%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRA165-1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 06:34:21 PM UTC 2026
% Result : Unsatisfiable 0.47s 0.68s
% Output : Proof 0.96s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRA165-1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.11 % Command : run_E %s %d THM
% 0.14/0.32 % Computer : n009.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 00:39:42 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.47/0.68 % SZS status Unsatisfiable
% 0.47/0.68 % SZS output start Proof
% 0.47/0.68 tff(b_type, type, (
% 0.47/0.68 b: ( $i * $i ) > $o)).
% 0.47/0.68 tff(s_type, type, (
% 0.47/0.68 s: $i > $i)).
% 0.47/0.68 tff(z_type, type, (
% 0.47/0.68 z: $i)).
% 0.47/0.68 tff(r_type, type, (
% 0.47/0.68 r: ( $i * $i ) > $o)).
% 0.47/0.68 tff(inj_0_type, type, (
% 0.47/0.68 inj_0: $i > $i)).
% 0.47/0.68 tff(1,assumption,(b(s(s(s(s(s(s(z)))))), z)), introduced(assumption)).
% 0.47/0.68 tff(2,assumption,(r(s(s(s(s(s(s(z)))))), s(z))), introduced(assumption)).
% 0.47/0.68 tff(3,assumption,(r(z, s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 0.47/0.68 tff(4,assumption,(r(z, s(z))), introduced(assumption)).
% 0.47/0.68 tff(5,plain,
% 0.47/0.68 (^[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))))),
% 0.47/0.68 inference(bind,[status(th)],[])).
% 0.47/0.68 tff(6,plain,
% 0.47/0.68 (![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)))),
% 0.47/0.68 inference(quant_intro,[status(thm)],[5])).
% 0.47/0.68 tff(7,plain,
% 0.47/0.68 (![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)))),
% 0.47/0.68 inference(rewrite,[status(thm)],[])).
% 0.47/0.68 tff(8,plain,
% 0.47/0.68 (^[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))))),
% 0.47/0.68 inference(bind,[status(th)],[])).
% 0.47/0.68 tff(9,plain,
% 0.47/0.68 (![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)))),
% 0.47/0.68 inference(quant_intro,[status(thm)],[8])).
% 0.47/0.68 tff(10,axiom,(![X0: $i, X2: $i, X1: $i] : (((~r(X0, X1)) | (~r(X0, X2))) | (~r(X1, X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axr')).
% 0.47/0.68 tff(11,plain,
% 0.47/0.68 (![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 0.47/0.68 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.47/0.68 tff(12,plain,
% 0.47/0.68 (![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 0.47/0.68 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.47/0.68 tff(13,plain,(
% 0.47/0.68 ![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 0.47/0.68 inference(skolemize,[status(sab)],[12])).
% 0.47/0.68 tff(14,plain,
% 0.47/0.68 (![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 0.47/0.68 inference(modus_ponens,[status(thm)],[13, 6])).
% 0.47/0.68 tff(15,plain,
% 0.47/0.68 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(z, s(s(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(s(s(s(s(s(s(z)))))), s(z))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(z, s(z))))),
% 0.47/0.68 inference(rewrite,[status(thm)],[])).
% 0.47/0.68 tff(16,plain,
% 0.47/0.68 (((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(z, s(z))))),
% 0.47/0.68 inference(rewrite,[status(thm)],[])).
% 0.47/0.68 tff(17,plain,
% 0.47/0.68 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(z, s(z))) | (~r(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(s(s(z)))))), s(z))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(z, s(z)))))),
% 0.47/0.68 inference(monotonicity,[status(thm)],[16])).
% 0.47/0.68 tff(18,plain,
% 0.47/0.68 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(z, s(z))) | (~r(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(s(s(z)))))), s(z))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(z, s(z))))),
% 0.47/0.68 inference(transitivity,[status(thm)],[17, 15])).
% 0.47/0.68 tff(19,plain,
% 0.47/0.68 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 0.47/0.68 inference(quant_inst,[status(thm)],[])).
% 0.47/0.68 tff(20,plain,
% 0.47/0.68 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(z, s(z)))),
% 0.47/0.68 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.47/0.68 tff(21,plain,
% 0.47/0.68 ($false),
% 0.47/0.68 inference(unit_resolution,[status(thm)],[20, 14, 4, 3, 2])).
% 0.47/0.68 tff(22,plain,((~r(z, s(z))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.68 tff(23,plain,
% 0.47/0.68 (~r(z, s(z))),
% 0.47/0.68 inference(unit_resolution,[status(thm)],[22, 3, 2])).
% 0.47/0.68 tff(24,plain,
% 0.47/0.68 ((z = s(z)) <=> (s(z) = z)),
% 0.47/0.68 inference(commutativity,[status(thm)],[])).
% 0.47/0.68 tff(25,plain,
% 0.47/0.68 ((s(z) = z) <=> (z = s(z))),
% 0.47/0.68 inference(symmetry,[status(thm)],[24])).
% 0.47/0.68 tff(26,plain,
% 0.47/0.68 ((~(s(z) = z)) <=> (~(z = s(z)))),
% 0.47/0.68 inference(monotonicity,[status(thm)],[25])).
% 0.47/0.68 tff(27,plain,
% 0.47/0.68 (^[X: $i] : refl((~(s(X) = z)) <=> (~(s(X) = z)))),
% 0.47/0.68 inference(bind,[status(th)],[])).
% 0.47/0.68 tff(28,plain,
% 0.47/0.68 (![X: $i] : (~(s(X) = z)) <=> ![X: $i] : (~(s(X) = z))),
% 0.47/0.68 inference(quant_intro,[status(thm)],[27])).
% 0.47/0.68 tff(29,plain,
% 0.47/0.68 (![X: $i] : (~(s(X) = z)) <=> ![X: $i] : (~(s(X) = z))),
% 0.47/0.68 inference(rewrite,[status(thm)],[])).
% 0.47/0.68 tff(30,axiom,(![X: $i] : (~(s(X) = z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','snz')).
% 0.47/0.68 tff(31,plain,
% 0.47/0.68 (![X: $i] : (~(s(X) = z))),
% 0.47/0.68 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.47/0.68 tff(32,plain,(
% 0.47/0.68 ![X: $i] : (~(s(X) = z))),
% 0.47/0.68 inference(skolemize,[status(sab)],[31])).
% 0.47/0.68 tff(33,plain,
% 0.47/0.68 (![X: $i] : (~(s(X) = z))),
% 0.47/0.68 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.47/0.68 tff(34,plain,
% 0.47/0.68 ((~![X: $i] : (~(s(X) = z))) | (~(s(z) = z))),
% 0.47/0.68 inference(quant_inst,[status(thm)],[])).
% 0.47/0.68 tff(35,plain,
% 0.47/0.68 (~(s(z) = z)),
% 0.47/0.68 inference(unit_resolution,[status(thm)],[34, 33])).
% 0.47/0.68 tff(36,plain,
% 0.47/0.68 (~(z = s(z))),
% 0.47/0.68 inference(modus_ponens,[status(thm)],[35, 26])).
% 0.47/0.68 tff(37,plain,
% 0.47/0.68 (^[Y: $i, X: $i] : refl(((X = Y) | b(X, Y) | r(X, Y)) <=> ((X = Y) | b(X, Y) | r(X, Y)))),
% 0.47/0.68 inference(bind,[status(th)],[])).
% 0.47/0.68 tff(38,plain,
% 0.47/0.68 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.47/0.68 inference(quant_intro,[status(thm)],[37])).
% 0.47/0.68 tff(39,plain,
% 0.47/0.68 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.47/0.68 inference(rewrite,[status(thm)],[])).
% 0.47/0.68 tff(40,plain,
% 0.47/0.68 (^[Y: $i, X: $i] : rewrite((((X = Y) | r(X, Y)) | b(X, Y)) <=> ((X = Y) | b(X, Y) | r(X, Y)))),
% 0.47/0.68 inference(bind,[status(th)],[])).
% 0.47/0.68 tff(41,plain,
% 0.47/0.68 (![Y: $i, X: $i] : (((X = Y) | r(X, Y)) | b(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.47/0.68 inference(quant_intro,[status(thm)],[40])).
% 0.47/0.68 tff(42,axiom,(![Y: $i, X: $i] : (((X = Y) | r(X, Y)) | b(X, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','rb')).
% 0.47/0.68 tff(43,plain,
% 0.47/0.68 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.47/0.68 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.47/0.68 tff(44,plain,
% 0.47/0.68 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.47/0.68 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.47/0.68 tff(45,plain,(
% 0.47/0.68 ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.47/0.68 inference(skolemize,[status(sab)],[44])).
% 0.47/0.68 tff(46,plain,
% 0.47/0.68 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.47/0.68 inference(modus_ponens,[status(thm)],[45, 38])).
% 0.47/0.68 tff(47,plain,
% 0.47/0.68 (((~![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)))),
% 0.47/0.68 inference(rewrite,[status(thm)],[])).
% 0.47/0.68 tff(48,plain,
% 0.47/0.68 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(z)) | b(z, s(z)) | r(z, s(z)))),
% 0.47/0.68 inference(quant_inst,[status(thm)],[])).
% 0.47/0.68 tff(49,plain,
% 0.47/0.68 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(z)) | b(z, s(z)) | r(z, s(z))),
% 0.47/0.68 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.47/0.68 tff(50,plain,
% 0.47/0.68 ((z = s(z)) | b(z, s(z)) | r(z, s(z))),
% 0.47/0.68 inference(unit_resolution,[status(thm)],[49, 46])).
% 0.47/0.68 tff(51,plain,
% 0.47/0.68 (b(z, s(z)) | r(z, s(z))),
% 0.47/0.68 inference(unit_resolution,[status(thm)],[50, 36])).
% 0.47/0.68 tff(52,plain,
% 0.47/0.68 (b(z, s(z))),
% 0.47/0.68 inference(unit_resolution,[status(thm)],[51, 23])).
% 0.47/0.68 tff(53,assumption,(r(s(s(s(z))), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 0.47/0.68 tff(54,plain,
% 0.47/0.68 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(z))))) | (~r(s(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(z, s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 0.47/0.68 inference(rewrite,[status(thm)],[])).
% 0.47/0.68 tff(55,plain,
% 0.47/0.68 (((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(z)))))) <=> ((~r(z, s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 0.47/0.68 inference(rewrite,[status(thm)],[])).
% 0.47/0.68 tff(56,plain,
% 0.47/0.68 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(z, 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(s(s(z)))))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))))),
% 0.47/0.68 inference(monotonicity,[status(thm)],[55])).
% 0.47/0.68 tff(57,plain,
% 0.47/0.68 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(z, 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(s(s(z)))))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 0.47/0.68 inference(transitivity,[status(thm)],[56, 54])).
% 0.47/0.68 tff(58,plain,
% 0.47/0.68 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(z))))))),
% 0.47/0.68 inference(quant_inst,[status(thm)],[])).
% 0.47/0.68 tff(59,plain,
% 0.47/0.68 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 0.47/0.68 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.47/0.68 tff(60,plain,
% 0.47/0.68 (~r(z, s(s(s(z))))),
% 0.47/0.68 inference(unit_resolution,[status(thm)],[59, 14, 3, 53])).
% 0.47/0.68 tff(61,plain,
% 0.47/0.68 ((z = s(s(s(z)))) <=> (s(s(s(z))) = z)),
% 0.47/0.68 inference(commutativity,[status(thm)],[])).
% 0.47/0.68 tff(62,plain,
% 0.47/0.68 ((s(s(s(z))) = z) <=> (z = s(s(s(z))))),
% 0.47/0.68 inference(symmetry,[status(thm)],[61])).
% 0.47/0.68 tff(63,plain,
% 0.47/0.68 ((~(s(s(s(z))) = z)) <=> (~(z = s(s(s(z)))))),
% 0.47/0.68 inference(monotonicity,[status(thm)],[62])).
% 0.47/0.68 tff(64,plain,
% 0.47/0.68 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(z))) = z))),
% 0.47/0.68 inference(quant_inst,[status(thm)],[])).
% 0.47/0.68 tff(65,plain,
% 0.47/0.68 (~(s(s(s(z))) = z)),
% 0.47/0.68 inference(unit_resolution,[status(thm)],[64, 33])).
% 0.47/0.68 tff(66,plain,
% 0.47/0.68 (~(z = s(s(s(z))))),
% 0.47/0.68 inference(modus_ponens,[status(thm)],[65, 63])).
% 0.47/0.68 tff(67,plain,
% 0.47/0.68 (((~![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)))))),
% 0.47/0.68 inference(rewrite,[status(thm)],[])).
% 0.47/0.68 tff(68,plain,
% 0.47/0.68 ((~![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)))))),
% 0.47/0.68 inference(quant_inst,[status(thm)],[])).
% 0.47/0.68 tff(69,plain,
% 0.47/0.68 ((~![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))))),
% 0.47/0.68 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.47/0.68 tff(70,plain,
% 0.47/0.68 ((z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z))))),
% 0.47/0.68 inference(unit_resolution,[status(thm)],[69, 46])).
% 0.47/0.68 tff(71,plain,
% 0.47/0.68 (b(z, s(s(s(z)))) | r(z, s(s(s(z))))),
% 0.47/0.68 inference(unit_resolution,[status(thm)],[70, 66])).
% 0.47/0.68 tff(72,plain,
% 0.47/0.68 (b(z, s(s(s(z))))),
% 0.47/0.68 inference(unit_resolution,[status(thm)],[71, 60])).
% 0.47/0.68 tff(73,assumption,(b(s(s(s(s(s(s(z)))))), s(s(s(z))))), introduced(assumption)).
% 0.47/0.68 tff(74,assumption,(r(s(s(s(z))), s(z))), introduced(assumption)).
% 0.47/0.68 tff(75,plain,
% 0.47/0.68 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(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(s(s(z)))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 0.47/0.69 inference(rewrite,[status(thm)],[])).
% 0.47/0.69 tff(76,plain,
% 0.47/0.69 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 0.47/0.69 inference(quant_inst,[status(thm)],[])).
% 0.47/0.69 tff(77,plain,
% 0.47/0.69 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 0.47/0.69 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.47/0.69 tff(78,plain,
% 0.47/0.69 ($false),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[77, 14, 74, 53, 2])).
% 0.47/0.69 tff(79,plain,((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.69 tff(80,plain,
% 0.47/0.69 (~r(s(s(s(z))), s(z))),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[79, 2, 53])).
% 0.47/0.69 tff(81,plain,
% 0.47/0.69 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0) <=> ![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 0.47/0.69 inference(rewrite,[status(thm)],[])).
% 0.47/0.69 tff(82,plain,
% 0.47/0.69 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y)) <=> ![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 0.47/0.69 inference(rewrite,[status(thm)],[])).
% 0.47/0.69 tff(83,plain,
% 0.47/0.69 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y)) <=> ![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 0.47/0.69 inference(rewrite,[status(thm)],[])).
% 0.47/0.69 tff(84,axiom,(![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sinj')).
% 0.47/0.69 tff(85,plain,
% 0.47/0.69 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 0.47/0.69 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.47/0.69 tff(86,plain,(
% 0.47/0.69 ![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 0.47/0.69 inference(skolemize,[status(sab)],[85])).
% 0.47/0.69 tff(87,plain,
% 0.47/0.69 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 0.47/0.69 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.47/0.69 tff(88,plain,
% 0.47/0.69 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 0.47/0.69 inference(modus_ponens,[status(thm)],[87, 81])).
% 0.47/0.69 tff(89,plain,
% 0.47/0.69 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(z)) = z)),
% 0.47/0.69 inference(quant_inst,[status(thm)],[])).
% 0.47/0.69 tff(90,plain,
% 0.47/0.69 (inj_0(s(z)) = z),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[89, 88])).
% 0.47/0.69 tff(91,assumption,(s(s(s(z))) = s(z)), introduced(assumption)).
% 0.47/0.69 tff(92,plain,
% 0.47/0.69 (inj_0(s(s(s(z)))) = inj_0(s(z))),
% 0.47/0.69 inference(monotonicity,[status(thm)],[91])).
% 0.47/0.69 tff(93,plain,
% 0.47/0.69 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(z)))) = s(s(z)))),
% 0.47/0.69 inference(quant_inst,[status(thm)],[])).
% 0.47/0.69 tff(94,plain,
% 0.47/0.69 (inj_0(s(s(s(z)))) = s(s(z))),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[93, 88])).
% 0.47/0.69 tff(95,plain,
% 0.47/0.69 (s(s(z)) = inj_0(s(s(s(z))))),
% 0.47/0.69 inference(symmetry,[status(thm)],[94])).
% 0.47/0.69 tff(96,plain,
% 0.47/0.69 (s(s(z)) = z),
% 0.47/0.69 inference(transitivity,[status(thm)],[95, 92, 90])).
% 0.47/0.69 tff(97,plain,
% 0.47/0.69 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(z)) = z))),
% 0.47/0.69 inference(quant_inst,[status(thm)],[])).
% 0.47/0.69 tff(98,plain,
% 0.47/0.69 (~(s(s(z)) = z)),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[97, 33])).
% 0.47/0.69 tff(99,plain,
% 0.47/0.69 ($false),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[98, 96])).
% 0.47/0.69 tff(100,plain,(~(s(s(s(z))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.69 tff(101,plain,
% 0.47/0.69 (((~![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)))),
% 0.47/0.69 inference(rewrite,[status(thm)],[])).
% 0.47/0.69 tff(102,plain,
% 0.47/0.69 ((~![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)))),
% 0.47/0.69 inference(quant_inst,[status(thm)],[])).
% 0.47/0.69 tff(103,plain,
% 0.47/0.69 ((~![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))),
% 0.47/0.69 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.47/0.69 tff(104,plain,
% 0.47/0.69 ((s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z))),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[103, 46])).
% 0.47/0.69 tff(105,plain,
% 0.47/0.69 (b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z))),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[104, 100])).
% 0.47/0.69 tff(106,plain,
% 0.47/0.69 (b(s(s(s(z))), s(z))),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[105, 80])).
% 0.47/0.69 tff(107,plain,
% 0.47/0.69 (~r(z, s(z))),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[22, 2, 3])).
% 0.47/0.69 tff(108,plain,
% 0.47/0.69 (b(z, s(z))),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[51, 107])).
% 0.47/0.69 tff(109,plain,
% 0.47/0.69 (^[X0: $i, X3: $i, X2: $i, X1: $i] : refl(((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) <=> ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))))),
% 0.47/0.69 inference(bind,[status(th)],[])).
% 0.47/0.69 tff(110,plain,
% 0.47/0.69 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 0.47/0.69 inference(quant_intro,[status(thm)],[109])).
% 0.47/0.69 tff(111,plain,
% 0.47/0.69 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 0.47/0.69 inference(rewrite,[status(thm)],[])).
% 0.47/0.69 tff(112,plain,
% 0.47/0.69 (^[X0: $i, X3: $i, X2: $i, X1: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) <=> ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))), (((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X1, X3))) <=> (((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X1, X3))))), rewrite((((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X1, X3))) <=> ((~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))), (((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X1, X3))) <=> ((~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))))), ((((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X1, X3))) | (~b(X2, X3))) <=> (((~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X2, X3))))), rewrite((((~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X2, X3))) <=> ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))), ((((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X1, X3))) | (~b(X2, X3))) <=> ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))))),
% 0.47/0.69 inference(bind,[status(th)],[])).
% 0.47/0.69 tff(113,plain,
% 0.47/0.69 (![X0: $i, X3: $i, X2: $i, X1: $i] : (((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X1, X3))) | (~b(X2, X3))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 0.47/0.69 inference(quant_intro,[status(thm)],[112])).
% 0.47/0.69 tff(114,axiom,(![X0: $i, X3: $i, X2: $i, X1: $i] : (((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X1, X3))) | (~b(X2, X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axb')).
% 0.47/0.69 tff(115,plain,
% 0.47/0.69 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 0.47/0.69 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.47/0.69 tff(116,plain,
% 0.47/0.69 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 0.47/0.69 inference(modus_ponens,[status(thm)],[115, 111])).
% 0.47/0.69 tff(117,plain,(
% 0.47/0.69 ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 0.47/0.69 inference(skolemize,[status(sab)],[116])).
% 0.47/0.69 tff(118,plain,
% 0.47/0.69 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 0.47/0.69 inference(modus_ponens,[status(thm)],[117, 110])).
% 0.47/0.69 tff(119,plain,
% 0.47/0.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 0.47/0.69 inference(rewrite,[status(thm)],[])).
% 0.47/0.69 tff(120,plain,
% 0.47/0.69 (((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z))) <=> ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 0.47/0.69 inference(rewrite,[status(thm)],[])).
% 0.47/0.69 tff(121,plain,
% 0.47/0.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z)))))))),
% 0.47/0.69 inference(monotonicity,[status(thm)],[120])).
% 0.47/0.69 tff(122,plain,
% 0.47/0.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 0.47/0.69 inference(transitivity,[status(thm)],[121, 119])).
% 0.47/0.69 tff(123,plain,
% 0.47/0.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 0.47/0.69 inference(quant_inst,[status(thm)],[])).
% 0.47/0.69 tff(124,plain,
% 0.47/0.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z)))))),
% 0.47/0.69 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.47/0.69 tff(125,plain,
% 0.47/0.69 ($false),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[124, 118, 108, 106, 73, 1, 72])).
% 0.47/0.69 tff(126,plain,((~r(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(s(s(s(z)))))), z)) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.69 tff(127,plain,
% 0.47/0.69 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[126, 53, 1, 2, 3])).
% 0.47/0.69 tff(128,plain,
% 0.47/0.69 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(z)))))) = s(s(s(s(z)))))),
% 0.47/0.69 inference(quant_inst,[status(thm)],[])).
% 0.47/0.69 tff(129,plain,
% 0.47/0.69 (inj_0(s(s(s(s(s(z)))))) = s(s(s(s(z))))),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[128, 88])).
% 0.47/0.69 tff(130,plain,
% 0.47/0.69 ((~![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))))))),
% 0.47/0.69 inference(quant_inst,[status(thm)],[])).
% 0.47/0.69 tff(131,plain,
% 0.47/0.69 (inj_0(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[130, 88])).
% 0.47/0.69 tff(132,assumption,(s(s(s(s(s(s(z)))))) = s(s(s(z)))), introduced(assumption)).
% 0.47/0.69 tff(133,plain,
% 0.47/0.69 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(s(s(z))))),
% 0.47/0.69 inference(monotonicity,[status(thm)],[132])).
% 0.47/0.69 tff(134,plain,
% 0.47/0.69 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(s(s(z)))))))),
% 0.47/0.69 inference(symmetry,[status(thm)],[133])).
