).
% 0.74/0.95 tff(1170,plain,
% 0.74/0.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 0.74/0.95 inference(monotonicity,[status(thm)],[1169])).
% 0.74/0.95 tff(1171,plain,
% 0.74/0.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 0.74/0.95 inference(transitivity,[status(thm)],[1170, 1168])).
% 0.74/0.95 tff(1172,plain,
% 0.74/0.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 0.74/0.95 inference(quant_inst,[status(thm)],[])).
% 0.74/0.95 tff(1173,plain,
% 0.74/0.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 0.74/0.95 inference(modus_ponens,[status(thm)],[1172, 1171])).
% 0.74/0.95 tff(1174,plain,
% 0.74/0.95 ($false),
% 0.74/0.95 inference(unit_resolution,[status(thm)],[1173, 180, 225, 224, 400, 222])).
% 0.74/0.95 tff(1175,plain,((~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.95 tff(1176,plain,
% 0.74/0.95 (~b(s(s(s(s(z)))), s(s(z)))),
% 0.74/0.95 inference(unit_resolution,[status(thm)],[1175, 1167, 1064, 224])).
% 0.74/0.95 tff(1177,plain,
% 0.74/0.95 (r(s(s(s(s(z)))), s(s(z)))),
% 0.74/0.95 inference(unit_resolution,[status(thm)],[220, 73, 203, 1176])).
% 0.74/0.95 tff(1178,assumption,(r(s(s(s(s(z)))), s(s(z)))), introduced(assumption)).
% 0.74/0.95 tff(1179,plain,
% 0.74/0.95 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 0.74/0.95 inference(rewrite,[status(thm)],[])).
% 0.74/0.95 tff(1180,plain,
% 0.74/0.95 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 0.74/0.95 inference(quant_inst,[status(thm)],[])).
% 0.74/0.95 tff(1181,plain,
% 0.74/0.95 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 0.74/0.95 inference(modus_ponens,[status(thm)],[1180, 1179])).
% 0.74/0.95 tff(1182,plain,
% 0.74/0.95 ($false),
% 0.74/0.95 inference(unit_resolution,[status(thm)],[1181, 53, 40, 1178, 785])).
% 0.74/0.95 tff(1183,plain,((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.95 tff(1184,plain,
% 0.74/0.95 (~r(s(s(s(z))), s(s(z)))),
% 0.74/0.95 inference(unit_resolution,[status(thm)],[1183, 1177, 40])).
% 0.74/0.95 tff(1185,assumption,(~r(s(s(s(s(s(s(z)))))), s(s(s(z))))), introduced(assumption)).
% 0.74/0.95 tff(1186,plain,
% 0.74/0.95 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.74/0.95 inference(unit_resolution,[status(thm)],[487, 73, 484, 1185])).
% 0.74/0.95 tff(1187,assumption,(~r(s(s(s(z))), s(s(z)))), introduced(assumption)).
% 0.74/0.95 tff(1188,plain,
% 0.74/0.95 (b(s(s(s(z))), s(s(z)))),
% 0.74/0.95 inference(unit_resolution,[status(thm)],[330, 73, 1187, 323])).
% 0.74/0.95 tff(1189,plain,
% 0.74/0.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 0.74/0.95 inference(rewrite,[status(thm)],[])).
% 0.74/0.95 tff(1190,plain,
% 0.74/0.95 (((~b(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(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 0.74/0.95 inference(rewrite,[status(thm)],[])).
% 0.74/0.95 tff(1191,plain,
% 0.74/0.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))))),
% 0.74/0.95 inference(monotonicity,[status(thm)],[1190])).
% 0.74/0.95 tff(1192,plain,
% 0.74/0.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 0.74/0.95 inference(transitivity,[status(thm)],[1191, 1189])).
% 0.74/0.95 tff(1193,plain,
% 0.74/0.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 0.74/0.95 inference(quant_inst,[status(thm)],[])).
% 0.74/0.95 tff(1194,plain,
% 0.74/0.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))),
% 0.74/0.95 inference(modus_ponens,[status(thm)],[1193, 1192])).
% 0.74/0.95 tff(1195,plain,
% 0.74/0.95 ($false),
% 0.74/0.95 inference(unit_resolution,[status(thm)],[1194, 180, 169, 1188, 409, 1186])).
% 0.74/0.95 tff(1196,plain,(r(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)))) | r(s(s(s(z))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.95 tff(1197,plain,
% 0.74/0.95 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.74/0.95 inference(unit_resolution,[status(thm)],[1196, 1113, 151, 1184])).
% 0.74/0.95 tff(1198,plain,
% 0.74/0.95 ($false),
% 0.74/0.95 inference(unit_resolution,[status(thm)],[984, 53, 40, 1108, 1197])).
% 0.74/0.95 tff(1199,plain,((~b(s(z), 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)), z))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.95 tff(1200,plain,
% 0.74/0.95 (~b(s(z), s(s(s(s(z)))))),
% 0.74/0.95 inference(unit_resolution,[status(thm)],[1199, 1060, 41, 40])).
% 0.74/0.95 tff(1201,plain,
% 0.74/0.95 (r(s(z), s(s(s(s(z)))))),
% 0.74/0.95 inference(unit_resolution,[status(thm)],[523, 1200])).
% 0.74/0.95 tff(1202,plain,
% 0.74/0.95 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 0.74/0.95 inference(unit_resolution,[status(thm)],[579, 1201, 309])).
% 0.74/0.95 tff(1203,plain,
% 0.74/0.95 (b(s(s(s(z))), s(s(s(s(z)))))),
% 0.74/0.95 inference(unit_resolution,[status(thm)],[468, 1202])).
% 0.74/0.95 tff(1204,plain,
% 0.74/0.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)))),
% 0.74/0.95 inference(rewrite,[status(thm)],[])).
% 0.74/0.95 tff(1205,plain,
% 0.74/0.95 (((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z))) <=> ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)))),
% 0.74/0.95 inference(rewrite,[status(thm)],[])).
% 0.74/0.95 tff(1206,plain,
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% 0.74/0.95 inference(monotonicity,[status(thm)],[1205])).
% 0.74/0.95 tff(1207,plain,
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% 0.74/0.95 inference(transitivity,[status(thm)],[1206, 1204])).
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% 0.74/0.95 inference(quant_inst,[status(thm)],[])).
% 0.74/0.95 tff(1209,plain,
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% 0.74/0.95 inference(modus_ponens,[status(thm)],[1208, 1207])).
% 0.74/0.95 tff(1210,plain,
% 0.74/0.95 ($false),
% 0.74/0.95 inference(unit_resolution,[status(thm)],[1209, 180, 718, 1203, 1062, 1058])).
% 0.74/0.95 tff(1211,plain,((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.95 tff(1212,plain,
% 0.74/0.95 (~r(s(s(s(z))), s(z))),
% 0.74/0.95 inference(unit_resolution,[status(thm)],[1211, 41, 40])).
% 0.74/0.95 tff(1213,plain,
% 0.74/0.95 (b(s(s(s(z))), s(z))),
% 0.74/0.95 inference(unit_resolution,[status(thm)],[307, 1212])).
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% 0.74/0.95 inference(unit_resolution,[status(thm)],[848, 856, 620, 1213, 151])).
% 0.74/0.95 tff(1215,plain,((~r(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)))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.95 tff(1216,plain,
% 0.74/0.95 (~r(s(z), s(s(s(s(z)))))),
% 0.74/0.95 inference(unit_resolution,[status(thm)],[1215, 41, 40])).
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% 0.74/0.95 (b(s(z), s(s(s(s(z)))))),
% 0.74/0.95 inference(unit_resolution,[status(thm)],[523, 1216])).
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% 0.74/0.95 inference(unit_resolution,[status(thm)],[1199, 1217, 41, 40])).
% 0.74/0.95 tff(1219,plain,
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% 0.74/0.95 inference(unit_resolution,[status(thm)],[165, 1218])).
% 0.74/0.95 tff(1220,plain,
% 0.74/0.95 (~b(s(s(s(z))), z)),
% 0.74/0.95 inference(unit_resolution,[status(thm)],[188, 1219, 151, 992])).
% 0.74/0.95 tff(1221,plain,
% 0.74/0.95 (r(s(s(s(z))), z)),
% 0.74/0.95 inference(unit_resolution,[status(thm)],[117, 1220])).
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% 0.74/0.95 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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)))))))),
% 0.74/0.95 inference(rewrite,[status(thm)],[])).
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% 0.74/0.95 (((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(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)))))))),
% 0.74/0.95 inference(rewrite,[status(thm)],[])).
% 0.74/0.95 tff(1224,plain,
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% 0.74/0.95 inference(monotonicity,[status(thm)],[1223])).
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% 0.74/0.95 inference(transitivity,[status(thm)],[1224, 1222])).
% 0.74/0.95 tff(1226,plain,
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% 0.74/0.95 inference(quant_inst,[status(thm)],[])).
% 0.74/0.95 tff(1227,plain,
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% 0.74/0.95 inference(modus_ponens,[status(thm)],[1226, 1225])).
% 0.74/0.95 tff(1228,plain,
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% 0.74/0.95 inference(unit_resolution,[status(thm)],[1227, 53, 104, 571, 43])).
% 0.74/0.95 tff(1229,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.95 tff(1230,plain,
% 0.74/0.95 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 0.74/0.95 inference(unit_resolution,[status(thm)],[1229, 43, 104])).
% 0.74/0.95 tff(1231,plain,
% 0.74/0.95 (b(s(s(s(z))), s(s(s(s(z)))))),
% 0.74/0.95 inference(unit_resolution,[status(thm)],[468, 1230])).
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% 0.74/0.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), 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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 0.74/0.95 inference(rewrite,[status(thm)],[])).
% 0.74/0.95 tff(1233,plain,
% 0.74/0.95 (((~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(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(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(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 0.74/0.95 inference(rewrite,[status(thm)],[])).
% 0.74/0.95 tff(1234,plain,
% 0.74/0.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), 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(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 0.74/0.95 inference(monotonicity,[status(thm)],[1233])).
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% 0.74/0.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), 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(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 0.74/0.95 inference(transitivity,[status(thm)],[1234, 1232])).
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% 0.74/0.95 inference(quant_inst,[status(thm)],[])).
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% 0.74/0.95 inference(modus_ponens,[status(thm)],[1236, 1235])).
% 0.74/0.95 tff(1238,plain,
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% 0.74/0.95 inference(unit_resolution,[status(thm)],[1237, 180, 224, 289, 539, 400])).
% 0.74/0.95 tff(1239,plain,((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.95 tff(1240,plain,
% 0.74/0.95 (~b(s(s(s(s(z)))), s(z))),
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% 0.74/0.95 ((s(s(s(s(z)))) = s(z)) | r(s(s(s(s(z)))), s(z))),
% 0.74/0.95 inference(unit_resolution,[status(thm)],[381, 73, 1240])).
% 0.74/0.95 tff(1242,plain,
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% 0.74/0.95 inference(unit_resolution,[status(thm)],[1241, 352])).
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% 0.74/0.95 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))),
% 0.74/0.96 inference(rewrite,[status(thm)],[])).
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% 0.74/0.96 (((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(z, s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))),
% 0.74/0.96 inference(rewrite,[status(thm)],[])).
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% 0.74/0.96 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z)))))),
% 0.74/0.96 inference(monotonicity,[status(thm)],[1244])).
% 0.74/0.96 tff(1246,plain,
% 0.74/0.96 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))),
% 0.74/0.96 inference(transitivity,[status(thm)],[1245, 1243])).
% 0.74/0.96 tff(1247,plain,
% 0.74/0.96 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))))),
% 0.74/0.96 inference(quant_inst,[status(thm)],[])).
% 0.74/0.96 tff(1248,plain,
% 0.74/0.96 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z)))),
% 0.74/0.96 inference(modus_ponens,[status(thm)],[1247, 1246])).
% 0.74/0.96 tff(1249,plain,
% 0.74/0.96 ($false),
% 0.74/0.96 inference(unit_resolution,[status(thm)],[1248, 53, 269, 43, 1242])).
% 0.74/0.96 tff(1250,plain,((~r(z, s(s(s(s(z)))))) | (~r(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.96 tff(1251,plain,
% 0.74/0.96 (~r(z, s(s(s(s(z)))))),
% 0.74/0.96 inference(unit_resolution,[status(thm)],[1250, 1051, 1213, 1217, 1221])).
% 0.74/0.96 tff(1252,plain,
% 0.74/0.96 (b(z, s(s(s(s(z)))))),
% 0.74/0.96 inference(unit_resolution,[status(thm)],[78, 1251])).
% 0.74/0.96 tff(1253,plain,
% 0.74/0.96 (~b(s(z), z)),
% 0.74/0.96 inference(unit_resolution,[status(thm)],[1081, 180, 1217, 718, 1252])).
% 0.74/0.96 tff(1254,plain,
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% 0.74/0.96 inference(unit_resolution,[status(thm)],[267, 1253])).
% 0.74/0.96 tff(1255,plain,
% 0.74/0.96 (~r(s(z), s(s(s(z))))),
% 0.74/0.96 inference(unit_resolution,[status(thm)],[1039, 53, 1254, 1221])).
% 0.74/0.96 tff(1256,plain,
% 0.74/0.96 (b(s(z), s(s(s(z))))),
% 0.74/0.96 inference(unit_resolution,[status(thm)],[373, 1255])).
% 0.74/0.96 tff(1257,plain,
% 0.74/0.96 (~b(s(s(z)), s(z))),
% 0.74/0.96 inference(unit_resolution,[status(thm)],[848, 1256, 1213, 151])).
% 0.74/0.96 tff(1258,plain,
% 0.74/0.96 (r(s(s(z)), s(z))),
% 0.74/0.96 inference(unit_resolution,[status(thm)],[253, 1257])).
% 0.74/0.96 tff(1259,plain,
% 0.74/0.96 ((s(s(s(z))) = s(s(z))) <=> (s(s(z)) = s(s(s(z))))),
% 0.74/0.96 inference(commutativity,[status(thm)],[])).
% 0.74/0.96 tff(1260,plain,
% 0.74/0.96 ((s(s(z)) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(z)))),
% 0.74/0.96 inference(symmetry,[status(thm)],[1259])).
% 0.74/0.96 tff(1261,plain,
% 0.74/0.96 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(z))))),
% 0.74/0.96 inference(monotonicity,[status(thm)],[1260])).
% 0.74/0.96 tff(1262,plain,
% 0.74/0.96 (~(s(s(s(z))) = s(s(z)))),
% 0.74/0.96 inference(modus_ponens,[status(thm)],[145, 1261])).
% 0.74/0.96 tff(1263,plain,
% 0.74/0.96 (~r(z, s(s(z)))),
% 0.74/0.96 inference(unit_resolution,[status(thm)],[693, 269, 39])).
% 0.74/0.96 tff(1264,plain,
% 0.74/0.96 (b(z, s(s(z)))),
% 0.74/0.96 inference(unit_resolution,[status(thm)],[703, 1263])).
% 0.74/0.96 tff(1265,plain,
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% 0.74/0.96 inference(rewrite,[status(thm)],[])).
% 0.74/0.96 tff(1266,plain,
% 0.74/0.96 (((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 0.74/0.96 inference(rewrite,[status(thm)],[])).
% 0.74/0.96 tff(1267,plain,
% 0.74/0.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))))),
% 0.74/0.96 inference(monotonicity,[status(thm)],[1266])).
% 0.74/0.96 tff(1268,plain,
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% 0.74/0.96 inference(transitivity,[status(thm)],[1267, 1265])).
% 0.74/0.96 tff(1269,plain,
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% 0.74/0.96 inference(quant_inst,[status(thm)],[])).
% 0.74/0.96 tff(1270,plain,
% 0.74/0.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))),
% 0.74/0.96 inference(modus_ponens,[status(thm)],[1269, 1268])).
% 0.74/0.96 tff(1271,plain,
% 0.74/0.96 (~b(s(s(z)), s(s(s(s(z)))))),
% 0.74/0.96 inference(unit_resolution,[status(thm)],[1270, 180, 872, 1264, 719])).
% 0.74/0.96 tff(1272,plain,
% 0.74/0.96 (r(s(s(z)), s(s(s(s(z)))))),
% 0.74/0.96 inference(unit_resolution,[status(thm)],[212, 1271])).
% 0.74/0.96 tff(1273,plain,
% 0.74/0.96 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))))),
% 0.74/0.96 inference(rewrite,[status(thm)],[])).
% 0.74/0.96 tff(1274,plain,
% 0.74/0.96 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))))),
% 0.74/0.96 inference(quant_inst,[status(thm)],[])).
% 0.74/0.96 tff(1275,plain,
% 0.74/0.96 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z))))),
% 0.74/0.96 inference(modus_ponens,[status(thm)],[1274, 1273])).
% 0.74/0.96 tff(1276,plain,
% 0.74/0.96 (~r(s(s(s(z))), s(s(z)))),
% 0.74/0.96 inference(unit_resolution,[status(thm)],[1275, 53, 571, 1272])).
% 0.74/0.96 tff(1277,plain,
% 0.74/0.96 ((s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z)))),
% 0.74/0.96 inference(unit_resolution,[status(thm)],[330, 73, 1276])).
% 0.74/0.96 tff(1278,plain,
% 0.74/0.96 (b(s(s(s(z))), s(s(z)))),
% 0.74/0.96 inference(unit_resolution,[status(thm)],[1277, 1262])).
% 0.74/0.96 tff(1279,plain,
% 0.74/0.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)))),
% 0.74/0.96 inference(rewrite,[status(thm)],[])).
% 0.74/0.96 tff(1280,plain,
% 0.74/0.96 (((~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)))),
% 0.74/0.96 inference(rewrite,[status(thm)],[])).
% 0.74/0.96 tff(1281,plain,
% 0.74/0.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z))))),
% 0.74/0.96 inference(monotonicity,[status(thm)],[1280])).
% 0.74/0.96 tff(1282,plain,
% 0.74/0.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)))),
% 0.74/0.96 inference(transitivity,[status(thm)],[1281, 1279])).
% 0.74/0.96 tff(1283,plain,
% 0.74/0.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))))),
% 0.74/0.96 inference(quant_inst,[status(thm)],[])).
% 0.74/0.96 tff(1284,plain,
% 0.74/0.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z))),
% 0.74/0.96 inference(modus_ponens,[status(thm)],[1283, 1282])).
% 0.74/0.96 tff(1285,plain,
% 0.74/0.96 ($false),
% 0.74/0.96 inference(unit_resolution,[status(thm)],[1284, 180, 872, 1264, 167, 1278])).
% 0.74/0.96 tff(1286,plain,((~r(z, s(z))) | (~b(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.96 tff(1287,plain,
% 0.74/0.96 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 0.74/0.96 inference(unit_resolution,[status(thm)],[1286, 1258, 718, 992, 1051])).
% 0.74/0.96 tff(1288,plain,
% 0.74/0.96 (b(s(s(s(z))), s(s(s(s(z)))))),
% 0.74/0.96 inference(unit_resolution,[status(thm)],[468, 1287])).
% 0.74/0.96 tff(1289,plain,
% 0.74/0.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 0.74/0.96 inference(rewrite,[status(thm)],[])).
% 0.74/0.96 tff(1290,plain,
% 0.74/0.96 (((~b(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(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(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(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 0.74/0.96 inference(rewrite,[status(thm)],[])).
% 0.74/0.96 tff(1291,plain,
% 0.74/0.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(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)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z))))))))),
% 0.74/0.96 inference(monotonicity,[status(thm)],[1290])).
% 0.74/0.96 tff(1292,plain,
% 0.74/0.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(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)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 0.74/0.96 inference(transitivity,[status(thm)],[1291, 1289])).
% 0.74/0.96 tff(1293,plain,
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% 0.74/0.96 inference(quant_inst,[status(thm)],[])).
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% 0.74/0.96 inference(modus_ponens,[status(thm)],[1293, 1292])).
% 0.74/0.96 tff(1295,plain,
% 0.74/0.96 ($false),
% 0.74/0.96 inference(unit_resolution,[status(thm)],[1294, 180, 1217, 1213, 718, 1288, 1252])).
% 0.74/0.96 tff(1296,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.96 tff(1297,plain,
% 0.74/0.96 (~r(s(s(z)), s(s(s(s(z)))))),
% 0.74/0.96 inference(unit_resolution,[status(thm)],[1296, 40])).
% 0.74/0.96 tff(1298,plain,
% 0.74/0.96 (b(s(s(z)), s(s(s(s(z)))))),
% 0.74/0.96 inference(unit_resolution,[status(thm)],[212, 1297])).
% 0.74/0.96 tff(1299,plain,
% 0.74/0.96 (~r(z, s(s(s(z))))),
% 0.74/0.96 inference(unit_resolution,[status(thm)],[58, 43, 40])).
% 0.74/0.96 tff(1300,plain,
% 0.74/0.96 (b(z, s(s(s(z))))),
% 0.74/0.96 inference(unit_resolution,[status(thm)],[102, 1299])).
% 0.74/0.96 tff(1301,plain,
% 0.74/0.96 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 0.74/0.96 inference(rewrite,[status(thm)],[])).
% 0.74/0.96 tff(1302,plain,
% 0.74/0.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))))),
% 0.74/0.96 inference(monotonicity,[status(thm)],[1301])).
% 0.74/0.96 tff(1303,plain,
% 0.74/0.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 0.74/0.96 inference(transitivity,[status(thm)],[1302, 891])).
% 0.74/0.96 tff(1304,plain,
% 0.74/0.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 0.74/0.96 inference(quant_inst,[status(thm)],[])).
% 0.74/0.96 tff(1305,plain,
% 0.74/0.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))),
% 0.74/0.96 inference(modus_ponens,[status(thm)],[1304, 1303])).
% 0.74/0.96 tff(1306,plain,
% 0.74/0.96 ($false),
% 0.74/0.96 inference(unit_resolution,[status(thm)],[1305, 180, 170, 719, 540, 223])).
% 0.74/0.96 tff(1307,plain,((~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.96 tff(1308,plain,
% 0.74/0.96 (~b(z, s(s(s(s(z)))))),
% 0.74/0.96 inference(unit_resolution,[status(thm)],[1307, 170, 718, 1298])).
% 0.74/0.96 tff(1309,plain,
% 0.74/0.96 (r(z, s(s(s(s(z)))))),
% 0.74/0.96 inference(unit_resolution,[status(thm)],[78, 1308])).
% 0.74/0.96 tff(1310,plain,
% 0.74/0.96 ($false),
% 0.74/0.96 inference(unit_resolution,[status(thm)],[1270, 180, 170, 751, 719, 223])).
% 0.74/0.96 tff(1311,plain,((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.96 tff(1312,plain,
% 0.74/0.96 (~b(z, s(s(z)))),
% 0.74/0.96 inference(unit_resolution,[status(thm)],[1311, 170, 718, 1298])).
% 0.74/0.96 tff(1313,plain,
% 0.74/0.96 (r(z, s(s(z)))),
% 0.74/0.96 inference(unit_resolution,[status(thm)],[703, 1312])).
% 0.74/0.96 tff(1314,plain,
% 0.74/0.96 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 0.74/0.96 inference(rewrite,[status(thm)],[])).
% 0.74/0.96 tff(1315,plain,
% 0.74/0.96 (((~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 0.74/0.96 inference(rewrite,[status(thm)],[])).
% 0.74/0.96 tff(1316,plain,
% 0.74/0.96 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 0.74/0.96 inference(monotonicity,[status(thm)],[1315])).
% 0.74/0.96 tff(1317,plain,
% 0.74/0.96 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 0.74/0.96 inference(transitivity,[status(thm)],[1316, 1314])).
% 0.74/0.96 tff(1318,plain,
% 0.74/0.96 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))))),
% 0.74/0.96 inference(quant_inst,[status(thm)],[])).
% 0.74/0.96 tff(1319,plain,
% 0.74/0.96 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 0.74/0.96 inference(modus_ponens,[status(thm)],[1318, 1317])).
% 0.74/0.96 tff(1320,plain,
% 0.74/0.96 ($false),
% 0.74/0.96 inference(unit_resolution,[status(thm)],[1319, 53, 688, 43, 1178])).
% 0.74/0.96 tff(1321,plain,((~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.96 tff(1322,plain,
% 0.74/0.96 (~r(s(s(s(s(z)))), s(s(z)))),
% 0.74/0.96 inference(unit_resolution,[status(thm)],[1321, 1313, 1309])).
% 0.74/0.96 tff(1323,assumption,(~r(s(s(s(s(z)))), s(s(z)))), introduced(assumption)).
% 0.74/0.96 tff(1324,assumption,(~b(s(s(s(s(z)))), s(s(z)))), introduced(assumption)).
% 0.74/0.96 tff(1325,plain,
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% 0.74/0.96 inference(unit_resolution,[status(thm)],[220, 73, 203, 1324, 1323])).
% 0.74/0.96 tff(1326,plain,(b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.96 tff(1327,plain,
% 0.74/0.96 (b(s(s(s(s(z)))), s(s(z)))),
% 0.74/0.96 inference(unit_resolution,[status(thm)],[1326, 1322])).
% 0.74/0.96 tff(1328,plain,
% 0.74/0.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 0.74/0.96 inference(rewrite,[status(thm)],[])).
% 0.74/0.96 tff(1329,plain,
% 0.74/0.96 (((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 0.74/0.96 inference(rewrite,[status(thm)],[])).
% 0.74/0.96 tff(1330,plain,
% 0.74/0.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))))),
% 0.74/0.96 inference(monotonicity,[status(thm)],[1329])).
% 0.74/0.96 tff(1331,plain,
% 0.74/0.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 0.74/0.96 inference(transitivity,[status(thm)],[1330, 1328])).
% 0.74/0.96 tff(1332,plain,
% 0.74/0.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 0.74/0.96 inference(quant_inst,[status(thm)],[])).
% 0.74/0.96 tff(1333,plain,
% 0.74/0.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))),
% 0.74/0.96 inference(modus_ponens,[status(thm)],[1332, 1331])).
% 0.74/0.96 tff(1334,plain,
% 0.74/0.96 ($false),
% 0.74/0.96 inference(unit_resolution,[status(thm)],[1333, 180, 291, 170, 290, 719, 223])).
% 0.74/0.96 tff(1335,plain,((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.96 tff(1336,plain,
% 0.74/0.96 (~b(s(z), z)),
% 0.74/0.96 inference(unit_resolution,[status(thm)],[1335, 170, 291, 719, 223])).
% 0.74/0.96 tff(1337,plain,
% 0.74/0.96 (r(s(z), z)),
% 0.74/0.96 inference(unit_resolution,[status(thm)],[267, 1336])).
% 0.74/0.96 tff(1338,plain,
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% 0.74/0.97 inference(monotonicity,[status(thm)],[1339])).
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% 0.74/0.97 inference(transitivity,[status(thm)],[1340, 1338])).
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% 0.74/0.97 inference(quant_inst,[status(thm)],[])).
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% 0.74/0.97 tff(1346,plain,
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% 0.74/0.97 inference(unit_resolution,[status(thm)],[1345, 1337, 526])).
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% 0.74/0.97 (b(z, s(s(s(s(z)))))),
% 0.74/0.97 inference(unit_resolution,[status(thm)],[78, 1346])).
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% 0.74/0.97 inference(unit_resolution,[status(thm)],[1305, 180, 170, 719, 1347, 223])).
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% 0.74/0.97 tff(1350,plain,
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% 0.74/0.97 inference(unit_resolution,[status(thm)],[1349, 170, 719, 223, 526])).
% 0.74/0.97 tff(1351,plain,
% 0.74/0.97 (r(z, s(z))),
% 0.74/0.97 inference(unit_resolution,[status(thm)],[287, 1350])).
% 0.74/0.97 tff(1352,plain,
% 0.74/0.97 (~b(z, s(s(s(s(z)))))),
% 0.74/0.97 inference(unit_resolution,[status(thm)],[616, 170, 223, 222])).
% 0.74/0.97 tff(1353,plain,
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% 0.74/0.97 inference(unit_resolution,[status(thm)],[78, 1352])).
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% 0.74/0.97 inference(unit_resolution,[status(thm)],[558, 1353, 1351, 526])).
% 0.74/0.97 tff(1355,plain,((~b(s(s(z)), z)) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.97 tff(1356,plain,
% 0.74/0.97 (~r(s(z), s(s(s(s(z)))))),
% 0.74/0.97 inference(unit_resolution,[status(thm)],[1355, 1327, 1298, 170, 718])).
% 0.74/0.97 tff(1357,plain,
% 0.74/0.97 (~r(s(s(s(s(z)))), s(s(z)))),
% 0.74/0.97 inference(unit_resolution,[status(thm)],[606, 53, 40, 119])).
% 0.74/0.97 tff(1358,plain,
% 0.74/0.97 (b(s(s(s(s(z)))), s(s(z)))),
% 0.74/0.97 inference(unit_resolution,[status(thm)],[220, 73, 203, 1357])).
% 0.74/0.97 tff(1359,plain,
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% 0.74/0.97 inference(unit_resolution,[status(thm)],[1355, 526, 1298, 1358, 718])).
% 0.74/0.97 tff(1360,plain,
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% 0.74/0.97 inference(unit_resolution,[status(thm)],[165, 1359])).
% 0.74/0.97 tff(1361,plain,
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% 0.74/0.97 inference(unit_resolution,[status(thm)],[86, 53, 40, 42])).
% 0.74/0.97 tff(1362,plain,
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% 0.74/0.97 inference(unit_resolution,[status(thm)],[717, 1361])).
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% 0.74/0.97 inference(rewrite,[status(thm)],[])).
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% 0.74/0.97 inference(rewrite,[status(thm)],[])).
% 0.74/0.97 tff(1365,plain,
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% 0.74/0.97 inference(monotonicity,[status(thm)],[1364])).
% 0.74/0.97 tff(1366,plain,
% 0.74/0.97 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 0.74/0.97 inference(transitivity,[status(thm)],[1365, 1363])).
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% 0.74/0.97 inference(quant_inst,[status(thm)],[])).
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% 0.74/0.97 inference(modus_ponens,[status(thm)],[1367, 1366])).
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% 0.74/0.97 inference(unit_resolution,[status(thm)],[1368, 53, 119, 42])).
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% 0.74/0.97 inference(unit_resolution,[status(thm)],[703, 1369])).
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% 0.74/0.97 inference(rewrite,[status(thm)],[])).
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% 0.74/0.97 inference(rewrite,[status(thm)],[])).
% 0.74/0.97 tff(1373,plain,
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% 0.74/0.97 inference(monotonicity,[status(thm)],[1372])).
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% 0.74/0.97 inference(transitivity,[status(thm)],[1373, 1371])).
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% 0.74/0.97 inference(quant_inst,[status(thm)],[])).
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% 0.74/0.97 inference(modus_ponens,[status(thm)],[1375, 1374])).
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% 0.74/0.97 inference(unit_resolution,[status(thm)],[1376, 53, 119, 42])).
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% 0.74/0.97 tff(1380,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.97 tff(1381,plain,
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% 0.74/0.97 inference(unit_resolution,[status(thm)],[102, 1381])).
% 0.74/0.97 tff(1383,plain,
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% 0.74/0.97 inference(unit_resolution,[status(thm)],[579, 309, 526])).
% 0.74/0.97 tff(1384,plain,
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% 0.74/0.97 inference(unit_resolution,[status(thm)],[468, 1383])).
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% 0.74/0.97 inference(rewrite,[status(thm)],[])).
% 0.74/0.97 tff(1386,plain,
% 0.74/0.97 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 0.74/0.97 inference(rewrite,[status(thm)],[])).
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% 0.74/0.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 0.74/0.97 inference(monotonicity,[status(thm)],[1386])).
% 0.74/0.97 tff(1388,plain,
% 0.74/0.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 0.74/0.97 inference(transitivity,[status(thm)],[1387, 1385])).
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% 0.74/0.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))),
% 0.74/0.97 inference(quant_inst,[status(thm)],[])).
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% 0.74/0.97 inference(modus_ponens,[status(thm)],[1389, 1388])).
% 0.74/0.97 tff(1391,plain,
% 0.74/0.97 (~b(s(s(s(z))), s(s(z)))),
% 0.74/0.97 inference(unit_resolution,[status(thm)],[1390, 180, 1384, 222, 223])).
% 0.74/0.97 tff(1392,plain,
% 0.74/0.97 (r(s(s(s(z))), s(s(z)))),
% 0.74/0.97 inference(unit_resolution,[status(thm)],[330, 73, 1391, 323])).
% 0.74/0.97 tff(1393,plain,
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% 0.74/0.97 inference(unit_resolution,[status(thm)],[568, 1384, 223, 167, 222, 353])).
% 0.74/0.97 tff(1394,plain,
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% 0.74/0.97 inference(unit_resolution,[status(thm)],[287, 1393])).
% 0.74/0.97 tff(1395,plain,
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% 0.74/0.97 inference(unit_resolution,[status(thm)],[361, 1394, 167, 353])).
% 0.74/0.97 tff(1396,plain,
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% 0.74/0.97 inference(unit_resolution,[status(thm)],[117, 1395])).
% 0.74/0.97 tff(1397,plain,
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% 0.74/0.97 inference(unit_resolution,[status(thm)],[317, 309, 119])).
% 0.74/0.97 tff(1398,plain,
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% 0.74/0.97 inference(unit_resolution,[status(thm)],[1349, 1394, 719, 223, 526])).
% 0.74/0.97 tff(1399,plain,
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% 0.74/0.97 inference(unit_resolution,[status(thm)],[165, 1398])).
% 0.74/0.97 tff(1400,plain,
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% 0.74/0.97 inference(unit_resolution,[status(thm)],[782, 1399, 1394, 1397])).
% 0.74/0.97 tff(1401,plain,
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% 0.74/0.97 inference(unit_resolution,[status(thm)],[703, 1400])).
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% 0.74/0.97 inference(rewrite,[status(thm)],[])).
% 0.74/0.97 tff(1403,plain,
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% 0.74/0.97 inference(rewrite,[status(thm)],[])).
% 0.74/0.97 tff(1404,plain,
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% 0.74/0.97 inference(monotonicity,[status(thm)],[1403])).
% 0.74/0.97 tff(1405,plain,
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% 0.74/0.97 inference(transitivity,[status(thm)],[1404, 1402])).
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% 0.74/0.97 inference(quant_inst,[status(thm)],[])).
% 0.74/0.97 tff(1407,plain,
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% 0.74/0.97 inference(modus_ponens,[status(thm)],[1406, 1405])).
% 0.74/0.97 tff(1408,plain,
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% 0.74/0.97 inference(unit_resolution,[status(thm)],[1407, 53, 1401, 1396, 1392])).
% 0.74/0.97 tff(1409,plain,((~r(s(s(s(z))), 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)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.97 tff(1410,plain,
% 0.74/0.97 (~r(s(s(s(z))), s(z))),
% 0.74/0.97 inference(unit_resolution,[status(thm)],[1409, 526, 1298, 718, 1358, 1382, 620, 119])).
% 0.74/0.97 tff(1411,plain,
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% 0.74/0.97 inference(unit_resolution,[status(thm)],[307, 1410])).
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% 0.74/0.97 tff(1413,plain,
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% 0.74/0.97 inference(unit_resolution,[status(thm)],[267, 1412])).
% 0.74/0.97 tff(1414,plain,
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% 0.74/0.97 inference(unit_resolution,[status(thm)],[780, 53, 152, 1413])).
% 0.74/0.97 tff(1415,plain,
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% 0.74/0.97 inference(unit_resolution,[status(thm)],[341, 73, 247, 1414])).
% 0.74/0.97 tff(1416,plain,
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% 0.74/0.97 inference(unit_resolution,[status(thm)],[260, 1413, 152])).
% 0.74/0.97 tff(1417,plain,
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% 0.74/0.97 inference(unit_resolution,[status(thm)],[253, 1416])).
% 0.74/0.97 tff(1418,plain,
% 0.74/0.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))))),
% 0.74/0.97 inference(rewrite,[status(thm)],[])).
% 0.74/0.97 tff(1419,plain,
% 0.74/0.97 (((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))))),
% 0.74/0.97 inference(rewrite,[status(thm)],[])).
% 0.74/0.97 tff(1420,plain,
% 0.74/0.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z)))))),
% 0.74/0.97 inference(monotonicity,[status(thm)],[1419])).
% 0.74/0.97 tff(1421,plain,
% 0.74/0.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))))),
% 0.74/0.97 inference(transitivity,[status(thm)],[1420, 1418])).
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% 0.74/0.97 inference(modus_ponens,[status(thm)],[1422, 1421])).
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% 0.74/0.97 tff(1425,plain,((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.97 tff(1426,plain,
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% 0.74/0.97 inference(unit_resolution,[status(thm)],[287, 1426])).
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% 0.74/0.97 inference(unit_resolution,[status(thm)],[558, 1427, 526])).
% 0.74/0.97 tff(1429,plain,
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% 0.74/0.97 inference(unit_resolution,[status(thm)],[78, 1428])).
% 0.74/0.97 tff(1430,plain,
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% 0.74/0.97 tff(1431,plain,
% 0.74/0.97 (b(s(s(z)), s(z))),
% 0.74/0.97 inference(unit_resolution,[status(thm)],[253, 1430])).
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% 0.74/0.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 0.74/0.97 inference(rewrite,[status(thm)],[])).
% 0.74/0.97 tff(1433,plain,
% 0.74/0.97 (((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 0.74/0.97 inference(rewrite,[status(thm)],[])).
% 0.74/0.97 tff(1434,plain,
% 0.74/0.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))))),
% 0.74/0.97 inference(monotonicity,[status(thm)],[1433])).
% 0.74/0.97 tff(1435,plain,
% 0.74/0.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 0.74/0.97 inference(transitivity,[status(thm)],[1434, 1432])).
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% 0.74/0.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 0.74/0.97 inference(quant_inst,[status(thm)],[])).
% 0.74/0.97 tff(1437,plain,
% 0.74/0.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))),
% 0.74/0.97 inference(modus_ponens,[status(thm)],[1436, 1435])).
% 0.74/0.97 tff(1438,plain,
% 0.74/0.97 (~b(s(s(s(z))), s(s(z)))),
% 0.74/0.97 inference(unit_resolution,[status(thm)],[1437, 180, 1431, 620, 1411])).
% 0.74/0.97 tff(1439,plain,
% 0.74/0.97 (r(s(s(s(z))), s(s(z)))),
% 0.74/0.97 inference(unit_resolution,[status(thm)],[330, 73, 1438, 323])).
% 0.74/0.97 tff(1440,plain,
% 0.74/0.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 0.74/0.97 inference(rewrite,[status(thm)],[])).
% 0.74/0.97 tff(1441,plain,
% 0.74/0.97 (((~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(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z))))) <=> ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 0.74/0.97 inference(rewrite,[status(thm)],[])).
% 0.74/0.97 tff(1442,plain,
% 0.74/0.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))))),
% 0.74/0.97 inference(monotonicity,[status(thm)],[1441])).
% 0.74/0.97 tff(1443,plain,
% 0.74/0.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 0.74/0.98 inference(transitivity,[status(thm)],[1442, 1440])).
% 0.74/0.98 tff(1444,plain,
% 0.74/0.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))))),
% 0.74/0.98 inference(quant_inst,[status(thm)],[])).
% 0.74/0.98 tff(1445,plain,
% 0.74/0.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))),
% 0.74/0.98 inference(modus_ponens,[status(thm)],[1444, 1443])).
% 0.74/0.98 tff(1446,plain,
% 0.74/0.98 (~b(z, s(s(z)))),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[1445, 180, 718, 1429, 1298])).
% 0.74/0.98 tff(1447,plain,
% 0.74/0.98 (r(z, s(s(z)))),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[703, 1446])).
% 0.74/0.98 tff(1448,plain,
% 0.74/0.98 (~r(s(s(s(z))), z)),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[1407, 53, 1447, 1439])).
% 0.74/0.98 tff(1449,plain,
% 0.74/0.98 (b(s(s(s(z))), z)),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[117, 1448])).
% 0.74/0.98 tff(1450,plain,
% 0.74/0.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))))),
% 0.74/0.98 inference(rewrite,[status(thm)],[])).
% 0.74/0.98 tff(1451,plain,
% 0.74/0.98 (((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))))),
% 0.74/0.98 inference(rewrite,[status(thm)],[])).
% 0.74/0.98 tff(1452,plain,
% 0.74/0.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z)))))))),
% 0.74/0.98 inference(monotonicity,[status(thm)],[1451])).
% 0.74/0.98 tff(1453,plain,
% 0.74/0.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))))),
% 0.74/0.98 inference(transitivity,[status(thm)],[1452, 1450])).
% 0.74/0.98 tff(1454,plain,
% 0.74/0.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)))),
% 0.74/0.98 inference(quant_inst,[status(thm)],[])).
% 0.74/0.98 tff(1455,plain,
% 0.74/0.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z)))))),
% 0.74/0.98 inference(modus_ponens,[status(thm)],[1454, 1453])).
% 0.74/0.98 tff(1456,plain,
% 0.74/0.98 (~b(s(z), z)),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[1455, 180, 620, 1449, 1382])).
% 0.74/0.98 tff(1457,plain,
% 0.74/0.98 (r(s(z), z)),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[267, 1456])).
% 0.74/0.98 tff(1458,plain,
% 0.74/0.98 (~r(s(z), s(s(z)))),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[780, 53, 1360, 1457])).
% 0.74/0.98 tff(1459,plain,
% 0.74/0.98 (b(s(z), s(s(z)))),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[341, 73, 247, 1458])).
% 0.74/0.98 tff(1460,plain,
% 0.74/0.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 0.74/0.98 inference(rewrite,[status(thm)],[])).
% 0.74/0.98 tff(1461,plain,
% 0.74/0.98 (((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 0.74/0.98 inference(rewrite,[status(thm)],[])).
% 0.74/0.98 tff(1462,plain,
% 0.74/0.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), 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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))))),
% 0.74/0.98 inference(monotonicity,[status(thm)],[1461])).
% 0.74/0.98 tff(1463,plain,
% 0.74/0.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), 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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 0.74/0.98 inference(transitivity,[status(thm)],[1462, 1460])).
% 0.74/0.98 tff(1464,plain,
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% 0.74/0.98 inference(quant_inst,[status(thm)],[])).
% 0.74/0.98 tff(1465,plain,
% 0.74/0.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))),
% 0.74/0.98 inference(modus_ponens,[status(thm)],[1464, 1463])).
% 0.74/0.98 tff(1466,plain,
% 0.74/0.98 ($false),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[1465, 180, 225, 752, 222, 409, 399])).
% 0.74/0.98 tff(1467,plain,((~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.98 tff(1468,plain,
% 0.74/0.98 (~b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[1467, 384, 222, 752, 225])).
% 0.74/0.98 tff(1469,plain,
% 0.74/0.98 (r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[1096, 1468])).
% 0.74/0.98 tff(1470,plain,
% 0.74/0.98 ($false),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[1091, 53, 152, 1075, 1469])).
% 0.74/0.98 tff(1471,plain,(r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) | (~r(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.98 tff(1472,plain,
% 0.74/0.98 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[1471, 1360, 1358, 1459, 1431, 1429, 718])).
% 0.74/0.98 tff(1473,plain,
% 0.74/0.98 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[568, 1427, 1298, 1382, 1358, 620])).
% 0.74/0.98 tff(1474,plain,
% 0.74/0.98 (r(s(s(s(z))), s(s(s(s(z)))))),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[468, 1473])).
% 0.74/0.98 tff(1475,assumption,(r(s(s(s(s(s(s(z)))))), s(s(s(z))))), introduced(assumption)).
% 0.74/0.98 tff(1476,assumption,(r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))), introduced(assumption)).
% 0.74/0.98 tff(1477,plain,
% 0.74/0.98 ($false),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[472, 53, 571, 1476, 1475])).
% 0.74/0.98 tff(1478,plain,((~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(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.98 tff(1479,plain,
% 0.74/0.98 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[1478, 1474, 1472])).
% 0.74/0.98 tff(1480,plain,
% 0.74/0.98 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[487, 73, 484, 1479])).
% 0.74/0.98 tff(1481,plain,
% 0.74/0.98 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 0.74/0.98 inference(rewrite,[status(thm)],[])).
% 0.74/0.98 tff(1482,plain,
% 0.74/0.98 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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(s(s(s(s(s(z)))))), s(z))))),
% 0.74/0.98 inference(quant_inst,[status(thm)],[])).
% 0.74/0.98 tff(1483,plain,
% 0.74/0.98 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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(s(s(s(s(s(z)))))), s(z)))),
% 0.74/0.98 inference(modus_ponens,[status(thm)],[1482, 1481])).
% 0.74/0.98 tff(1484,plain,
% 0.74/0.98 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[1483, 53, 526, 1472])).
% 0.74/0.98 tff(1485,plain,
% 0.74/0.98 (b(s(s(s(s(s(s(z)))))), s(z))),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[947, 1484])).
% 0.74/0.98 tff(1486,plain,
% 0.74/0.98 (((~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(z))), 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(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))))),
% 0.74/0.98 inference(rewrite,[status(thm)],[])).
% 0.74/0.98 tff(1487,plain,
% 0.74/0.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z))), 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))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))))),
% 0.74/0.98 inference(monotonicity,[status(thm)],[1486])).
% 0.74/0.98 tff(1488,plain,
% 0.74/0.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z))), 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))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 0.74/0.98 inference(transitivity,[status(thm)],[1487, 949])).
% 0.74/0.98 tff(1489,plain,
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% 0.74/0.98 inference(quant_inst,[status(thm)],[])).
% 0.74/0.98 tff(1490,plain,
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% 0.74/0.98 inference(modus_ponens,[status(thm)],[1489, 1488])).
% 0.74/0.98 tff(1491,plain,
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% 0.74/0.98 inference(unit_resolution,[status(thm)],[1490, 180, 620, 1411, 1485, 1480])).
% 0.74/0.98 tff(1492,plain,((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.98 tff(1493,plain,
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% 0.74/0.98 inference(unit_resolution,[status(thm)],[1492, 119, 40])).
% 0.74/0.98 tff(1494,plain,
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% 0.74/0.98 inference(unit_resolution,[status(thm)],[523, 1493])).
% 0.74/0.98 tff(1495,plain,
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% 0.74/0.98 inference(unit_resolution,[status(thm)],[233, 1494, 1298, 1358])).
% 0.74/0.98 tff(1496,plain,
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% 0.74/0.98 inference(unit_resolution,[status(thm)],[253, 1495])).
% 0.74/0.98 tff(1497,plain,
% 0.74/0.98 (~r(s(s(s(z))), s(z))),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[317, 1496, 119])).
% 0.74/0.98 tff(1498,plain,
% 0.74/0.98 (b(s(s(s(z))), s(z))),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[307, 1497])).
% 0.74/0.98 tff(1499,plain,
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% 0.74/0.98 inference(rewrite,[status(thm)],[])).
% 0.74/0.98 tff(1500,plain,
% 0.74/0.98 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), 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(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(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 0.74/0.98 inference(rewrite,[status(thm)],[])).
% 0.74/0.98 tff(1501,plain,
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% 0.74/0.98 inference(monotonicity,[status(thm)],[1500])).
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% 0.74/0.98 inference(transitivity,[status(thm)],[1501, 1499])).
% 0.74/0.98 tff(1503,plain,
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% 0.74/0.98 inference(quant_inst,[status(thm)],[])).
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% 0.74/0.98 tff(1505,plain,
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% 0.74/0.98 inference(unit_resolution,[status(thm)],[1504, 180, 224, 289, 539, 222, 223])).
% 0.74/0.98 tff(1506,plain,((~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(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.98 tff(1507,plain,
% 0.74/0.98 (~b(s(s(s(z))), s(s(s(s(z)))))),
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% 0.74/0.98 tff(1511,plain,
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% 0.74/0.98 tff(1512,plain,
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% 0.74/0.98 tff(1513,plain,
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% 0.74/0.98 inference(unit_resolution,[status(thm)],[361, 1512, 1382, 1510])).
% 0.74/0.98 tff(1514,plain,
% 0.74/0.98 (r(s(s(s(z))), z)),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[117, 1513])).
% 0.74/0.98 tff(1515,plain,
% 0.74/0.98 (~b(z, s(s(s(s(z)))))),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[747, 1512, 718, 1494])).
% 0.74/0.98 tff(1516,plain,
% 0.74/0.98 (r(z, s(s(s(s(z)))))),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[78, 1515])).
% 0.74/0.98 tff(1517,plain,
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% 0.74/0.98 inference(unit_resolution,[status(thm)],[1229, 1516, 1514, 1508])).
% 0.74/0.98 tff(1518,plain,((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.98 tff(1519,plain,
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% 0.74/0.98 tff(1521,plain,
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% 0.74/0.98 tff(1522,plain,
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% 0.74/0.98 tff(1523,plain,
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% 0.74/0.98 tff(1524,plain,
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% 0.74/0.98 tff(1526,plain,
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% 0.74/0.98 tff(1527,plain,
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% 0.74/0.98 tff(1528,plain,
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% 0.74/0.98 tff(1529,plain,
% 0.74/0.98 (~b(z, s(s(s(s(z)))))),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[747, 1528, 718, 291])).
% 0.74/0.98 tff(1530,plain,
% 0.74/0.98 (r(z, s(s(s(s(z)))))),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[78, 1529])).
% 0.74/0.98 tff(1531,plain,
% 0.74/0.98 (~r(z, s(s(s(z))))),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[58, 1530, 40])).
% 0.74/0.98 tff(1532,plain,
% 0.74/0.98 (b(z, s(s(s(z))))),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[102, 1531])).
% 0.74/0.98 tff(1533,plain,
% 0.74/0.98 (~b(s(s(s(z))), z)),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[188, 1532, 1520, 170])).
% 0.74/0.98 tff(1534,plain,
% 0.74/0.98 (r(s(s(s(z))), z)),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[117, 1533])).
% 0.74/0.98 tff(1535,plain,
% 0.74/0.98 (~b(s(z), z)),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[1335, 291, 1298, 718, 170])).
% 0.74/0.98 tff(1536,plain,
% 0.74/0.98 (r(s(z), z)),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[267, 1535])).
% 0.74/0.98 tff(1537,plain,
% 0.74/0.98 ($false),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[1031, 53, 1536, 1534, 309])).
% 0.74/0.98 tff(1538,plain,((~b(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~b(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.98 tff(1539,plain,
% 0.74/0.98 (~b(z, s(z))),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[1538, 309, 170, 40])).
% 0.74/0.98 tff(1540,plain,
% 0.74/0.98 (r(z, s(z))),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[287, 1539])).
% 0.74/0.98 tff(1541,plain,
% 0.74/0.98 (~r(z, s(s(s(z))))),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[986, 1540, 40, 1520, 170])).
% 0.74/0.98 tff(1542,plain,
% 0.74/0.98 (b(z, s(s(s(z))))),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[102, 1541])).
% 0.74/0.98 tff(1543,plain,
% 0.74/0.98 (~r(s(s(s(z))), z)),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[1056, 1540, 309])).
% 0.74/0.98 tff(1544,plain,
% 0.74/0.98 (b(s(s(s(z))), z)),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[117, 1543])).
% 0.74/0.98 tff(1545,plain,
% 0.74/0.98 ($false),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[188, 1544, 1542, 1520, 170])).
% 0.74/0.98 tff(1546,plain,((~r(s(s(s(z))), s(z))) | (~b(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.98 tff(1547,plain,
% 0.74/0.98 (~r(s(s(s(z))), s(z))),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[1546, 170, 40])).
% 0.74/0.98 tff(1548,plain,
% 0.74/0.98 (b(s(s(s(z))), s(z))),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[307, 1547])).
% 0.74/0.98 tff(1549,plain,
% 0.74/0.98 (~b(s(z), s(s(s(s(z)))))),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[1506, 1327, 1548, 1526, 1298])).
% 0.74/0.98 tff(1550,plain,
% 0.74/0.98 ($false),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[523, 1549, 1356])).
% 0.74/0.98 tff(1551,plain,((~b(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.98 tff(1552,plain,
% 0.74/0.98 (~b(s(s(z)), z)),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[1551, 40])).
% 0.74/0.98 tff(1553,plain,
% 0.74/0.98 (r(s(s(z)), z)),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[165, 1552])).
% 0.74/0.98 tff(1554,plain,
% 0.74/0.98 (~r(s(z), z)),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[1345, 526, 43])).
% 0.74/0.98 tff(1555,plain,
% 0.74/0.98 (b(s(z), z)),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[267, 1554])).
% 0.74/0.98 tff(1556,plain,
% 0.74/0.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 0.74/0.99 inference(rewrite,[status(thm)],[])).
% 0.74/0.99 tff(1557,plain,
% 0.74/0.99 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 0.74/0.99 inference(rewrite,[status(thm)],[])).
% 0.74/0.99 tff(1558,plain,
% 0.74/0.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))))),
% 0.74/0.99 inference(monotonicity,[status(thm)],[1557])).
% 0.74/0.99 tff(1559,plain,
% 0.74/0.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 0.74/0.99 inference(transitivity,[status(thm)],[1558, 1556])).
% 0.74/0.99 tff(1560,plain,
% 0.74/0.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 0.74/0.99 inference(quant_inst,[status(thm)],[])).
% 0.74/0.99 tff(1561,plain,
% 0.74/0.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))),
% 0.74/0.99 inference(modus_ponens,[status(thm)],[1560, 1559])).
% 0.74/0.99 tff(1562,plain,
% 0.74/0.99 (~b(s(s(s(s(z)))), s(z))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[1561, 180, 622, 1555, 719])).
% 0.74/0.99 tff(1563,plain,
% 0.74/0.99 ((s(s(s(s(z)))) = s(z)) | r(s(s(s(s(z)))), s(z))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[381, 73, 1562])).
% 0.74/0.99 tff(1564,plain,
% 0.74/0.99 (r(s(s(s(s(z)))), s(z))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[1563, 352])).
% 0.74/0.99 tff(1565,assumption,(r(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 0.74/0.99 tff(1566,plain,
% 0.74/0.99 (~r(z, s(s(z)))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[1321, 1178, 43])).
% 0.74/0.99 tff(1567,plain,
% 0.74/0.99 (b(z, s(s(z)))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[703, 1566])).
% 0.74/0.99 tff(1568,plain,
% 0.74/0.99 (r(s(s(z)), s(z))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[782, 1567, 152, 291])).
% 0.74/0.99 tff(1569,plain,
% 0.74/0.99 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 0.74/0.99 inference(rewrite,[status(thm)],[])).
% 0.74/0.99 tff(1570,plain,
% 0.74/0.99 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 0.74/0.99 inference(quant_inst,[status(thm)],[])).
% 0.74/0.99 tff(1571,plain,
% 0.74/0.99 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 0.74/0.99 inference(modus_ponens,[status(thm)],[1570, 1569])).
% 0.74/0.99 tff(1572,plain,
% 0.74/0.99 ($false),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[1571, 53, 1568, 1178, 1565])).
% 0.74/0.99 tff(1573,plain,((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), z)) | (~b(z, s(z))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.99 tff(1574,plain,
% 0.74/0.99 (~r(s(s(s(s(z)))), s(s(z)))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[1573, 1564, 152, 622, 43])).
% 0.74/0.99 tff(1575,plain,
% 0.74/0.99 (b(s(s(s(s(z)))), s(s(z)))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[1326, 1574])).
% 0.74/0.99 tff(1576,plain,
% 0.74/0.99 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[579, 526, 309])).
% 0.74/0.99 tff(1577,plain,
% 0.74/0.99 (b(s(s(s(z))), s(s(s(s(z)))))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[468, 1576])).
% 0.74/0.99 tff(1578,plain,
% 0.74/0.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 0.74/0.99 inference(rewrite,[status(thm)],[])).
% 0.74/0.99 tff(1579,plain,
% 0.74/0.99 (((~b(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(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 0.74/0.99 inference(rewrite,[status(thm)],[])).
% 0.74/0.99 tff(1580,plain,
% 0.74/0.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(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(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 0.74/0.99 inference(monotonicity,[status(thm)],[1579])).
% 0.74/0.99 tff(1581,plain,
% 0.74/0.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(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(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 0.74/0.99 inference(transitivity,[status(thm)],[1580, 1578])).
% 0.74/0.99 tff(1582,plain,
% 0.74/0.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(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(z)), s(s(s(z))))))),
% 0.74/0.99 inference(quant_inst,[status(thm)],[])).
% 0.74/0.99 tff(1583,plain,
% 0.74/0.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 0.74/0.99 inference(modus_ponens,[status(thm)],[1582, 1581])).
% 0.74/0.99 tff(1584,plain,
% 0.74/0.99 ($false),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[1583, 180, 1577, 169, 1575, 223])).
% 0.74/0.99 tff(1585,plain,((~r(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.99 tff(1586,plain,
% 0.74/0.99 (~r(s(z), s(s(s(s(z)))))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[1585, 309, 223, 152, 43, 719, 169])).
% 0.74/0.99 tff(1587,plain,
% 0.74/0.99 (b(s(z), s(s(s(s(z)))))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[523, 1586])).
% 0.74/0.99 tff(1588,plain,
% 0.74/0.99 (~r(s(s(s(z))), z)),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[1056, 269, 309])).
% 0.74/0.99 tff(1589,plain,
% 0.74/0.99 (b(s(s(s(z))), z)),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[117, 1588])).
% 0.74/0.99 tff(1590,plain,
% 0.74/0.99 (~r(s(s(z)), s(z))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[277, 269, 152])).
% 0.74/0.99 tff(1591,plain,
% 0.74/0.99 (b(s(s(z)), s(z))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[253, 1590])).
% 0.74/0.99 tff(1592,plain,
% 0.74/0.99 (~b(s(s(s(s(z)))), s(s(z)))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[233, 1591, 223, 224])).
% 0.74/0.99 tff(1593,plain,
% 0.74/0.99 (r(s(s(s(s(z)))), s(s(z)))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[1326, 1592])).
% 0.74/0.99 tff(1594,plain,
% 0.74/0.99 (~r(z, s(s(z)))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[1321, 1593, 43])).
% 0.74/0.99 tff(1595,plain,
% 0.74/0.99 (b(z, s(s(z)))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[703, 1594])).
% 0.74/0.99 tff(1596,plain,
% 0.74/0.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))))),
% 0.74/0.99 inference(rewrite,[status(thm)],[])).
% 0.74/0.99 tff(1597,plain,
% 0.74/0.99 (((~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(z))))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))))),
% 0.74/0.99 inference(rewrite,[status(thm)],[])).
% 0.74/0.99 tff(1598,plain,
% 0.74/0.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z))))))),
% 0.74/0.99 inference(monotonicity,[status(thm)],[1597])).
% 0.74/0.99 tff(1599,plain,
% 0.74/0.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))))),
% 0.74/0.99 inference(transitivity,[status(thm)],[1598, 1596])).
% 0.74/0.99 tff(1600,plain,
% 0.74/0.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(z)))))),
% 0.74/0.99 inference(quant_inst,[status(thm)],[])).
% 0.74/0.99 tff(1601,plain,
% 0.74/0.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z))))),
% 0.74/0.99 inference(modus_ponens,[status(thm)],[1600, 1599])).
% 0.74/0.99 tff(1602,plain,
% 0.74/0.99 ($false),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[1601, 180, 1595, 169, 1589, 167])).
% 0.74/0.99 tff(1603,plain,((~r(z, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.99 tff(1604,plain,
% 0.74/0.99 (~r(z, s(z))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[1603, 1587, 167, 43, 223, 169, 309, 152])).
% 0.74/0.99 tff(1605,plain,
% 0.74/0.99 (b(z, s(z))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[287, 1604])).
% 0.74/0.99 tff(1606,plain,
% 0.74/0.99 (~b(s(z), z)),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[1026, 1605, 719, 1587])).
% 0.74/0.99 tff(1607,plain,
% 0.74/0.99 (r(s(z), z)),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[267, 1606])).
% 0.74/0.99 tff(1608,plain,
% 0.74/0.99 (~r(s(s(z)), s(z))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[260, 1607, 152])).