% 0.47/0.69 tff(135,plain,
% 0.47/0.69 (s(s(z)) = s(s(s(s(s(z)))))),
% 0.47/0.69 inference(transitivity,[status(thm)],[95, 134, 131])).
% 0.47/0.69 tff(136,plain,
% 0.47/0.69 (inj_0(s(s(z))) = inj_0(s(s(s(s(s(z))))))),
% 0.47/0.69 inference(monotonicity,[status(thm)],[135])).
% 0.47/0.69 tff(137,plain,
% 0.47/0.69 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(z))) = s(z))),
% 0.47/0.69 inference(quant_inst,[status(thm)],[])).
% 0.47/0.69 tff(138,plain,
% 0.47/0.69 (inj_0(s(s(z))) = s(z)),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[137, 88])).
% 0.47/0.69 tff(139,plain,
% 0.47/0.69 (s(z) = inj_0(s(s(z)))),
% 0.47/0.69 inference(symmetry,[status(thm)],[138])).
% 0.47/0.69 tff(140,plain,
% 0.47/0.69 (s(z) = s(s(s(s(z))))),
% 0.47/0.69 inference(transitivity,[status(thm)],[139, 136, 129])).
% 0.47/0.69 tff(141,assumption,(s(z) = s(s(s(s(z))))), introduced(assumption)).
% 0.47/0.69 tff(142,plain,
% 0.47/0.69 (s(s(s(s(z)))) = s(z)),
% 0.47/0.69 inference(symmetry,[status(thm)],[141])).
% 0.47/0.69 tff(143,plain,
% 0.47/0.69 (inj_0(s(s(s(s(z))))) = inj_0(s(z))),
% 0.47/0.69 inference(monotonicity,[status(thm)],[142])).
% 0.47/0.69 tff(144,plain,
% 0.47/0.69 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(z))))) = s(s(s(z))))),
% 0.47/0.69 inference(quant_inst,[status(thm)],[])).
% 0.47/0.69 tff(145,plain,
% 0.47/0.69 (inj_0(s(s(s(s(z))))) = s(s(s(z)))),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[144, 88])).
% 0.47/0.69 tff(146,plain,
% 0.47/0.69 (s(s(s(z))) = inj_0(s(s(s(s(z)))))),
% 0.47/0.69 inference(symmetry,[status(thm)],[145])).
% 0.47/0.69 tff(147,plain,
% 0.47/0.69 (s(s(s(z))) = z),
% 0.47/0.69 inference(transitivity,[status(thm)],[146, 143, 90])).
% 0.47/0.69 tff(148,plain,
% 0.47/0.69 ($false),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[65, 147])).
% 0.47/0.69 tff(149,plain,(~(s(z) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.69 tff(150,plain,
% 0.47/0.69 ($false),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[149, 140])).
% 0.47/0.69 tff(151,plain,(~(s(s(s(s(s(s(z)))))) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.69 tff(152,plain,
% 0.47/0.69 (((~![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)))))),
% 0.47/0.69 inference(rewrite,[status(thm)],[])).
% 0.47/0.69 tff(153,plain,
% 0.47/0.69 ((~![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)))))),
% 0.47/0.69 inference(quant_inst,[status(thm)],[])).
% 0.47/0.69 tff(154,plain,
% 0.47/0.69 ((~![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))))),
% 0.47/0.69 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.47/0.69 tff(155,plain,
% 0.47/0.69 ((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))))),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[154, 46])).
% 0.47/0.69 tff(156,plain,
% 0.47/0.69 (b(s(s(s(s(s(s(z)))))), s(s(s(z)))) | r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[155, 151])).
% 0.47/0.69 tff(157,plain,
% 0.47/0.69 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[156, 127])).
% 0.47/0.69 tff(158,plain,
% 0.47/0.69 (~r(s(s(s(z))), s(z))),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[79, 53, 2])).
% 0.47/0.69 tff(159,plain,
% 0.47/0.69 (b(s(s(s(z))), s(z))),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[105, 158])).
% 0.47/0.69 tff(160,assumption,(r(s(s(s(s(s(s(z)))))), s(s(s(z))))), introduced(assumption)).
% 0.47/0.69 tff(161,assumption,(r(z, s(s(s(z))))), introduced(assumption)).
% 0.47/0.69 tff(162,plain,
% 0.47/0.69 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 0.47/0.69 inference(rewrite,[status(thm)],[])).
% 0.47/0.69 tff(163,plain,
% 0.47/0.69 (((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(z))))))))) <=> ((~r(z, s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 0.47/0.69 inference(rewrite,[status(thm)],[])).
% 0.47/0.69 tff(164,plain,
% 0.47/0.69 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))))),
% 0.47/0.69 inference(monotonicity,[status(thm)],[163])).
% 0.47/0.69 tff(165,plain,
% 0.47/0.69 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 0.47/0.69 inference(transitivity,[status(thm)],[164, 162])).
% 0.47/0.69 tff(166,plain,
% 0.47/0.69 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 0.47/0.69 inference(quant_inst,[status(thm)],[])).
% 0.47/0.69 tff(167,plain,
% 0.47/0.69 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 0.47/0.69 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.47/0.69 tff(168,plain,
% 0.47/0.69 ($false),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[167, 14, 3, 160, 161])).
% 0.47/0.69 tff(169,plain,((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.69 tff(170,plain,
% 0.47/0.69 (~r(z, s(s(s(z))))),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[169, 160, 3])).
% 0.47/0.69 tff(171,plain,
% 0.47/0.69 (b(z, s(s(s(z))))),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[71, 170])).
% 0.47/0.69 tff(172,assumption,(b(s(z), s(s(s(z))))), introduced(assumption)).
% 0.47/0.69 tff(173,assumption,(b(s(s(s(z))), s(z))), introduced(assumption)).
% 0.47/0.69 tff(174,assumption,(b(z, s(z))), introduced(assumption)).
% 0.47/0.69 tff(175,assumption,(r(s(s(s(z))), z)), introduced(assumption)).
% 0.47/0.69 tff(176,assumption,(r(s(z), s(s(s(z))))), introduced(assumption)).
% 0.47/0.69 tff(177,assumption,(r(s(z), z)), introduced(assumption)).
% 0.47/0.69 tff(178,plain,
% 0.47/0.69 (((~![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(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))),
% 0.47/0.69 inference(rewrite,[status(thm)],[])).
% 0.47/0.69 tff(179,plain,
% 0.47/0.69 ((~![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))))))),
% 0.47/0.69 inference(quant_inst,[status(thm)],[])).
% 0.47/0.69 tff(180,plain,
% 0.47/0.69 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z)))))),
% 0.47/0.69 inference(modus_ponens,[status(thm)],[179, 178])).
% 0.47/0.69 tff(181,plain,
% 0.47/0.69 ($false),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[180, 14, 177, 176, 175])).
% 0.47/0.69 tff(182,plain,((~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.69 tff(183,plain,
% 0.47/0.69 (~r(s(z), z)),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[182, 176, 175])).
% 0.47/0.69 tff(184,plain,
% 0.47/0.69 (((~![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))),
% 0.47/0.69 inference(rewrite,[status(thm)],[])).
% 0.47/0.69 tff(185,plain,
% 0.47/0.69 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = z) | b(s(z), z) | r(s(z), z))),
% 0.47/0.69 inference(quant_inst,[status(thm)],[])).
% 0.47/0.69 tff(186,plain,
% 0.47/0.69 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = z) | b(s(z), z) | r(s(z), z)),
% 0.47/0.69 inference(modus_ponens,[status(thm)],[185, 184])).
% 0.47/0.69 tff(187,plain,
% 0.47/0.69 (b(s(z), z) | r(s(z), z)),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[186, 46, 35])).
% 0.47/0.69 tff(188,plain,
% 0.47/0.69 (b(s(z), z)),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[187, 183])).
% 0.47/0.69 tff(189,plain,
% 0.47/0.69 (((~![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(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(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 0.47/0.69 inference(rewrite,[status(thm)],[])).
% 0.47/0.69 tff(190,plain,
% 0.47/0.69 (((~r(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(z)))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 0.47/0.69 inference(rewrite,[status(thm)],[])).
% 0.47/0.70 tff(191,plain,
% 0.47/0.70 (((~![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(s(s(z)))))), 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(z))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))))),
% 0.47/0.70 inference(monotonicity,[status(thm)],[190])).
% 0.47/0.70 tff(192,plain,
% 0.47/0.70 (((~![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(s(s(z)))))), 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(z))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 0.47/0.70 inference(transitivity,[status(thm)],[191, 189])).
% 0.47/0.70 tff(193,plain,
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% 0.47/0.70 inference(quant_inst,[status(thm)],[])).
% 0.47/0.70 tff(194,plain,
% 0.47/0.70 ((~![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(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 0.47/0.70 inference(modus_ponens,[status(thm)],[193, 192])).
% 0.47/0.70 tff(195,plain,
% 0.47/0.70 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 0.47/0.70 inference(unit_resolution,[status(thm)],[194, 14, 176, 160])).
% 0.47/0.70 tff(196,assumption,(~b(s(s(s(s(s(s(z)))))), s(z))), introduced(assumption)).
% 0.47/0.70 tff(197,assumption,(~r(s(s(s(s(s(s(z)))))), s(z))), introduced(assumption)).
% 0.47/0.70 tff(198,assumption,(s(s(s(s(s(s(z)))))) = s(z)), introduced(assumption)).
% 0.47/0.70 tff(199,plain,
% 0.47/0.70 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(z))),
% 0.47/0.70 inference(monotonicity,[status(thm)],[198])).
% 0.47/0.70 tff(200,plain,
% 0.47/0.70 (s(s(s(s(s(z))))) = inj_0(s(s(s(s(s(s(z)))))))),
% 0.47/0.70 inference(symmetry,[status(thm)],[131])).
% 0.47/0.70 tff(201,plain,
% 0.47/0.70 (s(s(s(s(s(z))))) = z),
% 0.47/0.70 inference(transitivity,[status(thm)],[200, 199, 90])).
% 0.47/0.70 tff(202,plain,
% 0.47/0.70 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(z))))) = z))),
% 0.47/0.70 inference(quant_inst,[status(thm)],[])).
% 0.47/0.70 tff(203,plain,
% 0.47/0.70 (~(s(s(s(s(s(z))))) = z)),
% 0.47/0.70 inference(unit_resolution,[status(thm)],[202, 33])).
% 0.47/0.70 tff(204,plain,
% 0.47/0.70 ($false),
% 0.47/0.70 inference(unit_resolution,[status(thm)],[203, 201])).
% 0.47/0.70 tff(205,plain,(~(s(s(s(s(s(s(z)))))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.70 tff(206,plain,
% 0.47/0.70 (((~![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)))),
% 0.47/0.70 inference(rewrite,[status(thm)],[])).
% 0.47/0.70 tff(207,plain,
% 0.47/0.70 ((~![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)))),
% 0.47/0.70 inference(quant_inst,[status(thm)],[])).
% 0.47/0.70 tff(208,plain,
% 0.47/0.70 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(z)) | b(s(s(s(s(s(s(z)))))), s(z)) | r(s(s(s(s(s(s(z)))))), s(z))),
% 0.47/0.70 inference(modus_ponens,[status(thm)],[207, 206])).
% 0.47/0.70 tff(209,plain,
% 0.47/0.70 ($false),
% 0.47/0.70 inference(unit_resolution,[status(thm)],[208, 46, 205, 197, 196])).
% 0.47/0.70 tff(210,plain,(b(s(s(s(s(s(s(z)))))), s(z)) | r(s(s(s(s(s(s(z)))))), s(z))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.70 tff(211,plain,
% 0.47/0.70 (b(s(s(s(s(s(s(z)))))), s(z))),
% 0.47/0.70 inference(unit_resolution,[status(thm)],[210, 195])).
% 0.47/0.70 tff(212,assumption,(r(s(z), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 0.47/0.70 tff(213,plain,
% 0.47/0.70 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(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(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 0.47/0.70 inference(rewrite,[status(thm)],[])).
% 0.47/0.70 tff(214,plain,
% 0.47/0.70 (((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(z))))))))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 0.54/0.70 inference(rewrite,[status(thm)],[])).
% 0.54/0.70 tff(215,plain,
% 0.54/0.70 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(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), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))))),
% 0.54/0.70 inference(monotonicity,[status(thm)],[214])).
% 0.54/0.70 tff(216,plain,
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% 0.54/0.70 inference(transitivity,[status(thm)],[215, 213])).
% 0.54/0.70 tff(217,plain,
% 0.54/0.70 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 0.54/0.70 inference(quant_inst,[status(thm)],[])).
% 0.54/0.70 tff(218,plain,
% 0.54/0.70 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 0.54/0.70 inference(modus_ponens,[status(thm)],[217, 216])).
% 0.54/0.70 tff(219,plain,
% 0.54/0.70 ($false),
% 0.54/0.70 inference(unit_resolution,[status(thm)],[218, 14, 176, 160, 212])).
% 0.54/0.70 tff(220,plain,((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.70 tff(221,plain,
% 0.54/0.70 (~r(s(z), s(s(s(s(s(s(z)))))))),
% 0.54/0.70 inference(unit_resolution,[status(thm)],[220, 176, 160])).
% 0.54/0.70 tff(222,assumption,(s(z) = s(s(s(s(s(s(z))))))), introduced(assumption)).
% 0.54/0.70 tff(223,plain,
% 0.54/0.70 (s(s(s(s(s(s(z)))))) = s(z)),
% 0.54/0.70 inference(symmetry,[status(thm)],[222])).
% 0.54/0.70 tff(224,plain,
% 0.54/0.70 ($false),
% 0.54/0.70 inference(unit_resolution,[status(thm)],[205, 223])).
% 0.54/0.70 tff(225,plain,(~(s(z) = s(s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.70 tff(226,assumption,(~r(s(z), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 0.54/0.70 tff(227,assumption,(~b(s(z), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 0.54/0.70 tff(228,plain,
% 0.54/0.70 (((~![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))))))))),
% 0.54/0.70 inference(rewrite,[status(thm)],[])).
% 0.54/0.70 tff(229,plain,
% 0.54/0.70 ((~![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))))))))),
% 0.54/0.70 inference(quant_inst,[status(thm)],[])).
% 0.54/0.70 tff(230,plain,
% 0.54/0.70 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(s(s(z))))))) | b(s(z), s(s(s(s(s(s(z))))))) | r(s(z), s(s(s(s(s(s(z)))))))),
% 0.54/0.70 inference(modus_ponens,[status(thm)],[229, 228])).
% 0.54/0.70 tff(231,plain,
% 0.54/0.70 ($false),
% 0.54/0.70 inference(unit_resolution,[status(thm)],[230, 46, 227, 226, 225])).
% 0.54/0.70 tff(232,plain,(r(s(z), s(s(s(s(s(s(z))))))) | b(s(z), s(s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.70 tff(233,plain,
% 0.54/0.70 (b(s(z), s(s(s(s(s(s(z)))))))),
% 0.54/0.70 inference(unit_resolution,[status(thm)],[232, 221])).
% 0.54/0.70 tff(234,assumption,(b(s(z), z)), introduced(assumption)).
% 0.54/0.70 tff(235,assumption,(b(z, s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 0.54/0.70 tff(236,assumption,(b(s(s(s(s(s(s(z)))))), s(z))), introduced(assumption)).
% 0.54/0.70 tff(237,assumption,(b(s(z), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 0.54/0.70 tff(238,plain,
% 0.54/0.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 0.54/0.70 inference(rewrite,[status(thm)],[])).
% 0.54/0.70 tff(239,plain,
% 0.54/0.70 (((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z)))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 0.54/0.70 inference(rewrite,[status(thm)],[])).
% 0.54/0.70 tff(240,plain,
% 0.54/0.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z))))))))))),
% 0.54/0.70 inference(monotonicity,[status(thm)],[239])).
% 0.54/0.70 tff(241,plain,
% 0.54/0.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 0.54/0.70 inference(transitivity,[status(thm)],[240, 238])).
% 0.54/0.70 tff(242,plain,
% 0.54/0.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 0.54/0.70 inference(quant_inst,[status(thm)],[])).
% 0.54/0.70 tff(243,plain,
% 0.54/0.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z))))))))),
% 0.54/0.70 inference(modus_ponens,[status(thm)],[242, 241])).
% 0.54/0.70 tff(244,plain,
% 0.54/0.70 ($false),
% 0.54/0.70 inference(unit_resolution,[status(thm)],[243, 118, 234, 237, 1, 235, 236])).
% 0.54/0.70 tff(245,plain,((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.70 tff(246,plain,
% 0.54/0.70 (~b(s(s(s(s(s(s(z)))))), z)),
% 0.54/0.70 inference(unit_resolution,[status(thm)],[245, 235, 233, 234, 211])).
% 0.54/0.70 tff(247,plain,
% 0.54/0.70 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(s(z)))))) = z))),
% 0.54/0.70 inference(quant_inst,[status(thm)],[])).
% 0.54/0.70 tff(248,plain,
% 0.54/0.70 (~(s(s(s(s(s(s(z)))))) = z)),
% 0.54/0.70 inference(unit_resolution,[status(thm)],[247, 33])).
% 0.54/0.70 tff(249,plain,
% 0.54/0.70 (((~![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))),
% 0.54/0.70 inference(rewrite,[status(thm)],[])).
% 0.54/0.70 tff(250,plain,
% 0.54/0.70 ((~![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))),
% 0.54/0.70 inference(quant_inst,[status(thm)],[])).
% 0.54/0.70 tff(251,plain,
% 0.54/0.70 ((~![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)),
% 0.54/0.70 inference(modus_ponens,[status(thm)],[250, 249])).
% 0.54/0.70 tff(252,plain,
% 0.54/0.70 (b(s(s(s(s(s(s(z)))))), z) | r(s(s(s(s(s(s(z)))))), z)),
% 0.54/0.70 inference(unit_resolution,[status(thm)],[251, 46, 248])).
% 0.54/0.70 tff(253,plain,
% 0.54/0.70 (r(s(s(s(s(s(s(z)))))), z)),
% 0.54/0.70 inference(unit_resolution,[status(thm)],[252, 246])).
% 0.54/0.70 tff(254,plain,
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% 0.54/0.70 inference(rewrite,[status(thm)],[])).
% 0.54/0.70 tff(255,plain,
% 0.54/0.70 (((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), z))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 0.54/0.70 inference(rewrite,[status(thm)],[])).
% 0.54/0.70 tff(256,plain,
% 0.54/0.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z))))))))))),
% 0.54/0.70 inference(monotonicity,[status(thm)],[255])).
% 0.54/0.70 tff(257,plain,
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% 0.54/0.70 inference(transitivity,[status(thm)],[256, 254])).
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% 0.54/0.70 inference(quant_inst,[status(thm)],[])).
% 0.54/0.70 tff(259,plain,
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% 0.54/0.70 inference(modus_ponens,[status(thm)],[258, 257])).
% 0.54/0.70 tff(260,plain,
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% 0.54/0.70 inference(unit_resolution,[status(thm)],[259, 118, 174, 234, 237, 235, 236])).
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% 0.54/0.70 tff(262,plain,
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% 0.54/0.70 inference(unit_resolution,[status(thm)],[261, 235, 234, 211, 233])).
% 0.54/0.70 tff(263,plain,
% 0.54/0.70 (r(z, s(z))),
% 0.54/0.70 inference(unit_resolution,[status(thm)],[51, 262])).
% 0.54/0.70 tff(264,plain,
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% 0.54/0.70 inference(rewrite,[status(thm)],[])).
% 0.54/0.70 tff(265,plain,
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% 0.54/0.70 inference(quant_inst,[status(thm)],[])).
% 0.54/0.70 tff(266,plain,
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% 0.54/0.70 inference(modus_ponens,[status(thm)],[265, 264])).
% 0.54/0.70 tff(267,plain,
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% 0.54/0.70 inference(unit_resolution,[status(thm)],[266, 14, 4, 176, 161])).
% 0.54/0.70 tff(268,plain,((~r(s(z), s(s(s(z))))) | (~r(z, s(z))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.70 tff(269,plain,
% 0.54/0.70 (~r(z, s(s(s(z))))),
% 0.54/0.70 inference(unit_resolution,[status(thm)],[268, 263, 176])).
% 0.54/0.70 tff(270,plain,
% 0.54/0.70 (b(z, s(s(s(z))))),
% 0.54/0.70 inference(unit_resolution,[status(thm)],[71, 269])).
% 0.54/0.70 tff(271,assumption,(b(z, s(s(s(z))))), introduced(assumption)).
% 0.54/0.70 tff(272,assumption,(r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))), introduced(assumption)).
% 0.54/0.70 tff(273,assumption,(r(s(s(s(s(s(s(z)))))), z)), introduced(assumption)).
% 0.54/0.70 tff(274,assumption,(r(s(s(s(s(z)))), z)), introduced(assumption)).
% 0.54/0.70 tff(275,plain,
% 0.54/0.70 (((~![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)))))))),
% 0.54/0.70 inference(rewrite,[status(thm)],[])).
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% 0.54/0.70 inference(quant_inst,[status(thm)],[])).
% 0.54/0.70 tff(277,plain,
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% 0.54/0.70 inference(modus_ponens,[status(thm)],[276, 275])).
% 0.54/0.70 tff(278,plain,
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% 0.54/0.70 inference(unit_resolution,[status(thm)],[277, 14, 272, 274, 273])).
% 0.54/0.70 tff(279,plain,((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.70 tff(280,plain,
% 0.54/0.70 (~r(s(s(s(s(z)))), z)),
% 0.54/0.70 inference(unit_resolution,[status(thm)],[279, 272, 273])).
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% 0.54/0.70 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(z)))) = z))),
% 0.54/0.70 inference(quant_inst,[status(thm)],[])).
% 0.54/0.70 tff(282,plain,
% 0.54/0.70 (~(s(s(s(s(z)))) = z)),
% 0.54/0.70 inference(unit_resolution,[status(thm)],[281, 33])).
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% 0.54/0.70 (((~![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))),
% 0.54/0.70 inference(rewrite,[status(thm)],[])).
% 0.54/0.70 tff(284,plain,
% 0.54/0.70 ((~![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))),
% 0.54/0.70 inference(quant_inst,[status(thm)],[])).
% 0.54/0.70 tff(285,plain,
% 0.54/0.70 ((~![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)),
% 0.54/0.70 inference(modus_ponens,[status(thm)],[284, 283])).
% 0.54/0.70 tff(286,plain,
% 0.54/0.70 (b(s(s(s(s(z)))), z) | r(s(s(s(s(z)))), z)),
% 0.54/0.70 inference(unit_resolution,[status(thm)],[285, 46, 282])).
% 0.54/0.70 tff(287,plain,
% 0.54/0.70 (b(s(s(s(s(z)))), z)),
% 0.54/0.70 inference(unit_resolution,[status(thm)],[286, 280])).
% 0.54/0.70 tff(288,assumption,(r(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
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% 0.54/0.70 inference(rewrite,[status(thm)],[])).
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% 0.54/0.70 inference(quant_inst,[status(thm)],[])).
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% 0.54/0.71 inference(modus_ponens,[status(thm)],[290, 289])).
% 0.54/0.71 tff(292,plain,
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% 0.54/0.71 inference(unit_resolution,[status(thm)],[291, 14, 272, 160, 288])).
% 0.54/0.71 tff(293,plain,((~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)))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.71 tff(294,plain,
% 0.54/0.71 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 0.54/0.71 inference(unit_resolution,[status(thm)],[293, 272, 160])).
% 0.54/0.71 tff(295,plain,
% 0.54/0.71 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(s(z)))))),
% 0.54/0.71 inference(commutativity,[status(thm)],[])).
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% 0.54/0.71 ((s(s(s(z))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(z))))),
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% 0.54/0.71 inference(monotonicity,[status(thm)],[296])).
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% 0.54/0.71 tff(299,plain,
% 0.54/0.71 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(z)))))),
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% 0.54/0.71 (inj_0(s(s(z))) = inj_0(s(s(s(s(z)))))),
% 0.54/0.71 inference(monotonicity,[status(thm)],[300])).
% 0.54/0.71 tff(302,plain,
% 0.54/0.71 (s(z) = s(s(s(s(z))))),
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% 0.54/0.71 tff(303,plain,
% 0.54/0.71 ($false),
% 0.54/0.71 inference(unit_resolution,[status(thm)],[149, 302])).
% 0.54/0.71 tff(304,plain,(~(s(s(s(z))) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.71 tff(305,plain,
% 0.54/0.71 (~(s(s(s(s(z)))) = s(s(s(z))))),
% 0.54/0.71 inference(modus_ponens,[status(thm)],[304, 297])).
% 0.54/0.71 tff(306,plain,
% 0.54/0.71 (((~![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)))))),
% 0.54/0.71 inference(rewrite,[status(thm)],[])).
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% 0.54/0.71 ((~![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)))))),
% 0.54/0.71 inference(quant_inst,[status(thm)],[])).
% 0.54/0.71 tff(308,plain,
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% 0.54/0.71 inference(modus_ponens,[status(thm)],[307, 306])).
% 0.54/0.71 tff(309,plain,
% 0.54/0.71 ((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))))),
% 0.54/0.71 inference(unit_resolution,[status(thm)],[308, 46])).
% 0.54/0.71 tff(310,plain,
% 0.54/0.71 (b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z))))),
% 0.54/0.71 inference(unit_resolution,[status(thm)],[309, 305])).
% 0.54/0.71 tff(311,plain,
% 0.54/0.71 (b(s(s(s(s(z)))), s(s(s(z))))),
% 0.54/0.71 inference(unit_resolution,[status(thm)],[310, 294])).
% 0.54/0.71 tff(312,plain,
% 0.54/0.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(z))))))),
% 0.54/0.71 inference(rewrite,[status(thm)],[])).
% 0.54/0.71 tff(313,plain,
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% 0.54/0.71 inference(monotonicity,[status(thm)],[313])).
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% 0.54/0.71 inference(modus_ponens,[status(thm)],[320, 319])).
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% 0.54/0.71 inference(unit_resolution,[status(thm)],[321, 46])).
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% 0.54/0.71 inference(modus_ponens,[status(thm)],[205, 327])).
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% 0.54/0.71 inference(monotonicity,[status(thm)],[359])).
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% 0.54/0.71 inference(transitivity,[status(thm)],[360, 358])).
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% 0.54/0.71 inference(quant_inst,[status(thm)],[])).
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% 0.54/0.71 inference(modus_ponens,[status(thm)],[362, 361])).
% 0.54/0.71 tff(364,plain,
% 0.54/0.71 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 0.54/0.71 inference(unit_resolution,[status(thm)],[363, 14, 329, 272])).
% 0.54/0.71 tff(365,plain,
% 0.54/0.71 (b(s(s(s(s(s(s(z)))))), s(z))),
% 0.54/0.71 inference(unit_resolution,[status(thm)],[210, 364])).
% 0.54/0.71 tff(366,plain,
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% 0.54/0.71 inference(rewrite,[status(thm)],[])).
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% 0.54/0.72 inference(quant_inst,[status(thm)],[])).
% 0.54/0.72 tff(368,plain,
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% 0.54/0.72 inference(modus_ponens,[status(thm)],[367, 366])).
% 0.54/0.72 tff(369,plain,
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% 0.54/0.72 inference(unit_resolution,[status(thm)],[368, 14, 329, 339])).
% 0.54/0.72 tff(370,plain,
% 0.54/0.72 (b(z, s(z))),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[51, 369])).
% 0.54/0.72 tff(371,plain,
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% 0.54/0.72 inference(rewrite,[status(thm)],[])).
% 0.54/0.72 tff(372,plain,
% 0.54/0.72 (((~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 0.54/0.72 inference(rewrite,[status(thm)],[])).
% 0.54/0.72 tff(373,plain,
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% 0.54/0.72 inference(monotonicity,[status(thm)],[372])).
% 0.54/0.72 tff(374,plain,
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% 0.54/0.72 inference(transitivity,[status(thm)],[373, 371])).
% 0.54/0.72 tff(375,plain,
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% 0.54/0.72 inference(quant_inst,[status(thm)],[])).
% 0.54/0.72 tff(376,plain,
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% 0.54/0.72 inference(modus_ponens,[status(thm)],[375, 374])).
% 0.54/0.72 tff(377,plain,
% 0.54/0.72 (~r(s(z), z)),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[376, 14, 329, 339])).
% 0.54/0.72 tff(378,plain,
% 0.54/0.72 (b(s(z), z)),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[187, 377])).
% 0.54/0.72 tff(379,plain,
% 0.54/0.72 ($false),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[261, 378, 370, 365, 357, 338])).
% 0.54/0.72 tff(380,plain,((~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.72 tff(381,plain,
% 0.54/0.72 (~r(z, s(s(s(s(z)))))),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[380, 324, 272])).
% 0.54/0.72 tff(382,assumption,(z = s(s(s(s(z))))), introduced(assumption)).
% 0.54/0.72 tff(383,plain,
% 0.54/0.72 (s(s(s(s(z)))) = z),
% 0.54/0.72 inference(symmetry,[status(thm)],[382])).
% 0.54/0.72 tff(384,plain,
% 0.54/0.72 ($false),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[282, 383])).
% 0.54/0.72 tff(385,plain,(~(z = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.72 tff(386,plain,
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% 0.54/0.72 inference(rewrite,[status(thm)],[])).
% 0.54/0.72 tff(387,plain,
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% 0.54/0.72 inference(quant_inst,[status(thm)],[])).
% 0.54/0.72 tff(388,plain,
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% 0.54/0.72 inference(modus_ponens,[status(thm)],[387, 386])).
% 0.54/0.72 tff(389,plain,
% 0.54/0.72 (b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z)))))),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[388, 46, 385])).
% 0.54/0.72 tff(390,plain,
% 0.54/0.72 (b(z, s(s(s(s(z)))))),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[389, 381])).
% 0.54/0.72 tff(391,assumption,(r(s(s(s(z))), s(s(s(s(z)))))), introduced(assumption)).
% 0.54/0.72 tff(392,plain,
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% 0.54/0.72 inference(rewrite,[status(thm)],[])).
% 0.54/0.72 tff(393,plain,
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% 0.54/0.72 inference(quant_inst,[status(thm)],[])).
% 0.54/0.72 tff(394,plain,
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% 0.54/0.72 inference(modus_ponens,[status(thm)],[393, 392])).
% 0.54/0.72 tff(395,plain,
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% 0.54/0.72 inference(unit_resolution,[status(thm)],[394, 14, 272, 391, 160])).
% 0.54/0.72 tff(396,plain,((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.72 tff(397,plain,
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% 0.54/0.72 inference(unit_resolution,[status(thm)],[396, 272, 160])).
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% 0.54/0.72 inference(rewrite,[status(thm)],[])).
% 0.54/0.72 tff(399,plain,
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% 0.54/0.72 inference(quant_inst,[status(thm)],[])).
% 0.54/0.72 tff(400,plain,
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% 0.54/0.72 inference(modus_ponens,[status(thm)],[399, 398])).
% 0.54/0.72 tff(401,plain,
% 0.54/0.72 ((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)))))),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[400, 46])).
% 0.54/0.72 tff(402,plain,
% 0.54/0.72 (b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z)))))),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[401, 304])).
% 0.54/0.72 tff(403,plain,
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% 0.54/0.72 inference(unit_resolution,[status(thm)],[402, 397])).
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% 0.54/0.72 inference(rewrite,[status(thm)],[])).
% 0.54/0.72 tff(405,plain,
% 0.54/0.72 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))))),
% 0.54/0.72 inference(rewrite,[status(thm)],[])).
% 0.54/0.72 tff(406,plain,
% 0.54/0.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z)))))))),
% 0.54/0.72 inference(monotonicity,[status(thm)],[405])).
% 0.54/0.72 tff(407,plain,
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% 0.54/0.72 inference(transitivity,[status(thm)],[406, 404])).
% 0.54/0.72 tff(408,plain,
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% 0.54/0.72 inference(quant_inst,[status(thm)],[])).
% 0.54/0.72 tff(409,plain,
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% 0.54/0.72 inference(modus_ponens,[status(thm)],[408, 407])).
% 0.54/0.72 tff(410,plain,
% 0.54/0.72 ($false),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[409, 118, 403, 311, 287, 390, 271])).
% 0.54/0.72 tff(411,plain,((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.72 tff(412,plain,
% 0.54/0.72 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[411, 270, 234, 253, 160])).
% 0.54/0.72 tff(413,assumption,(~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))), introduced(assumption)).
% 0.54/0.72 tff(414,assumption,(s(s(s(s(s(s(z)))))) = s(s(s(s(z))))), introduced(assumption)).
% 0.54/0.72 tff(415,plain,
% 0.54/0.72 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(s(s(s(z)))))),
% 0.54/0.72 inference(monotonicity,[status(thm)],[414])).
% 0.54/0.72 tff(416,plain,
% 0.54/0.72 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(s(s(z)))))))),
% 0.54/0.72 inference(symmetry,[status(thm)],[415])).
% 0.54/0.72 tff(417,plain,
% 0.54/0.72 (s(s(s(z))) = s(s(s(s(s(z)))))),
% 0.54/0.72 inference(transitivity,[status(thm)],[146, 416, 131])).
% 0.54/0.72 tff(418,plain,
% 0.54/0.72 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(s(z))))))),
% 0.54/0.72 inference(monotonicity,[status(thm)],[417])).
% 0.54/0.72 tff(419,plain,
% 0.54/0.72 (s(s(z)) = s(s(s(s(z))))),
% 0.54/0.72 inference(transitivity,[status(thm)],[95, 418, 129])).
% 0.54/0.72 tff(420,plain,
% 0.54/0.72 (inj_0(s(s(z))) = inj_0(s(s(s(s(z)))))),
% 0.54/0.72 inference(monotonicity,[status(thm)],[419])).
% 0.54/0.72 tff(421,plain,
% 0.54/0.72 (s(z) = s(s(s(z)))),
% 0.54/0.72 inference(transitivity,[status(thm)],[139, 420, 145])).
% 0.54/0.72 tff(422,plain,
% 0.54/0.72 (inj_0(s(z)) = inj_0(s(s(s(z))))),
% 0.54/0.72 inference(monotonicity,[status(thm)],[421])).
% 0.54/0.72 tff(423,plain,
% 0.54/0.72 (inj_0(s(s(s(z)))) = inj_0(s(z))),
% 0.54/0.72 inference(symmetry,[status(thm)],[422])).
% 0.54/0.72 tff(424,plain,
% 0.54/0.72 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(s(z))))),
% 0.54/0.72 inference(symmetry,[status(thm)],[418])).
% 0.54/0.72 tff(425,plain,
% 0.54/0.72 (s(s(s(s(z)))) = inj_0(s(s(s(s(s(z))))))),
% 0.54/0.72 inference(symmetry,[status(thm)],[129])).
% 0.54/0.72 tff(426,plain,
% 0.54/0.72 (s(s(s(s(z)))) = z),
% 0.54/0.72 inference(transitivity,[status(thm)],[425, 424, 423, 90])).
% 0.54/0.72 tff(427,plain,
% 0.54/0.72 ($false),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[282, 426])).
% 0.54/0.72 tff(428,plain,(~(s(s(s(s(s(s(z)))))) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.72 tff(429,assumption,(~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))), introduced(assumption)).
% 0.54/0.72 tff(430,plain,
% 0.54/0.72 (((~![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))))))),
% 0.54/0.72 inference(rewrite,[status(thm)],[])).
% 0.54/0.72 tff(431,plain,
% 0.54/0.72 ((~![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))))))),
% 0.54/0.72 inference(quant_inst,[status(thm)],[])).
% 0.54/0.72 tff(432,plain,
% 0.54/0.72 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 0.54/0.72 inference(modus_ponens,[status(thm)],[431, 430])).
% 0.54/0.72 tff(433,plain,
% 0.54/0.72 ($false),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[432, 46, 429, 428, 413])).
% 0.54/0.72 tff(434,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,[]))).
% 0.54/0.72 tff(435,plain,
% 0.54/0.72 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[434, 412])).
% 0.54/0.72 tff(436,assumption,(b(z, s(s(s(s(z)))))), introduced(assumption)).
% 0.54/0.72 tff(437,assumption,(b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))), introduced(assumption)).
% 0.54/0.72 tff(438,plain,
% 0.54/0.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 0.54/0.72 inference(rewrite,[status(thm)],[])).
% 0.54/0.72 tff(439,plain,
% 0.54/0.72 (((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(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(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 0.54/0.72 inference(rewrite,[status(thm)],[])).
% 0.54/0.72 tff(440,plain,
% 0.54/0.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z))))))))))),
% 0.54/0.72 inference(monotonicity,[status(thm)],[439])).
% 0.54/0.72 tff(441,plain,
% 0.54/0.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 0.54/0.72 inference(transitivity,[status(thm)],[440, 438])).
% 0.54/0.72 tff(442,plain,
% 0.54/0.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), z)))),
% 0.54/0.72 inference(quant_inst,[status(thm)],[])).
% 0.54/0.72 tff(443,plain,
% 0.54/0.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z))))))))),
% 0.54/0.72 inference(modus_ponens,[status(thm)],[442, 441])).
% 0.54/0.72 tff(444,plain,
% 0.54/0.72 ($false),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[443, 118, 234, 437, 237, 436, 235])).
% 0.54/0.72 tff(445,plain,((~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.73 tff(446,plain,
% 0.54/0.73 (~b(z, s(s(s(s(z)))))),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[445, 435, 234, 233, 235])).
% 0.54/0.73 tff(447,plain,
% 0.54/0.73 (r(z, s(s(s(s(z)))))),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[389, 446])).
% 0.54/0.73 tff(448,plain,
% 0.54/0.73 ($false),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[368, 14, 329, 4, 339])).
% 0.54/0.73 tff(449,plain,((~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.73 tff(450,plain,
% 0.54/0.73 (~r(s(z), s(s(s(s(z)))))),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[449, 447, 263])).
% 0.54/0.73 tff(451,plain,
% 0.54/0.73 (b(s(z), s(s(s(s(z)))))),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[323, 450])).
% 0.54/0.73 tff(452,plain,
% 0.54/0.73 (((~![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(z), s(s(s(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(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(453,plain,
% 0.54/0.73 ((~![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(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 0.54/0.73 inference(quant_inst,[status(thm)],[])).
% 0.54/0.73 tff(454,plain,
% 0.54/0.73 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z))))))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[453, 452])).
% 0.54/0.73 tff(455,plain,
% 0.54/0.73 ($false),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[454, 14, 329, 176, 288])).
% 0.54/0.73 tff(456,plain,((~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.73 tff(457,plain,
% 0.54/0.73 (~r(s(z), s(s(s(s(z)))))),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[456, 288, 176])).
% 0.54/0.73 tff(458,plain,
% 0.54/0.73 (b(s(z), s(s(s(s(z)))))),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[323, 457])).
% 0.54/0.73 tff(459,assumption,(b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 0.54/0.73 tff(460,assumption,(b(s(z), s(s(s(s(z)))))), introduced(assumption)).
% 0.54/0.73 tff(461,plain,
% 0.54/0.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(462,plain,
% 0.54/0.73 (((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(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(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(463,plain,
% 0.54/0.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))))),
% 0.54/0.73 inference(monotonicity,[status(thm)],[462])).
% 0.54/0.73 tff(464,plain,
% 0.54/0.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 0.54/0.73 inference(transitivity,[status(thm)],[463, 461])).
% 0.54/0.73 tff(465,plain,
% 0.54/0.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 0.54/0.73 inference(quant_inst,[status(thm)],[])).
% 0.54/0.73 tff(466,plain,
% 0.54/0.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[465, 464])).
% 0.54/0.73 tff(467,plain,
% 0.54/0.73 ($false),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[466, 118, 460, 437, 459, 237, 236])).
% 0.54/0.73 tff(468,plain,((~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(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.73 tff(469,plain,
% 0.54/0.73 (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[468, 458, 211, 233, 437])).
% 0.54/0.73 tff(470,assumption,(s(s(s(s(z)))) = s(s(s(s(s(s(z))))))), introduced(assumption)).
% 0.54/0.73 tff(471,plain,
% 0.54/0.73 (s(s(s(s(s(s(z)))))) = s(s(s(s(z))))),
% 0.54/0.73 inference(symmetry,[status(thm)],[470])).
% 0.54/0.73 tff(472,plain,
% 0.54/0.73 ($false),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[428, 471])).
% 0.54/0.73 tff(473,plain,(~(s(s(s(s(z)))) = s(s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.73 tff(474,assumption,(~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 0.54/0.73 tff(475,assumption,(~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 0.54/0.73 tff(476,plain,
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% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(477,plain,
% 0.54/0.73 ((~![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))))))))),
% 0.54/0.73 inference(quant_inst,[status(thm)],[])).
% 0.54/0.73 tff(478,plain,
% 0.54/0.73 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[477, 476])).
% 0.54/0.73 tff(479,plain,
% 0.54/0.73 ($false),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[478, 46, 475, 474, 473])).
% 0.54/0.73 tff(480,plain,(r(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)))))))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.73 tff(481,plain,
% 0.54/0.73 (r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[480, 469])).
% 0.54/0.73 tff(482,plain,
% 0.54/0.73 (((~![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(z)))), s(s(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(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(483,plain,
% 0.54/0.73 (((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(484,plain,
% 0.54/0.73 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(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(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))))),
% 0.54/0.73 inference(monotonicity,[status(thm)],[483])).
% 0.54/0.73 tff(485,plain,
% 0.54/0.73 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(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(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 0.54/0.73 inference(transitivity,[status(thm)],[484, 482])).
% 0.54/0.73 tff(486,plain,
% 0.54/0.73 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 0.54/0.73 inference(quant_inst,[status(thm)],[])).
% 0.54/0.73 tff(487,plain,
% 0.54/0.73 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[486, 485])).
% 0.54/0.73 tff(488,plain,
% 0.54/0.73 ($false),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[487, 14, 160, 288, 481])).
% 0.54/0.73 tff(489,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.73 tff(490,plain,
% 0.54/0.73 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[489, 435, 160, 176])).
% 0.54/0.73 tff(491,plain,
% 0.54/0.73 (b(s(s(s(s(z)))), s(s(s(z))))),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[310, 490])).
% 0.54/0.73 tff(492,plain,
% 0.54/0.73 ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[317, 118, 234, 491, 270])).
% 0.54/0.73 tff(493,plain,
% 0.54/0.73 (~b(s(s(s(s(z)))), z)),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[492, 451])).
% 0.54/0.73 tff(494,plain,
% 0.54/0.73 (r(s(s(s(s(z)))), z)),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[286, 493])).
% 0.54/0.73 tff(495,assumption,(r(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 0.54/0.73 tff(496,plain,
% 0.54/0.73 (((~![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(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(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(497,plain,
% 0.54/0.73 (((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(498,plain,
% 0.54/0.73 (((~![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(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z))))),
% 0.54/0.73 inference(monotonicity,[status(thm)],[497])).
% 0.54/0.73 tff(499,plain,
% 0.54/0.73 (((~![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(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)))),
% 0.54/0.73 inference(transitivity,[status(thm)],[498, 496])).
% 0.54/0.73 tff(500,plain,
% 0.54/0.73 ((~![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)))),
% 0.54/0.73 inference(quant_inst,[status(thm)],[])).
% 0.54/0.73 tff(501,plain,
% 0.54/0.73 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[500, 499])).
% 0.54/0.73 tff(502,plain,
% 0.54/0.73 ($false),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[501, 14, 495, 4, 274])).
% 0.54/0.73 tff(503,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.73 tff(504,plain,
% 0.54/0.73 (~r(s(s(s(s(z)))), s(z))),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[503, 494, 263])).
% 0.54/0.73 tff(505,plain,
% 0.54/0.73 ((s(s(s(s(z)))) = s(z)) <=> (s(z) = s(s(s(s(z)))))),
% 0.54/0.73 inference(commutativity,[status(thm)],[])).
% 0.54/0.73 tff(506,plain,
% 0.54/0.73 ((s(z) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(z))),
% 0.54/0.73 inference(symmetry,[status(thm)],[505])).
% 0.54/0.73 tff(507,plain,
% 0.54/0.73 ((~(s(z) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(z)))),
% 0.54/0.73 inference(monotonicity,[status(thm)],[506])).
% 0.54/0.73 tff(508,plain,
% 0.54/0.73 (~(s(s(s(s(z)))) = s(z))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[149, 507])).
% 0.54/0.73 tff(509,plain,
% 0.54/0.73 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z)))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(510,plain,
% 0.54/0.73 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z)))),
% 0.54/0.73 inference(quant_inst,[status(thm)],[])).
% 0.54/0.73 tff(511,plain,
% 0.54/0.73 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[510, 509])).
% 0.54/0.73 tff(512,plain,
% 0.54/0.73 ((s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z))),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[511, 46])).
% 0.54/0.73 tff(513,plain,
% 0.54/0.73 (b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z))),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[512, 508])).