% 0.74/0.99 tff(1609,plain,
% 0.74/0.99 (~b(z, s(s(z)))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[782, 1608, 152, 1605])).
% 0.74/0.99 tff(1610,plain,
% 0.74/0.99 (r(z, s(s(z)))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[703, 1609])).
% 0.74/0.99 tff(1611,plain,
% 0.74/0.99 (b(s(s(z)), s(z))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[253, 1608])).
% 0.74/0.99 tff(1612,plain,
% 0.74/0.99 (~b(s(s(s(s(z)))), s(s(z)))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[233, 1611, 223, 1587])).
% 0.74/0.99 tff(1613,plain,
% 0.74/0.99 (r(s(s(s(s(z)))), s(s(z)))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[1326, 1612])).
% 0.74/0.99 tff(1614,plain,
% 0.74/0.99 ($false),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[1321, 1613, 1610, 43])).
% 0.74/0.99 tff(1615,plain,((~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.99 tff(1616,plain,
% 0.74/0.99 (~r(s(s(s(z))), s(z))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[1615, 43, 1298, 1553, 718, 1300, 1520])).
% 0.74/0.99 tff(1617,plain,
% 0.74/0.99 (b(s(s(s(z))), s(z))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[307, 1616])).
% 0.74/0.99 tff(1618,plain,
% 0.74/0.99 (~b(z, s(z))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[1425, 1617, 1553, 1300])).
% 0.74/0.99 tff(1619,plain,
% 0.74/0.99 (r(z, s(z))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[287, 1618])).
% 0.74/0.99 tff(1620,plain,
% 0.74/0.99 (~r(s(z), s(s(s(s(z)))))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[558, 1619, 43])).
% 0.74/0.99 tff(1621,plain,
% 0.74/0.99 (b(s(z), s(s(s(s(z)))))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[523, 1620])).
% 0.74/0.99 tff(1622,plain,
% 0.74/0.99 (~r(s(s(s(z))), z)),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[1250, 1621, 43, 1617, 1619])).
% 0.74/0.99 tff(1623,plain,
% 0.74/0.99 (b(s(s(s(z))), z)),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[117, 1622])).
% 0.74/0.99 tff(1624,plain,
% 0.74/0.99 (~r(s(s(z)), s(z))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[277, 1619, 1553])).
% 0.74/0.99 tff(1625,plain,
% 0.74/0.99 (b(s(s(z)), s(z))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[253, 1624])).
% 0.74/0.99 tff(1626,plain,
% 0.74/0.99 (~b(s(s(s(s(z)))), s(s(z)))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[233, 1625, 1298, 1621])).
% 0.74/0.99 tff(1627,plain,
% 0.74/0.99 (r(s(s(s(s(z)))), s(s(z)))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[1326, 1626])).
% 0.74/0.99 tff(1628,plain,
% 0.74/0.99 (~r(z, s(s(z)))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[1321, 1627, 43])).
% 0.74/0.99 tff(1629,plain,
% 0.74/0.99 (b(z, s(s(z)))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[703, 1628])).
% 0.74/0.99 tff(1630,plain,
% 0.74/0.99 ($false),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[1601, 180, 1629, 1520, 1623, 1300])).
% 0.74/0.99 tff(1631,plain,((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.99 tff(1632,plain,
% 0.74/0.99 (~r(z, s(s(s(s(z)))))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[1631, 40])).
% 0.74/0.99 tff(1633,plain,
% 0.74/0.99 (b(z, s(s(s(s(z)))))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[78, 1632])).
% 0.74/0.99 tff(1634,plain,
% 0.74/0.99 (~b(z, s(s(z)))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[1445, 180, 718, 1633, 1298])).
% 0.74/0.99 tff(1635,plain,
% 0.74/0.99 (r(z, s(s(z)))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[703, 1634])).
% 0.74/0.99 tff(1636,plain,
% 0.74/0.99 (~r(s(s(z)), s(z))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[277, 269, 1553])).
% 0.74/0.99 tff(1637,plain,
% 0.74/0.99 (b(s(s(z)), s(z))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[253, 1636])).
% 0.74/0.99 tff(1638,plain,
% 0.74/0.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 0.74/0.99 inference(rewrite,[status(thm)],[])).
% 0.74/0.99 tff(1639,plain,
% 0.74/0.99 (((~b(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(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z)))) <=> ((~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 0.74/0.99 inference(rewrite,[status(thm)],[])).
% 0.74/0.99 tff(1640,plain,
% 0.74/0.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(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(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z))))))))),
% 0.74/0.99 inference(monotonicity,[status(thm)],[1639])).
% 0.74/0.99 tff(1641,plain,
% 0.74/0.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(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(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 0.74/0.99 inference(transitivity,[status(thm)],[1640, 1638])).
% 0.74/0.99 tff(1642,plain,
% 0.74/0.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(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(s(z)), s(z))))),
% 0.74/0.99 inference(quant_inst,[status(thm)],[])).
% 0.74/0.99 tff(1643,plain,
% 0.74/0.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z))))))),
% 0.74/0.99 inference(modus_ponens,[status(thm)],[1642, 1641])).
% 0.74/0.99 tff(1644,plain,
% 0.74/0.99 ($false),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[1643, 180, 225, 224, 719, 540, 223])).
% 0.74/0.99 tff(1645,plain,((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.99 tff(1646,plain,
% 0.74/0.99 (~b(s(z), s(s(s(s(z)))))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[1645, 1637, 718, 1633, 1298])).
% 0.74/0.99 tff(1647,plain,
% 0.74/0.99 (r(s(z), s(s(s(s(z)))))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[523, 1646])).
% 0.74/0.99 tff(1648,plain,
% 0.74/0.99 (~r(s(z), s(s(s(z))))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[534, 1647, 40])).
% 0.74/0.99 tff(1649,plain,
% 0.74/0.99 (b(s(z), s(s(s(z))))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[373, 1648])).
% 0.74/0.99 tff(1650,plain,
% 0.74/0.99 (~b(s(s(s(z))), s(z))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[848, 1649, 1520, 1637])).
% 0.74/0.99 tff(1651,plain,
% 0.74/0.99 (r(s(s(s(z))), s(z))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[307, 1650])).
% 0.74/0.99 tff(1652,plain,
% 0.74/0.99 (~r(s(s(s(z))), z)),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[1056, 1651, 269])).
% 0.74/0.99 tff(1653,plain,
% 0.74/0.99 (b(s(s(s(z))), z)),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[117, 1652])).
% 0.74/0.99 tff(1654,plain,
% 0.74/0.99 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[579, 1651, 1647])).
% 0.74/0.99 tff(1655,plain,
% 0.74/0.99 (b(s(s(s(z))), s(s(s(s(z)))))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[468, 1654])).
% 0.74/0.99 tff(1656,plain,
% 0.74/0.99 ($false),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[1209, 180, 718, 1655, 1633, 1653])).
% 0.74/0.99 tff(1657,plain,((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.99 tff(1658,plain,
% 0.74/0.99 (~r(z, s(z))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[1657, 40])).
% 0.74/0.99 tff(1659,plain,
% 0.74/0.99 (b(z, s(z))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[287, 1658])).
% 0.74/0.99 tff(1660,plain,
% 0.74/0.99 (~b(s(z), s(s(s(s(z)))))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[747, 1659, 718, 1633])).
% 0.74/0.99 tff(1661,plain,
% 0.74/0.99 (r(s(z), s(s(s(s(z)))))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[523, 1660])).
% 0.74/0.99 tff(1662,plain,
% 0.74/0.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 0.74/0.99 inference(rewrite,[status(thm)],[])).
% 0.74/0.99 tff(1663,plain,
% 0.74/0.99 (((~b(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(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 0.74/0.99 inference(rewrite,[status(thm)],[])).
% 0.74/0.99 tff(1664,plain,
% 0.74/0.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(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(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))))),
% 0.74/0.99 inference(monotonicity,[status(thm)],[1663])).
% 0.74/0.99 tff(1665,plain,
% 0.74/0.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(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(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 0.74/0.99 inference(transitivity,[status(thm)],[1664, 1662])).
% 0.74/0.99 tff(1666,plain,
% 0.74/0.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(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(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))),
% 0.74/0.99 inference(quant_inst,[status(thm)],[])).
% 0.74/0.99 tff(1667,plain,
% 0.74/1.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))),
% 0.74/1.00 inference(modus_ponens,[status(thm)],[1666, 1665])).
% 0.74/1.00 tff(1668,plain,
% 0.74/1.00 ($false),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[1667, 180, 719, 539, 540, 169, 223])).
% 0.74/1.00 tff(1669,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.74/1.00 tff(1670,plain,
% 0.74/1.00 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[1669, 718, 1633, 1520, 1298])).
% 0.74/1.00 tff(1671,plain,
% 0.74/1.00 (r(s(s(s(z))), s(s(s(s(z)))))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[468, 1670])).
% 0.74/1.00 tff(1672,plain,
% 0.74/1.00 (~r(s(s(s(z))), s(z))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[579, 1671, 1661])).
% 0.74/1.00 tff(1673,plain,
% 0.74/1.00 (b(s(s(s(z))), s(z))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[307, 1672])).
% 0.74/1.00 tff(1674,plain,
% 0.74/1.00 (~b(z, s(s(s(z))))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[1425, 1673, 1553, 1659])).
% 0.74/1.00 tff(1675,plain,
% 0.74/1.00 (r(z, s(s(s(z))))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[102, 1674])).
% 0.74/1.00 tff(1676,plain,
% 0.74/1.00 (~r(s(s(s(z))), s(s(z)))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[793, 1675, 1635])).
% 0.74/1.00 tff(1677,plain,
% 0.74/1.00 (~r(s(z), s(s(s(z))))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[534, 1661, 40])).
% 0.74/1.00 tff(1678,plain,
% 0.74/1.00 (b(s(z), s(s(s(z))))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[373, 1677])).
% 0.74/1.00 tff(1679,plain,
% 0.74/1.00 (~b(s(s(z)), s(z))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[848, 1673, 1520, 1678])).
% 0.74/1.00 tff(1680,plain,
% 0.74/1.00 (r(s(s(z)), s(z))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[253, 1679])).
% 0.74/1.00 tff(1681,plain,
% 0.74/1.00 (~r(s(z), z)),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[260, 1680, 1553])).
% 0.74/1.00 tff(1682,plain,
% 0.74/1.00 (b(s(z), z)),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[267, 1681])).
% 0.74/1.00 tff(1683,plain,
% 0.74/1.00 (~r(s(z), z)),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[260, 39, 152])).
% 0.74/1.00 tff(1684,plain,
% 0.74/1.00 (b(s(z), z)),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[267, 1683])).
% 0.74/1.00 tff(1685,plain,
% 0.74/1.00 (~b(s(s(s(s(z)))), s(z))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[1561, 180, 291, 1684, 719])).
% 0.74/1.00 tff(1686,plain,
% 0.74/1.00 ((s(s(s(s(z)))) = s(z)) | r(s(s(s(s(z)))), s(z))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[381, 73, 1685])).
% 0.74/1.00 tff(1687,plain,
% 0.74/1.00 (r(s(s(s(s(z)))), s(z))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[1686, 352])).
% 0.74/1.00 tff(1688,plain,
% 0.74/1.00 ($false),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[1571, 53, 39, 1178, 1687])).
% 0.74/1.00 tff(1689,plain,((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 0.74/1.00 tff(1690,plain,
% 0.74/1.00 (~r(s(s(s(s(z)))), s(s(z)))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[1689, 1680, 1659, 718, 1553])).
% 0.74/1.00 tff(1691,plain,
% 0.74/1.00 (b(s(s(s(s(z)))), s(s(z)))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[1326, 1690])).
% 0.74/1.00 tff(1692,plain,
% 0.74/1.00 (~b(s(s(s(s(z)))), s(z))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[1561, 180, 291, 290, 718])).
% 0.74/1.00 tff(1693,plain,
% 0.74/1.00 ((s(s(s(s(z)))) = s(z)) | r(s(s(s(s(z)))), s(z))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[381, 73, 1692])).
% 0.74/1.00 tff(1694,plain,
% 0.74/1.00 (r(s(s(s(s(z)))), s(z))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[1693, 352])).
% 0.74/1.00 tff(1695,plain,
% 0.74/1.00 (~b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[417, 384, 222, 408, 169])).
% 0.74/1.00 tff(1696,plain,
% 0.74/1.00 (r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[1096, 1695])).
% 0.74/1.00 tff(1697,assumption,(~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))), introduced(assumption)).
% 0.74/1.00 tff(1698,plain,
% 0.74/1.00 ($false),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[398, 73, 395, 384, 1697])).
% 0.74/1.00 tff(1699,plain,(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)))))), inference(lemma,lemma(discharge,[]))).
% 0.74/1.00 tff(1700,plain,
% 0.74/1.00 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[1699, 384])).
% 0.74/1.00 tff(1701,assumption,(b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))), introduced(assumption)).
% 0.74/1.00 tff(1702,plain,
% 0.74/1.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 0.74/1.00 inference(rewrite,[status(thm)],[])).
% 0.74/1.00 tff(1703,plain,
% 0.74/1.00 (((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, 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(z), z)) | (~b(z, 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)))))))),
% 0.74/1.00 inference(rewrite,[status(thm)],[])).
% 0.74/1.00 tff(1704,plain,
% 0.74/1.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, 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)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 0.74/1.00 inference(monotonicity,[status(thm)],[1703])).
% 0.74/1.00 tff(1705,plain,
% 0.74/1.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, 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)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 0.74/1.00 inference(transitivity,[status(thm)],[1704, 1702])).
% 0.74/1.00 tff(1706,plain,
% 0.74/1.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, 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)))))))),
% 0.74/1.00 inference(quant_inst,[status(thm)],[])).
% 0.74/1.00 tff(1707,plain,
% 0.74/1.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 0.74/1.00 inference(modus_ponens,[status(thm)],[1706, 1705])).
% 0.74/1.00 tff(1708,plain,
% 0.74/1.00 ($false),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[1707, 180, 291, 290, 719, 1065, 1701])).
% 0.74/1.00 tff(1709,plain,((~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.74/1.00 tff(1710,plain,
% 0.74/1.00 (~b(s(s(s(s(s(s(z)))))), z)),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[1709, 1700, 290, 719, 291])).
% 0.74/1.00 tff(1711,plain,
% 0.74/1.00 (r(s(s(s(s(s(s(z)))))), z)),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[509, 1710])).
% 0.74/1.00 tff(1712,assumption,(r(s(s(s(s(s(s(z)))))), s(s(z)))), introduced(assumption)).
% 0.74/1.00 tff(1713,assumption,(r(s(s(s(s(s(s(z)))))), z)), introduced(assumption)).
% 0.74/1.00 tff(1714,plain,
% 0.74/1.00 ($false),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[1091, 53, 152, 1713, 1712])).
% 0.74/1.00 tff(1715,plain,((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.74/1.00 tff(1716,plain,
% 0.74/1.00 ($false),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[1715, 1711, 1696, 152])).
% 0.74/1.00 tff(1717,plain,(r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) | (~r(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.74/1.00 tff(1718,plain,
% 0.74/1.00 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[1717, 1188, 290, 718, 291, 222, 1553, 1520])).
% 0.74/1.00 tff(1719,plain,
% 0.74/1.00 ($false),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[984, 53, 40, 1476, 1475])).
% 0.74/1.00 tff(1720,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,[]))).
% 0.74/1.00 tff(1721,plain,
% 0.74/1.00 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[1720, 1718, 40])).
% 0.74/1.00 tff(1722,plain,
% 0.74/1.00 (~b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[1196, 1721, 1520, 1187])).
% 0.74/1.00 tff(1723,plain,
% 0.74/1.00 (r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[1096, 1722])).
% 0.74/1.00 tff(1724,plain,
% 0.74/1.00 (~r(s(s(s(s(s(s(z)))))), z)),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[1715, 1723, 1553])).
% 0.74/1.00 tff(1725,plain,
% 0.74/1.00 (b(s(s(s(s(s(s(z)))))), z)),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[509, 1724])).
% 0.74/1.00 tff(1726,plain,
% 0.74/1.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 0.74/1.00 inference(rewrite,[status(thm)],[])).
% 0.74/1.00 tff(1727,plain,
% 0.74/1.00 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~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(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 0.74/1.00 inference(rewrite,[status(thm)],[])).
% 0.74/1.00 tff(1728,plain,
% 0.74/1.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~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))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z))))),
% 0.74/1.00 inference(monotonicity,[status(thm)],[1727])).
% 0.74/1.00 tff(1729,plain,
% 0.74/1.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~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))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 0.74/1.00 inference(transitivity,[status(thm)],[1728, 1726])).
% 0.74/1.00 tff(1730,plain,
% 0.74/1.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~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))))),
% 0.74/1.00 inference(quant_inst,[status(thm)],[])).
% 0.74/1.00 tff(1731,plain,
% 0.74/1.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z))),
% 0.74/1.00 inference(modus_ponens,[status(thm)],[1730, 1729])).
% 0.74/1.00 tff(1732,plain,
% 0.74/1.00 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[1731, 180, 291, 290, 1725])).
% 0.74/1.00 tff(1733,plain,
% 0.74/1.00 (r(s(s(s(s(s(s(z)))))), s(z))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[947, 1732])).
% 0.74/1.00 tff(1734,plain,
% 0.74/1.00 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 0.74/1.00 inference(rewrite,[status(thm)],[])).
% 0.74/1.00 tff(1735,plain,
% 0.74/1.00 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 0.74/1.00 inference(quant_inst,[status(thm)],[])).
% 0.74/1.00 tff(1736,plain,
% 0.74/1.00 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 0.74/1.00 inference(modus_ponens,[status(thm)],[1735, 1734])).
% 0.74/1.00 tff(1737,plain,
% 0.74/1.00 ($false),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[1736, 53, 1718, 1733, 1694])).
% 0.74/1.00 tff(1738,plain,(r(s(s(s(z))), s(s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.74/1.00 tff(1739,plain,
% 0.74/1.00 ($false),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[1738, 1691, 1682, 1659, 40, 1676])).
% 0.74/1.00 tff(1740,plain,(~r(s(s(s(s(z)))), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.74/1.00 tff(1741,plain,
% 0.74/1.00 (b(s(s(s(s(z)))), s(s(s(z))))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[887, 1740])).
% 0.74/1.00 tff(1742,plain,
% 0.74/1.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 0.74/1.00 inference(rewrite,[status(thm)],[])).
% 0.74/1.00 tff(1743,plain,
% 0.74/1.00 (((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 0.74/1.00 inference(rewrite,[status(thm)],[])).
% 0.74/1.00 tff(1744,plain,
% 0.74/1.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 0.74/1.00 inference(monotonicity,[status(thm)],[1743])).
% 0.74/1.00 tff(1745,plain,
% 0.74/1.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 0.74/1.00 inference(transitivity,[status(thm)],[1744, 1742])).
% 0.74/1.00 tff(1746,plain,
% 0.74/1.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 0.74/1.00 inference(quant_inst,[status(thm)],[])).
% 0.74/1.00 tff(1747,plain,
% 0.74/1.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 0.74/1.00 inference(modus_ponens,[status(thm)],[1746, 1745])).
% 0.74/1.00 tff(1748,plain,
% 0.74/1.00 ($false),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[1747, 180, 873, 719, 168, 167])).
% 0.74/1.00 tff(1749,plain,((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.74/1.00 tff(1750,plain,
% 0.74/1.00 (~b(s(s(s(z))), z)),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[1749, 167, 873, 719])).
% 0.74/1.00 tff(1751,plain,
% 0.74/1.00 (r(s(s(s(z))), z)),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[117, 1750])).
% 0.74/1.00 tff(1752,plain,
% 0.74/1.00 (~r(s(s(s(z))), s(s(z)))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[326, 53, 39, 309])).
% 0.74/1.00 tff(1753,plain,
% 0.74/1.00 ((s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z)))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[330, 73, 1752])).
% 0.74/1.00 tff(1754,plain,
% 0.74/1.00 (b(s(s(s(z))), s(s(z)))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[1753, 1262])).
% 0.74/1.00 tff(1755,plain,
% 0.74/1.00 (~r(s(s(z)), s(s(s(z))))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[317, 309, 39])).
% 0.74/1.00 tff(1756,plain,
% 0.74/1.00 (b(s(s(z)), s(s(s(z))))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[150, 1755])).
% 0.74/1.00 tff(1757,plain,
% 0.74/1.00 (~r(z, s(z))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[1056, 309, 1751])).
% 0.74/1.00 tff(1758,plain,
% 0.74/1.00 (b(z, s(z))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[287, 1757])).
% 0.74/1.00 tff(1759,plain,
% 0.74/1.00 (~b(s(z), s(s(s(s(z)))))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[747, 540, 1758, 719])).
% 0.74/1.00 tff(1760,plain,
% 0.74/1.00 (r(s(z), s(s(s(s(z)))))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[523, 1759])).
% 0.74/1.00 tff(1761,plain,
% 0.74/1.00 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[579, 1760, 309])).
% 0.74/1.00 tff(1762,plain,
% 0.74/1.00 (b(s(s(s(z))), s(s(s(s(z)))))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[468, 1761])).
% 0.74/1.00 tff(1763,plain,
% 0.74/1.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, 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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 0.74/1.00 inference(rewrite,[status(thm)],[])).
% 0.74/1.00 tff(1764,plain,
% 0.74/1.00 (((~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(s(s(s(s(z)))), 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(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(s(z)))), s(s(s(z))))))),
% 0.74/1.00 inference(rewrite,[status(thm)],[])).
% 0.74/1.00 tff(1765,plain,
% 0.74/1.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 0.74/1.00 inference(monotonicity,[status(thm)],[1764])).
% 0.74/1.00 tff(1766,plain,
% 0.74/1.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 0.74/1.00 inference(transitivity,[status(thm)],[1765, 1763])).
% 0.74/1.00 tff(1767,plain,
% 0.74/1.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))),
% 0.74/1.00 inference(quant_inst,[status(thm)],[])).
% 0.74/1.00 tff(1768,plain,
% 0.74/1.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 0.74/1.00 inference(modus_ponens,[status(thm)],[1767, 1766])).
% 0.74/1.00 tff(1769,plain,
% 0.74/1.00 ($false),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[1768, 180, 873, 1762, 540, 167])).
% 0.74/1.00 tff(1770,plain,((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 0.74/1.01 tff(1771,plain,
% 0.74/1.01 (~b(z, s(s(s(s(z)))))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[1770, 309, 167, 873, 719])).
% 0.74/1.01 tff(1772,plain,
% 0.74/1.01 (r(z, s(s(s(s(z)))))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[78, 1771])).
% 0.74/1.01 tff(1773,plain,
% 0.74/1.01 (~r(s(s(s(s(z)))), s(s(z)))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[1321, 43, 688])).
% 0.74/1.01 tff(1774,plain,
% 0.74/1.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), 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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 0.74/1.01 inference(rewrite,[status(thm)],[])).
% 0.74/1.01 tff(1775,plain,
% 0.74/1.01 (((~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(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 0.74/1.01 inference(rewrite,[status(thm)],[])).
% 0.74/1.01 tff(1776,plain,
% 0.74/1.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 0.74/1.01 inference(monotonicity,[status(thm)],[1775])).
% 0.74/1.01 tff(1777,plain,
% 0.74/1.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 0.74/1.01 inference(transitivity,[status(thm)],[1776, 1774])).
% 0.74/1.01 tff(1778,plain,
% 0.74/1.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 0.74/1.01 inference(quant_inst,[status(thm)],[])).
% 0.74/1.01 tff(1779,plain,
% 0.74/1.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 0.74/1.01 inference(modus_ponens,[status(thm)],[1778, 1777])).
% 0.74/1.01 tff(1780,plain,
% 0.74/1.01 (~b(s(s(s(s(z)))), s(s(z)))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[1779, 180, 873, 1231, 169])).
% 0.74/1.01 tff(1781,plain,
% 0.74/1.01 ($false),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[220, 73, 203, 1780, 1773])).
% 0.74/1.01 tff(1782,plain,((~r(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.74/1.01 tff(1783,plain,
% 0.74/1.01 (~r(z, s(s(z)))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[1782, 1772, 1756, 1751, 873])).
% 0.74/1.01 tff(1784,plain,
% 0.74/1.01 (b(z, s(s(z)))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[703, 1783])).
% 0.74/1.01 tff(1785,plain,
% 0.74/1.01 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[1229, 1772, 1751])).
% 0.74/1.01 tff(1786,plain,
% 0.74/1.01 (b(s(s(s(z))), s(s(s(s(z)))))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[468, 1785])).
% 0.74/1.01 tff(1787,plain,
% 0.74/1.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), 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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 0.74/1.01 inference(rewrite,[status(thm)],[])).
% 0.74/1.01 tff(1788,plain,
% 0.74/1.01 (((~b(s(s(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(z))), s(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(z)), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 0.74/1.01 inference(rewrite,[status(thm)],[])).
% 0.74/1.01 tff(1789,plain,
% 0.74/1.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 0.74/1.01 inference(monotonicity,[status(thm)],[1788])).
% 0.74/1.01 tff(1790,plain,
% 0.74/1.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 0.74/1.01 inference(transitivity,[status(thm)],[1789, 1787])).
% 0.74/1.01 tff(1791,plain,
% 0.74/1.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 0.74/1.01 inference(quant_inst,[status(thm)],[])).
% 0.74/1.01 tff(1792,plain,
% 0.74/1.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 0.74/1.01 inference(modus_ponens,[status(thm)],[1791, 1790])).
% 0.74/1.01 tff(1793,plain,
% 0.74/1.01 (~b(s(s(z)), s(s(s(s(z)))))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[1792, 180, 873, 1786, 1756])).
% 0.74/1.01 tff(1794,plain,
% 0.74/1.01 (r(s(s(z)), s(s(s(s(z)))))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[212, 1793])).
% 0.74/1.01 tff(1795,plain,
% 0.74/1.01 (~r(s(s(z)), z)),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[737, 1794, 1772])).
% 0.74/1.01 tff(1796,plain,
% 0.74/1.01 (b(s(s(z)), z)),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[165, 1795])).
% 0.74/1.01 tff(1797,plain,
% 0.74/1.01 ($false),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[1284, 180, 1796, 1784, 167, 1754])).
% 0.74/1.01 tff(1798,plain,((~r(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 0.74/1.01 tff(1799,plain,
% 0.74/1.01 (~r(s(s(s(z))), s(z))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[1798, 167, 39, 873, 719])).
% 0.74/1.01 tff(1800,plain,
% 0.74/1.01 (b(s(s(s(z))), s(z))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[307, 1799])).
% 0.74/1.01 tff(1801,plain,
% 0.74/1.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 0.74/1.01 inference(rewrite,[status(thm)],[])).
% 0.74/1.01 tff(1802,plain,
% 0.74/1.01 (((~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(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 0.74/1.01 inference(rewrite,[status(thm)],[])).
% 0.74/1.01 tff(1803,plain,
% 0.74/1.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z))))))))),
% 0.74/1.01 inference(monotonicity,[status(thm)],[1802])).
% 0.74/1.01 tff(1804,plain,
% 0.74/1.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 0.74/1.01 inference(transitivity,[status(thm)],[1803, 1801])).
% 0.74/1.01 tff(1805,plain,
% 0.74/1.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))),
% 0.74/1.01 inference(quant_inst,[status(thm)],[])).
% 0.74/1.01 tff(1806,plain,
% 0.74/1.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 0.74/1.01 inference(modus_ponens,[status(thm)],[1805, 1804])).
% 0.74/1.01 tff(1807,plain,
% 0.74/1.01 ($false),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[1806, 180, 873, 224, 289, 539])).
% 0.74/1.01 tff(1808,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.74/1.01 tff(1809,plain,
% 0.74/1.01 (~b(s(z), s(s(s(s(z)))))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[1808, 539, 873, 289])).
% 0.74/1.01 tff(1810,plain,
% 0.74/1.01 (r(s(z), s(s(s(s(z)))))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[523, 1809])).
% 0.74/1.01 tff(1811,plain,
% 0.74/1.01 ($false),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[1768, 180, 873, 539, 540, 167])).
% 0.74/1.01 tff(1812,plain,((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.74/1.01 tff(1813,plain,
% 0.74/1.01 (~b(z, s(s(s(s(z)))))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[1812, 539, 873, 167])).
% 0.74/1.01 tff(1814,plain,
% 0.74/1.01 (r(z, s(s(s(s(z)))))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[78, 1813])).
% 0.74/1.01 tff(1815,plain,
% 0.74/1.01 (~r(z, s(z))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[558, 1814, 1810])).
% 0.74/1.01 tff(1816,plain,
% 0.74/1.01 (b(z, s(z))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[287, 1815])).
% 0.74/1.01 tff(1817,plain,
% 0.74/1.01 (~b(s(z), z)),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[299, 1816, 167, 289])).
% 0.74/1.01 tff(1818,plain,
% 0.74/1.01 (r(s(z), z)),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[267, 1817])).
% 0.74/1.01 tff(1819,plain,
% 0.74/1.01 ($false),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[1343, 53, 1818, 1814, 1810])).
% 0.74/1.01 tff(1820,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.74/1.01 tff(1821,plain,
% 0.74/1.01 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[1820, 167, 1800, 873])).
% 0.74/1.01 tff(1822,plain,
% 0.74/1.01 (r(s(s(s(z))), s(s(s(s(z)))))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[468, 1821])).
% 0.74/1.01 tff(1823,plain,
% 0.74/1.01 (~r(z, s(s(s(s(z)))))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[1229, 1822, 1751])).
% 0.74/1.01 tff(1824,plain,
% 0.74/1.01 (b(z, s(s(s(s(z)))))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[78, 1823])).
% 0.74/1.01 tff(1825,plain,
% 0.74/1.01 (~r(z, s(z))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[1286, 167, 1822, 719, 39])).
% 0.74/1.01 tff(1826,plain,
% 0.74/1.01 (b(z, s(z))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[287, 1825])).
% 0.74/1.01 tff(1827,plain,
% 0.74/1.01 (~b(s(z), s(s(s(s(z)))))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[747, 1826, 1824, 719])).
% 0.74/1.01 tff(1828,plain,
% 0.74/1.01 (r(s(z), s(s(s(s(z)))))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[523, 1827])).