% 0.54/0.73 tff(514,plain,
% 0.54/0.73 (b(s(s(s(s(z)))), s(z))),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[513, 504])).
% 0.54/0.73 tff(515,plain,
% 0.54/0.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(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(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(516,plain,
% 0.54/0.73 (((~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(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(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(517,plain,
% 0.54/0.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(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(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(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(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))))),
% 0.54/0.73 inference(monotonicity,[status(thm)],[516])).
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% 0.54/0.74 tff(562,plain,
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% 0.54/0.74 tff(563,plain,
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% 0.54/0.74 inference(modus_ponens,[status(thm)],[568, 567])).
% 0.54/0.74 tff(570,plain,
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% 0.54/0.74 tff(571,plain,((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.74 tff(572,plain,
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% 0.54/0.74 inference(unit_resolution,[status(thm)],[571, 524, 175])).
% 0.54/0.74 tff(573,plain,
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% 0.54/0.74 inference(commutativity,[status(thm)],[])).
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% 0.54/0.74 inference(symmetry,[status(thm)],[573])).
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% 0.54/0.74 inference(monotonicity,[status(thm)],[574])).
% 0.54/0.74 tff(576,plain,
% 0.54/0.74 (~(s(s(s(z))) = s(s(s(s(s(s(z)))))))),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[151, 575])).
% 0.54/0.74 tff(577,plain,
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% 0.54/0.74 tff(578,plain,
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% 0.54/0.74 inference(quant_inst,[status(thm)],[])).
% 0.54/0.74 tff(579,plain,
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% 0.54/0.74 inference(modus_ponens,[status(thm)],[578, 577])).
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% 0.54/0.74 inference(unit_resolution,[status(thm)],[579, 46])).
% 0.54/0.74 tff(581,plain,
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% 0.54/0.74 inference(unit_resolution,[status(thm)],[580, 576])).
% 0.54/0.74 tff(582,plain,
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% 0.54/0.74 inference(unit_resolution,[status(thm)],[581, 572])).
% 0.54/0.74 tff(583,plain,
% 0.54/0.74 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[456, 563, 176])).
% 0.54/0.74 tff(584,plain,
% 0.54/0.74 (b(s(s(s(s(z)))), s(s(s(z))))),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[310, 583])).
% 0.54/0.74 tff(585,plain,
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% 0.54/0.74 inference(unit_resolution,[status(thm)],[411, 272, 234, 528, 160])).
% 0.54/0.74 tff(586,plain,
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% 0.54/0.74 inference(unit_resolution,[status(thm)],[252, 585])).
% 0.54/0.74 tff(587,assumption,(b(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 0.54/0.74 tff(588,plain,
% 0.54/0.74 (~b(s(s(s(s(z)))), z)),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[409, 118, 403, 587, 530, 528])).
% 0.54/0.74 tff(589,plain,
% 0.54/0.74 (r(s(s(s(s(z)))), z)),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[286, 588])).
% 0.54/0.74 tff(590,plain,
% 0.54/0.74 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[551, 589, 3])).
% 0.54/0.74 tff(591,plain,
% 0.54/0.74 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[480, 590])).
% 0.54/0.74 tff(592,plain,
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% 0.54/0.74 inference(unit_resolution,[status(thm)],[279, 274, 272])).
% 0.54/0.74 tff(593,plain,
% 0.54/0.74 (b(s(s(s(s(s(s(z)))))), z)),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[252, 592])).
% 0.54/0.74 tff(594,assumption,(b(s(s(s(z))), s(s(s(s(z)))))), introduced(assumption)).
% 0.54/0.74 tff(595,plain,
% 0.54/0.74 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[551, 274, 3])).
% 0.54/0.74 tff(596,plain,
% 0.54/0.74 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[480, 595])).
% 0.54/0.74 tff(597,plain,
% 0.54/0.74 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[169, 161, 3])).
% 0.54/0.74 tff(598,plain,
% 0.54/0.74 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[156, 597])).
% 0.54/0.74 tff(599,plain,
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% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(600,plain,
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% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(601,plain,
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% 0.54/0.74 inference(monotonicity,[status(thm)],[600])).
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% 0.54/0.74 inference(transitivity,[status(thm)],[601, 599])).
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% 0.54/0.74 inference(modus_ponens,[status(thm)],[603, 602])).
% 0.54/0.74 tff(605,plain,
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% 0.54/0.74 tff(606,plain,((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.74 tff(607,plain,
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% 0.54/0.74 inference(unit_resolution,[status(thm)],[606, 161, 274])).
% 0.54/0.74 tff(608,plain,
% 0.54/0.74 (b(s(s(s(s(z)))), s(s(s(z))))),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[310, 607])).
% 0.54/0.74 tff(609,assumption,(b(s(s(s(z))), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 0.54/0.74 tff(610,plain,
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% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(611,plain,
% 0.54/0.75 (((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(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(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(612,plain,
% 0.54/0.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))))),
% 0.54/0.75 inference(monotonicity,[status(thm)],[611])).
% 0.54/0.75 tff(613,plain,
% 0.54/0.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 0.54/0.75 inference(transitivity,[status(thm)],[612, 610])).
% 0.54/0.75 tff(614,plain,
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% 0.54/0.75 inference(quant_inst,[status(thm)],[])).
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% 0.54/0.75 inference(modus_ponens,[status(thm)],[614, 613])).
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% 0.54/0.75 inference(unit_resolution,[status(thm)],[615, 118, 594, 587, 73, 609, 459])).
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% 0.54/0.75 tff(618,plain,
% 0.54/0.75 (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[617, 608, 594, 598, 596])).
% 0.54/0.75 tff(619,plain,
% 0.54/0.75 (r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[581, 618])).
% 0.54/0.75 tff(620,plain,
% 0.54/0.75 ($false),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[59, 14, 3, 619, 161])).
% 0.54/0.75 tff(621,plain,((~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.75 tff(622,plain,
% 0.54/0.75 (~r(z, s(s(s(z))))),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[621, 274, 594, 3])).
% 0.54/0.75 tff(623,plain,
% 0.54/0.75 (b(z, s(s(s(z))))),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[71, 622])).
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% 0.54/0.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(625,plain,
% 0.54/0.75 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z))) <=> ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(626,plain,
% 0.54/0.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z)))))))),
% 0.54/0.75 inference(monotonicity,[status(thm)],[625])).
% 0.54/0.75 tff(627,plain,
% 0.54/0.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 0.54/0.75 inference(transitivity,[status(thm)],[626, 624])).
% 0.54/0.75 tff(628,plain,
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% 0.54/0.75 inference(quant_inst,[status(thm)],[])).
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% 0.54/0.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z)))))),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[628, 627])).
% 0.54/0.75 tff(630,plain,
% 0.54/0.75 ($false),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[629, 118, 594, 73, 1, 436, 271])).
% 0.54/0.75 tff(631,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)))))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.75 tff(632,plain,
% 0.54/0.75 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[631, 593, 594, 436, 623])).
% 0.54/0.75 tff(633,plain,
% 0.54/0.75 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[156, 632])).
% 0.54/0.75 tff(634,plain,
% 0.54/0.75 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[293, 633, 272])).
% 0.54/0.75 tff(635,plain,
% 0.54/0.75 (b(s(s(s(s(z)))), s(s(s(z))))),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[310, 634])).
% 0.54/0.75 tff(636,plain,
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% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(637,plain,
% 0.54/0.75 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z))) <=> ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(638,plain,
% 0.54/0.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z)))))))),
% 0.54/0.75 inference(monotonicity,[status(thm)],[637])).
% 0.54/0.75 tff(639,plain,
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% 0.54/0.75 inference(transitivity,[status(thm)],[638, 636])).
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% 0.54/0.75 (~b(s(s(s(z))), z)),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[641, 118, 594, 635, 436, 623])).
% 0.54/0.75 tff(643,assumption,(~r(s(s(s(z))), z)), introduced(assumption)).
% 0.54/0.75 tff(644,assumption,(~b(s(s(s(z))), z)), introduced(assumption)).
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% 0.54/0.75 (((~![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))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
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% 0.54/0.75 ((~![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))),
% 0.54/0.75 inference(quant_inst,[status(thm)],[])).
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% 0.54/0.75 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = z) | b(s(s(s(z))), z) | r(s(s(s(z))), z)),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[646, 645])).
% 0.54/0.75 tff(648,plain,
% 0.54/0.75 ($false),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[647, 46, 65, 644, 643])).
% 0.54/0.75 tff(649,plain,(r(s(s(s(z))), z) | b(s(s(s(z))), z)), inference(lemma,lemma(discharge,[]))).
% 0.54/0.75 tff(650,plain,
% 0.54/0.75 (r(s(s(s(z))), z)),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[649, 642])).
% 0.54/0.75 tff(651,plain,
% 0.54/0.75 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[571, 650, 3])).
% 0.54/0.75 tff(652,plain,
% 0.54/0.75 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[581, 651])).
% 0.54/0.75 tff(653,plain,
% 0.54/0.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(z))))))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(654,plain,
% 0.54/0.75 (((~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z)))) <=> ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(z))))))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(655,plain,
% 0.54/0.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(z)))))))),
% 0.54/0.75 inference(monotonicity,[status(thm)],[654])).
% 0.54/0.75 tff(656,plain,
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% 0.54/0.75 inference(modus_ponens,[status(thm)],[665, 664])).
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% 0.54/0.75 inference(unit_resolution,[status(thm)],[666, 46])).
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% 0.54/0.75 (b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z))))),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[667, 663])).
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% 0.54/0.75 inference(unit_resolution,[status(thm)],[668, 659])).
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% 0.54/0.75 inference(unit_resolution,[status(thm)],[182, 669, 650])).
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% 0.54/0.75 inference(unit_resolution,[status(thm)],[187, 670])).
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% 0.54/0.76 tff(674,plain,
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% 0.54/0.77 inference(unit_resolution,[status(thm)],[752, 46])).
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% 0.54/0.77 inference(monotonicity,[status(thm)],[793])).
% 0.54/0.77 tff(795,plain,
% 0.54/0.77 (s(s(s(z))) = s(s(s(s(s(z)))))),
% 0.54/0.77 inference(transitivity,[status(thm)],[146, 794, 129, 793])).
% 0.54/0.77 tff(796,assumption,(s(s(s(z))) = s(s(s(s(s(z)))))), introduced(assumption)).
% 0.54/0.77 tff(797,plain,
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% 0.54/0.77 inference(symmetry,[status(thm)],[796])).
% 0.54/0.77 tff(798,plain,
% 0.54/0.77 (s(s(s(s(s(s(z)))))) = s(s(s(s(z))))),
% 0.54/0.77 inference(monotonicity,[status(thm)],[797])).
% 0.54/0.77 tff(799,plain,
% 0.54/0.77 ($false),
% 0.54/0.77 inference(unit_resolution,[status(thm)],[428, 798])).
% 0.54/0.77 tff(800,plain,(~(s(s(s(z))) = s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.77 tff(801,plain,
% 0.54/0.77 ($false),
% 0.54/0.77 inference(unit_resolution,[status(thm)],[800, 795])).
% 0.54/0.77 tff(802,plain,(~(s(s(s(s(z)))) = s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.77 tff(803,plain,
% 0.54/0.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 0.54/0.77 inference(rewrite,[status(thm)],[])).
% 0.54/0.77 tff(804,plain,
% 0.54/0.77 (((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 0.54/0.77 inference(rewrite,[status(thm)],[])).
% 0.54/0.77 tff(805,plain,
% 0.54/0.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 0.54/0.77 inference(monotonicity,[status(thm)],[804])).
% 0.54/0.77 tff(806,plain,
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% 0.54/0.77 inference(transitivity,[status(thm)],[805, 803])).
% 0.54/0.77 tff(807,plain,
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% 0.54/0.77 inference(quant_inst,[status(thm)],[])).
% 0.54/0.77 tff(808,plain,
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% 0.54/0.77 inference(modus_ponens,[status(thm)],[807, 806])).
% 0.54/0.77 tff(809,plain,
% 0.54/0.77 ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))),
% 0.54/0.77 inference(unit_resolution,[status(thm)],[808, 118, 174, 721, 724])).
% 0.54/0.77 tff(810,plain,
% 0.54/0.77 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 0.54/0.77 inference(unit_resolution,[status(thm)],[809, 768])).
% 0.54/0.77 tff(811,plain,
% 0.54/0.77 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(s(s(z)))))) | b(s(s(s(s(z)))), s(s(s(s(s(z)))))) | r(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(s(s(z)))))) | b(s(s(s(s(z)))), s(s(s(s(s(z)))))) | r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 0.54/0.77 inference(rewrite,[status(thm)],[])).
% 0.54/0.77 tff(812,plain,
% 0.54/0.77 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(s(s(z)))))) | b(s(s(s(s(z)))), s(s(s(s(s(z)))))) | r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 0.54/0.77 inference(quant_inst,[status(thm)],[])).
% 0.54/0.77 tff(813,plain,
% 0.54/0.77 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(s(s(z)))))) | b(s(s(s(s(z)))), s(s(s(s(s(z)))))) | r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 0.54/0.77 inference(modus_ponens,[status(thm)],[812, 811])).
% 0.54/0.77 tff(814,plain,
% 0.54/0.77 ((s(s(s(s(z)))) = s(s(s(s(s(z)))))) | b(s(s(s(s(z)))), s(s(s(s(s(z)))))) | r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 0.54/0.77 inference(unit_resolution,[status(thm)],[813, 46])).
% 0.54/0.77 tff(815,plain,
% 0.54/0.77 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 0.54/0.77 inference(unit_resolution,[status(thm)],[814, 810, 802])).
% 0.54/0.77 tff(816,plain,
% 0.54/0.77 (((~![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(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(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(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 0.54/0.77 inference(rewrite,[status(thm)],[])).
% 0.54/0.77 tff(817,plain,
% 0.54/0.77 (((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 0.54/0.78 inference(rewrite,[status(thm)],[])).
% 0.54/0.78 tff(818,plain,
% 0.54/0.78 (((~![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(z))))))) | (~r(s(z), s(s(s(s(s(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), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 0.54/0.78 inference(monotonicity,[status(thm)],[817])).
% 0.54/0.78 tff(819,plain,
% 0.54/0.78 (((~![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(z))))))) | (~r(s(z), s(s(s(s(s(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), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 0.54/0.78 inference(transitivity,[status(thm)],[818, 816])).
% 0.54/0.78 tff(820,plain,
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% 0.54/0.78 inference(quant_inst,[status(thm)],[])).
% 0.54/0.78 tff(821,plain,
% 0.54/0.78 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 0.54/0.78 inference(modus_ponens,[status(thm)],[820, 819])).
% 0.54/0.78 tff(822,plain,
% 0.54/0.78 ($false),
% 0.54/0.78 inference(unit_resolution,[status(thm)],[821, 14, 329, 815, 792])).
% 0.54/0.78 tff(823,plain,((~b(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.78 tff(824,plain,
% 0.54/0.78 (~b(s(s(s(s(s(z))))), s(z))),
% 0.54/0.78 inference(unit_resolution,[status(thm)],[823, 174, 329, 721, 234, 236, 237])).
% 0.54/0.78 tff(825,plain,
% 0.54/0.78 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(z)) | b(s(s(s(s(s(z))))), s(z)) | r(s(s(s(s(s(z))))), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(z)) | b(s(s(s(s(s(z))))), s(z)) | r(s(s(s(s(s(z))))), s(z)))),
% 0.54/0.78 inference(rewrite,[status(thm)],[])).
% 0.54/0.78 tff(826,plain,
% 0.54/0.78 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(z)) | b(s(s(s(s(s(z))))), s(z)) | r(s(s(s(s(s(z))))), s(z)))),
% 0.54/0.78 inference(quant_inst,[status(thm)],[])).
% 0.54/0.78 tff(827,plain,
% 0.54/0.78 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(z)) | b(s(s(s(s(s(z))))), s(z)) | r(s(s(s(s(s(z))))), s(z))),
% 0.54/0.78 inference(modus_ponens,[status(thm)],[826, 825])).
% 0.54/0.78 tff(828,plain,
% 0.54/0.78 ((s(s(s(s(s(z))))) = s(z)) | b(s(s(s(s(s(z))))), s(z)) | r(s(s(s(s(s(z))))), s(z))),
% 0.54/0.78 inference(unit_resolution,[status(thm)],[827, 46])).
% 0.54/0.78 tff(829,plain,
% 0.54/0.78 (b(s(s(s(s(s(z))))), s(z)) | r(s(s(s(s(s(z))))), s(z))),
% 0.54/0.78 inference(unit_resolution,[status(thm)],[828, 785])).
% 0.54/0.78 tff(830,plain,
% 0.54/0.78 (r(s(s(s(s(s(z))))), s(z))),
% 0.54/0.78 inference(unit_resolution,[status(thm)],[829, 824])).
% 0.54/0.78 tff(831,plain,
% 0.54/0.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(z))))))),
% 0.54/0.78 inference(rewrite,[status(thm)],[])).
% 0.54/0.78 tff(832,plain,
% 0.54/0.78 (((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(z))))))),
% 0.54/0.78 inference(rewrite,[status(thm)],[])).
% 0.54/0.78 tff(833,plain,
% 0.54/0.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(z)))))))),
% 0.54/0.78 inference(monotonicity,[status(thm)],[832])).
% 0.54/0.78 tff(834,plain,
% 0.54/0.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(z))))))),
% 0.54/0.78 inference(transitivity,[status(thm)],[833, 831])).
% 0.54/0.78 tff(835,plain,
% 0.54/0.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))),
% 0.54/0.78 inference(quant_inst,[status(thm)],[])).
% 0.54/0.78 tff(836,plain,
% 0.54/0.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(z)))))),
% 0.54/0.78 inference(modus_ponens,[status(thm)],[835, 834])).
% 0.54/0.78 tff(837,plain,
% 0.54/0.78 (~b(s(s(s(z))), s(z))),
% 0.54/0.78 inference(unit_resolution,[status(thm)],[836, 118, 174, 609, 237, 271])).
% 0.54/0.78 tff(838,plain,
% 0.54/0.78 (r(s(s(s(z))), s(z))),
% 0.54/0.78 inference(unit_resolution,[status(thm)],[105, 837])).
% 0.54/0.78 tff(839,plain,
% 0.54/0.78 (((~![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(z))), s(s(s(s(s(z))))))) | (~r(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(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 0.54/0.78 inference(rewrite,[status(thm)],[])).
% 0.54/0.78 tff(840,plain,
% 0.54/0.78 (((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 0.54/0.78 inference(rewrite,[status(thm)],[])).
% 0.54/0.78 tff(841,plain,
% 0.54/0.78 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), 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(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z)))))),
% 0.54/0.78 inference(monotonicity,[status(thm)],[840])).
% 0.54/0.78 tff(842,plain,
% 0.54/0.78 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), 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(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 0.54/0.78 inference(transitivity,[status(thm)],[841, 839])).
% 0.54/0.78 tff(843,plain,
% 0.54/0.78 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 0.54/0.78 inference(quant_inst,[status(thm)],[])).
% 0.54/0.78 tff(844,plain,
% 0.54/0.78 ((~![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(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z)))),
% 0.54/0.78 inference(modus_ponens,[status(thm)],[843, 842])).
% 0.54/0.78 tff(845,plain,
% 0.54/0.78 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 0.54/0.78 inference(unit_resolution,[status(thm)],[844, 14, 838, 830])).
% 0.54/0.78 tff(846,plain,
% 0.54/0.78 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(s(z)))))) | b(s(s(s(z))), s(s(s(s(s(z)))))) | r(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(s(z)))))) | b(s(s(s(z))), s(s(s(s(s(z)))))) | r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 0.54/0.78 inference(rewrite,[status(thm)],[])).
% 0.54/0.78 tff(847,plain,
% 0.54/0.78 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(s(z)))))) | b(s(s(s(z))), s(s(s(s(s(z)))))) | r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 0.54/0.78 inference(quant_inst,[status(thm)],[])).
% 0.54/0.78 tff(848,plain,
% 0.54/0.78 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(s(z)))))) | b(s(s(s(z))), s(s(s(s(s(z)))))) | r(s(s(s(z))), s(s(s(s(s(z))))))),
% 0.54/0.78 inference(modus_ponens,[status(thm)],[847, 846])).
% 0.54/0.78 tff(849,plain,
% 0.54/0.78 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 0.54/0.78 inference(unit_resolution,[status(thm)],[848, 46, 800, 845])).
% 0.54/0.78 tff(850,plain,
% 0.54/0.78 (((~![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(z))))))) | (~r(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(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 0.54/0.78 inference(rewrite,[status(thm)],[])).
% 0.54/0.78 tff(851,plain,
% 0.54/0.78 (((~r(s(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(z)))))))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 0.54/0.78 inference(rewrite,[status(thm)],[])).
% 0.54/0.78 tff(852,plain,
% 0.54/0.78 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), 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(z))))))) | (~r(s(s(s(s(s(z))))), s(z)))))),
% 0.54/0.78 inference(monotonicity,[status(thm)],[851])).
% 0.54/0.78 tff(853,plain,
% 0.54/0.78 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), 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(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 0.54/0.78 inference(transitivity,[status(thm)],[852, 850])).
% 0.54/0.78 tff(854,plain,
% 0.54/0.78 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 0.54/0.78 inference(quant_inst,[status(thm)],[])).
% 0.54/0.78 tff(855,plain,
% 0.54/0.78 ((~![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(z))))))) | (~r(s(s(s(s(s(z))))), s(z)))),
% 0.54/0.78 inference(modus_ponens,[status(thm)],[854, 853])).
% 0.54/0.78 tff(856,plain,
% 0.54/0.78 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 0.54/0.78 inference(unit_resolution,[status(thm)],[855, 14, 495, 830])).
% 0.54/0.78 tff(857,plain,
% 0.54/0.78 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 0.54/0.78 inference(unit_resolution,[status(thm)],[814, 856, 802])).
% 0.54/0.78 tff(858,plain,
% 0.54/0.78 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(s(s(z))))))),
% 0.54/0.78 inference(commutativity,[status(thm)],[])).
% 0.54/0.78 tff(859,plain,
% 0.54/0.78 ((s(s(s(s(z)))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 0.54/0.78 inference(symmetry,[status(thm)],[858])).
% 0.54/0.78 tff(860,plain,
% 0.54/0.78 ((~(s(s(s(s(z)))) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(s(z))))) = s(s(s(s(z))))))),
% 0.54/0.78 inference(monotonicity,[status(thm)],[859])).
% 0.54/0.78 tff(861,plain,
% 0.54/0.78 (~(s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 0.54/0.78 inference(modus_ponens,[status(thm)],[802, 860])).
% 0.54/0.78 tff(862,plain,
% 0.54/0.78 (((~![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(z))))), s(z))) | (~r(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(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 0.54/0.78 inference(rewrite,[status(thm)],[])).
% 0.54/0.78 tff(863,plain,
% 0.54/0.78 ((~![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(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 0.54/0.78 inference(quant_inst,[status(thm)],[])).
% 0.54/0.78 tff(864,plain,
% 0.54/0.78 ((~![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(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 0.54/0.78 inference(modus_ponens,[status(thm)],[863, 862])).
% 0.54/0.78 tff(865,plain,
% 0.54/0.78 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 0.54/0.78 inference(unit_resolution,[status(thm)],[864, 14, 495, 830])).
% 0.54/0.78 tff(866,plain,
% 0.54/0.78 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(s(z))))) | b(s(s(s(s(s(z))))), s(s(s(s(z))))) | r(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(s(s(z))))) | b(s(s(s(s(s(z))))), s(s(s(s(z))))) | r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 0.54/0.78 inference(rewrite,[status(thm)],[])).
% 0.54/0.78 tff(867,plain,
% 0.54/0.78 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(s(z))))) | b(s(s(s(s(s(z))))), s(s(s(s(z))))) | r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 0.54/0.78 inference(quant_inst,[status(thm)],[])).
% 0.54/0.78 tff(868,plain,
% 0.54/0.78 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(s(s(z))))) | b(s(s(s(s(s(z))))), s(s(s(s(z))))) | r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 0.54/0.78 inference(modus_ponens,[status(thm)],[867, 866])).
% 0.54/0.78 tff(869,plain,
% 0.54/0.78 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) | b(s(s(s(s(s(z))))), s(s(s(s(z))))) | r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 0.54/0.78 inference(unit_resolution,[status(thm)],[868, 46])).
% 0.54/0.78 tff(870,plain,
% 0.54/0.78 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 0.54/0.78 inference(unit_resolution,[status(thm)],[869, 865, 861])).
% 0.54/0.78 tff(871,plain,
% 0.54/0.78 (((~![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(z)))), 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(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))))),
% 0.54/0.78 inference(rewrite,[status(thm)],[])).
% 0.54/0.78 tff(872,plain,
% 0.54/0.78 (((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))))),
% 0.54/0.78 inference(rewrite,[status(thm)],[])).
% 0.54/0.78 tff(873,plain,
% 0.54/0.78 (((~![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(z))), 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(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z)))))),
% 0.54/0.78 inference(monotonicity,[status(thm)],[872])).
% 0.54/0.78 tff(874,plain,
% 0.54/0.78 (((~![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(z))), 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(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))))),
% 0.54/0.78 inference(transitivity,[status(thm)],[873, 871])).
% 0.54/0.78 tff(875,plain,
% 0.54/0.78 ((~![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(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 0.54/0.78 inference(quant_inst,[status(thm)],[])).
% 0.54/0.78 tff(876,plain,
% 0.54/0.78 ((~![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(z)))), s(z))) | (~r(s(s(s(z))), s(z)))),
% 0.54/0.78 inference(modus_ponens,[status(thm)],[875, 874])).
% 0.54/0.78 tff(877,plain,
% 0.54/0.78 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 0.54/0.78 inference(unit_resolution,[status(thm)],[876, 14, 495, 838])).
% 0.54/0.78 tff(878,plain,
% 0.54/0.78 (b(s(s(s(z))), s(s(s(s(z)))))),
% 0.54/0.78 inference(unit_resolution,[status(thm)],[402, 877])).
% 0.54/0.78 tff(879,plain,
% 0.54/0.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 0.54/0.79 inference(rewrite,[status(thm)],[])).
% 0.54/0.79 tff(880,plain,
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% 0.54/0.79 inference(rewrite,[status(thm)],[])).
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% 0.54/0.79 inference(monotonicity,[status(thm)],[880])).
% 0.54/0.79 tff(882,plain,
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% 0.54/0.79 inference(transitivity,[status(thm)],[881, 879])).
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% 0.54/0.79 inference(quant_inst,[status(thm)],[])).
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% 0.54/0.79 inference(modus_ponens,[status(thm)],[883, 882])).
% 0.54/0.79 tff(885,plain,
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% 0.54/0.79 inference(unit_resolution,[status(thm)],[884, 118, 878, 587, 870, 857, 849])).
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% 0.54/0.79 tff(887,plain,
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% 0.54/0.79 inference(unit_resolution,[status(thm)],[886, 584, 720, 563, 715, 188, 211, 233, 582, 526])).
% 0.54/0.79 tff(888,plain,
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% 0.54/0.79 inference(unit_resolution,[status(thm)],[51, 887])).
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% 0.54/0.79 inference(unit_resolution,[status(thm)],[449, 888, 563])).
% 0.54/0.79 tff(890,plain,
% 0.54/0.79 (b(z, s(s(s(s(z)))))),
% 0.54/0.79 inference(unit_resolution,[status(thm)],[389, 889])).
% 0.54/0.79 tff(891,plain,
% 0.54/0.79 (((~![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(z), s(s(s(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(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 0.54/0.79 inference(rewrite,[status(thm)],[])).
% 0.54/0.79 tff(892,plain,
% 0.54/0.79 (((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 0.54/0.79 inference(rewrite,[status(thm)],[])).
% 0.54/0.79 tff(893,plain,
% 0.54/0.79 (((~![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(z), s(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(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z))))))))),
% 0.54/0.79 inference(monotonicity,[status(thm)],[892])).
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% 0.54/0.79 inference(transitivity,[status(thm)],[893, 891])).
% 0.54/0.79 tff(895,plain,
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% 0.54/0.79 inference(quant_inst,[status(thm)],[])).
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% 0.54/0.79 inference(modus_ponens,[status(thm)],[895, 894])).
% 0.54/0.79 tff(897,plain,
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% 0.54/0.79 inference(unit_resolution,[status(thm)],[896, 14, 329, 391, 176])).
% 0.54/0.79 tff(898,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.79 tff(899,plain,
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% 0.54/0.79 inference(unit_resolution,[status(thm)],[898, 563, 176])).
% 0.54/0.79 tff(900,plain,
% 0.54/0.79 (b(s(s(s(z))), s(s(s(s(z)))))),
% 0.54/0.79 inference(unit_resolution,[status(thm)],[402, 899])).
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% 0.54/0.79 tff(903,plain,
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% 0.54/0.79 inference(unit_resolution,[status(thm)],[902, 175, 160])).
% 0.54/0.79 tff(904,plain,
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% 0.54/0.79 inference(unit_resolution,[status(thm)],[668, 903])).
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% 0.54/0.79 inference(rewrite,[status(thm)],[])).
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% 0.54/0.79 inference(quant_inst,[status(thm)],[])).
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% 0.54/0.79 inference(modus_ponens,[status(thm)],[906, 905])).
% 0.54/0.79 tff(908,plain,
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% 0.54/0.79 inference(unit_resolution,[status(thm)],[907, 14, 160, 175, 273])).
% 0.54/0.79 tff(909,plain,((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.79 tff(910,plain,
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% 0.54/0.79 inference(unit_resolution,[status(thm)],[252, 910])).
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% 0.54/0.79 (((~![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))))))),
% 0.54/0.79 inference(rewrite,[status(thm)],[])).
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% 0.54/0.79 inference(quant_inst,[status(thm)],[])).
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% 0.54/0.79 inference(modus_ponens,[status(thm)],[913, 912])).
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% 0.54/0.79 inference(unit_resolution,[status(thm)],[914, 14, 175, 274])).
% 0.54/0.79 tff(916,plain,
% 0.54/0.79 (b(s(s(s(s(z)))), s(s(s(z))))),
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% 0.54/0.79 inference(rewrite,[status(thm)],[])).
% 0.54/0.79 tff(918,plain,
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% 0.54/0.79 inference(rewrite,[status(thm)],[])).
% 0.54/0.79 tff(919,plain,
% 0.54/0.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(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(s(z)))), s(z))) | (~b(s(z), s(s(s(z)))))))),
% 0.54/0.79 inference(monotonicity,[status(thm)],[918])).
% 0.54/0.79 tff(920,plain,
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% 0.54/0.79 inference(transitivity,[status(thm)],[919, 917])).
% 0.54/0.79 tff(921,plain,
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% 0.54/0.79 inference(quant_inst,[status(thm)],[])).
% 0.54/0.79 tff(922,plain,
% 0.54/0.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z)))))),
% 0.54/0.79 inference(modus_ponens,[status(thm)],[921, 920])).
% 0.54/0.79 tff(923,plain,
% 0.54/0.79 (~b(s(s(s(s(z)))), s(z))),
% 0.54/0.79 inference(unit_resolution,[status(thm)],[922, 118, 460, 705, 916, 904])).
% 0.54/0.79 tff(924,plain,
% 0.54/0.79 (r(s(s(s(s(z)))), s(z))),
% 0.54/0.79 inference(unit_resolution,[status(thm)],[513, 923])).
% 0.54/0.79 tff(925,plain,
% 0.54/0.79 (~r(z, s(z))),
% 0.54/0.79 inference(unit_resolution,[status(thm)],[503, 924, 274])).
% 0.54/0.79 tff(926,plain,
% 0.54/0.79 (b(z, s(z))),
% 0.54/0.79 inference(unit_resolution,[status(thm)],[51, 925])).
% 0.54/0.79 tff(927,plain,
% 0.54/0.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(z), s(s(s(z))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(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(z, s(z))))),
% 0.54/0.79 inference(rewrite,[status(thm)],[])).
% 0.54/0.79 tff(928,plain,
% 0.54/0.79 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z)))) <=> ((~b(z, s(s(s(s(z)))))) | (~b(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(z, s(z))))),
% 0.54/0.79 inference(rewrite,[status(thm)],[])).
% 0.54/0.79 tff(929,plain,
% 0.54/0.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(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(z, s(z)))))),
% 0.54/0.79 inference(monotonicity,[status(thm)],[928])).
% 0.54/0.79 tff(930,plain,
% 0.54/0.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(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(z, s(z))))),
% 0.54/0.79 inference(transitivity,[status(thm)],[929, 927])).
% 0.54/0.79 tff(931,plain,
% 0.54/0.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))),
% 0.54/0.79 inference(quant_inst,[status(thm)],[])).
% 0.54/0.79 tff(932,plain,
% 0.54/0.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z)))),
% 0.54/0.79 inference(modus_ponens,[status(thm)],[931, 930])).
% 0.54/0.79 tff(933,plain,
% 0.54/0.79 ($false),
% 0.54/0.79 inference(unit_resolution,[status(thm)],[932, 118, 460, 174, 587, 172, 436])).
% 0.54/0.79 tff(934,plain,((~b(z, s(s(s(s(z)))))) | (~b(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(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.79 tff(935,plain,
% 0.54/0.79 (~b(z, s(s(s(s(z)))))),
% 0.54/0.79 inference(unit_resolution,[status(thm)],[934, 926, 904, 460, 916])).
% 0.54/0.79 tff(936,plain,
% 0.54/0.79 (r(z, s(s(s(s(z)))))),
% 0.54/0.79 inference(unit_resolution,[status(thm)],[389, 935])).
% 0.54/0.79 tff(937,plain,
% 0.54/0.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))))),
% 0.54/0.79 inference(rewrite,[status(thm)],[])).
% 0.64/0.80 tff(938,plain,
% 0.64/0.80 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))))),
% 0.64/0.80 inference(rewrite,[status(thm)],[])).
% 0.64/0.80 tff(939,plain,
% 0.64/0.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z)))))))),
% 0.64/0.80 inference(monotonicity,[status(thm)],[938])).
% 0.64/0.80 tff(940,plain,
% 0.64/0.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))))),
% 0.64/0.80 inference(transitivity,[status(thm)],[939, 937])).
% 0.64/0.80 tff(941,plain,
% 0.64/0.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))),
% 0.64/0.80 inference(quant_inst,[status(thm)],[])).
% 0.64/0.80 tff(942,plain,
% 0.64/0.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z)))))),
% 0.64/0.80 inference(modus_ponens,[status(thm)],[941, 940])).
% 0.64/0.80 tff(943,plain,
% 0.64/0.80 ($false),
% 0.64/0.80 inference(unit_resolution,[status(thm)],[942, 118, 460, 594, 173, 587, 172])).
% 0.64/0.80 tff(944,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(s(z))))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.80 tff(945,plain,
% 0.64/0.80 (~b(s(s(s(z))), s(z))),
% 0.64/0.80 inference(unit_resolution,[status(thm)],[944, 916, 460, 705, 904])).
% 0.64/0.80 tff(946,plain,
% 0.64/0.80 (r(s(s(s(z))), s(z))),
% 0.64/0.80 inference(unit_resolution,[status(thm)],[105, 945])).
% 0.64/0.80 tff(947,plain,
% 0.64/0.80 (((~![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))))))),
% 0.64/0.80 inference(rewrite,[status(thm)],[])).
% 0.64/0.80 tff(948,plain,
% 0.64/0.80 ((~![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))))))),
% 0.64/0.80 inference(quant_inst,[status(thm)],[])).
% 0.64/0.80 tff(949,plain,
% 0.64/0.80 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 0.64/0.80 inference(modus_ponens,[status(thm)],[948, 947])).
% 0.64/0.80 tff(950,plain,
% 0.64/0.80 ($false),
% 0.64/0.80 inference(unit_resolution,[status(thm)],[949, 14, 74, 160, 2])).
% 0.64/0.80 tff(951,plain,((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.80 tff(952,plain,
% 0.64/0.80 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 0.64/0.80 inference(unit_resolution,[status(thm)],[951, 946, 160])).
% 0.64/0.80 tff(953,plain,
% 0.64/0.80 (b(s(s(s(s(s(s(z)))))), s(z))),
% 0.64/0.80 inference(unit_resolution,[status(thm)],[210, 952])).
% 0.64/0.80 tff(954,plain,
% 0.64/0.80 (((~![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))))),
% 0.64/0.80 inference(rewrite,[status(thm)],[])).
% 0.64/0.80 tff(955,plain,
% 0.64/0.80 ((~![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))))),
% 0.64/0.80 inference(quant_inst,[status(thm)],[])).
% 0.64/0.80 tff(956,plain,
% 0.64/0.80 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))),
% 0.64/0.80 inference(modus_ponens,[status(thm)],[955, 954])).
% 0.64/0.80 tff(957,plain,
% 0.64/0.80 ($false),
% 0.64/0.80 inference(unit_resolution,[status(thm)],[956, 14, 177, 74, 175])).
% 0.64/0.80 tff(958,plain,((~r(s(s(s(z))), s(z))) | (~r(s(z), z)) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.80 tff(959,plain,
% 0.64/0.80 (~r(s(s(s(z))), s(z))),
% 0.64/0.80 inference(unit_resolution,[status(thm)],[958, 177, 175])).
% 0.64/0.80 tff(960,plain,
% 0.64/0.80 (b(s(s(s(z))), s(z))),
% 0.64/0.80 inference(unit_resolution,[status(thm)],[105, 959])).
% 0.64/0.80 tff(961,assumption,(b(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 0.64/0.80 tff(962,plain,
% 0.64/0.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(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))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(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))) | (~b(s(z), s(s(s(z))))))),
% 0.64/0.80 inference(rewrite,[status(thm)],[])).
% 0.64/0.80 tff(963,plain,
% 0.64/0.80 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(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))) | (~b(s(z), s(s(s(z))))))),
% 0.64/0.80 inference(rewrite,[status(thm)],[])).
% 0.64/0.80 tff(964,plain,
% 0.64/0.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z)))))))),
% 0.64/0.80 inference(monotonicity,[status(thm)],[963])).
% 0.64/0.80 tff(965,plain,
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% 0.64/0.81 inference(unit_resolution,[status(thm)],[71, 1009])).
% 0.64/0.81 tff(1011,plain,
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% 0.64/0.81 inference(rewrite,[status(thm)],[])).
% 0.64/0.81 tff(1012,plain,
% 0.64/0.81 (((~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), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z))))))))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 0.64/0.81 inference(rewrite,[status(thm)],[])).
% 0.64/0.81 tff(1013,plain,
% 0.64/0.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), 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), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z))))),
% 0.64/0.81 inference(monotonicity,[status(thm)],[1012])).
% 0.64/0.81 tff(1014,plain,
% 0.64/0.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), 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), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 0.64/0.81 inference(transitivity,[status(thm)],[1013, 1011])).
% 0.64/0.81 tff(1015,plain,
% 0.64/0.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), 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), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))))),
% 0.64/0.81 inference(quant_inst,[status(thm)],[])).
% 0.64/0.81 tff(1016,plain,
% 0.64/0.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z))),
% 0.64/0.81 inference(modus_ponens,[status(thm)],[1015, 1014])).
% 0.64/0.81 tff(1017,plain,
% 0.64/0.81 ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z))))))))),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[1016, 118, 460, 721, 1])).
% 0.64/0.81 tff(1018,plain,
% 0.64/0.81 (~b(s(z), s(s(s(s(s(s(z)))))))),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[1017, 994])).
% 0.64/0.81 tff(1019,plain,
% 0.64/0.81 (r(s(z), s(s(s(s(s(s(z)))))))),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[232, 1018])).
% 0.64/0.81 tff(1020,plain,
% 0.64/0.81 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(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(z), z)) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 0.64/0.81 inference(rewrite,[status(thm)],[])).
% 0.64/0.81 tff(1021,plain,
% 0.64/0.81 (((~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 0.64/0.81 inference(rewrite,[status(thm)],[])).
% 0.64/0.81 tff(1022,plain,
% 0.64/0.81 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z))))))))))),
% 0.64/0.81 inference(monotonicity,[status(thm)],[1021])).
% 0.64/0.81 tff(1023,plain,
% 0.64/0.81 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 0.64/0.81 inference(transitivity,[status(thm)],[1022, 1020])).
% 0.64/0.81 tff(1024,plain,
% 0.64/0.81 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(z), z)))),
% 0.64/0.81 inference(quant_inst,[status(thm)],[])).
% 0.64/0.81 tff(1025,plain,
% 0.64/0.81 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z))))))))),
% 0.64/0.81 inference(modus_ponens,[status(thm)],[1024, 1023])).
% 0.64/0.81 tff(1026,plain,
% 0.64/0.81 ($false),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[1025, 14, 177, 3, 212])).
% 0.64/0.81 tff(1027,plain,((~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.81 tff(1028,plain,
% 0.64/0.81 (~r(s(z), z)),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[1027, 1019, 1008])).
% 0.64/0.81 tff(1029,plain,
% 0.64/0.81 (b(s(z), z)),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[187, 1028])).
% 0.64/0.81 tff(1030,plain,
% 0.64/0.81 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[559, 118, 460, 1029, 994, 721])).
% 0.64/0.81 tff(1031,plain,
% 0.64/0.81 (r(s(s(s(s(s(s(z)))))), s(z))),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[210, 1030])).
% 0.64/0.81 tff(1032,plain,
% 0.64/0.81 (~r(s(s(s(z))), s(z))),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[951, 1031, 160])).
% 0.64/0.81 tff(1033,plain,
% 0.64/0.81 (b(s(s(s(z))), s(z))),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[105, 1032])).
% 0.64/0.81 tff(1034,plain,
% 0.64/0.81 (~r(z, s(z))),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[22, 1031, 1008])).
% 0.64/0.81 tff(1035,plain,
% 0.64/0.81 (b(z, s(z))),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[51, 1034])).
% 0.64/0.81 tff(1036,plain,
% 0.64/0.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(z))))))),
% 0.64/0.81 inference(rewrite,[status(thm)],[])).
% 0.64/0.81 tff(1037,plain,
% 0.64/0.81 (((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(z))))))),
% 0.64/0.81 inference(rewrite,[status(thm)],[])).
% 0.64/0.81 tff(1038,plain,
% 0.64/0.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(z)))))))),
% 0.64/0.81 inference(monotonicity,[status(thm)],[1037])).
% 0.64/0.81 tff(1039,plain,
% 0.64/0.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(z))))))),
% 0.64/0.81 inference(transitivity,[status(thm)],[1038, 1036])).
% 0.64/0.81 tff(1040,plain,
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% 0.64/0.81 inference(quant_inst,[status(thm)],[])).
% 0.64/0.81 tff(1041,plain,
% 0.64/0.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(z)))))),
% 0.64/0.81 inference(modus_ponens,[status(thm)],[1040, 1039])).
% 0.64/0.81 tff(1042,plain,
% 0.64/0.81 ($false),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[1041, 118, 1035, 1029, 1033, 172, 1010])).
% 0.64/0.81 tff(1043,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.81 tff(1044,plain,
% 0.64/0.81 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[1043, 460, 160, 904, 992, 911])).
% 0.64/0.81 tff(1045,plain,
% 0.64/0.81 (b(s(s(s(s(z)))), s(s(s(z))))),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[310, 1044])).
% 0.64/0.81 tff(1046,plain,
% 0.64/0.81 (~b(s(s(s(z))), s(z))),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[944, 403, 460, 1045, 904])).
% 0.64/0.81 tff(1047,plain,
% 0.64/0.81 (r(s(s(s(z))), s(z))),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[105, 1046])).
% 0.64/0.81 tff(1048,plain,
% 0.64/0.81 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[951, 1047, 160])).
% 0.64/0.81 tff(1049,plain,
% 0.64/0.81 (b(s(s(s(s(s(s(z)))))), s(z))),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[210, 1048])).
% 0.64/0.81 tff(1050,plain,
% 0.64/0.81 (~r(s(z), z)),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[958, 1047, 175])).
% 0.64/0.81 tff(1051,plain,
% 0.64/0.81 (b(s(z), z)),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[187, 1050])).
% 0.64/0.81 tff(1052,plain,
% 0.64/0.81 (~r(z, s(s(s(s(s(s(z)))))))),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[538, 1051, 460, 272, 160])).
% 0.64/0.81 tff(1053,plain,
% 0.64/0.81 (b(z, s(s(s(s(s(s(z)))))))),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[356, 1052])).
% 0.64/0.81 tff(1054,plain,
% 0.64/0.81 (~b(s(s(s(s(z)))), s(z))),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[922, 118, 460, 403, 1045, 904])).
% 0.64/0.81 tff(1055,plain,
% 0.64/0.81 (r(s(s(s(s(z)))), s(z))),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[513, 1054])).
% 0.64/0.81 tff(1056,plain,
% 0.64/0.81 (((~![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(z))) | (~r(z, 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(z))) | (~r(z, s(z))))),
% 0.64/0.81 inference(rewrite,[status(thm)],[])).