% 0.74/1.01 tff(1829,plain,
% 0.74/1.01 (~r(s(s(z)), s(s(s(s(z)))))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[727, 1828, 39])).
% 0.74/1.01 tff(1830,plain,
% 0.74/1.01 (b(s(s(z)), s(s(s(s(z)))))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[212, 1829])).
% 0.74/1.01 tff(1831,plain,
% 0.74/1.01 (~b(s(z), z)),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[299, 1826, 167, 1800])).
% 0.74/1.01 tff(1832,plain,
% 0.74/1.01 (r(s(z), z)),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[267, 1831])).
% 0.74/1.01 tff(1833,plain,
% 0.74/1.01 (~r(s(s(z)), z)),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[260, 1832, 39])).
% 0.74/1.01 tff(1834,plain,
% 0.74/1.01 (b(s(s(z)), z)),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[165, 1833])).
% 0.74/1.01 tff(1835,plain,
% 0.74/1.01 ($false),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[1305, 180, 1834, 719, 1824, 1830])).
% 0.74/1.01 tff(1836,plain,((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.74/1.01 tff(1837,plain,
% 0.74/1.01 (~b(z, s(s(s(z))))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[1836, 39, 719, 873])).
% 0.74/1.01 tff(1838,plain,
% 0.74/1.01 (r(z, s(s(s(z))))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[102, 1837])).
% 0.74/1.01 tff(1839,plain,
% 0.74/1.01 (~r(s(s(s(z))), s(z))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[838, 269, 1838])).
% 0.74/1.01 tff(1840,plain,
% 0.74/1.01 (b(s(s(s(z))), s(z))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[307, 1839])).
% 0.74/1.01 tff(1841,plain,
% 0.74/1.01 (~r(s(z), s(s(s(z))))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[828, 269, 1838])).
% 0.74/1.01 tff(1842,plain,
% 0.74/1.01 (b(s(z), s(s(s(z))))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[373, 1841])).
% 0.74/1.01 tff(1843,plain,
% 0.74/1.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 0.74/1.01 inference(rewrite,[status(thm)],[])).
% 0.74/1.01 tff(1844,plain,
% 0.74/1.01 (((~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(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 0.74/1.01 inference(rewrite,[status(thm)],[])).
% 0.74/1.01 tff(1845,plain,
% 0.74/1.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))))),
% 0.74/1.01 inference(monotonicity,[status(thm)],[1844])).
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% 0.74/1.02 tff(1917,plain,
% 0.74/1.02 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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)))))))),
% 0.74/1.02 inference(rewrite,[status(thm)],[])).
% 0.74/1.02 tff(1918,plain,
% 0.74/1.02 (((~r(s(s(z)), s(s(s(s(z)))))) | (~r(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)))))))),
% 0.74/1.02 inference(rewrite,[status(thm)],[])).
% 0.74/1.02 tff(1919,plain,
% 0.74/1.02 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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))))))))),
% 0.74/1.02 inference(monotonicity,[status(thm)],[1918])).
% 0.74/1.02 tff(1920,plain,
% 0.74/1.02 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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)))))))),
% 0.74/1.02 inference(transitivity,[status(thm)],[1919, 1917])).
% 0.74/1.02 tff(1921,plain,
% 0.74/1.02 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(z)))))),
% 0.74/1.02 inference(quant_inst,[status(thm)],[])).
% 0.74/1.02 tff(1922,plain,
% 0.74/1.02 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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))))))),
% 0.74/1.02 inference(modus_ponens,[status(thm)],[1921, 1920])).
% 0.74/1.02 tff(1923,plain,
% 0.74/1.02 (~r(z, s(s(z)))),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[1922, 53, 1916, 1908])).
% 0.74/1.02 tff(1924,plain,
% 0.74/1.02 (b(z, s(s(z)))),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[703, 1923])).
% 0.74/1.02 tff(1925,plain,
% 0.74/1.02 (~r(s(s(s(z))), s(s(z)))),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[326, 53, 39, 1912])).
% 0.74/1.02 tff(1926,plain,
% 0.74/1.02 ((s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z)))),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[330, 73, 1925])).
% 0.74/1.02 tff(1927,plain,
% 0.74/1.02 (b(s(s(s(z))), s(s(z)))),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[1926, 1262])).
% 0.74/1.02 tff(1928,plain,
% 0.74/1.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)))),
% 0.74/1.02 inference(rewrite,[status(thm)],[])).
% 0.74/1.02 tff(1929,plain,
% 0.74/1.02 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)))),
% 0.74/1.02 inference(rewrite,[status(thm)],[])).
% 0.74/1.02 tff(1930,plain,
% 0.74/1.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z))))),
% 0.74/1.02 inference(monotonicity,[status(thm)],[1929])).
% 0.74/1.02 tff(1931,plain,
% 0.74/1.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)))),
% 0.74/1.02 inference(transitivity,[status(thm)],[1930, 1928])).
% 0.74/1.02 tff(1932,plain,
% 0.74/1.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))),
% 0.74/1.02 inference(quant_inst,[status(thm)],[])).
% 0.74/1.02 tff(1933,plain,
% 0.74/1.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z))),
% 0.74/1.02 inference(modus_ponens,[status(thm)],[1932, 1931])).
% 0.74/1.02 tff(1934,plain,
% 0.74/1.02 ($false),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[1933, 180, 170, 751, 168, 408])).
% 0.74/1.02 tff(1935,plain,((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 0.74/1.02 tff(1936,plain,
% 0.74/1.02 (~b(s(s(s(z))), z)),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[1935, 1927, 1924, 1914])).
% 0.74/1.02 tff(1937,plain,
% 0.74/1.02 (r(s(s(s(z))), z)),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[117, 1936])).
% 0.74/1.02 tff(1938,plain,
% 0.74/1.02 (~b(s(z), z)),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[1026, 1910, 1858, 719])).
% 0.74/1.02 tff(1939,plain,
% 0.74/1.02 (r(s(z), z)),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[267, 1938])).
% 0.74/1.02 tff(1940,plain,
% 0.74/1.02 ($false),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[1031, 53, 1939, 1937, 1912])).
% 0.74/1.02 tff(1941,plain,((~r(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.74/1.02 tff(1942,plain,
% 0.74/1.02 ((~r(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), z))),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[1941, 1741])).
% 0.74/1.02 tff(1943,plain,
% 0.74/1.02 (~b(s(s(s(s(z)))), z)),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[1942, 39])).
% 0.74/1.02 tff(1944,plain,
% 0.74/1.02 (r(s(s(s(s(z)))), z)),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[717, 1943])).
% 0.74/1.02 tff(1945,plain,
% 0.74/1.02 (~r(s(s(s(z))), s(z))),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[579, 571, 526])).
% 0.74/1.02 tff(1946,plain,
% 0.74/1.02 (b(s(s(s(z))), s(z))),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[307, 1945])).
% 0.74/1.02 tff(1947,plain,
% 0.74/1.02 (b(s(s(z)), s(s(s(s(z)))))),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[212, 900])).
% 0.74/1.02 tff(1948,plain,
% 0.74/1.02 (~r(s(z), z)),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[589, 1944, 526])).
% 0.74/1.02 tff(1949,plain,
% 0.74/1.02 (b(s(z), z)),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[267, 1948])).
% 0.74/1.02 tff(1950,plain,
% 0.74/1.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))))),
% 0.74/1.02 inference(rewrite,[status(thm)],[])).
% 0.74/1.02 tff(1951,plain,
% 0.74/1.02 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z))) <=> ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))))),
% 0.74/1.02 inference(rewrite,[status(thm)],[])).
% 0.74/1.02 tff(1952,plain,
% 0.74/1.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z)))))),
% 0.74/1.02 inference(monotonicity,[status(thm)],[1951])).
% 0.74/1.02 tff(1953,plain,
% 0.74/1.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))))),
% 0.74/1.02 inference(transitivity,[status(thm)],[1952, 1950])).
% 0.74/1.02 tff(1954,plain,
% 0.74/1.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 0.74/1.02 inference(quant_inst,[status(thm)],[])).
% 0.74/1.02 tff(1955,plain,
% 0.74/1.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z)))),
% 0.74/1.02 inference(modus_ponens,[status(thm)],[1954, 1953])).
% 0.74/1.02 tff(1956,plain,
% 0.74/1.02 (~b(s(s(s(z))), z)),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[1955, 180, 291, 290, 289])).
% 0.74/1.02 tff(1957,plain,
% 0.74/1.02 (r(s(s(s(z))), z)),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[117, 1956])).
% 0.74/1.02 tff(1958,plain,
% 0.74/1.02 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 0.74/1.02 inference(rewrite,[status(thm)],[])).
% 0.74/1.02 tff(1959,plain,
% 0.74/1.02 (((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 0.74/1.02 inference(rewrite,[status(thm)],[])).
% 0.74/1.02 tff(1960,plain,
% 0.74/1.02 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))))),
% 0.74/1.02 inference(monotonicity,[status(thm)],[1959])).
% 0.74/1.02 tff(1961,plain,
% 0.74/1.02 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 0.74/1.02 inference(transitivity,[status(thm)],[1960, 1958])).
% 0.74/1.02 tff(1962,plain,
% 0.74/1.02 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 0.74/1.02 inference(quant_inst,[status(thm)],[])).
% 0.74/1.02 tff(1963,plain,
% 0.74/1.02 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))),
% 0.74/1.02 inference(modus_ponens,[status(thm)],[1962, 1961])).
% 0.74/1.02 tff(1964,plain,
% 0.74/1.02 ($false),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[1963, 53, 1957, 80, 571])).
% 0.74/1.02 tff(1965,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.74/1.02 tff(1966,plain,
% 0.74/1.02 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[1965, 289, 291, 290, 1944])).
% 0.74/1.02 tff(1967,plain,
% 0.74/1.02 (b(s(s(s(z))), s(s(s(s(z)))))),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[468, 1966])).
% 0.74/1.02 tff(1968,plain,
% 0.74/1.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), 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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 0.74/1.02 inference(rewrite,[status(thm)],[])).
% 0.74/1.02 tff(1969,plain,
% 0.74/1.02 (((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), 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), z)) | (~b(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(s(s(s(z)))))), s(z))))),
% 0.74/1.02 inference(rewrite,[status(thm)],[])).
% 0.74/1.02 tff(1970,plain,
% 0.87/1.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), 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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))))),
% 0.87/1.02 inference(monotonicity,[status(thm)],[1969])).
% 0.87/1.02 tff(1971,plain,
% 0.87/1.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), 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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 0.87/1.02 inference(transitivity,[status(thm)],[1970, 1968])).
% 0.87/1.02 tff(1972,plain,
% 0.87/1.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), 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))))))),
% 0.87/1.02 inference(quant_inst,[status(thm)],[])).
% 0.87/1.02 tff(1973,plain,
% 0.87/1.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))),
% 0.87/1.02 inference(modus_ponens,[status(thm)],[1972, 1971])).
% 0.87/1.02 tff(1974,plain,
% 0.87/1.02 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.87/1.02 inference(unit_resolution,[status(thm)],[1973, 180, 291, 290, 289, 655])).
% 0.87/1.02 tff(1975,plain,
% 0.87/1.02 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.87/1.02 inference(unit_resolution,[status(thm)],[487, 73, 484, 1974])).
% 0.87/1.02 tff(1976,plain,
% 0.87/1.02 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), 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(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 0.87/1.02 inference(rewrite,[status(thm)],[])).
% 0.87/1.02 tff(1977,plain,
% 0.87/1.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z))))),
% 0.87/1.02 inference(monotonicity,[status(thm)],[1976])).
% 0.87/1.02 tff(1978,plain,
% 0.87/1.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 0.87/1.02 inference(transitivity,[status(thm)],[1977, 1726])).
% 0.87/1.02 tff(1979,plain,
% 0.87/1.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 0.87/1.03 inference(quant_inst,[status(thm)],[])).
% 0.87/1.03 tff(1980,plain,
% 0.87/1.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z))),
% 0.87/1.03 inference(modus_ponens,[status(thm)],[1979, 1978])).
% 0.87/1.03 tff(1981,plain,
% 0.87/1.03 (~b(s(s(s(s(s(s(z)))))), z)),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[1980, 180, 291, 290, 655])).
% 0.87/1.03 tff(1982,plain,
% 0.87/1.03 (r(s(s(s(s(s(s(z)))))), z)),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[509, 1981])).
% 0.87/1.03 tff(1983,plain,
% 0.87/1.03 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 0.87/1.03 inference(rewrite,[status(thm)],[])).
% 0.87/1.03 tff(1984,plain,
% 0.87/1.03 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 0.87/1.03 inference(quant_inst,[status(thm)],[])).
% 0.87/1.03 tff(1985,plain,
% 0.87/1.03 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 0.87/1.03 inference(modus_ponens,[status(thm)],[1984, 1983])).
% 0.87/1.03 tff(1986,plain,
% 0.87/1.03 ($false),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[1985, 53, 1957, 1982, 1975])).
% 0.87/1.03 tff(1987,plain,((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.87/1.03 tff(1988,plain,
% 0.87/1.03 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[1987, 289, 290, 291])).
% 0.87/1.03 tff(1989,plain,
% 0.87/1.03 (r(s(s(s(s(s(s(z)))))), s(z))),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[947, 1988])).
% 0.87/1.03 tff(1990,plain,
% 0.87/1.03 (~r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[668, 53, 39, 1989])).
% 0.87/1.03 tff(1991,plain,
% 0.87/1.03 (b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[1096, 1990])).
% 0.87/1.03 tff(1992,plain,
% 0.87/1.03 (~b(z, s(s(s(z))))),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[299, 289, 291, 290])).
% 0.87/1.03 tff(1993,plain,
% 0.87/1.03 (r(z, s(s(s(z))))),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[102, 1992])).
% 0.87/1.03 tff(1994,plain,
% 0.87/1.03 ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[1896, 1741])).
% 0.87/1.03 tff(1995,plain,
% 0.87/1.03 (~b(s(s(z)), s(s(s(z))))),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[1994, 1967, 223])).
% 0.87/1.03 tff(1996,plain,
% 0.87/1.03 (r(s(s(z)), s(s(s(z))))),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[150, 1995])).
% 0.87/1.03 tff(1997,plain,
% 0.87/1.03 (~r(z, s(s(z)))),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[1368, 53, 1996, 1993])).
% 0.87/1.03 tff(1998,plain,
% 0.87/1.03 (b(z, s(s(z)))),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[703, 1997])).
% 0.87/1.03 tff(1999,plain,
% 0.87/1.03 (~r(s(s(z)), z)),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[1376, 53, 1996, 1993])).
% 0.87/1.03 tff(2000,plain,
% 0.87/1.03 (b(s(s(z)), z)),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[165, 1999])).
% 0.87/1.03 tff(2001,plain,
% 0.87/1.03 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z))) <=> ((~b(z, s(s(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)))))),
% 0.87/1.03 inference(rewrite,[status(thm)],[])).
% 0.87/1.03 tff(2002,plain,
% 0.87/1.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), 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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))))),
% 0.87/1.03 inference(monotonicity,[status(thm)],[2001])).
% 0.87/1.03 tff(2003,plain,
% 0.87/1.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), 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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 0.87/1.03 inference(transitivity,[status(thm)],[2002, 935])).
% 0.87/1.03 tff(2004,plain,
% 0.87/1.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 0.87/1.03 inference(quant_inst,[status(thm)],[])).
% 0.87/1.03 tff(2005,plain,
% 0.87/1.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))),
% 0.87/1.03 inference(modus_ponens,[status(thm)],[2004, 2003])).
% 0.87/1.03 tff(2006,plain,
% 0.87/1.03 (~b(s(s(s(s(s(s(z)))))), z)),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[2005, 180, 2000, 1998, 1991])).
% 0.87/1.03 tff(2007,plain,
% 0.87/1.03 (r(s(s(s(s(s(s(z)))))), z)),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[509, 2006])).
% 0.87/1.03 tff(2008,plain,
% 0.87/1.03 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 0.87/1.03 inference(rewrite,[status(thm)],[])).
% 0.87/1.03 tff(2009,plain,
% 0.87/1.03 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 0.87/1.03 inference(quant_inst,[status(thm)],[])).
% 0.87/1.03 tff(2010,plain,
% 0.87/1.03 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 0.87/1.03 inference(modus_ponens,[status(thm)],[2009, 2008])).
% 0.87/1.03 tff(2011,plain,
% 0.87/1.03 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[2010, 53, 1944, 2007])).
% 0.87/1.03 tff(2012,plain,
% 0.87/1.03 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[1699, 2011])).
% 0.87/1.03 tff(2013,assumption,(b(s(s(s(s(s(s(z)))))), s(s(s(z))))), introduced(assumption)).
% 0.87/1.03 tff(2014,plain,
% 0.87/1.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(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)))))))),
% 0.87/1.03 inference(rewrite,[status(thm)],[])).
% 0.87/1.03 tff(2015,plain,
% 0.87/1.03 (((~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(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(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)))))))),
% 0.87/1.03 inference(rewrite,[status(thm)],[])).
% 0.87/1.03 tff(2016,plain,
% 0.87/1.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), 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(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(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))))))))),
% 0.87/1.03 inference(monotonicity,[status(thm)],[2015])).
% 0.87/1.03 tff(2017,plain,
% 0.87/1.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), 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(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(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)))))))),
% 0.87/1.03 inference(transitivity,[status(thm)],[2016, 2014])).
% 0.87/1.03 tff(2018,plain,
% 0.87/1.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), 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(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)))))))),
% 0.87/1.03 inference(quant_inst,[status(thm)],[])).
% 0.87/1.03 tff(2019,plain,
% 0.87/1.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 0.87/1.03 inference(modus_ponens,[status(thm)],[2018, 2017])).
% 0.87/1.03 tff(2020,plain,
% 0.87/1.03 ($false),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[2019, 180, 1741, 539, 1701, 2013])).
% 0.87/1.03 tff(2021,plain,((~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(s(s(s(z)))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.87/1.03 tff(2022,plain,
% 0.87/1.03 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[2021, 2012, 1967])).
% 0.87/1.03 tff(2023,plain,
% 0.87/1.03 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[1985, 53, 1957, 2007])).
% 0.87/1.03 tff(2024,plain,
% 0.87/1.03 ($false),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[487, 73, 484, 2023, 2022])).
% 0.87/1.03 tff(2025,plain,((~b(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.87/1.03 tff(2026,plain,
% 0.87/1.03 (~b(s(s(s(z))), s(z))),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[2025, 39, 1949, 291, 1947])).
% 0.87/1.03 tff(2027,plain,
% 0.87/1.03 (r(s(s(s(z))), s(z))),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[307, 2026])).
% 0.87/1.03 tff(2028,plain,
% 0.87/1.03 (~r(s(s(z)), s(s(s(z))))),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[317, 2027, 39])).
% 0.87/1.03 tff(2029,plain,
% 0.87/1.03 (b(s(s(z)), s(s(s(z))))),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[150, 2028])).
% 0.87/1.03 tff(2030,plain,
% 0.87/1.03 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[579, 2027, 526])).
% 0.87/1.03 tff(2031,plain,
% 0.87/1.03 (b(s(s(s(z))), s(s(s(s(z)))))),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[468, 2030])).
% 0.87/1.03 tff(2032,plain,
% 0.87/1.03 ($false),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[1994, 2031, 2029, 1947])).
% 0.87/1.03 tff(2033,plain,((~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.87/1.03 tff(2034,plain,
% 0.87/1.03 (~r(s(s(z)), s(z))),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[2033, 526, 291])).
% 0.87/1.03 tff(2035,plain,
% 0.87/1.03 (b(s(s(z)), s(z))),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[253, 2034])).
% 0.87/1.03 tff(2036,plain,
% 0.87/1.03 (~r(s(z), s(s(s(z))))),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[1880, 571, 526])).
% 0.87/1.03 tff(2037,plain,
% 0.87/1.03 (b(s(z), s(s(s(z))))),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[373, 2036])).
% 0.87/1.03 tff(2038,plain,
% 0.87/1.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 0.87/1.03 inference(rewrite,[status(thm)],[])).
% 0.87/1.03 tff(2039,plain,
% 0.87/1.03 (((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))) <=> ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 0.87/1.03 inference(rewrite,[status(thm)],[])).
% 0.87/1.03 tff(2040,plain,
% 0.87/1.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))))),
% 0.87/1.03 inference(monotonicity,[status(thm)],[2039])).
% 0.87/1.03 tff(2041,plain,
% 0.87/1.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 0.87/1.03 inference(transitivity,[status(thm)],[2040, 2038])).
% 0.87/1.03 tff(2042,plain,
% 0.87/1.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 0.87/1.03 inference(quant_inst,[status(thm)],[])).
% 0.87/1.03 tff(2043,plain,
% 0.87/1.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z)))))),
% 0.87/1.03 inference(modus_ponens,[status(thm)],[2042, 2041])).
% 0.87/1.03 tff(2044,plain,
% 0.87/1.03 ($false),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[2043, 180, 291, 170, 225, 353, 289])).
% 0.87/1.03 tff(2045,plain,((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.87/1.03 tff(2046,plain,
% 0.87/1.03 (~b(s(s(z)), z)),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[2045, 2037, 291, 2035, 1946])).
% 0.87/1.03 tff(2047,plain,
% 0.87/1.03 (r(s(s(z)), z)),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[165, 2046])).
% 0.87/1.03 tff(2048,plain,
% 0.87/1.03 (~b(z, s(s(s(z))))),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[1425, 2047, 1946, 291])).
% 0.87/1.03 tff(2049,plain,
% 0.87/1.03 (r(z, s(s(s(z))))),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[102, 2048])).
% 0.87/1.03 tff(2050,plain,
% 0.87/1.03 (~b(z, s(s(z)))),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[782, 2047, 291, 2034])).
% 0.87/1.03 tff(2051,plain,
% 0.87/1.03 (r(z, s(s(z)))),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[703, 2050])).
% 0.87/1.03 tff(2052,plain,
% 0.87/1.03 (~r(s(s(s(z))), s(s(z)))),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[793, 2051, 2049])).
% 0.87/1.03 tff(2053,assumption,(~b(s(s(s(z))), s(s(z)))), introduced(assumption)).
% 0.87/1.03 tff(2054,plain,
% 0.87/1.03 ($false),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[330, 73, 2053, 1187, 323])).
% 0.87/1.03 tff(2055,plain,(b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.87/1.03 tff(2056,plain,
% 0.87/1.03 (b(s(s(s(z))), s(s(z)))),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[2055, 2052])).
% 0.87/1.03 tff(2057,plain,
% 0.87/1.03 ($false),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[1437, 180, 2035, 2037, 1946, 2056])).
% 0.87/1.03 tff(2058,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(z))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.87/1.03 tff(2059,plain,
% 0.87/1.03 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[2058, 526, 291])).
% 0.87/1.03 tff(2060,plain,
% 0.87/1.03 (b(s(s(s(z))), s(s(s(s(z)))))),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[468, 2059])).
% 0.87/1.03 tff(2061,plain,
% 0.87/1.03 (~r(z, s(s(s(s(z)))))),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[1345, 255, 526])).
% 0.87/1.03 tff(2062,plain,
% 0.87/1.03 (b(z, s(s(s(s(z)))))),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[78, 2061])).
% 0.87/1.03 tff(2063,plain,
% 0.87/1.03 (~r(s(s(s(s(z)))), z)),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[589, 255, 526])).
% 0.87/1.03 tff(2064,plain,
% 0.87/1.03 (b(s(s(s(s(z)))), z)),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[717, 2063])).
% 0.87/1.03 tff(2065,plain,
% 0.87/1.03 ($false),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[1209, 180, 2064, 539, 2062, 168])).
% 0.87/1.03 tff(2066,plain,((~r(s(z), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.87/1.03 tff(2067,plain,
% 0.87/1.03 (~r(s(z), z)),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[2066, 168, 2060, 526])).
% 0.87/1.03 tff(2068,plain,
% 0.87/1.03 (b(s(z), z)),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[267, 2067])).
% 0.87/1.03 tff(2069,plain,
% 0.87/1.03 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[1731, 180, 291, 290, 1065])).
% 0.87/1.03 tff(2070,plain,
% 0.87/1.03 (r(s(s(s(s(s(s(z)))))), s(z))),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[947, 2069])).
% 0.87/1.03 tff(2071,plain,
% 0.87/1.03 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[516, 180, 291, 290, 1065, 168])).
% 0.87/1.03 tff(2072,plain,
% 0.87/1.03 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[487, 73, 484, 2071])).
% 0.87/1.03 tff(2073,plain,
% 0.87/1.03 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 0.87/1.03 inference(rewrite,[status(thm)],[])).
% 0.87/1.03 tff(2074,plain,
% 0.87/1.03 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 0.87/1.03 inference(quant_inst,[status(thm)],[])).
% 0.87/1.03 tff(2075,plain,
% 0.87/1.03 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 0.87/1.03 inference(modus_ponens,[status(thm)],[2074, 2073])).
% 0.87/1.03 tff(2076,plain,
% 0.87/1.03 ($false),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[2075, 53, 2072, 309, 2070])).
% 0.87/1.03 tff(2077,plain,((~b(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 0.87/1.03 tff(2078,plain,
% 0.87/1.03 (~b(s(s(s(s(s(s(z)))))), z)),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[2077, 2068, 291, 309, 168])).
% 0.87/1.03 tff(2079,plain,
% 0.87/1.03 (r(s(s(s(s(s(s(z)))))), z)),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[509, 2078])).
% 0.87/1.03 tff(2080,plain,
% 0.87/1.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), 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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)))),
% 0.87/1.03 inference(rewrite,[status(thm)],[])).
% 0.87/1.03 tff(2081,plain,
% 0.87/1.03 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))) <=> ((~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)))),
% 0.87/1.03 inference(rewrite,[status(thm)],[])).
% 0.87/1.03 tff(2082,plain,
% 0.87/1.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z))))),
% 0.87/1.03 inference(monotonicity,[status(thm)],[2081])).
% 0.87/1.03 tff(2083,plain,
% 0.87/1.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)))),
% 0.87/1.03 inference(transitivity,[status(thm)],[2082, 2080])).
% 0.87/1.03 tff(2084,plain,
% 0.87/1.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 0.87/1.03 inference(quant_inst,[status(thm)],[])).
% 0.87/1.03 tff(2085,plain,
% 0.87/1.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z))),
% 0.87/1.03 inference(modus_ponens,[status(thm)],[2084, 2083])).
% 0.87/1.03 tff(2086,plain,
% 0.87/1.03 (~b(s(s(z)), z)),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[2085, 180, 291, 2068, 2035])).
% 0.87/1.03 tff(2087,plain,
% 0.87/1.03 (r(s(s(z)), z)),
% 0.87/1.03 inference(unit_resolution,[status(thm)],[165, 2086])).
% 0.87/1.03 tff(2088,plain,
% 0.87/1.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))))),
% 0.87/1.03 inference(rewrite,[status(thm)],[])).
% 0.87/1.03 tff(2089,plain,
% 0.87/1.03 (((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))))),
% 0.87/1.03 inference(rewrite,[status(thm)],[])).
% 0.87/1.03 tff(2090,plain,
% 0.87/1.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(z)))))))),
% 0.87/1.04 inference(monotonicity,[status(thm)],[2089])).
% 0.87/1.04 tff(2091,plain,
% 0.87/1.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))))),
% 0.87/1.04 inference(transitivity,[status(thm)],[2090, 2088])).
% 0.87/1.04 tff(2092,plain,
% 0.87/1.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))),
% 0.87/1.04 inference(quant_inst,[status(thm)],[])).
% 0.87/1.04 tff(2093,plain,
% 0.87/1.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(z)))))),
% 0.87/1.04 inference(modus_ponens,[status(thm)],[2092, 2091])).
% 0.87/1.04 tff(2094,plain,
% 0.87/1.04 (~b(s(z), s(s(s(z))))),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[2093, 180, 291, 2068, 168])).
% 0.87/1.04 tff(2095,plain,
% 0.87/1.04 (r(s(z), s(s(s(z))))),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[373, 2094])).
% 0.87/1.04 tff(2096,plain,
% 0.87/1.04 (~r(s(s(z)), s(s(s(s(z)))))),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[160, 80, 152])).
% 0.87/1.04 tff(2097,plain,
% 0.87/1.04 (b(s(s(z)), s(s(s(s(z)))))),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[212, 2096])).
% 0.87/1.04 tff(2098,plain,
% 0.87/1.04 (~b(s(s(z)), s(s(s(z))))),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[1994, 2097, 539])).
% 0.87/1.04 tff(2099,plain,
% 0.87/1.04 (r(s(s(z)), s(s(s(z))))),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[150, 2098])).
% 0.87/1.04 tff(2100,plain,
% 0.87/1.04 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 0.87/1.04 inference(rewrite,[status(thm)],[])).
% 0.87/1.04 tff(2101,plain,
% 0.87/1.04 (((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 0.87/1.04 inference(rewrite,[status(thm)],[])).
% 0.87/1.04 tff(2102,plain,
% 0.87/1.04 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z)))))))),
% 0.87/1.04 inference(monotonicity,[status(thm)],[2101])).
% 0.87/1.04 tff(2103,plain,
% 0.87/1.04 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 0.87/1.04 inference(transitivity,[status(thm)],[2102, 2100])).
% 0.87/1.04 tff(2104,plain,
% 0.87/1.04 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z)))))),
% 0.87/1.04 inference(quant_inst,[status(thm)],[])).
% 0.87/1.04 tff(2105,plain,
% 0.87/1.04 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z)))))),
% 0.87/1.04 inference(modus_ponens,[status(thm)],[2104, 2103])).
% 0.87/1.04 tff(2106,plain,
% 0.87/1.04 (~r(s(z), s(s(z)))),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[2105, 53, 2099, 525])).
% 0.87/1.04 tff(2107,plain,
% 0.87/1.04 ($false),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[2010, 53, 80, 1713, 1476])).
% 0.87/1.04 tff(2108,plain,((~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))))))), inference(lemma,lemma(discharge,[]))).
% 0.87/1.04 tff(2109,plain,
% 0.87/1.04 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[2108, 80, 1713])).