% 0.64/0.81 tff(1057,plain,
% 0.64/0.81 (((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))))),
% 0.64/0.81 inference(rewrite,[status(thm)],[])).
% 0.64/0.81 tff(1058,plain,
% 0.64/0.81 (((~![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(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z)))))),
% 0.64/0.81 inference(monotonicity,[status(thm)],[1057])).
% 0.64/0.81 tff(1059,plain,
% 0.64/0.81 (((~![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(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))))),
% 0.64/0.81 inference(transitivity,[status(thm)],[1058, 1056])).
% 0.64/0.81 tff(1060,plain,
% 0.64/0.81 ((~![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)))),
% 0.64/0.81 inference(quant_inst,[status(thm)],[])).
% 0.64/0.81 tff(1061,plain,
% 0.64/0.81 ((~![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(z))) | (~r(z, s(z)))),
% 0.64/0.81 inference(modus_ponens,[status(thm)],[1060, 1059])).
% 0.64/0.81 tff(1062,plain,
% 0.64/0.81 (~r(s(s(s(z))), z)),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[1061, 14, 4, 74])).
% 0.64/0.81 tff(1063,plain,
% 0.64/0.81 (b(s(s(s(z))), z)),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[649, 1062])).
% 0.64/0.81 tff(1064,plain,
% 0.64/0.81 (((~![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(z)))), 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(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 0.64/0.81 inference(rewrite,[status(thm)],[])).
% 0.64/0.81 tff(1065,plain,
% 0.64/0.81 ((~![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(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 0.64/0.81 inference(quant_inst,[status(thm)],[])).
% 0.64/0.81 tff(1066,plain,
% 0.64/0.81 ((~![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(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 0.64/0.81 inference(modus_ponens,[status(thm)],[1065, 1064])).
% 0.64/0.81 tff(1067,plain,
% 0.64/0.81 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[1066, 14, 495, 74])).
% 0.64/0.81 tff(1068,plain,
% 0.64/0.81 (b(s(s(s(s(z)))), s(s(s(z))))),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[310, 1067])).
% 0.64/0.81 tff(1069,plain,
% 0.64/0.81 (((~![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(s(s(s(z)))))) | (~r(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(z, s(s(s(s(z)))))) | (~r(z, s(z))))),
% 0.64/0.81 inference(rewrite,[status(thm)],[])).
% 0.64/0.81 tff(1070,plain,
% 0.64/0.81 (((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(z))))),
% 0.64/0.81 inference(rewrite,[status(thm)],[])).
% 0.64/0.81 tff(1071,plain,
% 0.64/0.81 (((~![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(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(z)))))),
% 0.64/0.81 inference(monotonicity,[status(thm)],[1070])).
% 0.64/0.82 tff(1072,plain,
% 0.64/0.82 (((~![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(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(z))))),
% 0.64/0.82 inference(transitivity,[status(thm)],[1071, 1069])).
% 0.64/0.82 tff(1073,plain,
% 0.64/0.82 ((~![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)))))))),
% 0.64/0.82 inference(quant_inst,[status(thm)],[])).
% 0.64/0.82 tff(1074,plain,
% 0.64/0.82 ((~![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(s(s(s(z)))))) | (~r(z, s(z)))),
% 0.64/0.82 inference(modus_ponens,[status(thm)],[1073, 1072])).
% 0.64/0.82 tff(1075,plain,
% 0.64/0.82 (~r(z, s(s(s(s(z)))))),
% 0.64/0.82 inference(unit_resolution,[status(thm)],[1074, 14, 495, 4])).
% 0.64/0.82 tff(1076,plain,
% 0.64/0.82 (b(z, s(s(s(s(z)))))),
% 0.64/0.82 inference(unit_resolution,[status(thm)],[389, 1075])).
% 0.64/0.82 tff(1077,plain,
% 0.64/0.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 0.64/0.82 inference(rewrite,[status(thm)],[])).
% 0.64/0.82 tff(1078,plain,
% 0.64/0.82 (((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 0.64/0.82 inference(rewrite,[status(thm)],[])).
% 0.64/0.82 tff(1079,plain,
% 0.64/0.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))))),
% 0.64/0.82 inference(monotonicity,[status(thm)],[1078])).
% 0.64/0.82 tff(1080,plain,
% 0.64/0.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 0.64/0.82 inference(transitivity,[status(thm)],[1079, 1077])).
% 0.64/0.82 tff(1081,plain,
% 0.64/0.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 0.64/0.82 inference(quant_inst,[status(thm)],[])).
% 0.64/0.82 tff(1082,plain,
% 0.64/0.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))),
% 0.64/0.82 inference(modus_ponens,[status(thm)],[1081, 1080])).
% 0.64/0.82 tff(1083,plain,
% 0.64/0.82 ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 0.64/0.82 inference(unit_resolution,[status(thm)],[1082, 118, 594, 721, 1076])).
% 0.64/0.82 tff(1084,plain,
% 0.64/0.82 ($false),
% 0.64/0.82 inference(unit_resolution,[status(thm)],[1083, 1068, 1063])).
% 0.64/0.82 tff(1085,plain,((~r(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.82 tff(1086,plain,
% 0.64/0.82 (~r(z, s(z))),
% 0.64/0.82 inference(unit_resolution,[status(thm)],[1085, 1055, 992, 403, 1047])).
% 0.64/0.82 tff(1087,plain,
% 0.64/0.82 (b(z, s(z))),
% 0.64/0.82 inference(unit_resolution,[status(thm)],[51, 1086])).
% 0.64/0.82 tff(1088,plain,
% 0.64/0.82 ($false),
% 0.64/0.82 inference(unit_resolution,[status(thm)],[984, 118, 1087, 1051, 911, 1053, 1049])).
% 0.64/0.82 tff(1089,plain,((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.82 tff(1090,plain,
% 0.64/0.82 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 0.64/0.82 inference(unit_resolution,[status(thm)],[1089, 460, 160, 175])).
% 0.64/0.82 tff(1091,plain,
% 0.64/0.82 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 0.64/0.82 inference(unit_resolution,[status(thm)],[434, 1090])).
% 0.64/0.82 tff(1092,plain,
% 0.64/0.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(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(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 0.64/0.82 inference(rewrite,[status(thm)],[])).
% 0.64/0.82 tff(1093,plain,
% 0.64/0.82 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), 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))))),
% 0.64/0.82 inference(rewrite,[status(thm)],[])).
% 0.64/0.82 tff(1094,plain,
% 0.64/0.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))))),
% 0.64/0.82 inference(monotonicity,[status(thm)],[1093])).
% 0.64/0.82 tff(1095,plain,
% 0.64/0.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 0.64/0.82 inference(transitivity,[status(thm)],[1094, 1092])).
% 0.64/0.82 tff(1096,plain,
% 0.64/0.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 0.64/0.82 inference(quant_inst,[status(thm)],[])).
% 0.64/0.82 tff(1097,plain,
% 0.64/0.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(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(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))),
% 0.64/0.82 inference(modus_ponens,[status(thm)],[1096, 1095])).
% 0.64/0.82 tff(1098,plain,
% 0.64/0.82 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 0.64/0.82 inference(unit_resolution,[status(thm)],[1097, 118, 460, 1045, 904, 1091])).
% 0.64/0.82 tff(1099,plain,
% 0.64/0.82 (r(s(s(s(s(s(s(z)))))), s(z))),
% 0.64/0.82 inference(unit_resolution,[status(thm)],[210, 1098])).
% 0.64/0.82 tff(1100,plain,
% 0.64/0.82 (~r(s(s(s(z))), s(z))),
% 0.64/0.82 inference(unit_resolution,[status(thm)],[951, 1099, 160])).
% 0.64/0.82 tff(1101,plain,
% 0.64/0.82 (b(s(s(s(z))), s(z))),
% 0.64/0.82 inference(unit_resolution,[status(thm)],[105, 1100])).
% 0.64/0.82 tff(1102,plain,
% 0.64/0.82 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 0.64/0.82 inference(unit_resolution,[status(thm)],[944, 1101, 460, 1045, 904])).
% 0.64/0.82 tff(1103,plain,
% 0.64/0.82 (r(s(s(s(z))), s(s(s(s(z)))))),
% 0.64/0.82 inference(unit_resolution,[status(thm)],[402, 1102])).
% 0.64/0.82 tff(1104,plain,
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% 0.64/0.82 inference(unit_resolution,[status(thm)],[1097, 118, 460, 587, 172, 437])).
% 0.64/0.82 tff(1105,plain,
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% 0.64/0.82 inference(unit_resolution,[status(thm)],[210, 1104])).
% 0.64/0.82 tff(1106,plain,
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% 0.64/0.82 inference(unit_resolution,[status(thm)],[951, 1105, 160])).
% 0.64/0.82 tff(1107,plain,
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% 0.64/0.82 inference(unit_resolution,[status(thm)],[105, 1106])).
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% 0.64/0.82 inference(rewrite,[status(thm)],[])).
% 0.64/0.82 tff(1109,plain,
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% 0.64/0.82 inference(rewrite,[status(thm)],[])).
% 0.64/0.82 tff(1110,plain,
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% 0.64/0.82 inference(monotonicity,[status(thm)],[1109])).
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% 0.64/0.82 inference(transitivity,[status(thm)],[1110, 1108])).
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% 0.64/0.82 inference(quant_inst,[status(thm)],[])).
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% 0.64/0.82 inference(modus_ponens,[status(thm)],[1112, 1111])).
% 0.64/0.82 tff(1114,plain,
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% 0.64/0.82 inference(unit_resolution,[status(thm)],[1113, 118, 460, 961, 1107, 587, 172])).
% 0.64/0.82 tff(1115,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.82 tff(1116,plain,
% 0.64/0.82 (~b(s(s(s(s(z)))), s(z))),
% 0.64/0.82 inference(unit_resolution,[status(thm)],[1115, 1091, 160, 904, 460, 1045])).
% 0.64/0.82 tff(1117,plain,
% 0.64/0.82 (r(s(s(s(s(z)))), s(z))),
% 0.64/0.82 inference(unit_resolution,[status(thm)],[513, 1116])).
% 0.64/0.82 tff(1118,plain,
% 0.64/0.82 (((~![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(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(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 0.64/0.82 inference(rewrite,[status(thm)],[])).
% 0.64/0.82 tff(1119,plain,
% 0.64/0.82 (((~r(s(s(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(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 0.64/0.82 inference(rewrite,[status(thm)],[])).
% 0.64/0.82 tff(1120,plain,
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% 0.64/0.82 inference(monotonicity,[status(thm)],[1119])).
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% 0.64/0.82 inference(transitivity,[status(thm)],[1120, 1118])).
% 0.64/0.82 tff(1122,plain,
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% 0.64/0.82 inference(quant_inst,[status(thm)],[])).
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% 0.64/0.82 inference(modus_ponens,[status(thm)],[1122, 1121])).
% 0.64/0.82 tff(1124,plain,
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% 0.64/0.82 inference(unit_resolution,[status(thm)],[1123, 14, 495, 543, 2])).
% 0.64/0.82 tff(1125,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.82 tff(1126,plain,
% 0.64/0.82 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.64/0.82 inference(unit_resolution,[status(thm)],[1125, 1099, 1117])).
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% 0.64/0.82 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.64/0.82 inference(unit_resolution,[status(thm)],[480, 1126])).
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% 0.64/0.82 (~b(z, s(s(s(s(s(s(z)))))))),
% 0.64/0.82 inference(unit_resolution,[status(thm)],[1002, 1127, 911, 992, 1091])).
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% 0.64/0.82 inference(unit_resolution,[status(thm)],[356, 1128])).
% 0.64/0.82 tff(1130,plain,
% 0.64/0.82 (~r(z, s(z))),
% 0.64/0.82 inference(unit_resolution,[status(thm)],[22, 1129, 1099])).
% 0.64/0.82 tff(1131,plain,
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% 0.64/0.82 inference(unit_resolution,[status(thm)],[51, 1130])).
% 0.64/0.82 tff(1132,plain,
% 0.64/0.82 (~b(z, s(s(s(s(z)))))),
% 0.64/0.82 inference(unit_resolution,[status(thm)],[934, 1131, 904, 460, 1045])).
% 0.64/0.82 tff(1133,plain,
% 0.64/0.82 (r(z, s(s(s(s(z)))))),
% 0.64/0.82 inference(unit_resolution,[status(thm)],[389, 1132])).
% 0.64/0.82 tff(1134,plain,
% 0.64/0.82 (((~![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(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(z, s(s(s(s(z)))))))),
% 0.64/0.82 inference(rewrite,[status(thm)],[])).
% 0.64/0.82 tff(1135,plain,
% 0.64/0.82 (((~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(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 0.64/0.82 inference(rewrite,[status(thm)],[])).
% 0.64/0.82 tff(1136,plain,
% 0.64/0.82 (((~![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(z))), s(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(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))))),
% 0.64/0.82 inference(monotonicity,[status(thm)],[1135])).
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% 0.64/0.82 inference(transitivity,[status(thm)],[1136, 1134])).
% 0.64/0.82 tff(1138,plain,
% 0.64/0.82 ((~![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(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))),
% 0.64/0.82 inference(quant_inst,[status(thm)],[])).
% 0.64/0.82 tff(1139,plain,
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% 0.64/0.82 inference(modus_ponens,[status(thm)],[1138, 1137])).
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% 0.64/0.82 inference(unit_resolution,[status(thm)],[1139, 14, 1133, 1103, 175])).
% 0.64/0.82 tff(1141,plain,((~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.82 tff(1142,plain,
% 0.64/0.82 (~b(s(z), s(s(s(s(z)))))),
% 0.64/0.82 inference(unit_resolution,[status(thm)],[1141, 175, 160])).
% 0.64/0.82 tff(1143,plain,
% 0.64/0.82 (r(s(z), s(s(s(s(z)))))),
% 0.64/0.82 inference(unit_resolution,[status(thm)],[323, 1142])).
% 0.64/0.82 tff(1144,plain,
% 0.64/0.82 (((~![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)))),
% 0.64/0.82 inference(rewrite,[status(thm)],[])).
% 0.64/0.82 tff(1145,plain,
% 0.64/0.82 (((~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)))),
% 0.64/0.82 inference(rewrite,[status(thm)],[])).
% 0.64/0.82 tff(1146,plain,
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% 0.64/0.82 inference(monotonicity,[status(thm)],[1145])).
% 0.64/0.82 tff(1147,plain,
% 0.64/0.82 (((~![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)))),
% 0.64/0.82 inference(transitivity,[status(thm)],[1146, 1144])).
% 0.64/0.82 tff(1148,plain,
% 0.64/0.82 ((~![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)))))))),
% 0.64/0.82 inference(quant_inst,[status(thm)],[])).
% 0.64/0.82 tff(1149,plain,
% 0.64/0.82 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))),
% 0.64/0.82 inference(modus_ponens,[status(thm)],[1148, 1147])).
% 0.64/0.82 tff(1150,plain,
% 0.64/0.82 ($false),
% 0.64/0.82 inference(unit_resolution,[status(thm)],[1149, 14, 329, 177, 274])).
% 0.64/0.82 tff(1151,plain,((~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.82 tff(1152,plain,
% 0.64/0.82 (~r(s(z), z)),
% 0.64/0.82 inference(unit_resolution,[status(thm)],[1151, 274, 1143])).
% 0.64/0.82 tff(1153,plain,
% 0.64/0.82 (b(s(z), z)),
% 0.64/0.82 inference(unit_resolution,[status(thm)],[187, 1152])).
% 0.64/0.82 tff(1154,plain,
% 0.64/0.82 (~r(s(s(s(z))), s(z))),
% 0.64/0.82 inference(unit_resolution,[status(thm)],[951, 2, 160])).
% 0.64/0.83 tff(1155,plain,
% 0.64/0.83 (b(s(s(s(z))), s(z))),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[105, 1154])).
% 0.64/0.83 tff(1156,plain,
% 0.64/0.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))))),
% 0.64/0.83 inference(rewrite,[status(thm)],[])).
% 0.64/0.83 tff(1157,plain,
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% 0.64/0.83 inference(rewrite,[status(thm)],[])).
% 0.64/0.83 tff(1158,plain,
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% 0.64/0.83 inference(monotonicity,[status(thm)],[1157])).
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% 0.64/0.83 inference(transitivity,[status(thm)],[1158, 1156])).
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% 0.64/0.83 inference(quant_inst,[status(thm)],[])).
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% 0.64/0.83 inference(modus_ponens,[status(thm)],[1160, 1159])).
% 0.64/0.83 tff(1162,plain,
% 0.64/0.83 (~b(s(s(s(s(z)))), s(z))),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[1161, 118, 705, 1155, 916, 904])).
% 0.64/0.83 tff(1163,plain,
% 0.64/0.83 (r(s(s(s(s(z)))), s(z))),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[513, 1162])).
% 0.64/0.83 tff(1164,assumption,(r(s(s(s(s(s(z))))), s(z))), introduced(assumption)).
% 0.64/0.83 tff(1165,plain,
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% 0.64/0.83 inference(rewrite,[status(thm)],[])).
% 0.64/0.83 tff(1166,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(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(s(z))))))))),
% 0.64/0.83 inference(quant_inst,[status(thm)],[])).
% 0.64/0.83 tff(1167,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(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(s(z)))))))),
% 0.64/0.83 inference(modus_ponens,[status(thm)],[1166, 1165])).
% 0.64/0.83 tff(1168,plain,
% 0.64/0.83 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[1167, 14, 2, 1164])).
% 0.64/0.83 tff(1169,plain,
% 0.64/0.83 (b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[744, 1168, 735])).
% 0.64/0.83 tff(1170,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(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(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(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 0.64/0.83 inference(rewrite,[status(thm)],[])).
% 0.64/0.83 tff(1171,plain,
% 0.64/0.83 (((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 0.64/0.83 inference(rewrite,[status(thm)],[])).
% 0.64/0.83 tff(1172,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(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(z)))))),
% 0.64/0.83 inference(monotonicity,[status(thm)],[1171])).
% 0.64/0.83 tff(1173,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(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 0.64/0.83 inference(transitivity,[status(thm)],[1172, 1170])).
% 0.64/0.83 tff(1174,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(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 0.64/0.83 inference(quant_inst,[status(thm)],[])).
% 0.64/0.83 tff(1175,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(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(z)))),
% 0.64/0.83 inference(modus_ponens,[status(thm)],[1174, 1173])).
% 0.64/0.83 tff(1176,plain,
% 0.64/0.83 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[1175, 14, 2, 1164])).
% 0.64/0.83 tff(1177,plain,
% 0.64/0.83 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[753, 1176, 734])).
% 0.64/0.83 tff(1178,plain,
% 0.64/0.83 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[855, 14, 495, 1164])).
% 0.64/0.83 tff(1179,plain,
% 0.64/0.83 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[814, 1178, 802])).
% 0.64/0.83 tff(1180,plain,
% 0.64/0.83 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[864, 14, 495, 1164])).
% 0.64/0.83 tff(1181,plain,
% 0.64/0.83 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[869, 1180, 861])).
% 0.64/0.83 tff(1182,plain,
% 0.64/0.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 0.64/0.83 inference(rewrite,[status(thm)],[])).
% 0.64/0.83 tff(1183,plain,
% 0.64/0.83 (((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 0.64/0.83 inference(rewrite,[status(thm)],[])).
% 0.64/0.83 tff(1184,plain,
% 0.64/0.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))))),
% 0.64/0.83 inference(monotonicity,[status(thm)],[1183])).
% 0.64/0.83 tff(1185,plain,
% 0.64/0.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 0.64/0.83 inference(transitivity,[status(thm)],[1184, 1182])).
% 0.64/0.83 tff(1186,plain,
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% 0.64/0.83 inference(quant_inst,[status(thm)],[])).
% 0.64/0.83 tff(1187,plain,
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% 0.64/0.83 inference(modus_ponens,[status(thm)],[1186, 1185])).
% 0.64/0.83 tff(1188,plain,
% 0.64/0.83 ($false),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[1187, 118, 437, 1181, 1179, 1177, 1169])).
% 0.64/0.83 tff(1189,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.83 tff(1190,plain,
% 0.64/0.83 (~r(s(s(s(s(s(z))))), s(z))),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[1189, 2, 437, 1163])).
% 0.64/0.83 tff(1191,plain,
% 0.64/0.83 (b(s(s(s(s(s(z))))), s(z))),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[829, 1190])).
% 0.64/0.83 tff(1192,plain,
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% 0.64/0.83 inference(unit_resolution,[status(thm)],[503, 1163, 274])).
% 0.64/0.83 tff(1193,plain,
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% 0.64/0.83 inference(unit_resolution,[status(thm)],[51, 1192])).
% 0.64/0.83 tff(1194,plain,
% 0.64/0.83 (~r(z, s(s(s(s(s(s(z)))))))),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[713, 437, 274, 916, 175])).
% 0.64/0.83 tff(1195,plain,
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% 0.64/0.83 inference(unit_resolution,[status(thm)],[356, 1194])).
% 0.64/0.83 tff(1196,plain,
% 0.64/0.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 0.64/0.83 inference(rewrite,[status(thm)],[])).
% 0.64/0.83 tff(1197,plain,
% 0.64/0.83 (((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 0.64/0.83 inference(rewrite,[status(thm)],[])).
% 0.64/0.83 tff(1198,plain,
% 0.64/0.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z))))))))))),
% 0.64/0.83 inference(monotonicity,[status(thm)],[1197])).
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% 0.64/0.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 0.64/0.83 inference(transitivity,[status(thm)],[1198, 1196])).
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% 0.64/0.83 inference(quant_inst,[status(thm)],[])).
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% 0.64/0.83 inference(modus_ponens,[status(thm)],[1200, 1199])).
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% 0.64/0.83 inference(unit_resolution,[status(thm)],[1201, 118, 1153, 911, 1195])).
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% 0.64/0.83 inference(unit_resolution,[status(thm)],[1202, 1193])).
% 0.64/0.83 tff(1204,plain,
% 0.64/0.83 (r(s(z), s(s(s(s(s(s(z)))))))),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[232, 1203])).
% 0.64/0.83 tff(1205,assumption,(b(s(s(s(s(s(z))))), z)), introduced(assumption)).
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% 0.64/0.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 0.64/0.83 inference(rewrite,[status(thm)],[])).
% 0.64/0.83 tff(1207,plain,
% 0.64/0.83 (((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(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(s(z)))))))) <=> ((~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 0.64/0.83 inference(rewrite,[status(thm)],[])).
% 0.64/0.83 tff(1208,plain,
% 0.64/0.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(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(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 0.64/0.84 inference(monotonicity,[status(thm)],[1207])).