% 0.87/1.04 tff(2110,plain,
% 0.87/1.04 (~r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[1715, 1713, 152])).
% 0.87/1.04 tff(2111,plain,
% 0.87/1.04 (b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[1096, 2110])).
% 0.87/1.04 tff(2112,plain,
% 0.87/1.04 (b(s(s(s(s(z)))), s(s(z)))),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[1326, 217])).
% 0.87/1.04 tff(2113,plain,
% 0.87/1.04 (~b(s(z), s(s(z)))),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[1467, 2112, 2111, 2109, 225])).
% 0.87/1.04 tff(2114,plain,
% 0.87/1.04 ($false),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[341, 73, 247, 2113, 2106])).
% 0.87/1.04 tff(2115,plain,((~r(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), z))), inference(lemma,lemma(discharge,[]))).
% 0.87/1.04 tff(2116,plain,
% 0.87/1.04 (~r(s(s(s(s(z)))), z)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[2115, 2095, 2035, 2087, 2060, 2079])).
% 0.87/1.04 tff(2117,plain,
% 0.87/1.04 (b(s(s(s(s(z)))), z)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[717, 2116])).
% 0.87/1.04 tff(2118,plain,
% 0.87/1.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, 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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 0.87/1.04 inference(rewrite,[status(thm)],[])).
% 0.87/1.04 tff(2119,plain,
% 0.87/1.04 (((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 0.87/1.04 inference(rewrite,[status(thm)],[])).
% 0.87/1.04 tff(2120,plain,
% 0.87/1.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 0.87/1.04 inference(monotonicity,[status(thm)],[2119])).
% 0.87/1.04 tff(2121,plain,
% 0.87/1.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 0.87/1.04 inference(transitivity,[status(thm)],[2120, 2118])).
% 0.87/1.04 tff(2122,plain,
% 0.87/1.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 0.87/1.04 inference(quant_inst,[status(thm)],[])).
% 0.87/1.04 tff(2123,plain,
% 0.87/1.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 0.87/1.04 inference(modus_ponens,[status(thm)],[2122, 2121])).
% 0.87/1.04 tff(2124,plain,
% 0.87/1.04 ($false),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[2123, 180, 291, 2068, 1741, 2117, 168])).
% 0.87/1.04 tff(2125,plain,((~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.87/1.04 tff(2126,plain,
% 0.87/1.04 (~b(s(s(s(z))), z)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[2125, 309, 291, 526])).
% 0.87/1.04 tff(2127,plain,
% 0.87/1.04 (r(s(s(s(z))), z)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[117, 2126])).
% 0.87/1.04 tff(2128,plain,
% 0.87/1.04 ($false),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[1031, 53, 255, 104, 309])).
% 0.87/1.04 tff(2129,plain,((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.87/1.04 tff(2130,plain,
% 0.87/1.04 (~r(s(z), z)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[2129, 2127, 309])).
% 0.87/1.04 tff(2131,plain,
% 0.87/1.04 (b(s(z), z)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[267, 2130])).
% 0.87/1.04 tff(2132,plain,
% 0.87/1.04 (~b(z, s(s(z)))),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[772, 2131, 291, 2035])).
% 0.87/1.04 tff(2133,plain,
% 0.87/1.04 (r(z, s(s(z)))),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[703, 2132])).
% 0.87/1.04 tff(2134,plain,
% 0.87/1.04 (~b(s(s(z)), z)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[2085, 180, 291, 2131, 2035])).
% 0.87/1.04 tff(2135,plain,
% 0.87/1.04 (r(s(s(z)), z)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[165, 2134])).
% 0.87/1.04 tff(2136,plain,
% 0.87/1.04 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 0.87/1.04 inference(rewrite,[status(thm)],[])).
% 0.87/1.04 tff(2137,plain,
% 0.87/1.04 (((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 0.87/1.04 inference(rewrite,[status(thm)],[])).
% 0.87/1.04 tff(2138,plain,
% 0.87/1.04 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z))))),
% 0.87/1.04 inference(monotonicity,[status(thm)],[2137])).
% 0.87/1.04 tff(2139,plain,
% 0.87/1.04 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 0.87/1.04 inference(transitivity,[status(thm)],[2138, 2136])).
% 0.87/1.04 tff(2140,plain,
% 0.87/1.04 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 0.87/1.04 inference(quant_inst,[status(thm)],[])).
% 0.87/1.04 tff(2141,plain,
% 0.87/1.04 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z))),
% 0.87/1.04 inference(modus_ponens,[status(thm)],[2140, 2139])).
% 0.87/1.04 tff(2142,plain,
% 0.87/1.04 (~r(s(s(z)), s(s(s(z))))),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[2141, 53, 2135, 2127])).
% 0.87/1.04 tff(2143,plain,
% 0.87/1.04 (b(s(s(z)), s(s(s(z))))),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[150, 2142])).
% 0.87/1.04 tff(2144,plain,
% 0.87/1.04 ((~r(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(z))))),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[1782, 1741])).
% 0.87/1.04 tff(2145,plain,
% 0.87/1.04 (~r(z, s(s(s(s(z)))))),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[2144, 2143, 2127, 2133])).
% 0.87/1.04 tff(2146,plain,
% 0.87/1.04 (b(z, s(s(s(s(z)))))),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[78, 2145])).
% 0.87/1.04 tff(2147,plain,
% 0.87/1.04 (~b(s(s(z)), s(s(s(s(z)))))),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[1994, 2143, 2060])).
% 0.87/1.04 tff(2148,plain,
% 0.87/1.04 (r(s(s(z)), s(s(s(s(z)))))),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[212, 2147])).
% 0.87/1.04 tff(2149,plain,
% 0.87/1.04 (~r(s(s(s(s(z)))), z)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[160, 2148, 2135])).
% 0.87/1.04 tff(2150,plain,
% 0.87/1.04 (b(s(s(s(s(z)))), z)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[717, 2149])).
% 0.87/1.04 tff(2151,plain,
% 0.87/1.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 0.87/1.04 inference(rewrite,[status(thm)],[])).
% 0.87/1.04 tff(2152,plain,
% 0.87/1.04 (((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 0.87/1.04 inference(rewrite,[status(thm)],[])).
% 0.87/1.04 tff(2153,plain,
% 0.87/1.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))))),
% 0.87/1.04 inference(monotonicity,[status(thm)],[2152])).
% 0.87/1.04 tff(2154,plain,
% 0.87/1.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 0.87/1.04 inference(transitivity,[status(thm)],[2153, 2151])).
% 0.87/1.04 tff(2155,plain,
% 0.87/1.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 0.87/1.04 inference(quant_inst,[status(thm)],[])).
% 0.87/1.04 tff(2156,plain,
% 0.87/1.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))),
% 0.87/1.04 inference(modus_ponens,[status(thm)],[2155, 2154])).
% 0.87/1.04 tff(2157,plain,
% 0.87/1.04 (~b(s(s(s(s(z)))), s(z))),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[2156, 180, 2131, 2150, 2146])).
% 0.87/1.04 tff(2158,plain,
% 0.87/1.04 ((s(s(s(s(z)))) = s(z)) | r(s(s(s(s(z)))), s(z))),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[381, 73, 2157])).
% 0.87/1.04 tff(2159,plain,
% 0.87/1.04 (r(s(s(s(s(z)))), s(z))),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[2158, 352])).
% 0.87/1.04 tff(2160,plain,
% 0.87/1.04 ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z)))))),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[1812, 1741])).
% 0.87/1.04 tff(2161,plain,
% 0.87/1.04 (~b(z, s(s(s(z))))),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[2160, 2146, 2060])).
% 0.87/1.04 tff(2162,plain,
% 0.87/1.04 (r(z, s(s(s(z))))),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[102, 2161])).
% 0.87/1.04 tff(2163,plain,
% 0.87/1.04 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[2021, 1701, 539])).
% 0.87/1.04 tff(2164,plain,
% 0.87/1.04 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[487, 73, 484, 2163])).
% 0.87/1.04 tff(2165,plain,
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% 0.87/1.04 inference(rewrite,[status(thm)],[])).
% 0.87/1.04 tff(2166,plain,
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% 0.87/1.04 inference(rewrite,[status(thm)],[])).
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% 0.87/1.04 inference(monotonicity,[status(thm)],[2166])).
% 0.87/1.04 tff(2168,plain,
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% 0.87/1.04 inference(transitivity,[status(thm)],[2167, 2165])).
% 0.87/1.04 tff(2169,plain,
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% 0.87/1.04 inference(modus_ponens,[status(thm)],[2169, 2168])).
% 0.87/1.04 tff(2171,plain,
% 0.87/1.04 (~b(s(s(s(s(s(s(z)))))), z)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[2170, 180, 1741, 539, 540, 1701])).
% 0.87/1.04 tff(2172,plain,
% 0.87/1.04 (r(s(s(s(s(s(s(z)))))), z)),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[509, 2171])).
% 0.87/1.04 tff(2173,plain,
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% 0.87/1.04 inference(rewrite,[status(thm)],[])).
% 0.87/1.04 tff(2174,plain,
% 0.87/1.04 (((~r(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)))))), 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))))))),
% 0.87/1.04 inference(rewrite,[status(thm)],[])).
% 0.87/1.04 tff(2175,plain,
% 0.87/1.04 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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)))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))))),
% 0.87/1.04 inference(monotonicity,[status(thm)],[2174])).
% 0.87/1.04 tff(2176,plain,
% 0.87/1.04 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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)))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
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% 0.87/1.04 tff(2178,plain,
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% 0.87/1.04 tff(2179,plain,
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% 0.87/1.04 inference(unit_resolution,[status(thm)],[2178, 53, 2172, 42, 2164])).
% 0.87/1.04 tff(2180,plain,((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.87/1.04 tff(2181,plain,
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% 0.87/1.04 tff(2182,plain,
% 0.87/1.04 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[1699, 2181])).
% 0.87/1.04 tff(2183,plain,
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% 0.87/1.04 tff(2184,plain,((~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(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.87/1.04 tff(2185,plain,
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% 0.87/1.04 inference(unit_resolution,[status(thm)],[2184, 2182, 2159])).
% 0.87/1.04 tff(2186,plain,
% 0.87/1.04 (b(s(s(s(s(s(s(z)))))), s(z))),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[947, 2185])).
% 0.87/1.04 tff(2187,plain,
% 0.87/1.04 (~r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[1111, 53, 2182, 2148])).
% 0.87/1.04 tff(2188,plain,
% 0.87/1.04 (b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.87/1.04 inference(unit_resolution,[status(thm)],[1096, 2187])).
% 0.87/1.04 tff(2189,plain,
% 0.87/1.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(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)))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 0.87/1.04 inference(rewrite,[status(thm)],[])).
% 0.87/1.04 tff(2190,plain,
% 0.87/1.05 (((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))) <=> ((~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
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% 0.87/1.05 tff(2191,plain,
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% 0.87/1.05 inference(monotonicity,[status(thm)],[2190])).
% 0.87/1.05 tff(2192,plain,
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% 0.87/1.05 inference(transitivity,[status(thm)],[2191, 2189])).
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% 0.87/1.05 inference(modus_ponens,[status(thm)],[2193, 2192])).
% 0.87/1.05 tff(2195,plain,
% 0.87/1.05 ($false),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[2194, 180, 291, 2131, 2035, 2188, 2186])).
% 0.87/1.05 tff(2196,plain,((~r(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.87/1.05 tff(2197,plain,
% 0.87/1.05 (~r(s(s(s(z))), s(z))),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[2196, 526, 291])).
% 0.87/1.05 tff(2198,plain,
% 0.87/1.05 (b(s(s(s(z))), s(z))),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[307, 2197])).
% 0.87/1.05 tff(2199,plain,
% 0.87/1.05 ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[1820, 1741])).
% 0.87/1.05 tff(2200,plain,
% 0.87/1.05 (~b(z, s(s(s(z))))),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[2199, 2198, 2060])).
% 0.87/1.05 tff(2201,plain,
% 0.87/1.05 (r(z, s(s(s(z))))),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[102, 2200])).
% 0.87/1.05 tff(2202,plain,
% 0.87/1.05 (~b(s(s(s(z))), z)),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[2066, 255, 2060, 526])).
% 0.87/1.05 tff(2203,plain,
% 0.87/1.05 (r(s(s(s(z))), z)),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[117, 2202])).
% 0.87/1.05 tff(2204,plain,
% 0.87/1.05 (~r(s(z), s(s(s(z))))),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[1039, 53, 255, 2203])).
% 0.87/1.05 tff(2205,plain,
% 0.87/1.05 (b(s(z), s(s(s(z))))),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[373, 2204])).
% 0.87/1.05 tff(2206,plain,
% 0.87/1.05 (~b(s(s(z)), s(s(s(z))))),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[848, 2205, 2035, 2198])).
% 0.87/1.05 tff(2207,plain,
% 0.87/1.05 (r(s(s(z)), s(s(s(z))))),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[150, 2206])).
% 0.87/1.05 tff(2208,plain,
% 0.87/1.05 (~b(s(s(z)), z)),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[2045, 2205, 291, 2035, 2198])).
% 0.87/1.05 tff(2209,plain,
% 0.87/1.05 (r(s(s(z)), z)),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[165, 2208])).
% 0.87/1.05 tff(2210,plain,
% 0.87/1.05 ($false),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[2141, 53, 2209, 2203, 2207])).
% 0.87/1.05 tff(2211,plain,((~r(s(z), z)) | (~b(z, s(z))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.87/1.05 tff(2212,plain,
% 0.87/1.05 (~r(s(z), z)),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[2211, 526, 291])).
% 0.87/1.05 tff(2213,plain,
% 0.87/1.05 (b(s(z), z)),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[267, 2212])).
% 0.87/1.05 tff(2214,plain,
% 0.87/1.05 (~b(z, s(s(z)))),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[772, 2213, 291, 2035])).
% 0.87/1.05 tff(2215,plain,
% 0.87/1.05 (r(z, s(s(z)))),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[703, 2214])).
% 0.87/1.05 tff(2216,plain,
% 0.87/1.05 (~r(s(s(s(z))), s(s(z)))),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[793, 2215, 2201])).
% 0.87/1.05 tff(2217,plain,
% 0.87/1.05 (b(s(s(s(z))), s(s(z)))),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[2055, 2216])).
% 0.87/1.05 tff(2218,plain,
% 0.87/1.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(2219,plain,
% 0.87/1.05 (((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(2220,plain,
% 0.87/1.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z)))))),
% 0.87/1.05 inference(monotonicity,[status(thm)],[2219])).
% 0.87/1.05 tff(2221,plain,
% 0.87/1.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))),
% 0.87/1.05 inference(transitivity,[status(thm)],[2220, 2218])).
% 0.87/1.05 tff(2222,plain,
% 0.87/1.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 0.87/1.05 inference(quant_inst,[status(thm)],[])).
% 0.87/1.05 tff(2223,plain,
% 0.87/1.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z)))),
% 0.87/1.05 inference(modus_ponens,[status(thm)],[2222, 2221])).
% 0.87/1.05 tff(2224,plain,
% 0.87/1.05 ($false),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[2223, 180, 291, 2213, 2035, 2198, 2217])).
% 0.87/1.05 tff(2225,plain,((~r(s(z), s(s(s(s(z)))))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.87/1.05 tff(2226,plain,
% 0.87/1.05 (~r(s(z), s(s(s(s(z)))))),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[2225, 291])).
% 0.87/1.05 tff(2227,plain,
% 0.87/1.05 (b(s(z), s(s(s(s(z)))))),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[523, 2226])).
% 0.87/1.05 tff(2228,plain,
% 0.87/1.05 (~b(s(s(s(s(z)))), z)),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[1026, 290, 2227, 291])).
% 0.87/1.05 tff(2229,plain,
% 0.87/1.05 (r(s(s(s(s(z)))), z)),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[717, 2228])).
% 0.87/1.05 tff(2230,plain,
% 0.87/1.05 (~r(s(s(s(z))), s(z))),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[317, 39, 119])).
% 0.87/1.05 tff(2231,plain,
% 0.87/1.05 (b(s(s(s(z))), s(z))),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[307, 2230])).
% 0.87/1.05 tff(2232,plain,
% 0.87/1.05 (~r(s(z), s(s(s(z))))),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[636, 39, 119])).
% 0.87/1.05 tff(2233,plain,
% 0.87/1.05 (b(s(z), s(s(s(z))))),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[373, 2232])).
% 0.87/1.05 tff(2234,plain,
% 0.87/1.05 ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[1850, 1741])).
% 0.87/1.05 tff(2235,plain,
% 0.87/1.05 ($false),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[2234, 2233, 2231, 224])).
% 0.87/1.05 tff(2236,plain,((~r(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.87/1.05 tff(2237,plain,
% 0.87/1.05 (~r(s(s(z)), s(s(s(z))))),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[2236, 39, 2227])).
% 0.87/1.05 tff(2238,plain,
% 0.87/1.05 (b(s(s(z)), s(s(s(z))))),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[150, 2237])).
% 0.87/1.05 tff(2239,plain,
% 0.87/1.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(z), 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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(2240,plain,
% 0.87/1.05 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z)))) <=> ((~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(2241,plain,
% 0.87/1.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 0.87/1.05 inference(monotonicity,[status(thm)],[2240])).
% 0.87/1.05 tff(2242,plain,
% 0.87/1.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 0.87/1.05 inference(transitivity,[status(thm)],[2241, 2239])).
% 0.87/1.05 tff(2243,plain,
% 0.87/1.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))),
% 0.87/1.05 inference(quant_inst,[status(thm)],[])).
% 0.87/1.05 tff(2244,plain,
% 0.87/1.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 0.87/1.05 inference(modus_ponens,[status(thm)],[2243, 2242])).
% 0.87/1.05 tff(2245,plain,
% 0.87/1.05 ($false),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[2244, 180, 291, 2227, 540, 400])).
% 0.87/1.05 tff(2246,plain,((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.87/1.05 tff(2247,plain,
% 0.87/1.05 (~b(s(s(s(s(z)))), s(z))),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[2246, 540, 291])).
% 0.87/1.05 tff(2248,plain,
% 0.87/1.05 ((s(s(s(s(z)))) = s(z)) | r(s(s(s(s(z)))), s(z))),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[381, 73, 2247])).
% 0.87/1.05 tff(2249,plain,
% 0.87/1.05 (r(s(s(s(s(z)))), s(z))),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[2248, 352])).
% 0.87/1.05 tff(2250,plain,
% 0.87/1.05 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(2251,plain,
% 0.87/1.05 (((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(2252,plain,
% 0.87/1.05 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 0.87/1.05 inference(monotonicity,[status(thm)],[2251])).
% 0.87/1.05 tff(2253,plain,
% 0.87/1.05 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 0.87/1.05 inference(transitivity,[status(thm)],[2252, 2250])).
% 0.87/1.05 tff(2254,plain,
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% 0.87/1.05 inference(modus_ponens,[status(thm)],[2254, 2253])).
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% 0.87/1.05 inference(unit_resolution,[status(thm)],[2255, 53, 39, 41, 1565])).
% 0.87/1.05 tff(2257,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.87/1.05 tff(2258,plain,
% 0.87/1.05 (~r(s(s(z)), s(s(s(s(z)))))),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[2257, 2249, 39])).
% 0.87/1.05 tff(2259,plain,
% 0.87/1.05 (b(s(s(z)), s(s(s(s(z)))))),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[212, 2258])).
% 0.87/1.05 tff(2260,plain,
% 0.87/1.05 (~b(s(s(s(s(z)))), s(s(z)))),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[616, 2259, 170, 540])).
% 0.87/1.05 tff(2261,plain,
% 0.87/1.05 (r(s(s(s(s(z)))), s(s(z)))),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[1326, 2260])).
% 0.87/1.05 tff(2262,plain,
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% 0.87/1.05 inference(unit_resolution,[status(thm)],[1571, 53, 39, 2261, 2249])).
% 0.87/1.05 tff(2263,plain,((~b(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.87/1.05 tff(2264,plain,
% 0.87/1.05 (~b(z, s(s(s(s(z)))))),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[2263, 170, 39, 291])).
% 0.87/1.05 tff(2265,plain,
% 0.87/1.05 (r(z, s(s(s(s(z)))))),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[78, 2264])).
% 0.87/1.05 tff(2266,plain,
% 0.87/1.05 (~r(z, s(s(s(z))))),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[1866, 2265, 571])).
% 0.87/1.05 tff(2267,plain,
% 0.87/1.05 (b(z, s(s(s(z))))),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[102, 2266])).
% 0.87/1.05 tff(2268,plain,
% 0.87/1.05 (~r(s(s(s(z))), z)),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[1229, 2265, 571])).
% 0.87/1.05 tff(2269,plain,
% 0.87/1.05 (b(s(s(s(z))), z)),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[117, 2268])).
% 0.87/1.05 tff(2270,plain,
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% 0.87/1.05 inference(unit_resolution,[status(thm)],[188, 2269, 2267, 2238, 170])).
% 0.87/1.05 tff(2271,plain,((~b(s(s(z)), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.87/1.05 tff(2272,plain,
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% 0.87/1.05 inference(unit_resolution,[status(thm)],[2271, 39, 571, 291])).
% 0.87/1.05 tff(2273,plain,
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% 0.87/1.05 tff(2274,plain,
% 0.87/1.05 (~r(s(s(z)), s(s(s(s(z)))))),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[160, 2273, 80])).
% 0.87/1.05 tff(2275,plain,
% 0.87/1.05 (b(s(s(z)), s(s(s(s(z)))))),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[212, 2274])).
% 0.87/1.05 tff(2276,plain,
% 0.87/1.05 (~r(s(s(s(s(z)))), s(s(z)))),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[216, 53, 2273, 80])).
% 0.87/1.05 tff(2277,plain,
% 0.87/1.05 (b(s(s(s(s(z)))), s(s(z)))),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[1326, 2276])).
% 0.87/1.05 tff(2278,plain,
% 0.87/1.05 (~r(z, s(s(s(z))))),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[1866, 43, 571])).
% 0.87/1.05 tff(2279,plain,
% 0.87/1.05 (b(z, s(s(s(z))))),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[102, 2278])).
% 0.87/1.05 tff(2280,plain,
% 0.87/1.05 (~r(s(s(s(z))), z)),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[1229, 43, 571])).
% 0.87/1.05 tff(2281,plain,
% 0.87/1.05 (b(s(s(s(z))), z)),
% 0.87/1.05 inference(unit_resolution,[status(thm)],[117, 2280])).
% 0.87/1.05 tff(2282,plain,
% 0.87/1.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), 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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(2283,plain,
% 0.87/1.05 (((~b(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(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(2284,plain,
% 0.87/1.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 0.87/1.05 inference(monotonicity,[status(thm)],[2283])).
% 0.87/1.05 tff(2285,plain,
% 0.87/1.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 0.87/1.05 inference(transitivity,[status(thm)],[2284, 2282])).
% 0.87/1.05 tff(2286,plain,
% 0.87/1.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 0.87/1.05 inference(quant_inst,[status(thm)],[])).
% 0.87/1.05 tff(2287,plain,
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% 0.87/1.05 inference(modus_ponens,[status(thm)],[2286, 2285])).
% 0.87/1.05 tff(2288,plain,
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% 0.87/1.05 tff(2289,plain,((~r(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.87/1.05 tff(2290,plain,
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% 0.87/1.05 tff(2291,plain,
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% 0.87/1.05 tff(2292,plain,
% 0.87/1.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(2293,plain,
% 0.87/1.05 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), 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(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 0.87/1.05 inference(rewrite,[status(thm)],[])).
% 0.87/1.05 tff(2294,plain,
% 0.87/1.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))))),
% 0.87/1.05 inference(monotonicity,[status(thm)],[2293])).
% 0.87/1.05 tff(2295,plain,
% 0.87/1.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 0.87/1.05 inference(transitivity,[status(thm)],[2294, 2292])).
% 0.87/1.05 tff(2296,plain,
% 0.87/1.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))),
% 0.87/1.05 inference(quant_inst,[status(thm)],[])).
% 0.87/1.06 tff(2297,plain,
% 0.87/1.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[2296, 2295])).
% 0.87/1.06 tff(2298,plain,
% 0.87/1.06 ($false),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[2297, 180, 291, 2227, 2291, 2277, 2275])).
% 0.87/1.06 tff(2299,plain,((~r(s(s(z)), s(z))) | (~b(z, s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 0.87/1.06 tff(2300,plain,
% 0.87/1.06 (~r(s(s(z)), s(z))),
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% 0.87/1.06 tff(2301,plain,
% 0.87/1.06 (b(s(s(z)), s(z))),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[253, 2300])).
% 0.87/1.06 tff(2302,plain,
% 0.87/1.06 (~b(s(s(z)), z)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[2085, 180, 291, 290, 2301])).
% 0.87/1.06 tff(2303,plain,
% 0.87/1.06 (r(s(s(z)), z)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[165, 2302])).
% 0.87/1.06 tff(2304,plain,
% 0.87/1.06 (~r(s(s(z)), s(s(s(s(z)))))),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[160, 2303, 2229])).
% 0.87/1.06 tff(2305,plain,
% 0.87/1.06 (b(s(s(z)), s(s(s(s(z)))))),
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% 0.87/1.06 tff(2330,plain,
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% 0.87/1.06 tff(2367,plain,
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% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(2370,plain,
% 0.87/1.06 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(2371,plain,
% 0.87/1.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 0.87/1.06 inference(monotonicity,[status(thm)],[2370])).
% 0.87/1.06 tff(2372,plain,
% 0.87/1.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 0.87/1.06 inference(transitivity,[status(thm)],[2371, 2369])).
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% 0.87/1.06 inference(quant_inst,[status(thm)],[])).
% 0.87/1.06 tff(2374,plain,
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% 0.87/1.06 inference(modus_ponens,[status(thm)],[2373, 2372])).
% 0.87/1.06 tff(2375,plain,
% 0.87/1.06 ($false),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[2374, 180, 2368, 2227, 2346, 2340])).
% 0.87/1.06 tff(2376,plain,((~r(s(z), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.87/1.06 tff(2377,plain,
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% 0.87/1.06 tff(2378,plain,
% 0.87/1.06 (b(s(z), z)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[267, 2377])).
% 0.87/1.06 tff(2379,plain,
% 0.87/1.06 (~b(s(s(s(s(z)))), z)),
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% 0.87/1.06 (~r(s(s(s(s(z)))), z)),
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% 0.87/1.06 tff(2381,plain,
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% 0.87/1.06 tff(2382,plain,((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.87/1.06 tff(2383,plain,
% 0.87/1.06 (~b(s(s(s(z))), s(z))),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[2382, 571, 291])).
% 0.87/1.06 tff(2384,plain,
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% 0.87/1.06 inference(unit_resolution,[status(thm)],[2129, 2311, 2384])).
% 0.87/1.06 tff(2386,plain,
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% 0.87/1.06 inference(unit_resolution,[status(thm)],[117, 2385])).
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% 0.87/1.06 inference(unit_resolution,[status(thm)],[1866, 2320, 571])).
% 0.87/1.06 tff(2388,plain,
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% 0.87/1.06 tff(2389,plain,
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% 0.87/1.06 inference(unit_resolution,[status(thm)],[2341, 2388, 2386])).
% 0.87/1.06 tff(2390,plain,
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% 0.87/1.06 inference(unit_resolution,[status(thm)],[717, 2389])).
% 0.87/1.06 tff(2391,plain,
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% 0.87/1.06 tff(2392,plain,
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% 0.87/1.06 inference(unit_resolution,[status(thm)],[253, 2391])).
% 0.87/1.06 tff(2393,plain,
% 0.87/1.06 (~r(s(s(s(s(z)))), s(z))),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[651, 53, 2311, 2390])).
% 0.87/1.06 tff(2394,plain,
% 0.87/1.06 ((s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z))),
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% 0.87/1.06 tff(2395,plain,
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% 0.87/1.06 inference(unit_resolution,[status(thm)],[2394, 352])).
% 0.87/1.06 tff(2396,plain,
% 0.87/1.06 (~b(s(s(s(s(z)))), s(s(z)))),
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% 0.87/1.06 tff(2397,plain,
% 0.87/1.06 (r(s(s(s(s(z)))), s(s(z)))),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[1326, 2396])).
% 0.87/1.06 tff(2398,plain,
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% 0.87/1.06 inference(unit_resolution,[status(thm)],[1321, 2397, 2320])).
% 0.87/1.06 tff(2399,plain,
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% 0.87/1.06 inference(unit_resolution,[status(thm)],[703, 2398])).
% 0.87/1.06 tff(2400,plain,
% 0.87/1.06 (~r(s(s(z)), z)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[782, 2399, 291, 2391])).
% 0.87/1.06 tff(2401,plain,
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% 0.87/1.06 inference(unit_resolution,[status(thm)],[165, 2400])).
% 0.87/1.06 tff(2402,plain,
% 0.87/1.06 (~b(s(s(s(z))), s(s(z)))),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[1935, 2401, 2386, 2399])).
% 0.87/1.06 tff(2403,plain,
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% 0.87/1.06 inference(unit_resolution,[status(thm)],[2055, 2402])).
% 0.87/1.06 tff(2404,plain,
% 0.87/1.06 (~r(s(s(z)), s(s(s(s(z)))))),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[2338, 2403, 571])).
% 0.87/1.06 tff(2405,plain,
% 0.87/1.06 (b(s(s(z)), s(s(s(s(z)))))),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[212, 2404])).
% 0.87/1.06 tff(2406,plain,
% 0.87/1.06 ($false),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[2374, 180, 2392, 2227, 2395, 2405])).
% 0.87/1.06 tff(2407,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.87/1.06 tff(2408,plain,
% 0.87/1.06 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[2407, 291])).
% 0.87/1.06 tff(2409,plain,
% 0.87/1.06 (b(s(s(s(z))), s(s(s(s(z)))))),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[468, 2408])).
% 0.87/1.06 tff(2410,plain,
% 0.87/1.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(2411,plain,
% 0.87/1.06 (((~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(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(2412,plain,
% 0.87/1.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(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(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))))),
% 0.87/1.06 inference(monotonicity,[status(thm)],[2411])).
% 0.87/1.06 tff(2413,plain,
% 0.87/1.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(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(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 0.87/1.06 inference(transitivity,[status(thm)],[2412, 2410])).
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% 0.87/1.06 inference(quant_inst,[status(thm)],[])).
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% 0.87/1.06 inference(modus_ponens,[status(thm)],[2414, 2413])).
% 0.87/1.06 tff(2416,plain,
% 0.87/1.06 (~b(s(z), s(s(s(z))))),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[2415, 180, 1741, 2227, 2409])).
% 0.87/1.06 tff(2417,plain,
% 0.87/1.06 (r(s(z), s(s(s(z))))),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[373, 2416])).
% 0.87/1.06 tff(2418,plain,
% 0.87/1.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, 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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(2419,plain,
% 0.87/1.06 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(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(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(2420,plain,
% 0.87/1.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))))),
% 0.87/1.06 inference(monotonicity,[status(thm)],[2419])).
% 0.87/1.06 tff(2421,plain,
% 0.87/1.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 0.87/1.06 inference(transitivity,[status(thm)],[2420, 2418])).
% 0.87/1.06 tff(2422,plain,
% 0.87/1.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))),
% 0.87/1.06 inference(quant_inst,[status(thm)],[])).
% 0.87/1.06 tff(2423,plain,
% 0.87/1.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))),
% 0.87/1.06 inference(modus_ponens,[status(thm)],[2422, 2421])).
% 0.87/1.06 tff(2424,plain,
% 0.87/1.06 ($false),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[2423, 180, 291, 1741, 2227, 2409, 540])).
% 0.87/1.06 tff(2425,plain,((~b(z, s(s(s(s(z)))))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.87/1.06 tff(2426,plain,
% 0.87/1.06 (~b(z, s(s(s(s(z)))))),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[2425, 291])).
% 0.87/1.06 tff(2427,plain,
% 0.87/1.06 (r(z, s(s(s(s(z)))))),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[78, 2426])).
% 0.87/1.06 tff(2428,plain,
% 0.87/1.06 (~r(z, s(s(z)))),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[1922, 53, 2427, 41])).
% 0.87/1.06 tff(2429,plain,
% 0.87/1.06 (b(z, s(s(z)))),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[703, 2428])).
% 0.87/1.06 tff(2430,plain,
% 0.87/1.06 (~r(s(s(z)), z)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[737, 41, 2427])).
% 0.87/1.06 tff(2431,plain,
% 0.87/1.06 (b(s(s(z)), z)),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[165, 2430])).
% 0.87/1.06 tff(2432,plain,
% 0.87/1.06 (~b(s(s(s(s(z)))), s(s(z)))),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[964, 180, 2431, 2429, 719])).
% 0.87/1.06 tff(2433,plain,
% 0.87/1.06 (r(s(s(s(s(z)))), s(s(z)))),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[1326, 2432])).
% 0.87/1.06 tff(2434,plain,
% 0.87/1.06 (~b(s(z), s(s(z)))),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[761, 2429, 291, 235])).
% 0.87/1.06 tff(2435,assumption,(~r(s(z), s(s(z)))), introduced(assumption)).
% 0.87/1.06 tff(2436,assumption,(~b(s(z), s(s(z)))), introduced(assumption)).
% 0.87/1.06 tff(2437,plain,
% 0.87/1.06 ($false),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[341, 73, 247, 2436, 2435])).
% 0.87/1.06 tff(2438,plain,(r(s(z), s(s(z))) | b(s(z), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.87/1.06 tff(2439,plain,
% 0.87/1.06 (r(s(z), s(s(z)))),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[2438, 2434])).
% 0.87/1.06 tff(2440,plain,
% 0.87/1.06 (~r(s(s(s(s(z)))), s(z))),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[977, 53, 2439, 2433])).
% 0.87/1.06 tff(2441,plain,
% 0.87/1.06 ((s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z))),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[381, 73, 2440])).
% 0.87/1.06 tff(2442,plain,
% 0.87/1.06 (b(s(s(s(s(z)))), s(z))),
% 0.87/1.06 inference(unit_resolution,[status(thm)],[2441, 352])).
% 0.87/1.06 tff(2443,plain,
% 0.87/1.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 0.87/1.06 inference(rewrite,[status(thm)],[])).
% 0.87/1.06 tff(2444,plain,
% 0.87/1.06 (((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(2445,plain,
% 0.87/1.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 0.87/1.07 inference(monotonicity,[status(thm)],[2444])).
% 0.87/1.07 tff(2446,plain,
% 0.87/1.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 0.87/1.07 inference(transitivity,[status(thm)],[2445, 2443])).
% 0.87/1.07 tff(2447,plain,
% 0.87/1.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 0.87/1.07 inference(quant_inst,[status(thm)],[])).
% 0.87/1.07 tff(2448,plain,
% 0.87/1.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[2447, 2446])).
% 0.87/1.07 tff(2449,plain,
% 0.87/1.07 ($false),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[2448, 180, 291, 2227, 719, 2442])).
% 0.87/1.07 tff(2450,plain,((~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | r(s(s(z)), s(z)) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.87/1.07 tff(2451,plain,
% 0.87/1.07 (~b(s(s(s(s(z)))), z)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[2450, 235, 291, 41])).
% 0.87/1.07 tff(2452,plain,
% 0.87/1.07 (r(s(s(s(s(z)))), z)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[717, 2451])).
% 0.87/1.07 tff(2453,plain,
% 0.87/1.07 (~b(s(z), z)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[772, 2429, 291, 764])).
% 0.87/1.07 tff(2454,plain,
% 0.87/1.07 (r(s(z), z)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[267, 2453])).
% 0.87/1.07 tff(2455,plain,
% 0.87/1.07 (~r(s(s(s(s(z)))), s(z))),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[651, 53, 2454, 2452])).
% 0.87/1.07 tff(2456,plain,
% 0.87/1.07 ((s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z))),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[381, 73, 2455])).
% 0.87/1.07 tff(2457,plain,
% 0.87/1.07 (b(s(s(s(s(z)))), s(z))),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[2456, 352])).
% 0.87/1.07 tff(2458,plain,
% 0.87/1.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), 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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(2459,plain,
% 0.87/1.07 (((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))) <=> ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(2460,plain,
% 0.87/1.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 0.87/1.07 inference(monotonicity,[status(thm)],[2459])).
% 0.87/1.07 tff(2461,plain,
% 0.87/1.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 0.87/1.07 inference(transitivity,[status(thm)],[2460, 2458])).
% 0.87/1.07 tff(2462,plain,
% 0.87/1.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 0.87/1.07 inference(quant_inst,[status(thm)],[])).
% 0.87/1.07 tff(2463,plain,
% 0.87/1.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[2462, 2461])).
% 0.87/1.07 tff(2464,plain,
% 0.87/1.07 ($false),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[2463, 180, 291, 2431, 764, 2227, 2457])).
% 0.87/1.07 tff(2465,plain,(r(s(s(z)), s(z)) | (~b(z, s(z))) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.87/1.07 tff(2466,plain,
% 0.87/1.07 (r(s(s(z)), s(z))),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[2465, 41, 291])).
% 0.87/1.07 tff(2467,plain,
% 0.87/1.07 (~b(s(s(s(s(z)))), z)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[1942, 2466])).
% 0.87/1.07 tff(2468,plain,
% 0.87/1.07 (r(s(s(s(s(z)))), z)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[717, 2467])).
% 0.87/1.07 tff(2469,plain,
% 0.87/1.07 ((~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)))),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[1808, 1741])).
% 0.87/1.07 tff(2470,plain,
% 0.87/1.07 (~b(s(s(s(z))), s(z))),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[2469, 2409, 2227])).
% 0.87/1.07 tff(2471,plain,
% 0.87/1.07 (r(s(s(s(z))), s(z))),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[307, 2470])).
% 0.87/1.07 tff(2472,plain,
% 0.87/1.07 (~r(s(s(s(z))), s(s(z)))),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[326, 53, 2466, 2471])).
% 0.87/1.07 tff(2473,plain,
% 0.87/1.07 (b(s(s(s(z))), s(s(z)))),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[2055, 2472])).
% 0.87/1.07 tff(2474,plain,
% 0.87/1.07 (~b(s(s(s(z))), z)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[1935, 2473, 2431, 2429])).
% 0.87/1.07 tff(2475,plain,
% 0.87/1.07 (r(s(s(s(z))), z)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[117, 2474])).
% 0.87/1.07 tff(2476,plain,
% 0.87/1.07 (~r(s(z), z)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[2129, 2475, 2471])).
% 0.87/1.07 tff(2477,plain,
% 0.87/1.07 (b(s(z), z)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[267, 2476])).
% 0.87/1.07 tff(2478,plain,
% 0.87/1.07 (~b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[940, 180, 170, 751, 1065])).
% 0.87/1.07 tff(2479,plain,
% 0.87/1.07 (r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[1096, 2478])).
% 0.87/1.07 tff(2480,plain,
% 0.87/1.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(2481,plain,
% 0.87/1.07 (((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(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(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(2482,plain,
% 0.87/1.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(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))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z))))),
% 0.87/1.07 inference(monotonicity,[status(thm)],[2481])).
% 0.87/1.07 tff(2483,plain,
% 0.87/1.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(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))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 0.87/1.07 inference(transitivity,[status(thm)],[2482, 2480])).
% 0.87/1.07 tff(2484,plain,
% 0.87/1.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(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))))),
% 0.87/1.07 inference(quant_inst,[status(thm)],[])).
% 0.87/1.07 tff(2485,plain,
% 0.87/1.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z))),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[2484, 2483])).
% 0.87/1.07 tff(2486,plain,
% 0.87/1.07 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[2485, 180, 170, 290, 751, 1065])).
% 0.87/1.07 tff(2487,plain,
% 0.87/1.07 (r(s(s(s(s(s(s(z)))))), s(z))),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[947, 2486])).
% 0.87/1.07 tff(2488,plain,
% 0.87/1.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(2489,plain,
% 0.87/1.07 (((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(2490,plain,
% 0.87/1.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z))))),
% 0.87/1.07 inference(monotonicity,[status(thm)],[2489])).
% 0.87/1.07 tff(2491,plain,
% 0.87/1.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))),
% 0.87/1.07 inference(transitivity,[status(thm)],[2490, 2488])).
% 0.87/1.07 tff(2492,plain,
% 0.87/1.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))),
% 0.87/1.07 inference(quant_inst,[status(thm)],[])).
% 0.87/1.07 tff(2493,plain,
% 0.87/1.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z))),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[2492, 2491])).
% 0.87/1.07 tff(2494,plain,
% 0.87/1.07 (~b(s(z), s(s(z)))),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[2493, 180, 170, 290, 751])).
% 0.87/1.07 tff(2495,plain,
% 0.87/1.07 (r(s(z), s(s(z)))),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[2438, 2494])).
% 0.87/1.07 tff(2496,plain,
% 0.87/1.07 ($false),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[429, 53, 2495, 2487, 2479])).
% 0.87/1.07 tff(2497,plain,((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.87/1.07 tff(2498,plain,
% 0.87/1.07 (~b(s(s(s(s(s(s(z)))))), z)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[2497, 2431, 2477, 2429])).
% 0.87/1.07 tff(2499,plain,
% 0.87/1.07 (r(s(s(s(s(s(s(z)))))), z)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[509, 2498])).
% 0.87/1.07 tff(2500,plain,
% 0.87/1.07 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[2108, 2499, 2468])).
% 0.87/1.07 tff(2501,plain,
% 0.87/1.07 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[1699, 2500])).
% 0.87/1.07 tff(2502,plain,
% 0.87/1.07 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[2021, 2501, 2409])).
% 0.87/1.07 tff(2503,plain,
% 0.87/1.07 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[1985, 53, 2475, 2499])).
% 0.87/1.07 tff(2504,plain,
% 0.87/1.07 ($false),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[487, 73, 484, 2503, 2502])).
% 0.87/1.07 tff(2505,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.87/1.07 tff(2506,plain,
% 0.87/1.07 (~r(s(s(z)), s(s(s(s(z)))))),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[2505, 291])).
% 0.87/1.07 tff(2507,plain,
% 0.87/1.07 (b(s(s(z)), s(s(s(s(z)))))),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[212, 2506])).
% 0.87/1.07 tff(2508,plain,
% 0.87/1.07 (~b(s(s(z)), s(s(s(z))))),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[1994, 2507, 2409])).
% 0.87/1.07 tff(2509,plain,
% 0.87/1.07 (r(s(s(z)), s(s(s(z))))),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[150, 2508])).
% 0.87/1.07 tff(2510,plain,
% 0.87/1.07 (~r(s(s(z)), s(z))),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[317, 2509, 2471])).
% 0.87/1.07 tff(2511,plain,
% 0.87/1.07 (b(s(s(z)), s(z))),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[253, 2510])).
% 0.87/1.07 tff(2512,plain,
% 0.87/1.07 (~b(s(s(s(s(z)))), s(s(z)))),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[233, 2511, 2227, 2507])).
% 0.87/1.07 tff(2513,plain,
% 0.87/1.07 (r(s(s(s(s(z)))), s(s(z)))),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[1326, 2512])).
% 0.87/1.07 tff(2514,plain,
% 0.87/1.07 (~r(z, s(s(z)))),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[1321, 2513, 2427])).
% 0.87/1.07 tff(2515,plain,
% 0.87/1.07 (b(z, s(s(z)))),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[703, 2514])).
% 0.87/1.07 tff(2516,plain,
% 0.87/1.07 (~b(s(z), s(s(z)))),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[761, 2515, 291, 2510])).
% 0.87/1.07 tff(2517,plain,
% 0.87/1.07 (r(s(z), s(s(z)))),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[2438, 2516])).
% 0.87/1.07 tff(2518,plain,
% 0.87/1.07 ($false),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[2105, 53, 2517, 2509, 2417])).
% 0.87/1.07 tff(2519,plain,(~b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 0.87/1.07 tff(2520,plain,
% 0.87/1.07 (r(z, s(z))),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[287, 2519])).
% 0.87/1.07 tff(2521,plain,
% 0.87/1.07 ((~r(s(s(z)), z)) | (~r(s(s(z)), s(z)))),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[277, 2520])).
% 0.87/1.07 tff(2522,plain,
% 0.87/1.07 (~r(s(s(z)), z)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[2521, 39])).
% 0.87/1.07 tff(2523,plain,
% 0.87/1.07 (b(s(s(z)), z)),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[165, 2522])).
% 0.87/1.07 tff(2524,plain,
% 0.87/1.07 ((~r(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), z)) | (~r(s(s(z)), s(z)))),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[942, 2520])).
% 0.87/1.07 tff(2525,plain,
% 0.87/1.07 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[2524, 2523, 39])).
% 0.87/1.07 tff(2526,plain,
% 0.87/1.07 (b(s(s(s(s(s(s(z)))))), s(z))),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[947, 2525])).
% 0.87/1.07 tff(2527,plain,
% 0.87/1.07 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(2528,plain,
% 0.87/1.07 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 0.87/1.07 inference(quant_inst,[status(thm)],[])).
% 0.87/1.07 tff(2529,plain,
% 0.87/1.07 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[2528, 2527])).
% 0.87/1.07 tff(2530,plain,
% 0.87/1.07 ($false),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[2529, 53, 269, 80, 1565])).
% 0.87/1.07 tff(2531,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 0.87/1.07 tff(2532,plain,
% 0.87/1.07 ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[2531, 2520])).
% 0.87/1.07 tff(2533,plain,
% 0.87/1.07 (~r(s(s(s(s(z)))), s(z))),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[2532, 1944])).
% 0.87/1.07 tff(2534,assumption,(s(s(s(s(z)))) = s(z)), introduced(assumption)).
% 0.87/1.07 tff(2535,plain,
% 0.87/1.07 (s(z) = s(s(s(s(z))))),
% 0.87/1.07 inference(symmetry,[status(thm)],[2534])).
% 0.87/1.07 tff(2536,plain,
% 0.87/1.07 ($false),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[351, 2535])).
% 0.87/1.07 tff(2537,plain,(~(s(s(s(s(z)))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 0.87/1.07 tff(2538,assumption,(~r(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 0.87/1.07 tff(2539,assumption,(~b(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 0.87/1.07 tff(2540,plain,
% 0.87/1.07 ($false),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[381, 73, 2539, 2538, 2537])).
% 0.87/1.07 tff(2541,plain,(b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z))), inference(lemma,lemma(discharge,[]))).
% 0.87/1.07 tff(2542,plain,
% 0.87/1.07 (b(s(s(s(s(z)))), s(z))),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[2541, 2533])).
% 0.87/1.07 tff(2543,plain,
% 0.87/1.07 (~r(z, s(s(s(s(z)))))),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[558, 526, 2520])).
% 0.87/1.07 tff(2544,plain,
% 0.87/1.07 (b(z, s(s(s(s(z)))))),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[78, 2543])).
% 0.87/1.07 tff(2545,plain,
% 0.87/1.07 (~r(s(s(s(s(z)))), s(z))),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[2531, 80, 2520])).
% 0.87/1.07 tff(2546,plain,
% 0.87/1.07 (~r(z, s(s(s(s(z)))))),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[558, 526, 269])).
% 0.87/1.07 tff(2547,plain,
% 0.87/1.07 (b(z, s(s(s(s(z)))))),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[78, 2546])).
% 0.87/1.07 tff(2548,plain,
% 0.87/1.07 (~r(z, s(s(s(z))))),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[838, 309, 269])).
% 0.87/1.07 tff(2549,plain,
% 0.87/1.07 (b(z, s(s(s(z))))),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[102, 2548])).
% 0.87/1.07 tff(2550,plain,
% 0.87/1.07 ($false),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[2160, 2549, 1384, 2547])).
% 0.87/1.07 tff(2551,plain,((~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.87/1.07 tff(2552,plain,
% 0.87/1.07 (~r(s(s(s(z))), s(z))),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[2551, 526, 2520])).
% 0.87/1.07 tff(2553,plain,
% 0.87/1.07 (b(s(s(s(z))), s(z))),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[307, 2552])).
% 0.87/1.07 tff(2554,plain,
% 0.87/1.07 (~r(s(s(z)), s(z))),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[277, 152, 2520])).
% 0.87/1.07 tff(2555,plain,
% 0.87/1.07 (b(s(s(z)), s(z))),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[253, 2554])).
% 0.87/1.07 tff(2556,plain,
% 0.87/1.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(2557,plain,
% 0.87/1.07 (((~b(s(s(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(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(2558,plain,
% 0.87/1.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 0.87/1.07 inference(monotonicity,[status(thm)],[2557])).
% 0.87/1.07 tff(2559,plain,
% 0.87/1.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 0.87/1.07 inference(transitivity,[status(thm)],[2558, 2556])).
% 0.87/1.07 tff(2560,plain,
% 0.87/1.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))))),
% 0.87/1.07 inference(quant_inst,[status(thm)],[])).
% 0.87/1.07 tff(2561,plain,
% 0.87/1.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[2560, 2559])).
% 0.87/1.07 tff(2562,plain,
% 0.87/1.07 (~b(z, s(s(z)))),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[2561, 180, 2544, 2112, 223])).
% 0.87/1.07 tff(2563,plain,
% 0.87/1.07 (r(z, s(s(z)))),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[703, 2562])).
% 0.87/1.07 tff(2564,plain,
% 0.87/1.07 (~r(s(s(s(z))), s(s(z)))),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[793, 42, 688])).
% 0.87/1.07 tff(2565,plain,
% 0.87/1.07 (b(s(s(s(z))), s(s(z)))),
% 0.87/1.07 inference(unit_resolution,[status(thm)],[2055, 2564])).
% 0.87/1.07 tff(2566,plain,
% 0.87/1.07 (~r(s(z), s(s(s(z))))),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[828, 42, 269])).
% 0.87/1.08 tff(2567,plain,
% 0.87/1.08 (b(s(z), s(s(s(z))))),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[373, 2566])).
% 0.87/1.08 tff(2568,plain,
% 0.87/1.08 ($false),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[1437, 180, 225, 2567, 289, 2565])).
% 0.87/1.08 tff(2569,plain,((~r(z, s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.87/1.08 tff(2570,plain,
% 0.87/1.08 (~r(z, s(s(s(z))))),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[2569, 2563, 2520, 2555, 2553])).
% 0.87/1.08 tff(2571,plain,
% 0.87/1.08 (b(z, s(s(s(z))))),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[102, 2570])).
% 0.87/1.08 tff(2572,plain,
% 0.87/1.08 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[2199, 2571, 2553])).
% 0.87/1.08 tff(2573,plain,
% 0.87/1.08 (r(s(s(s(z))), s(s(s(s(z)))))),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[468, 2572])).
% 0.87/1.08 tff(2574,plain,
% 0.87/1.08 (~r(s(z), s(s(s(z))))),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[1880, 2573, 526])).
% 0.87/1.08 tff(2575,plain,
% 0.87/1.08 (b(s(z), s(s(s(z))))),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[373, 2574])).
% 0.87/1.08 tff(2576,plain,
% 0.87/1.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), 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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 0.87/1.08 inference(rewrite,[status(thm)],[])).
% 0.87/1.08 tff(2577,plain,
% 0.87/1.08 (((~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(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(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(s(z)))), s(z))))),
% 0.87/1.08 inference(rewrite,[status(thm)],[])).
% 0.87/1.08 tff(2578,plain,
% 0.87/1.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 0.87/1.08 inference(monotonicity,[status(thm)],[2577])).
% 0.87/1.08 tff(2579,plain,
% 0.87/1.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 0.87/1.08 inference(transitivity,[status(thm)],[2578, 2576])).
% 0.87/1.08 tff(2580,plain,
% 0.87/1.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 0.87/1.08 inference(quant_inst,[status(thm)],[])).
% 0.87/1.08 tff(2581,plain,
% 0.87/1.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))),
% 0.87/1.08 inference(modus_ponens,[status(thm)],[2580, 2579])).
% 0.87/1.08 tff(2582,plain,
% 0.87/1.08 (~b(s(s(s(s(z)))), s(z))),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[2581, 180, 1741, 2575, 2553])).
% 0.87/1.08 tff(2583,plain,
% 0.87/1.08 ($false),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[381, 73, 2582, 2545, 2537])).
% 0.87/1.08 tff(2584,plain,((~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 0.87/1.08 tff(2585,plain,
% 0.87/1.08 (~r(s(s(s(s(z)))), z)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[2584, 223, 526, 152])).
% 0.87/1.08 tff(2586,plain,
% 0.87/1.08 (b(s(s(s(s(z)))), z)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[717, 2585])).
% 0.87/1.08 tff(2587,plain,
% 0.87/1.08 (~b(z, s(s(z)))),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[1445, 180, 2586, 2544, 223])).
% 0.87/1.08 tff(2588,plain,
% 0.87/1.08 (r(z, s(s(z)))),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[703, 2587])).
% 0.87/1.08 tff(2589,plain,
% 0.87/1.08 (~r(z, s(s(s(z))))),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[2569, 2588, 2520, 2555, 2553])).
% 0.87/1.08 tff(2590,plain,
% 0.87/1.08 (b(z, s(s(s(z))))),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[102, 2589])).
% 0.87/1.08 tff(2591,plain,
% 0.87/1.08 (~b(s(s(s(z))), z)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[2341, 2590, 2586])).
% 0.87/1.08 tff(2592,plain,
% 0.87/1.08 (r(s(s(s(z))), z)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[117, 2591])).
% 0.87/1.08 tff(2593,plain,
% 0.87/1.08 ($false),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[1407, 53, 688, 104, 785])).
% 0.87/1.08 tff(2594,plain,((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 0.87/1.08 tff(2595,plain,
% 0.87/1.08 (~r(s(s(s(z))), s(s(z)))),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[2594, 2592, 2588])).
% 0.87/1.08 tff(2596,plain,
% 0.87/1.08 (b(s(s(s(z))), s(s(z)))),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[2055, 2595])).
% 0.87/1.08 tff(2597,plain,
% 0.87/1.08 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[2199, 2590, 2553])).
% 0.87/1.08 tff(2598,plain,
% 0.87/1.08 (r(s(s(s(z))), s(s(s(s(z)))))),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[468, 2597])).
% 0.87/1.08 tff(2599,plain,
% 0.87/1.08 (~r(s(z), s(s(s(z))))),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[1880, 2598, 526])).
% 0.87/1.08 tff(2600,plain,
% 0.87/1.08 (b(s(z), s(s(s(z))))),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[373, 2599])).
% 0.87/1.08 tff(2601,plain,
% 0.87/1.08 ($false),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[1437, 180, 2555, 2600, 2553, 2596])).
% 0.87/1.08 tff(2602,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 0.87/1.08 tff(2603,plain,
% 0.87/1.08 (~b(s(s(z)), s(s(s(s(z)))))),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[2602, 152, 526])).
% 0.87/1.08 tff(2604,plain,
% 0.87/1.08 (r(s(s(z)), s(s(s(s(z)))))),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[212, 2603])).
% 0.87/1.08 tff(2605,plain,
% 0.87/1.08 (~b(z, s(s(s(z))))),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[2160, 539, 2544])).
% 0.87/1.08 tff(2606,plain,
% 0.87/1.08 (r(z, s(s(s(z))))),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[102, 2605])).
% 0.87/1.08 tff(2607,plain,
% 0.87/1.08 (~b(s(s(z)), s(s(s(z))))),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[911, 2606, 2520, 526, 2553])).
% 0.87/1.08 tff(2608,plain,
% 0.87/1.08 (r(s(s(z)), s(s(s(z))))),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[150, 2607])).
% 0.87/1.08 tff(2609,plain,
% 0.87/1.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 0.87/1.08 inference(rewrite,[status(thm)],[])).
% 0.87/1.08 tff(2610,plain,
% 0.87/1.08 (((~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(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z))) <=> ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 0.87/1.08 inference(rewrite,[status(thm)],[])).
% 0.87/1.08 tff(2611,plain,
% 0.87/1.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 0.87/1.08 inference(monotonicity,[status(thm)],[2610])).
% 0.87/1.08 tff(2612,plain,
% 0.87/1.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 0.87/1.08 inference(transitivity,[status(thm)],[2611, 2609])).
% 0.87/1.08 tff(2613,plain,
% 0.87/1.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))),
% 0.87/1.08 inference(quant_inst,[status(thm)],[])).
% 0.87/1.08 tff(2614,plain,
% 0.87/1.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 0.87/1.08 inference(modus_ponens,[status(thm)],[2613, 2612])).
% 0.87/1.08 tff(2615,plain,
% 0.87/1.08 (~b(s(s(s(z))), z)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[2614, 180, 1741, 539, 2544])).
% 0.87/1.08 tff(2616,plain,
% 0.87/1.08 (r(s(s(s(z))), z)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[117, 2615])).
% 0.87/1.08 tff(2617,plain,
% 0.87/1.08 ($false),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[2141, 53, 152, 2616, 2608])).
% 0.87/1.08 tff(2618,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.87/1.08 tff(2619,plain,
% 0.87/1.08 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[2618, 152, 526])).
% 0.87/1.08 tff(2620,plain,
% 0.87/1.08 (r(s(s(s(z))), s(s(s(s(z)))))),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[468, 2619])).
% 0.87/1.08 tff(2621,plain,
% 0.87/1.08 (~r(s(z), s(s(s(z))))),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[1880, 2620, 526])).
% 0.87/1.08 tff(2622,plain,
% 0.87/1.08 (b(s(z), s(s(s(z))))),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[373, 2621])).
% 0.87/1.08 tff(2623,plain,
% 0.87/1.08 (~b(s(s(z)), s(s(s(z))))),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[848, 2622, 2555, 2553])).
% 0.87/1.08 tff(2624,plain,
% 0.87/1.08 (r(s(s(z)), s(s(s(z))))),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[150, 2623])).
% 0.87/1.08 tff(2625,plain,
% 0.87/1.08 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 0.87/1.08 inference(rewrite,[status(thm)],[])).
% 0.87/1.08 tff(2626,plain,
% 0.87/1.08 (((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 0.87/1.08 inference(rewrite,[status(thm)],[])).
% 0.87/1.08 tff(2627,plain,
% 0.87/1.08 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 0.87/1.08 inference(monotonicity,[status(thm)],[2626])).
% 0.87/1.08 tff(2628,plain,
% 0.87/1.08 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 0.87/1.08 inference(transitivity,[status(thm)],[2627, 2625])).
% 0.87/1.08 tff(2629,plain,
% 0.87/1.08 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))))),
% 0.87/1.08 inference(quant_inst,[status(thm)],[])).
% 0.87/1.08 tff(2630,plain,
% 0.87/1.08 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 0.87/1.08 inference(modus_ponens,[status(thm)],[2629, 2628])).
% 0.87/1.08 tff(2631,plain,
% 0.87/1.08 ($false),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[2630, 53, 2620, 2624, 2604])).
% 0.87/1.08 tff(2632,plain,((~r(s(s(z)), z)) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.87/1.08 tff(2633,plain,
% 0.87/1.08 (~r(s(s(z)), z)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[2632, 526])).
% 0.87/1.08 tff(2634,plain,
% 0.87/1.08 (b(s(s(z)), z)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[165, 2633])).
% 0.87/1.08 tff(2635,plain,
% 0.87/1.08 (~b(s(s(s(s(z)))), s(z))),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[2581, 180, 1741, 2037, 2553])).
% 0.87/1.08 tff(2636,plain,
% 0.87/1.08 (r(s(s(s(s(z)))), s(z))),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[381, 73, 2635, 2537])).
% 0.87/1.08 tff(2637,plain,
% 0.87/1.08 (~r(s(s(s(s(z)))), z)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[2531, 2636, 2520])).
% 0.87/1.08 tff(2638,plain,
% 0.87/1.08 (b(s(s(s(s(z)))), z)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[717, 2637])).
% 0.87/1.08 tff(2639,plain,
% 0.87/1.08 (~b(s(s(z)), s(s(s(s(z)))))),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[1307, 2638, 2544, 2634])).
% 0.87/1.08 tff(2640,plain,
% 0.87/1.08 (r(s(s(z)), s(s(s(s(z)))))),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[212, 2639])).
% 0.87/1.08 tff(2641,plain,
% 0.87/1.08 (~r(s(s(s(z))), s(s(z)))),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[2338, 2640, 571])).