% 0.64/0.84 tff(1209,plain,
% 0.64/0.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(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(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 0.64/0.84 inference(transitivity,[status(thm)],[1208, 1206])).
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% 0.64/0.84 inference(quant_inst,[status(thm)],[])).
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% 0.64/0.84 inference(modus_ponens,[status(thm)],[1210, 1209])).
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% 0.64/0.84 ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[1211, 118, 174, 1, 724])).
% 0.64/0.84 tff(1213,plain,
% 0.64/0.84 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[1212, 1205])).
% 0.64/0.84 tff(1214,plain,
% 0.64/0.84 (r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[744, 1213, 735])).
% 0.64/0.84 tff(1215,plain,
% 0.64/0.84 (~b(s(z), s(s(s(s(s(z))))))),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[775, 1205])).
% 0.64/0.84 tff(1216,plain,
% 0.64/0.84 (r(s(z), s(s(s(s(s(z))))))),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[791, 1215])).
% 0.64/0.84 tff(1217,plain,
% 0.64/0.84 (((~![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(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(z), s(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(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 0.64/0.84 inference(rewrite,[status(thm)],[])).
% 0.64/0.84 tff(1218,plain,
% 0.64/0.84 (((~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(s(z))))))))) <=> ((~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 0.64/0.84 inference(rewrite,[status(thm)],[])).
% 0.64/0.84 tff(1219,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(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(z), 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(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 0.64/0.84 inference(monotonicity,[status(thm)],[1218])).
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% 0.64/0.84 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(z), 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(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 0.64/0.84 inference(transitivity,[status(thm)],[1219, 1217])).
% 0.64/0.84 tff(1221,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(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 0.64/0.84 inference(quant_inst,[status(thm)],[])).
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% 0.64/0.84 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 0.64/0.84 inference(modus_ponens,[status(thm)],[1221, 1220])).
% 0.64/0.84 tff(1223,plain,
% 0.64/0.84 ($false),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[1222, 14, 212, 1216, 1214])).
% 0.64/0.84 tff(1224,plain,((~b(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.84 tff(1225,plain,
% 0.64/0.84 (~b(s(s(s(s(s(z))))), z)),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[1224, 1204, 1193, 911, 1191, 1153])).
% 0.64/0.84 tff(1226,plain,
% 0.64/0.84 (r(s(s(s(s(s(z))))), z)),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[767, 1225])).
% 0.64/0.84 tff(1227,plain,
% 0.64/0.84 (((~![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(z))))), z)) | (~r(s(s(s(z))), 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(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 0.64/0.84 inference(rewrite,[status(thm)],[])).
% 0.64/0.84 tff(1228,plain,
% 0.64/0.84 (((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 0.64/0.84 inference(rewrite,[status(thm)],[])).
% 0.64/0.84 tff(1229,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(s(z))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), 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(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 0.64/0.84 inference(monotonicity,[status(thm)],[1228])).
% 0.64/0.84 tff(1230,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(s(z))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), 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(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 0.64/0.84 inference(transitivity,[status(thm)],[1229, 1227])).
% 0.64/0.84 tff(1231,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(s(z))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 0.64/0.84 inference(quant_inst,[status(thm)],[])).
% 0.64/0.84 tff(1232,plain,
% 0.64/0.84 ((~![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(z))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 0.64/0.84 inference(modus_ponens,[status(thm)],[1231, 1230])).
% 0.64/0.84 tff(1233,plain,
% 0.64/0.84 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[1232, 14, 175, 1226])).
% 0.64/0.84 tff(1234,plain,
% 0.64/0.84 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[848, 46, 800, 1233])).
% 0.64/0.84 tff(1235,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(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), 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)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 0.64/0.84 inference(rewrite,[status(thm)],[])).
% 0.64/0.84 tff(1236,plain,
% 0.64/0.84 (((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 0.64/0.84 inference(rewrite,[status(thm)],[])).
% 0.64/0.84 tff(1237,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(s(z))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), 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)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 0.64/0.84 inference(monotonicity,[status(thm)],[1236])).
% 0.64/0.84 tff(1238,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(s(z))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), 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)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 0.64/0.84 inference(transitivity,[status(thm)],[1237, 1235])).
% 0.64/0.84 tff(1239,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(s(z))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 0.64/0.84 inference(quant_inst,[status(thm)],[])).
% 0.64/0.84 tff(1240,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(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 0.64/0.84 inference(modus_ponens,[status(thm)],[1239, 1238])).
% 0.64/0.84 tff(1241,plain,
% 0.64/0.84 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[1240, 14, 274, 1226])).
% 0.64/0.84 tff(1242,plain,
% 0.64/0.84 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[814, 1241, 802])).
% 0.64/0.84 tff(1243,plain,
% 0.64/0.84 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[1125, 1163, 2])).
% 0.64/0.84 tff(1244,plain,
% 0.64/0.84 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[480, 1243])).
% 0.64/0.84 tff(1245,plain,
% 0.64/0.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 0.64/0.84 inference(rewrite,[status(thm)],[])).
% 0.64/0.84 tff(1246,plain,
% 0.64/0.84 (((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z))) <=> ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 0.64/0.84 inference(rewrite,[status(thm)],[])).
% 0.64/0.84 tff(1247,plain,
% 0.64/0.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))))),
% 0.64/0.84 inference(monotonicity,[status(thm)],[1246])).
% 0.64/0.84 tff(1248,plain,
% 0.64/0.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 0.64/0.84 inference(transitivity,[status(thm)],[1247, 1245])).
% 0.64/0.84 tff(1249,plain,
% 0.64/0.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 0.64/0.84 inference(quant_inst,[status(thm)],[])).
% 0.64/0.84 tff(1250,plain,
% 0.64/0.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 0.64/0.84 inference(modus_ponens,[status(thm)],[1249, 1248])).
% 0.64/0.84 tff(1251,plain,
% 0.64/0.84 (~b(z, s(s(s(s(z)))))),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[1250, 118, 437, 1244, 911, 1195])).
% 0.64/0.84 tff(1252,plain,
% 0.64/0.84 (r(z, s(s(s(s(z)))))),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[389, 1251])).
% 0.64/0.84 tff(1253,assumption,(r(s(s(s(s(s(z))))), s(s(s(s(z)))))), introduced(assumption)).
% 0.64/0.84 tff(1254,plain,
% 0.64/0.84 (((~![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(z))))), z)) | (~r(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(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 0.64/0.84 inference(rewrite,[status(thm)],[])).
% 0.64/0.84 tff(1255,plain,
% 0.64/0.84 (((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z))) <=> ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 0.64/0.84 inference(rewrite,[status(thm)],[])).
% 0.64/0.84 tff(1256,plain,
% 0.64/0.84 (((~![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(z))))), s(s(s(s(z)))))) | (~r(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(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 0.64/0.84 inference(monotonicity,[status(thm)],[1255])).
% 0.64/0.84 tff(1257,plain,
% 0.64/0.84 (((~![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(z))))), s(s(s(s(z)))))) | (~r(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(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 0.64/0.84 inference(transitivity,[status(thm)],[1256, 1254])).
% 0.64/0.84 tff(1258,plain,
% 0.64/0.84 ((~![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(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)))),
% 0.64/0.84 inference(quant_inst,[status(thm)],[])).
% 0.64/0.84 tff(1259,plain,
% 0.64/0.84 ((~![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(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 0.64/0.84 inference(modus_ponens,[status(thm)],[1258, 1257])).
% 0.64/0.84 tff(1260,plain,
% 0.64/0.84 (~r(s(s(s(s(s(z))))), z)),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[1259, 14, 339, 1253])).
% 0.64/0.84 tff(1261,plain,
% 0.64/0.84 (b(s(s(s(s(s(z))))), z)),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[767, 1260])).
% 0.64/0.84 tff(1262,plain,
% 0.64/0.84 (((~![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(z), s(s(s(s(s(z))))))) | (~r(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(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 0.64/0.84 inference(rewrite,[status(thm)],[])).
% 0.64/0.84 tff(1263,plain,
% 0.64/0.84 (((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z)))))))) <=> ((~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 0.64/0.84 inference(rewrite,[status(thm)],[])).
% 0.64/0.84 tff(1264,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(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(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(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 0.64/0.84 inference(monotonicity,[status(thm)],[1263])).
% 0.64/0.84 tff(1265,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(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(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(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 0.64/0.84 inference(transitivity,[status(thm)],[1264, 1262])).
% 0.64/0.84 tff(1266,plain,
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% 0.64/0.84 inference(quant_inst,[status(thm)],[])).
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% 0.64/0.84 inference(modus_ponens,[status(thm)],[1266, 1265])).
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% 0.64/0.84 inference(unit_resolution,[status(thm)],[1267, 14, 329, 1253])).
% 0.64/0.84 tff(1269,plain,
% 0.64/0.84 (b(s(z), s(s(s(s(s(z))))))),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[791, 1268])).
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% 0.64/0.84 inference(unit_resolution,[status(thm)],[775, 1269, 1261])).
% 0.64/0.84 tff(1271,plain,((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
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% 0.64/0.84 inference(unit_resolution,[status(thm)],[1271, 1193, 1153, 1191, 1143, 1252])).
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% 0.64/0.84 inference(unit_resolution,[status(thm)],[210, 1276])).
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% 0.64/0.84 inference(rewrite,[status(thm)],[])).
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% 0.64/0.84 inference(rewrite,[status(thm)],[])).
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% 0.64/0.84 inference(monotonicity,[status(thm)],[1279])).
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% 0.64/0.85 inference(transitivity,[status(thm)],[1280, 1278])).
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% 0.64/0.85 inference(modus_ponens,[status(thm)],[1282, 1281])).
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% 0.64/0.85 tff(1290,plain,
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% 0.64/0.85 inference(unit_resolution,[status(thm)],[1289, 274, 175, 160])).
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% 0.64/0.85 inference(unit_resolution,[status(thm)],[434, 1290])).
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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)],[1315, 1314])).
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% 0.64/0.85 inference(monotonicity,[status(thm)],[1320])).
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% 0.64/0.85 inference(transitivity,[status(thm)],[1321, 1319])).
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% 0.64/0.85 tff(1326,plain,
% 0.64/0.85 (b(s(z), s(s(s(s(s(z))))))),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[791, 1325])).
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% 0.64/0.85 inference(unit_resolution,[status(thm)],[182, 177, 175])).
% 0.64/0.85 tff(1328,plain,
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% 0.64/0.85 inference(unit_resolution,[status(thm)],[668, 1327])).
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% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(1331,plain,
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% 0.64/0.85 inference(monotonicity,[status(thm)],[1330])).
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% 0.64/0.85 inference(transitivity,[status(thm)],[1331, 1329])).
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% 0.64/0.85 inference(modus_ponens,[status(thm)],[1333, 1332])).
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% 0.64/0.85 inference(unit_resolution,[status(thm)],[1334, 118, 960, 1328, 1326, 1318, 1313])).
% 0.64/0.85 tff(1336,plain,((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.85 tff(1337,plain,
% 0.64/0.85 (~r(s(s(s(s(s(z))))), z)),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[1336, 177, 175])).
% 0.64/0.85 tff(1338,plain,
% 0.64/0.85 (b(s(s(s(s(s(z))))), z)),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[767, 1337])).
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% 0.64/0.85 inference(unit_resolution,[status(thm)],[376, 14, 329, 177, 339])).
% 0.64/0.85 tff(1340,plain,((~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.85 tff(1341,plain,
% 0.64/0.85 (~r(z, s(s(s(s(z)))))),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[1340, 177, 1143])).
% 0.64/0.85 tff(1342,plain,
% 0.64/0.85 (b(z, s(s(s(s(z)))))),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[389, 1341])).
% 0.64/0.85 tff(1343,plain,
% 0.64/0.85 (b(s(z), s(s(s(s(s(s(z)))))))),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[232, 336])).
% 0.64/0.85 tff(1344,plain,
% 0.64/0.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
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% 0.64/0.85 (((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
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% 0.64/0.85 inference(monotonicity,[status(thm)],[1345])).
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% 0.64/0.85 inference(transitivity,[status(thm)],[1346, 1344])).
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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)],[1348, 1347])).
% 0.64/0.85 tff(1350,plain,
% 0.64/0.85 (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[1349, 118, 173, 172, 1343, 365])).
% 0.64/0.85 tff(1351,plain,
% 0.64/0.85 (r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[581, 1350])).
% 0.64/0.85 tff(1352,assumption,(b(s(s(s(s(s(z))))), s(s(s(s(z)))))), introduced(assumption)).
% 0.64/0.85 tff(1353,plain,
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% 0.64/0.85 inference(rewrite,[status(thm)],[])).
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% 0.64/0.85 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
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% 0.64/0.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 0.64/0.85 inference(monotonicity,[status(thm)],[1354])).
% 0.64/0.85 tff(1356,plain,
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% 0.64/0.85 inference(transitivity,[status(thm)],[1355, 1353])).
% 0.64/0.85 tff(1357,plain,
% 0.64/0.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 0.64/0.85 inference(quant_inst,[status(thm)],[])).
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% 0.64/0.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 0.64/0.85 inference(modus_ponens,[status(thm)],[1357, 1356])).
% 0.64/0.85 tff(1359,plain,
% 0.64/0.85 ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[1358, 118, 594, 721, 1205])).
% 0.64/0.85 tff(1360,plain,
% 0.64/0.85 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[1359, 1352])).
% 0.64/0.85 tff(1361,plain,
% 0.64/0.86 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[848, 46, 800, 1360])).
% 0.64/0.86 tff(1362,plain,
% 0.64/0.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 0.64/0.86 inference(rewrite,[status(thm)],[])).
% 0.64/0.86 tff(1363,plain,
% 0.64/0.86 (((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))))) <=> ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 0.64/0.86 inference(rewrite,[status(thm)],[])).
% 0.64/0.86 tff(1364,plain,
% 0.64/0.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))))),
% 0.64/0.86 inference(monotonicity,[status(thm)],[1363])).
% 0.64/0.86 tff(1365,plain,
% 0.64/0.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 0.64/0.86 inference(transitivity,[status(thm)],[1364, 1362])).
% 0.64/0.86 tff(1366,plain,
% 0.64/0.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))),
% 0.64/0.86 inference(quant_inst,[status(thm)],[])).
% 0.64/0.86 tff(1367,plain,
% 0.64/0.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))),
% 0.64/0.86 inference(modus_ponens,[status(thm)],[1366, 1365])).
% 0.64/0.86 tff(1368,plain,
% 0.64/0.86 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[1367, 118, 1, 436, 1205, 1352])).
% 0.64/0.86 tff(1369,plain,
% 0.64/0.86 (r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[744, 1368, 735])).
% 0.64/0.86 tff(1370,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(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), 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(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))),
% 0.64/0.86 inference(rewrite,[status(thm)],[])).
% 0.64/0.86 tff(1371,plain,
% 0.64/0.86 (((~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))),
% 0.64/0.86 inference(rewrite,[status(thm)],[])).
% 0.64/0.86 tff(1372,plain,
% 0.64/0.86 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(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(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))))))),
% 0.64/0.86 inference(monotonicity,[status(thm)],[1371])).
% 0.64/0.86 tff(1373,plain,
% 0.64/0.86 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(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(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))),
% 0.64/0.86 inference(transitivity,[status(thm)],[1372, 1370])).
% 0.64/0.86 tff(1374,plain,
% 0.64/0.86 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 0.64/0.86 inference(quant_inst,[status(thm)],[])).
% 0.64/0.86 tff(1375,plain,
% 0.64/0.86 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))))),
% 0.64/0.86 inference(modus_ponens,[status(thm)],[1374, 1373])).
% 0.64/0.86 tff(1376,plain,
% 0.64/0.86 ($false),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[1375, 14, 53, 1369, 1361])).
% 0.64/0.86 tff(1377,plain,((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.86 tff(1378,plain,
% 0.64/0.86 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[1377, 1351, 1, 436, 1205, 403, 721])).
% 0.64/0.86 tff(1379,plain,
% 0.64/0.86 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[869, 1378, 861])).
% 0.64/0.86 tff(1380,plain,
% 0.64/0.86 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(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(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 0.64/0.86 inference(rewrite,[status(thm)],[])).
% 0.64/0.86 tff(1381,plain,
% 0.64/0.86 (((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 0.64/0.86 inference(rewrite,[status(thm)],[])).
% 0.64/0.86 tff(1382,plain,
% 0.64/0.86 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(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(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 0.64/0.86 inference(monotonicity,[status(thm)],[1381])).
% 0.64/0.86 tff(1383,plain,
% 0.64/0.86 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(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(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 0.64/0.86 inference(transitivity,[status(thm)],[1382, 1380])).
% 0.64/0.86 tff(1384,plain,
% 0.64/0.86 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 0.64/0.86 inference(quant_inst,[status(thm)],[])).
% 0.64/0.86 tff(1385,plain,
% 0.64/0.86 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 0.64/0.86 inference(modus_ponens,[status(thm)],[1384, 1383])).
% 0.64/0.86 tff(1386,plain,
% 0.64/0.86 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[1385, 14, 272, 1379])).
% 0.64/0.86 tff(1387,plain,
% 0.64/0.86 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[753, 1386, 734])).
% 0.64/0.86 tff(1388,plain,
% 0.64/0.86 (~r(s(z), s(s(s(s(s(z))))))),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[1267, 14, 329, 1379])).
% 0.64/0.86 tff(1389,plain,
% 0.64/0.86 (b(s(z), s(s(s(s(s(z))))))),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[791, 1388])).
% 0.64/0.86 tff(1390,plain,
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% 0.64/0.86 inference(rewrite,[status(thm)],[])).
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% 0.64/0.86 inference(commutativity,[status(thm)],[])).
% 0.64/0.86 tff(1424,plain,
% 0.64/0.86 ((s(s(s(s(s(z))))) = z) <=> (z = s(s(s(s(s(z))))))),
% 0.64/0.86 inference(symmetry,[status(thm)],[1423])).
% 0.64/0.86 tff(1425,plain,
% 0.64/0.86 ((~(s(s(s(s(s(z))))) = z)) <=> (~(z = s(s(s(s(s(z)))))))),
% 0.64/0.86 inference(monotonicity,[status(thm)],[1424])).
% 0.64/0.86 tff(1426,plain,
% 0.64/0.86 (~(z = s(s(s(s(s(z))))))),
% 0.64/0.86 inference(modus_ponens,[status(thm)],[203, 1425])).
% 0.64/0.86 tff(1427,plain,
% 0.64/0.86 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(s(z)))))) | b(z, s(s(s(s(s(z)))))) | r(z, s(s(s(s(s(z)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(s(z)))))) | b(z, s(s(s(s(s(z)))))) | r(z, s(s(s(s(s(z)))))))),
% 0.64/0.86 inference(rewrite,[status(thm)],[])).
% 0.64/0.86 tff(1428,plain,
% 0.64/0.86 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(s(z)))))) | b(z, s(s(s(s(s(z)))))) | r(z, s(s(s(s(s(z)))))))),
% 0.64/0.86 inference(quant_inst,[status(thm)],[])).
% 0.64/0.86 tff(1429,plain,
% 0.64/0.86 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(s(z)))))) | b(z, s(s(s(s(s(z)))))) | r(z, s(s(s(s(s(z))))))),
% 0.64/0.86 inference(modus_ponens,[status(thm)],[1428, 1427])).
% 0.64/0.86 tff(1430,plain,
% 0.64/0.86 ((z = s(s(s(s(s(z)))))) | b(z, s(s(s(s(s(z)))))) | r(z, s(s(s(s(s(z))))))),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[1429, 46])).
% 0.64/0.86 tff(1431,plain,
% 0.64/0.86 (b(z, s(s(s(s(s(z)))))) | r(z, s(s(s(s(s(z))))))),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[1430, 1426])).
% 0.64/0.86 tff(1432,plain,
% 0.64/0.86 (b(z, s(s(s(s(s(z))))))),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[1431, 1422])).
% 0.64/0.86 tff(1433,plain,
% 0.64/0.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))))),
% 0.64/0.87 inference(rewrite,[status(thm)],[])).
% 0.64/0.87 tff(1434,plain,
% 0.64/0.87 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z)))))))) <=> ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))))),
% 0.64/0.87 inference(rewrite,[status(thm)],[])).
% 0.64/0.87 tff(1435,plain,
% 0.64/0.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z)))))))))),
% 0.64/0.87 inference(monotonicity,[status(thm)],[1434])).
% 0.64/0.87 tff(1436,plain,
% 0.64/0.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))))),
% 0.64/0.87 inference(transitivity,[status(thm)],[1435, 1433])).
% 0.64/0.87 tff(1437,plain,
% 0.64/0.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))))),
% 0.64/0.87 inference(quant_inst,[status(thm)],[])).
% 0.64/0.87 tff(1438,plain,
% 0.64/0.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z)))))))),
% 0.64/0.87 inference(modus_ponens,[status(thm)],[1437, 1436])).
% 0.64/0.87 tff(1439,plain,
% 0.64/0.87 ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z)))))))),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[1438, 118, 1311, 1342, 1338])).
% 0.64/0.87 tff(1440,plain,
% 0.64/0.87 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[1439, 1432])).
% 0.64/0.87 tff(1441,plain,
% 0.64/0.87 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[869, 1440, 861])).
% 0.64/0.87 tff(1442,plain,
% 0.64/0.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 0.64/0.87 inference(rewrite,[status(thm)],[])).
% 0.64/0.87 tff(1443,plain,
% 0.64/0.87 (((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))) <=> ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 0.64/0.87 inference(rewrite,[status(thm)],[])).
% 0.64/0.87 tff(1444,plain,
% 0.64/0.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))))),
% 0.64/0.87 inference(monotonicity,[status(thm)],[1443])).
% 0.64/0.87 tff(1445,plain,
% 0.64/0.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 0.64/0.87 inference(transitivity,[status(thm)],[1444, 1442])).
% 0.64/0.87 tff(1446,plain,
% 0.64/0.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 0.64/0.87 inference(quant_inst,[status(thm)],[])).
% 0.64/0.87 tff(1447,plain,
% 0.64/0.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 0.64/0.87 inference(modus_ponens,[status(thm)],[1446, 1445])).
% 0.64/0.87 tff(1448,plain,
% 0.64/0.87 (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[1447, 118, 1400, 1311, 911, 1342])).
% 0.64/0.87 tff(1449,plain,
% 0.64/0.87 (r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[480, 1448])).
% 0.64/0.87 tff(1450,plain,
% 0.64/0.87 (((~![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(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(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(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 0.64/0.87 inference(rewrite,[status(thm)],[])).
% 0.64/0.87 tff(1451,plain,
% 0.64/0.87 ((~![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(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 0.64/0.87 inference(quant_inst,[status(thm)],[])).