% 0.87/1.08 tff(2642,plain,
% 0.87/1.08 (b(s(s(s(z))), s(s(z)))),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[2055, 2641])).
% 0.87/1.08 tff(2643,plain,
% 0.87/1.08 (~r(s(s(z)), s(z))),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[1942, 2638])).
% 0.87/1.08 tff(2644,plain,
% 0.87/1.08 (b(s(s(z)), s(z))),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[253, 2643])).
% 0.87/1.08 tff(2645,plain,
% 0.87/1.08 ($false),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[1437, 180, 2644, 2037, 2553, 2642])).
% 0.87/1.08 tff(2646,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.87/1.08 tff(2647,plain,
% 0.87/1.08 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[2646, 526])).
% 0.87/1.08 tff(2648,plain,
% 0.87/1.08 (b(s(s(s(z))), s(s(s(s(z)))))),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[468, 2647])).
% 0.87/1.08 tff(2649,plain,
% 0.87/1.08 (~b(z, s(s(s(z))))),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[2160, 2648, 2544])).
% 0.87/1.08 tff(2650,plain,
% 0.87/1.08 (r(z, s(s(s(z))))),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[102, 2649])).
% 0.87/1.08 tff(2651,plain,
% 0.87/1.08 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[2180, 2650, 2544, 2648])).
% 0.87/1.08 tff(2652,plain,
% 0.87/1.08 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[1699, 2651])).
% 0.87/1.08 tff(2653,plain,
% 0.87/1.08 (~r(s(z), s(s(s(z))))),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[828, 2650, 2520])).
% 0.87/1.08 tff(2654,plain,
% 0.87/1.08 (b(s(z), s(s(s(z))))),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[373, 2653])).
% 0.87/1.08 tff(2655,plain,
% 0.87/1.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 0.87/1.08 inference(rewrite,[status(thm)],[])).
% 0.87/1.08 tff(2656,plain,
% 0.87/1.08 (((~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(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 0.87/1.08 inference(rewrite,[status(thm)],[])).
% 0.87/1.08 tff(2657,plain,
% 0.87/1.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), 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(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 0.87/1.08 inference(monotonicity,[status(thm)],[2656])).
% 0.87/1.08 tff(2658,plain,
% 0.87/1.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), 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(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 0.87/1.08 inference(transitivity,[status(thm)],[2657, 2655])).
% 0.87/1.08 tff(2659,plain,
% 0.87/1.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), 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(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 0.87/1.08 inference(quant_inst,[status(thm)],[])).
% 0.87/1.08 tff(2660,plain,
% 0.87/1.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))),
% 0.87/1.08 inference(modus_ponens,[status(thm)],[2659, 2658])).
% 0.87/1.08 tff(2661,plain,
% 0.87/1.08 (~b(s(s(s(s(z)))), s(z))),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[2660, 180, 1741, 2654, 2648])).
% 0.87/1.08 tff(2662,plain,
% 0.87/1.08 (r(s(s(s(s(z)))), s(z))),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[381, 73, 2661, 2537])).
% 0.87/1.08 tff(2663,plain,
% 0.87/1.08 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[2184, 2662, 2652])).
% 0.87/1.08 tff(2664,plain,
% 0.87/1.08 (b(s(s(s(s(s(s(z)))))), s(z))),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[947, 2663])).
% 0.87/1.08 tff(2665,plain,
% 0.87/1.08 (~b(s(s(z)), s(s(s(z))))),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[911, 2650, 2520, 526, 2553])).
% 0.87/1.08 tff(2666,plain,
% 0.87/1.08 (r(s(s(z)), s(s(s(z))))),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[150, 2665])).
% 0.87/1.08 tff(2667,plain,
% 0.87/1.08 (~r(z, s(s(z)))),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[1368, 53, 2666, 2650])).
% 0.87/1.08 tff(2668,plain,
% 0.87/1.08 (b(z, s(s(z)))),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[703, 2667])).
% 0.87/1.08 tff(2669,plain,
% 0.87/1.08 (~r(s(z), z)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[589, 80, 526])).
% 0.87/1.08 tff(2670,plain,
% 0.87/1.08 (b(s(z), z)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[267, 2669])).
% 0.87/1.08 tff(2671,plain,
% 0.87/1.08 (~r(s(s(s(s(s(s(z)))))), z)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[2108, 80, 2652])).
% 0.87/1.08 tff(2672,plain,
% 0.87/1.08 (b(s(s(s(s(s(s(z)))))), z)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[509, 2671])).
% 0.87/1.08 tff(2673,plain,
% 0.87/1.08 ($false),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[2497, 2672, 2670, 2634, 2668])).
% 0.87/1.08 tff(2674,plain,((~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.87/1.08 tff(2675,plain,
% 0.87/1.08 (~r(s(s(s(s(z)))), z)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[2674, 526])).
% 0.87/1.08 tff(2676,plain,
% 0.87/1.08 (b(s(s(s(s(z)))), z)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[717, 2675])).
% 0.87/1.08 tff(2677,plain,
% 0.87/1.08 (~b(s(s(z)), s(s(s(s(z)))))),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[1307, 2676, 2544, 2634])).
% 0.87/1.08 tff(2678,plain,
% 0.87/1.08 (r(s(s(z)), s(s(s(s(z)))))),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[212, 2677])).
% 0.87/1.08 tff(2679,plain,
% 0.87/1.08 (~r(s(z), s(s(z)))),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[805, 53, 526, 2678])).
% 0.87/1.08 tff(2680,plain,
% 0.87/1.08 (b(s(z), s(s(z)))),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[2438, 2679])).
% 0.87/1.08 tff(2681,plain,
% 0.87/1.08 (~r(s(s(z)), s(z))),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[1942, 2676])).
% 0.87/1.08 tff(2682,plain,
% 0.87/1.08 (b(s(s(z)), s(z))),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[253, 2681])).
% 0.87/1.08 tff(2683,plain,
% 0.87/1.08 (((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(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(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 0.87/1.08 inference(rewrite,[status(thm)],[])).
% 0.87/1.08 tff(2684,plain,
% 0.87/1.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z), s(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)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))))),
% 0.87/1.08 inference(monotonicity,[status(thm)],[2683])).
% 0.87/1.08 tff(2685,plain,
% 0.87/1.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z), s(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)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 0.87/1.08 inference(transitivity,[status(thm)],[2684, 1118])).
% 0.87/1.08 tff(2686,plain,
% 0.87/1.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z), s(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)))))),
% 0.87/1.08 inference(quant_inst,[status(thm)],[])).
% 0.87/1.08 tff(2687,plain,
% 0.87/1.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))),
% 0.87/1.08 inference(modus_ponens,[status(thm)],[2686, 2685])).
% 0.87/1.08 tff(2688,plain,
% 0.87/1.08 (~b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[2687, 180, 2682, 2680, 2664])).
% 0.87/1.08 tff(2689,plain,
% 0.87/1.08 (r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.87/1.09 inference(unit_resolution,[status(thm)],[1096, 2688])).
% 0.87/1.09 tff(2690,plain,
% 0.87/1.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(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))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(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))))),
% 0.87/1.09 inference(rewrite,[status(thm)],[])).
% 0.87/1.09 tff(2691,plain,
% 0.87/1.09 (((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), 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(z)))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), s(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(s(s(s(z)))))), s(z))))),
% 0.87/1.09 inference(rewrite,[status(thm)],[])).
% 0.87/1.09 tff(2692,plain,
% 0.87/1.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), 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(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(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)))))),
% 0.87/1.09 inference(monotonicity,[status(thm)],[2691])).
% 0.87/1.09 tff(2693,plain,
% 0.87/1.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), 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(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(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))))),
% 0.87/1.09 inference(transitivity,[status(thm)],[2692, 2690])).
% 0.87/1.09 tff(2694,plain,
% 0.87/1.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), 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(z))))))),
% 0.87/1.09 inference(quant_inst,[status(thm)],[])).
% 0.87/1.09 tff(2695,plain,
% 0.87/1.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))),
% 0.87/1.09 inference(modus_ponens,[status(thm)],[2694, 2693])).
% 0.87/1.09 tff(2696,plain,
% 0.87/1.09 ($false),
% 0.87/1.09 inference(unit_resolution,[status(thm)],[2695, 180, 225, 752, 289, 655, 2013])).
% 0.87/1.09 tff(2697,plain,((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.87/1.09 tff(2698,plain,
% 0.87/1.09 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.87/1.09 inference(unit_resolution,[status(thm)],[2697, 2682, 2680, 2553, 2664])).
% 0.87/1.09 tff(2699,plain,
% 0.87/1.09 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.87/1.09 inference(unit_resolution,[status(thm)],[487, 73, 484, 2698])).
% 0.87/1.09 tff(2700,plain,
% 0.87/1.09 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 0.87/1.09 inference(rewrite,[status(thm)],[])).
% 0.87/1.09 tff(2701,plain,
% 0.87/1.09 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 0.87/1.09 inference(quant_inst,[status(thm)],[])).
% 0.87/1.09 tff(2702,plain,
% 0.87/1.09 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z))))),
% 0.87/1.09 inference(modus_ponens,[status(thm)],[2701, 2700])).
% 0.87/1.09 tff(2703,plain,
% 0.87/1.09 ($false),
% 0.87/1.09 inference(unit_resolution,[status(thm)],[2702, 53, 2666, 2699, 2689])).
% 0.87/1.09 tff(2704,plain,(~r(s(z), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.87/1.09 tff(2705,plain,
% 0.87/1.09 (b(s(z), s(s(s(s(z)))))),
% 0.87/1.09 inference(unit_resolution,[status(thm)],[523, 2704])).
% 0.87/1.09 tff(2706,plain,
% 0.87/1.09 (((~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(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)))))), s(s(s(s(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)))))), s(s(s(s(z)))))))),
% 0.87/1.09 inference(rewrite,[status(thm)],[])).
% 0.87/1.09 tff(2707,plain,
% 0.87/1.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 0.87/1.09 inference(monotonicity,[status(thm)],[2706])).
% 0.87/1.09 tff(2708,plain,
% 0.87/1.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 0.87/1.09 inference(transitivity,[status(thm)],[2707, 401])).
% 0.87/1.09 tff(2709,plain,
% 0.87/1.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 0.87/1.09 inference(quant_inst,[status(thm)],[])).
% 0.87/1.09 tff(2710,plain,
% 0.87/1.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 0.87/1.09 inference(modus_ponens,[status(thm)],[2709, 2708])).
% 0.87/1.09 tff(2711,plain,
% 0.87/1.09 ($false),
% 0.87/1.09 inference(unit_resolution,[status(thm)],[2710, 180, 2705, 400, 655, 1701])).
% 0.87/1.09 tff(2712,plain,((~b(s(s(s(s(s(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)))), inference(lemma,lemma(discharge,[]))).
% 0.87/1.09 tff(2713,plain,
% 0.87/1.09 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 0.87/1.09 inference(unit_resolution,[status(thm)],[2712, 2542, 2526])).
% 0.87/1.09 tff(2714,plain,
% 0.87/1.09 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 0.87/1.09 inference(unit_resolution,[status(thm)],[1699, 2713])).
% 0.87/1.09 tff(2715,plain,
% 0.87/1.09 (~r(s(s(s(s(s(s(z)))))), z)),
% 0.87/1.09 inference(unit_resolution,[status(thm)],[2108, 2714, 1944])).
% 0.87/1.09 tff(2716,plain,
% 0.87/1.09 (b(s(s(s(s(s(s(z)))))), z)),
% 0.87/1.09 inference(unit_resolution,[status(thm)],[509, 2715])).
% 0.87/1.09 tff(2717,plain,
% 0.87/1.09 ((~r(z, s(s(z)))) | (~r(s(s(z)), s(z)))),
% 0.87/1.09 inference(unit_resolution,[status(thm)],[693, 2520])).
% 0.87/1.09 tff(2718,plain,
% 0.87/1.09 (~r(z, s(s(z)))),
% 0.87/1.09 inference(unit_resolution,[status(thm)],[2717, 39])).
% 0.87/1.09 tff(2719,plain,
% 0.87/1.09 (b(z, s(s(z)))),
% 0.87/1.09 inference(unit_resolution,[status(thm)],[703, 2718])).
% 0.87/1.09 tff(2720,plain,
% 0.87/1.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), 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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 0.87/1.09 inference(rewrite,[status(thm)],[])).
% 0.87/1.09 tff(2721,plain,
% 0.87/1.09 (((~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(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(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 0.87/1.09 inference(rewrite,[status(thm)],[])).
% 0.87/1.09 tff(2722,plain,
% 0.87/1.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(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)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))))),
% 0.87/1.09 inference(monotonicity,[status(thm)],[2721])).
% 0.87/1.09 tff(2723,plain,
% 0.87/1.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(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)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 0.87/1.09 inference(transitivity,[status(thm)],[2722, 2720])).
% 0.87/1.09 tff(2724,plain,
% 0.87/1.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(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)))))))))),
% 0.87/1.09 inference(quant_inst,[status(thm)],[])).
% 0.87/1.09 tff(2725,plain,
% 0.87/1.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))),
% 0.87/1.09 inference(modus_ponens,[status(thm)],[2724, 2723])).
% 0.87/1.09 tff(2726,plain,
% 0.87/1.09 (~b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 0.87/1.09 inference(unit_resolution,[status(thm)],[2725, 180, 2523, 2719, 2716])).
% 0.87/1.09 tff(2727,plain,
% 0.87/1.09 (((~![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))))))))),
% 0.87/1.09 inference(rewrite,[status(thm)],[])).
% 0.87/1.09 tff(2728,plain,
% 0.87/1.09 ((~![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))))))))),
% 0.87/1.09 inference(quant_inst,[status(thm)],[])).
% 0.87/1.09 tff(2729,plain,
% 0.87/1.09 ((~![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)))))))),
% 0.87/1.09 inference(modus_ponens,[status(thm)],[2728, 2727])).
% 0.87/1.09 tff(2730,plain,
% 0.87/1.09 ((s(s(z)) = s(s(s(s(s(s(z))))))) | r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 0.87/1.09 inference(unit_resolution,[status(thm)],[2729, 73, 2726])).
% 0.87/1.09 tff(2731,plain,
% 0.87/1.09 (r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 0.87/1.09 inference(unit_resolution,[status(thm)],[2730, 38])).
% 0.87/1.09 tff(2732,plain,
% 0.87/1.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 0.87/1.09 inference(rewrite,[status(thm)],[])).
% 0.87/1.09 tff(2733,plain,
% 0.87/1.09 (((~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(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(z)))), s(s(s(s(s(s(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(z)))), s(s(s(s(s(s(z)))))))))),
% 0.87/1.09 inference(rewrite,[status(thm)],[])).
% 0.87/1.09 tff(2734,plain,
% 0.87/1.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), 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(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))))),
% 0.87/1.09 inference(monotonicity,[status(thm)],[2733])).
% 0.87/1.09 tff(2735,plain,
% 0.87/1.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), 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(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 0.87/1.09 inference(transitivity,[status(thm)],[2734, 2732])).
% 0.87/1.09 tff(2736,plain,
% 0.87/1.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), 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(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 0.87/1.09 inference(quant_inst,[status(thm)],[])).
% 0.87/1.09 tff(2737,plain,
% 0.87/1.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 0.87/1.09 inference(modus_ponens,[status(thm)],[2736, 2735])).
% 0.87/1.09 tff(2738,plain,
% 0.87/1.09 (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.87/1.09 inference(unit_resolution,[status(thm)],[2737, 180, 2705, 2542, 2526])).
% 0.87/1.09 tff(2739,plain,
% 0.87/1.09 (r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.87/1.09 inference(unit_resolution,[status(thm)],[1141, 73, 1138, 2738])).
% 0.87/1.09 tff(2740,plain,
% 0.87/1.09 ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z)))))),
% 0.87/1.09 inference(unit_resolution,[status(thm)],[2236, 2705])).
% 0.87/1.09 tff(2741,plain,
% 0.87/1.09 (~r(s(s(z)), s(s(s(z))))),
% 0.87/1.09 inference(unit_resolution,[status(thm)],[2740, 39])).
% 0.87/1.09 tff(2742,plain,
% 0.87/1.09 (b(s(s(z)), s(s(s(z))))),
% 0.87/1.09 inference(unit_resolution,[status(thm)],[150, 2741])).
% 0.87/1.09 tff(2743,plain,
% 0.87/1.09 ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))),
% 0.87/1.09 inference(unit_resolution,[status(thm)],[1056, 2520])).
% 0.87/1.09 tff(2744,plain,
% 0.87/1.09 (~r(s(s(s(z))), z)),
% 0.87/1.09 inference(unit_resolution,[status(thm)],[2743, 309])).
% 0.87/1.09 tff(2745,plain,
% 0.87/1.09 (b(s(s(s(z))), z)),
% 0.87/1.09 inference(unit_resolution,[status(thm)],[117, 2744])).
% 0.87/1.09 tff(2746,plain,
% 0.87/1.09 ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))),
% 0.87/1.09 inference(unit_resolution,[status(thm)],[838, 2520])).
% 0.87/1.09 tff(2747,plain,
% 0.87/1.09 (~r(z, s(s(s(z))))),
% 0.87/1.09 inference(unit_resolution,[status(thm)],[2746, 309])).
% 0.87/1.09 tff(2748,plain,
% 0.87/1.09 (b(z, s(s(s(z))))),
% 0.87/1.09 inference(unit_resolution,[status(thm)],[102, 2747])).
% 0.87/1.09 tff(2749,plain,
% 0.87/1.09 ($false),
% 0.87/1.09 inference(unit_resolution,[status(thm)],[188, 2748, 2745, 170, 169])).
% 0.87/1.09 tff(2750,plain,((~r(s(s(s(z))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.87/1.09 tff(2751,plain,
% 0.87/1.09 (~r(s(s(s(z))), s(z))),
% 0.87/1.09 inference(unit_resolution,[status(thm)],[2750, 2523, 2742])).
% 0.87/1.09 tff(2752,plain,
% 0.87/1.09 (b(s(s(s(z))), s(z))),
% 0.87/1.09 inference(unit_resolution,[status(thm)],[307, 2751])).
% 0.87/1.09 tff(2753,plain,
% 0.87/1.09 ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 0.87/1.09 inference(unit_resolution,[status(thm)],[2234, 2705])).
% 0.87/1.09 tff(2754,plain,
% 0.87/1.09 (~b(s(z), s(s(s(z))))),
% 0.87/1.09 inference(unit_resolution,[status(thm)],[2753, 2752])).
% 0.87/1.09 tff(2755,plain,
% 0.87/1.09 (r(s(z), s(s(s(z))))),
% 0.87/1.09 inference(unit_resolution,[status(thm)],[373, 2754])).
% 0.87/1.09 tff(2756,plain,
% 0.87/1.09 ((~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z)))))),
% 0.87/1.09 inference(unit_resolution,[status(thm)],[828, 2520])).
% 0.87/1.09 tff(2757,plain,
% 0.87/1.09 (~r(z, s(s(s(z))))),
% 0.87/1.09 inference(unit_resolution,[status(thm)],[2756, 2755])).
% 0.87/1.09 tff(2758,plain,
% 0.87/1.09 (b(z, s(s(s(z))))),
% 0.87/1.09 inference(unit_resolution,[status(thm)],[102, 2757])).
% 0.87/1.09 tff(2759,plain,
% 0.87/1.09 (~b(s(s(s(z))), z)),
% 0.87/1.09 inference(unit_resolution,[status(thm)],[188, 167, 169, 170])).
% 0.87/1.09 tff(2760,plain,
% 0.87/1.09 (r(s(s(s(z))), z)),
% 0.87/1.09 inference(unit_resolution,[status(thm)],[117, 2759])).
% 0.87/1.09 tff(2761,plain,
% 0.87/1.09 (~r(z, s(s(s(s(z)))))),
% 0.87/1.09 inference(unit_resolution,[status(thm)],[1250, 224, 269, 289, 2760])).
% 0.87/1.09 tff(2762,plain,
% 0.87/1.09 (b(z, s(s(s(s(z)))))),
% 0.87/1.09 inference(unit_resolution,[status(thm)],[78, 2761])).
% 0.87/1.09 tff(2763,plain,
% 0.87/1.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 0.87/1.09 inference(rewrite,[status(thm)],[])).
% 0.87/1.09 tff(2764,plain,
% 0.87/1.09 (((~b(s(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(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z))) <=> ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 0.87/1.10 inference(rewrite,[status(thm)],[])).
% 0.87/1.10 tff(2765,plain,
% 0.87/1.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z))))))))),
% 0.87/1.10 inference(monotonicity,[status(thm)],[2764])).
% 0.87/1.10 tff(2766,plain,
% 0.87/1.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))))),
% 0.87/1.10 inference(transitivity,[status(thm)],[2765, 2763])).
% 0.87/1.10 tff(2767,plain,
% 0.87/1.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)))),
% 0.87/1.10 inference(quant_inst,[status(thm)],[])).
% 0.87/1.10 tff(2768,plain,
% 0.87/1.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z))))))),
% 0.87/1.10 inference(modus_ponens,[status(thm)],[2767, 2766])).
% 0.87/1.10 tff(2769,plain,
% 0.87/1.10 ($false),
% 0.87/1.10 inference(unit_resolution,[status(thm)],[2768, 180, 170, 224, 289, 2762, 169, 167, 223])).
% 0.87/1.10 tff(2770,plain,((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.87/1.10 tff(2771,plain,
% 0.87/1.10 ((~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 0.87/1.10 inference(unit_resolution,[status(thm)],[2770, 2520, 2705])).
% 0.87/1.10 tff(2772,plain,
% 0.87/1.10 (~b(s(s(z)), s(s(s(s(z)))))),
% 0.87/1.10 inference(unit_resolution,[status(thm)],[2771, 2758, 2742, 2523, 2752])).
% 0.87/1.10 tff(2773,plain,
% 0.87/1.10 (r(s(s(z)), s(s(s(s(z)))))),
% 0.87/1.10 inference(unit_resolution,[status(thm)],[212, 2772])).
% 0.87/1.10 tff(2774,plain,
% 0.87/1.10 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 0.87/1.10 inference(rewrite,[status(thm)],[])).
% 0.87/1.10 tff(2775,plain,
% 0.87/1.10 (((~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(z)), s(s(s(s(z))))))) <=> ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 0.87/1.10 inference(rewrite,[status(thm)],[])).
% 0.87/1.10 tff(2776,plain,
% 0.87/1.10 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(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))))))))))),
% 0.87/1.10 inference(monotonicity,[status(thm)],[2775])).
% 0.87/1.10 tff(2777,plain,
% 0.87/1.10 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(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)))))))))),
% 0.87/1.10 inference(transitivity,[status(thm)],[2776, 2774])).
% 0.87/1.10 tff(2778,plain,
% 0.87/1.10 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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(z)), s(s(s(s(z)))))))),
% 0.87/1.10 inference(quant_inst,[status(thm)],[])).
% 0.87/1.10 tff(2779,plain,
% 0.87/1.10 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))),
% 0.87/1.10 inference(modus_ponens,[status(thm)],[2778, 2777])).
% 0.87/1.10 tff(2780,plain,
% 0.87/1.10 ($false),
% 0.87/1.10 inference(unit_resolution,[status(thm)],[2779, 53, 2773, 2739, 2731])).
% 0.87/1.10 tff(2781,plain,(~r(s(s(z)), s(z))), inference(lemma,lemma(discharge,[]))).
% 0.87/1.10 tff(2782,plain,
% 0.87/1.10 (b(s(s(z)), s(z))),
% 0.87/1.10 inference(unit_resolution,[status(thm)],[253, 2781])).
% 0.87/1.10 tff(2783,plain,
% 0.87/1.10 (~b(s(s(s(s(z)))), z)),
% 0.87/1.10 inference(unit_resolution,[status(thm)],[2341, 2748, 2745])).
% 0.87/1.10 tff(2784,plain,
% 0.87/1.10 (r(s(s(s(s(z)))), z)),
% 0.87/1.10 inference(unit_resolution,[status(thm)],[717, 2783])).
% 0.87/1.10 tff(2785,plain,
% 0.87/1.10 (~r(s(s(s(s(z)))), s(z))),
% 0.87/1.10 inference(unit_resolution,[status(thm)],[2532, 2784])).
% 0.87/1.10 tff(2786,plain,
% 0.87/1.10 (b(s(s(s(s(z)))), s(z))),
% 0.87/1.10 inference(unit_resolution,[status(thm)],[2541, 2785])).
% 0.87/1.10 tff(2787,plain,
% 0.87/1.10 ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 0.87/1.10 inference(unit_resolution,[status(thm)],[1175, 2705])).
% 0.87/1.10 tff(2788,plain,
% 0.87/1.10 (~b(s(s(s(s(z)))), s(s(z)))),
% 0.87/1.10 inference(unit_resolution,[status(thm)],[2787, 2786, 2782])).
% 0.87/1.10 tff(2789,plain,
% 0.87/1.10 (r(s(s(s(s(z)))), s(s(z)))),
% 0.87/1.10 inference(unit_resolution,[status(thm)],[1326, 2788])).
% 0.87/1.10 tff(2790,plain,
% 0.87/1.10 (~r(s(s(s(s(z)))), s(z))),
% 0.87/1.10 inference(unit_resolution,[status(thm)],[2532, 80])).
% 0.87/1.10 tff(2791,plain,
% 0.87/1.10 (b(s(s(s(s(z)))), s(z))),
% 0.87/1.10 inference(unit_resolution,[status(thm)],[2541, 2790])).
% 0.87/1.10 tff(2792,plain,
% 0.87/1.10 (~b(s(s(s(s(z)))), s(s(z)))),
% 0.87/1.10 inference(unit_resolution,[status(thm)],[2787, 2791, 2782])).
% 0.87/1.10 tff(2793,plain,
% 0.87/1.10 (r(s(s(s(s(z)))), s(s(z)))),
% 0.87/1.10 inference(unit_resolution,[status(thm)],[1326, 2792])).
% 0.87/1.10 tff(2794,plain,
% 0.87/1.10 ($false),
% 0.87/1.10 inference(unit_resolution,[status(thm)],[216, 53, 152, 80, 2793])).
% 0.87/1.10 tff(2795,plain,((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 0.87/1.10 tff(2796,plain,
% 0.87/1.10 (~r(s(s(s(s(z)))), z)),
% 0.87/1.10 inference(unit_resolution,[status(thm)],[2795, 152])).
% 0.87/1.10 tff(2797,plain,
% 0.87/1.10 (b(s(s(s(s(z)))), z)),
% 0.87/1.10 inference(unit_resolution,[status(thm)],[717, 2796])).
% 0.87/1.10 tff(2798,plain,
% 0.87/1.10 (~r(z, s(s(s(s(z)))))),
% 0.87/1.10 inference(unit_resolution,[status(thm)],[1248, 53, 2520, 1565])).
% 0.87/1.10 tff(2799,plain,
% 0.87/1.10 (b(z, s(s(s(s(z)))))),
% 0.87/1.10 inference(unit_resolution,[status(thm)],[78, 2798])).
% 0.87/1.10 tff(2800,plain,
% 0.87/1.10 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))),
% 0.87/1.10 inference(unit_resolution,[status(thm)],[1107, 2705])).
% 0.87/1.10 tff(2801,plain,
% 0.87/1.10 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 0.87/1.10 inference(unit_resolution,[status(thm)],[2800, 2799, 2782, 152, 2797])).
% 0.87/1.10 tff(2802,plain,
% 0.87/1.10 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 0.87/1.10 inference(unit_resolution,[status(thm)],[2184, 2801, 1565])).
% 0.87/1.10 tff(2803,plain,
% 0.87/1.10 (b(s(s(s(s(s(s(z)))))), s(z))),
% 0.87/1.10 inference(unit_resolution,[status(thm)],[947, 2802])).
% 0.87/1.10 tff(2804,plain,
% 0.87/1.10 (~b(z, s(s(s(z))))),
% 0.87/1.10 inference(unit_resolution,[status(thm)],[1770, 309, 540, 873, 719])).
% 0.87/1.10 tff(2805,plain,
% 0.87/1.10 ($false),
% 0.87/1.10 inference(unit_resolution,[status(thm)],[102, 2804, 2548])).
% 0.87/1.10 tff(2806,plain,((~r(s(s(s(z))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.87/1.10 tff(2807,plain,
% 0.87/1.10 ((~r(s(s(s(z))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~r(z, s(z)))),
% 0.87/1.10 inference(unit_resolution,[status(thm)],[2806, 1741])).
% 0.87/1.10 tff(2808,plain,
% 0.87/1.10 ((~r(s(s(s(z))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))),
% 0.87/1.10 inference(unit_resolution,[status(thm)],[2807, 2520])).
% 0.87/1.10 tff(2809,plain,
% 0.87/1.10 (~r(s(s(s(z))), s(z))),
% 0.87/1.10 inference(unit_resolution,[status(thm)],[2808, 2799, 2797])).
% 0.87/1.10 tff(2810,plain,
% 0.87/1.10 (b(s(s(s(z))), s(z))),
% 0.87/1.10 inference(unit_resolution,[status(thm)],[307, 2809])).
% 0.87/1.10 tff(2811,plain,
% 0.87/1.10 (~b(s(z), z)),
% 0.87/1.10 inference(unit_resolution,[status(thm)],[1081, 180, 2705, 2797, 2799])).
% 0.87/1.10 tff(2812,plain,
% 0.87/1.10 (r(s(z), z)),
% 0.87/1.10 inference(unit_resolution,[status(thm)],[267, 2811])).
% 0.87/1.10 tff(2813,plain,
% 0.87/1.10 (~r(s(z), s(s(z)))),
% 0.87/1.10 inference(unit_resolution,[status(thm)],[780, 53, 152, 2812])).
% 0.87/1.10 tff(2814,plain,
% 0.87/1.10 (b(s(z), s(s(z)))),
% 0.87/1.10 inference(unit_resolution,[status(thm)],[2438, 2813])).
% 0.87/1.10 tff(2815,plain,
% 0.87/1.10 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.87/1.10 inference(unit_resolution,[status(thm)],[2697, 2814, 2782, 2810, 2803])).
% 0.87/1.10 tff(2816,plain,
% 0.87/1.10 ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z)))),
% 0.87/1.10 inference(unit_resolution,[status(thm)],[2469, 2705])).
% 0.87/1.10 tff(2817,plain,
% 0.87/1.10 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 0.87/1.10 inference(unit_resolution,[status(thm)],[2816, 2810])).
% 0.87/1.10 tff(2818,plain,
% 0.87/1.10 (r(s(s(s(z))), s(s(s(s(z)))))),
% 0.87/1.10 inference(unit_resolution,[status(thm)],[468, 2817])).
% 0.87/1.10 tff(2819,plain,
% 0.87/1.10 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.87/1.10 inference(unit_resolution,[status(thm)],[1478, 2818, 2801])).
% 0.87/1.10 tff(2820,plain,
% 0.87/1.10 ($false),
% 0.87/1.10 inference(unit_resolution,[status(thm)],[487, 73, 484, 2819, 2815])).
% 0.87/1.10 tff(2821,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 0.87/1.10 tff(2822,plain,
% 0.87/1.10 (~r(s(s(s(s(z)))), s(z))),
% 0.87/1.10 inference(unit_resolution,[status(thm)],[2821, 152])).
% 0.87/1.10 tff(2823,plain,
% 0.87/1.10 (b(s(s(s(s(z)))), s(z))),
% 0.87/1.10 inference(unit_resolution,[status(thm)],[2541, 2822])).
% 0.87/1.10 tff(2824,plain,
% 0.87/1.10 (~b(s(s(z)), s(s(s(s(z)))))),
% 0.87/1.10 inference(unit_resolution,[status(thm)],[2374, 180, 2782, 2705, 2823])).
% 0.87/1.10 tff(2825,plain,
% 0.87/1.10 (r(s(s(z)), s(s(s(s(z)))))),
% 0.87/1.10 inference(unit_resolution,[status(thm)],[212, 2824])).
% 0.87/1.10 tff(2826,plain,
% 0.87/1.10 (~r(z, s(s(s(s(z)))))),
% 0.87/1.10 inference(unit_resolution,[status(thm)],[737, 2825, 152])).
% 0.87/1.10 tff(2827,plain,
% 0.87/1.10 (b(z, s(s(s(s(z)))))),
% 0.87/1.10 inference(unit_resolution,[status(thm)],[78, 2826])).
% 0.87/1.10 tff(2828,plain,
% 0.87/1.10 (~r(s(s(s(z))), s(z))),
% 0.87/1.10 inference(unit_resolution,[status(thm)],[2808, 2827, 2797])).
% 0.87/1.10 tff(2829,plain,
% 0.87/1.10 (b(s(s(s(z))), s(z))),
% 0.87/1.10 inference(unit_resolution,[status(thm)],[307, 2828])).
% 0.87/1.10 tff(2830,plain,
% 0.87/1.10 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 0.87/1.10 inference(unit_resolution,[status(thm)],[2816, 2829])).
% 0.87/1.10 tff(2831,plain,
% 0.87/1.10 (r(s(s(s(z))), s(s(s(s(z)))))),
% 0.87/1.10 inference(unit_resolution,[status(thm)],[468, 2830])).
% 0.87/1.10 tff(2832,plain,
% 0.87/1.10 (~r(s(s(s(z))), s(s(z)))),
% 0.87/1.10 inference(unit_resolution,[status(thm)],[2338, 2831, 2825])).
% 0.87/1.10 tff(2833,plain,
% 0.87/1.10 (b(s(s(s(z))), s(s(z)))),
% 0.87/1.10 inference(unit_resolution,[status(thm)],[2055, 2832])).
% 0.87/1.10 tff(2834,plain,
% 0.87/1.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(z), 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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 0.87/1.10 inference(rewrite,[status(thm)],[])).
% 0.87/1.10 tff(2835,plain,
% 0.87/1.10 (((~b(s(z), s(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(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z))) <=> ((~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 0.87/1.10 inference(rewrite,[status(thm)],[])).
% 0.87/1.10 tff(2836,plain,
% 0.87/1.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 0.87/1.10 inference(monotonicity,[status(thm)],[2835])).
% 0.87/1.10 tff(2837,plain,
% 0.87/1.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 0.87/1.10 inference(transitivity,[status(thm)],[2836, 2834])).
% 0.87/1.10 tff(2838,plain,
% 0.87/1.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))),
% 0.87/1.10 inference(quant_inst,[status(thm)],[])).
% 0.87/1.10 tff(2839,plain,
% 0.87/1.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 0.87/1.10 inference(modus_ponens,[status(thm)],[2838, 2837])).
% 0.87/1.10 tff(2840,plain,
% 0.87/1.10 (~b(s(z), z)),
% 0.87/1.10 inference(unit_resolution,[status(thm)],[2839, 180, 2705, 2827, 2823])).
% 0.87/1.10 tff(2841,plain,
% 0.87/1.10 (r(s(z), z)),
% 0.87/1.10 inference(unit_resolution,[status(thm)],[267, 2840])).
% 0.87/1.10 tff(2842,plain,
% 0.87/1.10 (~r(s(z), s(s(z)))),
% 0.87/1.10 inference(unit_resolution,[status(thm)],[780, 53, 152, 2841])).
% 0.87/1.10 tff(2843,plain,
% 0.87/1.10 (b(s(z), s(s(z)))),
% 0.87/1.10 inference(unit_resolution,[status(thm)],[2438, 2842])).
% 0.87/1.10 tff(2844,plain,
% 0.87/1.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))),
% 0.87/1.10 inference(rewrite,[status(thm)],[])).
% 0.87/1.10 tff(2845,plain,
% 0.87/1.10 (((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))),
% 0.87/1.10 inference(rewrite,[status(thm)],[])).
% 0.87/1.10 tff(2846,plain,
% 0.87/1.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z)))))),
% 0.87/1.10 inference(monotonicity,[status(thm)],[2845])).
% 0.87/1.10 tff(2847,plain,
% 0.87/1.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))),
% 0.87/1.10 inference(transitivity,[status(thm)],[2846, 2844])).
% 0.87/1.10 tff(2848,plain,
% 0.87/1.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))),
% 0.87/1.10 inference(quant_inst,[status(thm)],[])).
% 0.87/1.10 tff(2849,plain,
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% 0.87/1.10 inference(unit_resolution,[status(thm)],[468, 2881])).
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% 0.87/1.10 inference(monotonicity,[status(thm)],[2894])).
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% 0.87/1.10 inference(quant_inst,[status(thm)],[])).
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% 0.87/1.11 inference(modus_ponens,[status(thm)],[2897, 2896])).
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% 0.87/1.11 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.87/1.11 inference(unit_resolution,[status(thm)],[2898, 180, 224, 539, 400, 1701])).
% 0.87/1.11 tff(2900,plain,
% 0.87/1.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(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(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 0.87/1.11 inference(rewrite,[status(thm)],[])).
% 0.87/1.11 tff(2901,plain,
% 0.87/1.11 (((~b(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(z), 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)))))), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), 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)))))), s(s(s(s(z)))))))),
% 0.87/1.11 inference(rewrite,[status(thm)],[])).
% 0.87/1.11 tff(2902,plain,
% 0.87/1.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), 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)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 0.87/1.11 inference(monotonicity,[status(thm)],[2901])).
% 0.87/1.11 tff(2903,plain,
% 0.87/1.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), 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)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 0.87/1.11 inference(transitivity,[status(thm)],[2902, 2900])).
% 0.87/1.11 tff(2904,plain,
% 0.87/1.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), 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)))))), s(s(s(s(z)))))))),
% 0.87/1.11 inference(quant_inst,[status(thm)],[])).
% 0.87/1.11 tff(2905,plain,
% 0.87/1.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 0.87/1.11 inference(modus_ponens,[status(thm)],[2904, 2903])).
% 0.87/1.11 tff(2906,plain,
% 0.87/1.11 ($false),
% 0.87/1.11 inference(unit_resolution,[status(thm)],[2905, 180, 225, 752, 400, 655, 1701])).
% 0.87/1.11 tff(2907,plain,((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.87/1.11 tff(2908,plain,
% 0.87/1.11 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 0.87/1.11 inference(unit_resolution,[status(thm)],[2907, 1701, 752, 400, 225])).
% 0.87/1.11 tff(2909,plain,
% 0.87/1.11 (r(s(s(s(s(s(s(z)))))), s(z))),
% 0.87/1.11 inference(unit_resolution,[status(thm)],[947, 2908])).
% 0.87/1.11 tff(2910,plain,
% 0.87/1.11 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.87/1.11 inference(unit_resolution,[status(thm)],[2075, 53, 309, 2909])).
% 0.87/1.11 tff(2911,plain,
% 0.87/1.11 ($false),
% 0.87/1.11 inference(unit_resolution,[status(thm)],[487, 73, 484, 2910, 2899])).
% 0.87/1.11 tff(2912,plain,((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.87/1.11 tff(2913,plain,
% 0.87/1.11 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 0.87/1.11 inference(unit_resolution,[status(thm)],[2912, 2876, 2860, 2882, 400, 2892, 2862])).
% 0.87/1.11 tff(2914,plain,
% 0.87/1.11 (r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 0.87/1.11 inference(unit_resolution,[status(thm)],[1699, 2913])).
% 0.87/1.11 tff(2915,plain,
% 0.87/1.11 (~r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.87/1.11 inference(unit_resolution,[status(thm)],[1111, 53, 2914, 41])).
% 0.87/1.11 tff(2916,plain,
% 0.87/1.11 (b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.87/1.11 inference(unit_resolution,[status(thm)],[1096, 2915])).
% 0.87/1.11 tff(2917,plain,
% 0.87/1.11 (~r(s(s(s(s(s(s(z)))))), z)),
% 0.87/1.11 inference(unit_resolution,[status(thm)],[502, 53, 43, 2914])).
% 0.87/1.11 tff(2918,plain,
% 0.87/1.11 (b(s(s(s(s(s(s(z)))))), z)),
% 0.87/1.11 inference(unit_resolution,[status(thm)],[509, 2917])).
% 0.87/1.11 tff(2919,plain,
% 0.87/1.11 ($false),
% 0.87/1.11 inference(unit_resolution,[status(thm)],[940, 180, 170, 2866, 2918, 2916])).
% 0.87/1.11 tff(2920,plain,((~r(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.87/1.11 tff(2921,plain,
% 0.87/1.11 ((~r(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(z)))))),
% 0.87/1.11 inference(unit_resolution,[status(thm)],[2920, 2520])).
% 0.87/1.11 tff(2922,plain,
% 0.87/1.11 (~r(z, s(s(s(s(z)))))),
% 0.87/1.11 inference(unit_resolution,[status(thm)],[2921, 2856, 2852, 2858, 2786])).
% 0.87/1.11 tff(2923,plain,
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% 0.87/1.11 inference(unit_resolution,[status(thm)],[78, 2922])).
% 0.87/1.11 tff(2924,plain,
% 0.87/1.11 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 0.87/1.11 inference(unit_resolution,[status(thm)],[2160, 2923, 2748])).
% 0.87/1.11 tff(2925,plain,
% 0.87/1.11 (r(s(s(s(z))), s(s(s(s(z)))))),
% 0.87/1.11 inference(unit_resolution,[status(thm)],[468, 2924])).
% 0.87/1.11 tff(2926,plain,
% 0.87/1.11 (~r(s(s(s(z))), s(s(z)))),
% 0.87/1.11 inference(unit_resolution,[status(thm)],[2338, 2925, 2856])).
% 0.87/1.11 tff(2927,plain,
% 0.87/1.11 (b(s(s(s(z))), s(s(z)))),
% 0.87/1.11 inference(unit_resolution,[status(thm)],[2055, 2926])).
% 0.87/1.11 tff(2928,plain,
% 0.87/1.11 (~b(z, s(s(z)))),
% 0.87/1.11 inference(unit_resolution,[status(thm)],[1935, 2927, 2852, 2745])).
% 0.87/1.11 tff(2929,plain,
% 0.87/1.11 (r(z, s(s(z)))),
% 0.87/1.11 inference(unit_resolution,[status(thm)],[703, 2928])).
% 0.87/1.11 tff(2930,plain,
% 0.87/1.11 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))),
% 0.87/1.11 inference(rewrite,[status(thm)],[])).
% 0.87/1.11 tff(2931,plain,
% 0.87/1.11 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))),
% 0.87/1.11 inference(quant_inst,[status(thm)],[])).
% 0.87/1.11 tff(2932,plain,
% 0.87/1.11 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z))),
% 0.87/1.11 inference(modus_ponens,[status(thm)],[2931, 2930])).
% 0.87/1.11 tff(2933,plain,
% 0.87/1.11 ($false),
% 0.87/1.11 inference(unit_resolution,[status(thm)],[2932, 53, 2929, 2784, 2789])).
% 0.87/1.11 tff(2934,plain,(~r(s(s(s(z))), s(z))), inference(lemma,lemma(discharge,[]))).
% 0.87/1.11 tff(2935,plain,
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% 0.87/1.11 inference(unit_resolution,[status(thm)],[307, 2934])).
% 0.87/1.11 tff(2936,plain,
% 0.87/1.11 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 0.87/1.11 inference(unit_resolution,[status(thm)],[2816, 2935])).
% 0.87/1.11 tff(2937,plain,
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% 0.87/1.11 inference(unit_resolution,[status(thm)],[468, 2936])).
% 0.87/1.11 tff(2938,plain,
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% 0.87/1.11 inference(unit_resolution,[status(thm)],[2532, 1565])).
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% 0.87/1.11 inference(unit_resolution,[status(thm)],[717, 2938])).
% 0.87/1.11 tff(2940,plain,
% 0.87/1.11 (~b(s(z), s(s(s(z))))),
% 0.87/1.11 inference(unit_resolution,[status(thm)],[2753, 2935])).
% 0.87/1.11 tff(2941,plain,
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% 0.87/1.11 inference(unit_resolution,[status(thm)],[373, 2940])).
% 0.87/1.11 tff(2942,plain,
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% 0.87/1.11 inference(unit_resolution,[status(thm)],[2756, 2941])).
% 0.87/1.11 tff(2943,plain,
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% 0.87/1.11 inference(unit_resolution,[status(thm)],[102, 2942])).
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% 0.87/1.11 inference(unit_resolution,[status(thm)],[2341, 2939, 2943])).
% 0.87/1.11 tff(2945,plain,
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% 0.87/1.11 inference(unit_resolution,[status(thm)],[117, 2944])).
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% 0.87/1.11 inference(unit_resolution,[status(thm)],[1229, 2945, 2937])).
% 0.87/1.11 tff(2947,plain,
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% 0.87/1.11 inference(unit_resolution,[status(thm)],[78, 2946])).
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% 0.87/1.11 ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 0.87/1.11 inference(unit_resolution,[status(thm)],[1645, 2705])).
% 0.87/1.11 tff(2949,plain,
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% 0.87/1.11 tff(2950,plain,
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% 0.87/1.11 tff(2951,plain,
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% 0.87/1.11 inference(unit_resolution,[status(thm)],[2338, 2950, 2937])).
% 0.87/1.11 tff(2952,plain,
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% 0.87/1.11 inference(unit_resolution,[status(thm)],[2055, 2951])).
% 0.87/1.11 tff(2953,plain,
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% 0.87/1.11 inference(unit_resolution,[status(thm)],[1081, 180, 2705, 2939, 2947])).
% 0.87/1.11 tff(2954,plain,
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% 0.87/1.11 tff(2955,plain,
% 0.87/1.11 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 0.87/1.11 inference(unit_resolution,[status(thm)],[2184, 922, 1565])).
% 0.87/1.11 tff(2956,plain,
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% 0.87/1.11 tff(2957,plain,
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% 0.87/1.11 tff(2959,plain,((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.87/1.11 tff(2960,plain,
% 0.87/1.11 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 0.87/1.11 inference(unit_resolution,[status(thm)],[2959, 1565])).
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% 0.87/1.11 tff(2962,plain,
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% 0.87/1.11 tff(2963,plain,
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% 0.87/1.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)))),
% 0.87/1.11 inference(rewrite,[status(thm)],[])).
% 0.87/1.11 tff(2965,plain,
% 0.87/1.11 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)))),
% 0.87/1.11 inference(rewrite,[status(thm)],[])).
% 0.87/1.11 tff(2966,plain,
% 0.87/1.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z))))),
% 0.87/1.11 inference(monotonicity,[status(thm)],[2965])).
% 0.87/1.11 tff(2967,plain,
% 0.87/1.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)))),
% 0.87/1.11 inference(transitivity,[status(thm)],[2966, 2964])).
% 0.87/1.11 tff(2968,plain,
% 0.87/1.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 0.87/1.11 inference(quant_inst,[status(thm)],[])).
% 0.87/1.11 tff(2969,plain,
% 0.87/1.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z))),
% 0.87/1.11 inference(modus_ponens,[status(thm)],[2968, 2967])).
% 0.87/1.11 tff(2970,plain,
% 0.87/1.11 (~b(s(s(s(s(z)))), s(s(z)))),
% 0.87/1.11 inference(unit_resolution,[status(thm)],[2969, 180, 2852, 2939, 2947])).
% 0.87/1.11 tff(2971,plain,
% 0.87/1.11 (r(s(s(s(s(z)))), s(s(z)))),
% 0.87/1.11 inference(unit_resolution,[status(thm)],[1326, 2970])).
% 0.87/1.11 tff(2972,plain,
% 0.87/1.11 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.87/1.11 inference(unit_resolution,[status(thm)],[1478, 1476, 2937])).
% 0.87/1.11 tff(2973,plain,
% 0.87/1.11 (~b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.87/1.11 inference(unit_resolution,[status(thm)],[1196, 2972, 169, 1187])).
% 0.87/1.11 tff(2974,plain,
% 0.87/1.11 (r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.87/1.11 inference(unit_resolution,[status(thm)],[1096, 2973])).
% 0.87/1.11 tff(2975,plain,
% 0.87/1.11 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 0.87/1.11 inference(rewrite,[status(thm)],[])).
% 0.87/1.11 tff(2976,plain,
% 0.87/1.11 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 0.87/1.11 inference(quant_inst,[status(thm)],[])).
% 0.87/1.11 tff(2977,plain,
% 0.87/1.11 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 0.87/1.11 inference(modus_ponens,[status(thm)],[2976, 2975])).
% 0.87/1.11 tff(2978,plain,
% 0.87/1.11 ($false),
% 0.87/1.11 inference(unit_resolution,[status(thm)],[2977, 53, 1476, 1178, 2974])).
% 0.87/1.11 tff(2979,plain,((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | r(s(s(s(z))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.87/1.11 tff(2980,plain,
% 0.87/1.11 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 0.87/1.11 inference(unit_resolution,[status(thm)],[2979, 2971, 2963, 2951])).
% 0.87/1.11 tff(2981,plain,
% 0.87/1.11 (~b(s(s(s(s(s(s(z)))))), z)),
% 0.87/1.11 inference(unit_resolution,[status(thm)],[1073, 2980, 2939, 2947])).
% 0.87/1.11 tff(2982,plain,
% 0.87/1.11 (r(s(s(s(s(s(s(z)))))), z)),
% 0.87/1.11 inference(unit_resolution,[status(thm)],[509, 2981])).
% 0.87/1.11 tff(2983,plain,
% 0.87/1.11 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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)))))))))),
% 0.87/1.11 inference(rewrite,[status(thm)],[])).
% 0.87/1.11 tff(2984,plain,
% 0.87/1.11 (((~r(s(s(s(s(s(s(z)))))), z)) | (~r(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)))))))))),
% 0.87/1.11 inference(rewrite,[status(thm)],[])).
% 0.87/1.11 tff(2985,plain,
% 0.87/1.11 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(z), s(s(s(s(s(s(z))))))))))),
% 0.87/1.11 inference(monotonicity,[status(thm)],[2984])).
% 0.87/1.11 tff(2986,plain,
% 0.87/1.11 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 0.87/1.11 inference(transitivity,[status(thm)],[2985, 2983])).
% 0.87/1.11 tff(2987,plain,
% 0.87/1.11 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 0.87/1.11 inference(quant_inst,[status(thm)],[])).
% 0.87/1.11 tff(2988,plain,
% 0.87/1.11 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, 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))))))))),
% 0.87/1.11 inference(modus_ponens,[status(thm)],[2987, 2986])).
% 0.87/1.11 tff(2989,plain,
% 0.87/1.11 (~r(s(z), s(s(s(s(s(s(z)))))))),
% 0.87/1.11 inference(unit_resolution,[status(thm)],[2988, 53, 255, 1713])).
% 0.87/1.11 tff(2990,plain,
% 0.87/1.11 ((s(z) = s(s(s(s(s(s(z))))))) | b(s(z), s(s(s(s(s(s(z)))))))),
% 0.87/1.11 inference(unit_resolution,[status(thm)],[1156, 73, 2989])).
% 0.87/1.11 tff(2991,plain,
% 0.87/1.11 (b(s(z), s(s(s(s(s(s(z)))))))),
% 0.87/1.11 inference(unit_resolution,[status(thm)],[2990, 1146])).
% 0.87/1.11 tff(2992,plain,
% 0.87/1.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(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(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(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(s(z)))))),
% 0.87/1.11 inference(rewrite,[status(thm)],[])).
% 0.87/1.11 tff(2993,plain,
% 0.87/1.11 (((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(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(s(z)), s(z))) | (~b(s(s(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(s(z)))))),
% 0.87/1.11 inference(rewrite,[status(thm)],[])).
% 0.87/1.11 tff(2994,plain,
% 0.87/1.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(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)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(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(s(z))))))),
% 0.87/1.11 inference(monotonicity,[status(thm)],[2993])).
% 0.87/1.11 tff(2995,plain,
% 0.87/1.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(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)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(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(s(z)))))),
% 0.87/1.11 inference(transitivity,[status(thm)],[2994, 2992])).
% 0.87/1.11 tff(2996,plain,
% 0.87/1.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(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)))))),
% 0.87/1.11 inference(quant_inst,[status(thm)],[])).
% 0.87/1.11 tff(2997,plain,
% 0.87/1.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(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(s(z))))),
% 0.87/1.11 inference(modus_ponens,[status(thm)],[2996, 2995])).
% 0.87/1.11 tff(2998,plain,
% 0.87/1.11 (~b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.87/1.11 inference(unit_resolution,[status(thm)],[2997, 180, 2782, 655, 2991])).
% 0.87/1.11 tff(2999,plain,
% 0.87/1.11 (r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.87/1.11 inference(unit_resolution,[status(thm)],[1096, 2998])).
% 0.87/1.11 tff(3000,plain,
% 0.87/1.11 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 0.87/1.11 inference(rewrite,[status(thm)],[])).
% 0.87/1.11 tff(3001,plain,
% 0.87/1.11 (((~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), z))) <=> ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 0.87/1.11 inference(rewrite,[status(thm)],[])).
% 0.87/1.11 tff(3002,plain,
% 0.87/1.11 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(z))))))),
% 0.87/1.11 inference(monotonicity,[status(thm)],[3001])).
% 0.87/1.11 tff(3003,plain,
% 0.87/1.11 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 0.87/1.11 inference(transitivity,[status(thm)],[3002, 3000])).
% 0.87/1.11 tff(3004,plain,
% 0.87/1.11 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), z)))),
% 0.87/1.11 inference(quant_inst,[status(thm)],[])).
% 0.87/1.11 tff(3005,plain,
% 0.87/1.11 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(z))))),
% 0.87/1.11 inference(modus_ponens,[status(thm)],[3004, 3003])).
% 0.87/1.11 tff(3006,plain,
% 0.87/1.11 ($false),
% 0.87/1.11 inference(unit_resolution,[status(thm)],[3005, 53, 688, 1713, 2999])).
% 0.87/1.11 tff(3007,plain,((~r(s(s(s(s(s(s(z)))))), z)) | (~r(z, s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 0.87/1.11 tff(3008,plain,
% 0.87/1.12 (~r(z, s(s(z)))),
% 0.87/1.12 inference(unit_resolution,[status(thm)],[3007, 2982, 2961, 2954])).
% 0.87/1.12 tff(3009,plain,
% 0.87/1.12 (b(z, s(s(z)))),
% 0.87/1.12 inference(unit_resolution,[status(thm)],[703, 3008])).
% 0.87/1.12 tff(3010,plain,
% 0.87/1.12 ($false),
% 0.87/1.12 inference(unit_resolution,[status(thm)],[1284, 180, 2852, 3009, 2943, 2952])).
% 0.87/1.12 tff(3011,plain,(~r(s(s(s(s(z)))), s(z))), inference(lemma,lemma(discharge,[]))).
% 0.87/1.12 tff(3012,plain,
% 0.87/1.12 (b(s(s(s(s(z)))), s(z))),
% 0.87/1.12 inference(unit_resolution,[status(thm)],[2541, 3011])).
% 0.87/1.12 tff(3013,plain,
% 0.87/1.12 (~b(s(s(z)), s(s(s(s(z)))))),
% 0.87/1.12 inference(unit_resolution,[status(thm)],[2854, 3012])).
% 0.87/1.12 tff(3014,plain,
% 0.87/1.12 (r(s(s(z)), s(s(s(s(z)))))),
% 0.87/1.12 inference(unit_resolution,[status(thm)],[212, 3013])).
% 0.87/1.12 tff(3015,plain,
% 0.87/1.12 (~r(s(s(s(z))), s(s(z)))),
% 0.87/1.12 inference(unit_resolution,[status(thm)],[2338, 3014, 2937])).
% 0.87/1.12 tff(3016,plain,
% 0.87/1.12 (~b(s(s(s(s(z)))), s(s(z)))),
% 0.87/1.12 inference(unit_resolution,[status(thm)],[2787, 3012, 2782])).
% 0.87/1.12 tff(3017,plain,
% 0.87/1.12 (r(s(s(s(s(z)))), s(s(z)))),
% 0.87/1.12 inference(unit_resolution,[status(thm)],[1326, 3016])).
% 0.87/1.12 tff(3018,plain,
% 0.87/1.12 (~r(s(s(z)), s(s(s(z))))),
% 0.87/1.12 inference(unit_resolution,[status(thm)],[2630, 53, 2937, 3014])).
% 0.87/1.12 tff(3019,plain,
% 0.87/1.12 (b(s(s(z)), s(s(s(z))))),
% 0.87/1.12 inference(unit_resolution,[status(thm)],[150, 3018])).
% 0.87/1.12 tff(3020,plain,
% 0.87/1.12 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 0.87/1.12 inference(unit_resolution,[status(thm)],[2979, 3019, 3017, 3015])).
% 0.87/1.12 tff(3021,plain,
% 0.87/1.12 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 0.87/1.12 inference(unit_resolution,[status(thm)],[1699, 3020])).
% 0.87/1.12 tff(3022,plain,
% 0.87/1.12 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 0.87/1.12 inference(unit_resolution,[status(thm)],[2712, 3021, 3012])).
% 0.87/1.12 tff(3023,plain,
% 0.87/1.12 (r(s(s(s(s(s(s(z)))))), s(z))),
% 0.87/1.12 inference(unit_resolution,[status(thm)],[947, 3022])).
% 0.87/1.12 tff(3024,plain,
% 0.87/1.12 (~b(s(s(s(z))), z)),
% 0.87/1.12 inference(unit_resolution,[status(thm)],[188, 3019, 2852, 2943])).
% 0.87/1.12 tff(3025,plain,
% 0.87/1.12 (r(s(s(s(z))), z)),
% 0.87/1.12 inference(unit_resolution,[status(thm)],[117, 3024])).
% 0.87/1.12 tff(3026,plain,
% 0.87/1.12 (~r(z, s(s(s(s(z)))))),
% 0.87/1.12 inference(unit_resolution,[status(thm)],[1229, 3025, 2937])).
% 0.87/1.12 tff(3027,plain,
% 0.87/1.12 (b(z, s(s(s(s(z)))))),
% 0.87/1.12 inference(unit_resolution,[status(thm)],[78, 3026])).
% 0.87/1.12 tff(3028,plain,
% 0.87/1.12 (b(s(s(s(z))), s(s(z)))),
% 0.87/1.12 inference(unit_resolution,[status(thm)],[2055, 3015])).
% 0.87/1.12 tff(3029,plain,
% 0.87/1.12 ($false),
% 0.87/1.12 inference(unit_resolution,[status(thm)],[1284, 180, 2852, 751, 2943, 3028])).
% 0.87/1.12 tff(3030,plain,(~b(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.87/1.12 tff(3031,plain,
% 0.87/1.12 (r(z, s(s(z)))),
% 0.87/1.12 inference(unit_resolution,[status(thm)],[703, 3030])).
% 0.87/1.12 tff(3032,plain,
% 0.87/1.12 (~r(s(s(s(s(z)))), z)),
% 0.87/1.12 inference(unit_resolution,[status(thm)],[2932, 53, 3031, 3017])).
% 0.87/1.12 tff(3033,plain,
% 0.87/1.12 (b(s(s(s(s(z)))), z)),
% 0.87/1.12 inference(unit_resolution,[status(thm)],[717, 3032])).
% 0.87/1.12 tff(3034,plain,
% 0.87/1.12 (~b(s(s(s(s(s(s(z)))))), z)),
% 0.87/1.12 inference(unit_resolution,[status(thm)],[1073, 3033, 3020, 3027])).
% 0.87/1.12 tff(3035,plain,
% 0.87/1.12 (r(s(s(s(s(s(s(z)))))), z)),
% 0.87/1.12 inference(unit_resolution,[status(thm)],[509, 3034])).
% 0.87/1.12 tff(3036,plain,
% 0.87/1.12 (~b(s(z), z)),
% 0.87/1.12 inference(unit_resolution,[status(thm)],[2839, 180, 2705, 3027, 3012])).
% 0.87/1.12 tff(3037,plain,
% 0.87/1.12 (r(s(z), z)),
% 0.87/1.12 inference(unit_resolution,[status(thm)],[267, 3036])).
% 0.87/1.12 tff(3038,plain,
% 0.87/1.12 ($false),
% 0.87/1.12 inference(unit_resolution,[status(thm)],[1086, 53, 3037, 3035, 3023])).
% 0.87/1.12 % SZS output end Proof
% 0.87/1.12 % E exiting
%------------------------------------------------------------------------------