% 0.64/0.87 tff(1452,plain,
% 0.64/0.87 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 0.64/0.87 inference(modus_ponens,[status(thm)],[1451, 1450])).
% 0.64/0.87 tff(1453,plain,
% 0.64/0.87 ($false),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[1452, 14, 1449, 1405, 1441])).
% 0.64/0.87 tff(1454,plain,((~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.87 tff(1455,plain,
% 0.64/0.87 (~r(s(z), z)),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[1454, 175, 160])).
% 0.64/0.87 tff(1456,plain,
% 0.64/0.87 (b(s(z), z)),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[187, 1455])).
% 0.64/0.87 tff(1457,plain,
% 0.64/0.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(z))))))),
% 0.64/0.87 inference(rewrite,[status(thm)],[])).
% 0.64/0.87 tff(1458,plain,
% 0.64/0.87 (((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z)))) <=> ((~b(s(z), s(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(z, s(s(s(z))))))),
% 0.64/0.87 inference(rewrite,[status(thm)],[])).
% 0.64/0.87 tff(1459,plain,
% 0.64/0.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(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(z, s(s(s(z)))))))),
% 0.64/0.87 inference(monotonicity,[status(thm)],[1458])).
% 0.64/0.87 tff(1460,plain,
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% 0.64/0.87 inference(transitivity,[status(thm)],[1459, 1457])).
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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)],[1461, 1460])).
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% 0.64/0.87 inference(unit_resolution,[status(thm)],[1462, 118, 234, 172, 1, 271, 236])).
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% 0.64/0.87 tff(1465,plain,
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% 0.64/0.87 inference(unit_resolution,[status(thm)],[1464, 236, 172, 1, 234])).
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% 0.64/0.87 inference(unit_resolution,[status(thm)],[71, 1465])).
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% 0.64/0.87 inference(unit_resolution,[status(thm)],[169, 1466, 160])).
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% 0.64/0.87 inference(unit_resolution,[status(thm)],[356, 1467])).
% 0.64/0.87 tff(1469,plain,
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% 0.64/0.87 inference(unit_resolution,[status(thm)],[691, 365, 234, 272, 1343, 311, 160])).
% 0.64/0.87 tff(1470,plain,
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% 0.64/0.87 inference(unit_resolution,[status(thm)],[245, 1343, 1, 234, 365])).
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% 0.64/0.87 tff(1473,plain,
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% 0.64/0.87 inference(unit_resolution,[status(thm)],[1472, 1, 234, 160, 329])).
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% 0.64/0.87 inference(unit_resolution,[status(thm)],[434, 1473])).
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% 0.64/0.87 inference(unit_resolution,[status(thm)],[389, 1475])).
% 0.64/0.87 tff(1477,plain,
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% 0.64/0.87 inference(unit_resolution,[status(thm)],[449, 1476, 329])).
% 0.64/0.87 tff(1478,plain,
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% 0.64/0.87 inference(unit_resolution,[status(thm)],[51, 1477])).
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% 0.64/0.87 tff(1480,plain,((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.87 tff(1481,plain,
% 0.64/0.87 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[1480, 1456, 911, 1143, 1311, 160, 904])).
% 0.64/0.87 tff(1482,plain,
% 0.64/0.87 (r(s(s(s(s(s(s(z)))))), s(z))),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[210, 1481])).
% 0.64/0.87 tff(1483,plain,
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% 0.64/0.87 inference(unit_resolution,[status(thm)],[1472, 911, 1456, 160, 1143])).
% 0.64/0.87 tff(1484,plain,
% 0.64/0.87 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[434, 1483])).
% 0.64/0.87 tff(1485,plain,
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% 0.64/0.87 tff(1486,plain,((~r(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.87 tff(1487,plain,
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% 0.64/0.87 inference(unit_resolution,[status(thm)],[1486, 1456, 904, 1482, 160])).
% 0.64/0.87 tff(1488,plain,
% 0.64/0.87 (b(z, s(s(s(s(s(s(z)))))))),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[356, 1487])).
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% 0.64/0.87 inference(unit_resolution,[status(thm)],[1002, 1488, 911, 1311, 1484])).
% 0.64/0.87 tff(1490,plain,
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% 0.64/0.87 inference(unit_resolution,[status(thm)],[480, 1489])).
% 0.64/0.87 tff(1491,plain,
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% 0.64/0.87 inference(unit_resolution,[status(thm)],[1125, 1490, 1482])).
% 0.64/0.87 tff(1492,plain,
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% 0.64/0.87 inference(unit_resolution,[status(thm)],[513, 1491])).
% 0.64/0.87 tff(1493,plain,
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% 0.64/0.87 inference(unit_resolution,[status(thm)],[951, 1482, 160])).
% 0.64/0.87 tff(1494,plain,
% 0.64/0.87 (b(s(s(s(z))), s(z))),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[105, 1493])).
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% 0.64/0.87 inference(rewrite,[status(thm)],[])).
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% 0.64/0.87 (((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)))),
% 0.64/0.87 inference(rewrite,[status(thm)],[])).
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% 0.64/0.87 inference(monotonicity,[status(thm)],[1496])).
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% 0.64/0.87 inference(transitivity,[status(thm)],[1497, 1495])).
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% 0.64/0.87 inference(modus_ponens,[status(thm)],[1499, 1498])).
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% 0.64/0.87 inference(unit_resolution,[status(thm)],[402, 1502])).
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% 0.64/0.87 inference(unit_resolution,[status(thm)],[1413, 1488, 911, 1311, 1484])).
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% 0.64/0.87 tff(1507,plain,((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.87 tff(1508,plain,
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% 0.64/0.87 inference(rewrite,[status(thm)],[])).
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% 0.64/0.87 (((~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))),
% 0.64/0.87 inference(rewrite,[status(thm)],[])).
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% 0.64/0.87 inference(monotonicity,[status(thm)],[1511])).
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% 0.64/0.87 inference(transitivity,[status(thm)],[1512, 1510])).
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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)],[1514, 1513])).
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% 0.64/0.88 inference(modus_ponens,[status(thm)],[1527, 1526])).
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% 0.64/0.88 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
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% 0.64/0.88 inference(unit_resolution,[status(thm)],[581, 1560])).
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% 0.64/0.88 inference(rewrite,[status(thm)],[])).
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% 0.64/0.88 (((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 0.64/0.88 inference(rewrite,[status(thm)],[])).
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% 0.64/0.88 inference(monotonicity,[status(thm)],[1563])).
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% 0.64/0.88 inference(transitivity,[status(thm)],[1564, 1562])).
% 0.64/0.88 tff(1566,plain,
% 0.64/0.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(z))))),
% 0.64/0.88 inference(quant_inst,[status(thm)],[])).
% 0.64/0.88 tff(1567,plain,
% 0.64/0.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 0.64/0.88 inference(modus_ponens,[status(thm)],[1566, 1565])).
% 0.64/0.88 tff(1568,plain,
% 0.64/0.88 (~b(s(z), s(s(s(s(s(s(z)))))))),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[1567, 118, 1542, 1534, 1544, 1561])).
% 0.64/0.88 tff(1569,plain,
% 0.64/0.88 (r(s(z), s(s(s(s(s(s(z)))))))),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[232, 1568])).
% 0.64/0.88 tff(1570,plain,
% 0.64/0.88 (~r(s(z), z)),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[1027, 1569, 3])).
% 0.64/0.88 tff(1571,plain,
% 0.64/0.88 (b(s(z), z)),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[187, 1570])).
% 0.64/0.88 tff(1572,plain,
% 0.64/0.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(z), z)))),
% 0.64/0.88 inference(rewrite,[status(thm)],[])).
% 0.64/0.88 tff(1573,plain,
% 0.64/0.88 (((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(z), z)))),
% 0.64/0.88 inference(rewrite,[status(thm)],[])).
% 0.64/0.88 tff(1574,plain,
% 0.64/0.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(z), z))))),
% 0.64/0.88 inference(monotonicity,[status(thm)],[1573])).
% 0.64/0.88 tff(1575,plain,
% 0.64/0.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(z), z)))),
% 0.64/0.88 inference(transitivity,[status(thm)],[1574, 1572])).
% 0.64/0.88 tff(1576,plain,
% 0.64/0.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))),
% 0.64/0.88 inference(quant_inst,[status(thm)],[])).
% 0.64/0.88 tff(1577,plain,
% 0.64/0.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(z), z))),
% 0.64/0.88 inference(modus_ponens,[status(thm)],[1576, 1575])).
% 0.64/0.88 tff(1578,plain,
% 0.64/0.88 ($false),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[1577, 118, 961, 174, 234, 721, 436])).
% 0.64/0.88 tff(1579,plain,((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.88 tff(1580,plain,
% 0.64/0.88 (~b(s(s(s(s(z)))), s(z))),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[1579, 1571, 1559, 1548, 52])).
% 0.64/0.88 tff(1581,plain,
% 0.64/0.88 (r(s(s(s(s(z)))), s(z))),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[513, 1580])).
% 0.64/0.88 tff(1582,plain,
% 0.64/0.88 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[1125, 1581, 2])).
% 0.64/0.88 tff(1583,plain,
% 0.64/0.88 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[480, 1582])).
% 0.64/0.88 tff(1584,assumption,(r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))), introduced(assumption)).
% 0.64/0.88 tff(1585,plain,
% 0.64/0.88 ($false),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[1167, 14, 2, 1584, 1164])).
% 0.64/0.88 tff(1586,plain,((~r(s(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(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.88 tff(1587,plain,
% 0.64/0.88 (~r(s(s(s(s(s(z))))), s(z))),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[1586, 1584, 2])).
% 0.64/0.88 tff(1588,plain,
% 0.64/0.88 (b(s(s(s(s(s(z))))), s(z))),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[829, 1587])).
% 0.64/0.88 tff(1589,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(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(s(s(z))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(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(s(s(z))))))))),
% 0.64/0.88 inference(rewrite,[status(thm)],[])).
% 0.64/0.88 tff(1590,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(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(s(s(z))))))))),
% 0.64/0.88 inference(quant_inst,[status(thm)],[])).
% 0.64/0.88 tff(1591,plain,
% 0.64/0.88 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))))),
% 0.64/0.88 inference(modus_ponens,[status(thm)],[1590, 1589])).
% 0.64/0.88 tff(1592,plain,
% 0.64/0.88 ($false),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[1591, 14, 272, 1584, 1253])).
% 0.64/0.88 tff(1593,plain,((~r(s(s(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(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.88 tff(1594,plain,
% 0.64/0.88 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[1593, 1584, 272])).
% 0.64/0.88 tff(1595,plain,
% 0.64/0.88 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) | r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[869, 861])).
% 0.64/0.88 tff(1596,plain,
% 0.64/0.88 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[1595, 1594])).
% 0.64/0.88 tff(1597,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)))), 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)))))))),
% 0.64/0.88 inference(rewrite,[status(thm)],[])).
% 0.64/0.88 tff(1598,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)))), 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)))))))),
% 0.64/0.88 inference(quant_inst,[status(thm)],[])).
% 0.64/0.88 tff(1599,plain,
% 0.64/0.88 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 0.64/0.88 inference(modus_ponens,[status(thm)],[1598, 1597])).
% 0.64/0.88 tff(1600,plain,
% 0.64/0.88 ($false),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[1599, 14, 495, 272, 2])).
% 0.64/0.88 tff(1601,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.88 tff(1602,plain,
% 0.64/0.88 (~r(s(s(s(s(z)))), s(z))),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[1601, 2, 272])).
% 0.64/0.88 tff(1603,plain,
% 0.64/0.88 (b(s(s(s(s(z)))), s(z))),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[513, 1602])).
% 0.64/0.88 tff(1604,plain,
% 0.64/0.88 ($false),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[363, 14, 329, 272, 2])).
% 0.64/0.88 tff(1605,plain,((~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)))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.88 tff(1606,plain,
% 0.64/0.88 (~r(s(z), s(s(s(s(z)))))),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[1605, 2, 272])).
% 0.64/0.88 tff(1607,plain,
% 0.64/0.88 (b(s(z), s(s(s(s(z)))))),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[323, 1606])).
% 0.64/0.88 tff(1608,plain,
% 0.64/0.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 0.64/0.88 inference(rewrite,[status(thm)],[])).
% 0.64/0.88 tff(1609,plain,
% 0.64/0.88 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 0.64/0.88 inference(rewrite,[status(thm)],[])).
% 0.64/0.88 tff(1610,plain,
% 0.64/0.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 0.64/0.88 inference(monotonicity,[status(thm)],[1609])).
% 0.64/0.88 tff(1611,plain,
% 0.64/0.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 0.64/0.88 inference(transitivity,[status(thm)],[1610, 1608])).
% 0.64/0.88 tff(1612,plain,
% 0.64/0.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 0.64/0.88 inference(quant_inst,[status(thm)],[])).
% 0.64/0.88 tff(1613,plain,
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% 0.64/0.88 inference(modus_ponens,[status(thm)],[1612, 1611])).
% 0.64/0.88 tff(1614,plain,
% 0.64/0.88 ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[1613, 118, 1607, 1603, 1596])).
% 0.64/0.88 tff(1615,plain,
% 0.64/0.88 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[1614, 1588])).
% 0.64/0.88 tff(1616,plain,
% 0.64/0.88 (b(s(s(s(s(z)))), s(s(s(s(s(z)))))) | r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[814, 802])).
% 0.64/0.88 tff(1617,plain,
% 0.64/0.88 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[1616, 1615])).
% 0.64/0.88 tff(1618,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(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), 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(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 0.64/0.88 inference(rewrite,[status(thm)],[])).
% 0.64/0.88 tff(1619,plain,
% 0.64/0.88 (((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(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(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 0.64/0.88 inference(rewrite,[status(thm)],[])).
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% 0.64/0.88 inference(monotonicity,[status(thm)],[1619])).
% 0.64/0.88 tff(1621,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)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(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(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 0.64/0.88 inference(transitivity,[status(thm)],[1620, 1618])).
% 0.64/0.88 tff(1622,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)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 0.64/0.88 inference(quant_inst,[status(thm)],[])).
% 0.64/0.88 tff(1623,plain,
% 0.64/0.88 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 0.64/0.88 inference(modus_ponens,[status(thm)],[1622, 1621])).
% 0.64/0.88 tff(1624,plain,
% 0.64/0.88 ($false),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[1623, 14, 272, 1617, 1584])).
% 0.64/0.88 tff(1625,plain,((~r(s(s(s(s(s(s(z)))))), s(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)))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.88 tff(1626,plain,
% 0.64/0.88 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[1625, 2, 272])).
% 0.64/0.89 tff(1627,plain,
% 0.64/0.89 (b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))) | r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[744, 735])).
% 0.64/0.89 tff(1628,plain,
% 0.64/0.89 (b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[1627, 1626])).
% 0.64/0.89 tff(1629,plain,
% 0.64/0.89 (~r(z, s(s(s(s(z)))))),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[347, 3, 272])).
% 0.64/0.89 tff(1630,plain,
% 0.64/0.89 (b(z, s(s(s(s(z)))))),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[389, 1629])).
% 0.64/0.89 tff(1631,plain,
% 0.64/0.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(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(z)))), z)) | (~b(z, s(z))))),
% 0.64/0.89 inference(rewrite,[status(thm)],[])).
% 0.64/0.89 tff(1632,plain,
% 0.64/0.89 (((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, s(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(z)))), z)) | (~b(z, s(z))))),
% 0.64/0.89 inference(rewrite,[status(thm)],[])).
% 0.64/0.89 tff(1633,plain,
% 0.64/0.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(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(z)))), z)) | (~b(z, s(z)))))),
% 0.64/0.89 inference(monotonicity,[status(thm)],[1632])).
% 0.64/0.89 tff(1634,plain,
% 0.64/0.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(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(z)))), z)) | (~b(z, s(z))))),
% 0.64/0.89 inference(transitivity,[status(thm)],[1633, 1631])).
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% 0.64/0.89 inference(quant_inst,[status(thm)],[])).
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% 0.64/0.89 inference(modus_ponens,[status(thm)],[1635, 1634])).
% 0.64/0.89 tff(1637,plain,
% 0.64/0.89 (~b(s(s(s(s(z)))), z)),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[1636, 118, 1607, 1603, 52, 1630])).
% 0.64/0.89 tff(1638,plain,
% 0.64/0.89 (r(s(s(s(s(z)))), z)),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[286, 1637])).
% 0.64/0.89 tff(1639,plain,
% 0.64/0.89 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[551, 1638, 3])).
% 0.64/0.89 tff(1640,plain,
% 0.64/0.89 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[480, 1639])).
% 0.64/0.89 tff(1641,plain,
% 0.64/0.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 0.64/0.89 inference(rewrite,[status(thm)],[])).
% 0.64/0.89 tff(1642,plain,
% 0.64/0.89 (((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 0.64/0.89 inference(rewrite,[status(thm)],[])).
% 0.64/0.89 tff(1643,plain,
% 0.64/0.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z))))),
% 0.64/0.89 inference(monotonicity,[status(thm)],[1642])).
% 0.64/0.89 tff(1644,plain,
% 0.64/0.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 0.64/0.89 inference(transitivity,[status(thm)],[1643, 1641])).
% 0.64/0.89 tff(1645,plain,
% 0.64/0.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 0.64/0.89 inference(quant_inst,[status(thm)],[])).
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% 0.64/0.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z))),
% 0.64/0.89 inference(modus_ponens,[status(thm)],[1645, 1644])).
% 0.64/0.89 tff(1647,plain,
% 0.64/0.89 ($false),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[1646, 118, 961, 174, 436, 1205, 1352])).
% 0.64/0.89 tff(1648,plain,((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.89 tff(1649,plain,
% 0.64/0.89 (~b(s(s(s(s(s(z))))), z)),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[1648, 52, 1603, 1352, 1630])).
% 0.64/0.89 tff(1650,plain,
% 0.64/0.89 (r(s(s(s(s(s(z))))), z)),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[767, 1649])).
% 0.64/0.89 tff(1651,plain,
% 0.64/0.89 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[1240, 14, 274, 736])).
% 0.64/0.89 tff(1652,plain,
% 0.64/0.89 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[1616, 1651])).
% 0.64/0.89 tff(1653,plain,
% 0.64/0.89 (((~![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(z))))), z)) | (~r(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(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 0.64/0.89 inference(rewrite,[status(thm)],[])).
% 0.64/0.89 tff(1654,plain,
% 0.64/0.89 ((~![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(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 0.64/0.89 inference(quant_inst,[status(thm)],[])).
% 0.64/0.89 tff(1655,plain,
% 0.64/0.89 ((~![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(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 0.64/0.89 inference(modus_ponens,[status(thm)],[1654, 1653])).
% 0.64/0.89 tff(1656,plain,
% 0.64/0.89 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[1655, 14, 274, 736])).
% 0.64/0.89 tff(1657,plain,
% 0.64/0.89 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[1595, 1656])).
% 0.64/0.89 tff(1658,plain,
% 0.64/0.89 (~r(s(s(s(s(z)))), s(z))),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[974, 14, 177, 274])).
% 0.64/0.89 tff(1659,plain,
% 0.64/0.89 (b(s(s(s(s(z)))), s(z))),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[513, 1658])).
% 0.64/0.89 tff(1660,plain,
% 0.64/0.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 0.64/0.89 inference(rewrite,[status(thm)],[])).
% 0.64/0.89 tff(1661,plain,
% 0.64/0.89 (((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 0.64/0.89 inference(rewrite,[status(thm)],[])).
% 0.64/0.89 tff(1662,plain,
% 0.64/0.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 0.64/0.89 inference(monotonicity,[status(thm)],[1661])).
% 0.64/0.89 tff(1663,plain,
% 0.64/0.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 0.64/0.89 inference(transitivity,[status(thm)],[1662, 1660])).
% 0.64/0.89 tff(1664,plain,
% 0.64/0.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 0.64/0.89 inference(quant_inst,[status(thm)],[])).
% 0.64/0.89 tff(1665,plain,
% 0.64/0.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 0.64/0.89 inference(modus_ponens,[status(thm)],[1664, 1663])).
% 0.64/0.89 tff(1666,plain,
% 0.64/0.89 ($false),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[1665, 118, 1659, 1657, 1652, 1326, 1318])).
% 0.64/0.89 tff(1667,plain,((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.89 tff(1668,plain,
% 0.64/0.89 (~r(s(z), z)),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[1667, 1650, 274])).
% 0.64/0.89 tff(1669,plain,
% 0.64/0.89 (b(s(z), z)),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[187, 1668])).
% 0.64/0.89 tff(1670,plain,
% 0.64/0.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(z), z)))),
% 0.64/0.89 inference(rewrite,[status(thm)],[])).
% 0.64/0.89 tff(1671,plain,
% 0.64/0.89 (((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z))) <=> ((~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(z), z)))),
% 0.64/0.89 inference(rewrite,[status(thm)],[])).
% 0.64/0.89 tff(1672,plain,
% 0.64/0.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(z), z))))),
% 0.64/0.89 inference(monotonicity,[status(thm)],[1671])).
% 0.64/0.89 tff(1673,plain,
% 0.64/0.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(z), z)))),
% 0.64/0.89 inference(transitivity,[status(thm)],[1672, 1670])).
% 0.64/0.89 tff(1674,plain,
% 0.64/0.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))),
% 0.64/0.89 inference(quant_inst,[status(thm)],[])).
% 0.64/0.89 tff(1675,plain,
% 0.64/0.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(z), z))),
% 0.64/0.89 inference(modus_ponens,[status(thm)],[1674, 1673])).
% 0.64/0.89 tff(1676,plain,
% 0.64/0.89 ($false),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[1675, 118, 1607, 1603, 52, 1669, 1630])).
% 0.64/0.89 tff(1677,plain,((~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.89 tff(1678,plain,
% 0.64/0.89 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[1677, 1638, 3, 2, 272])).
% 0.64/0.89 tff(1679,plain,
% 0.64/0.89 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[1595, 1678])).
% 0.64/0.89 tff(1680,assumption,(r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 0.64/0.89 tff(1681,plain,
% 0.64/0.89 ($false),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[1385, 14, 272, 1680, 1253])).
% 0.64/0.89 tff(1682,plain,((~r(s(s(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(z))))), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.89 tff(1683,plain,
% 0.64/0.89 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[1682, 1679, 272])).
% 0.64/0.89 tff(1684,plain,
% 0.64/0.89 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[753, 734])).
% 0.64/0.89 tff(1685,plain,
% 0.64/0.89 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[1684, 1683])).
% 0.64/0.89 tff(1686,plain,
% 0.64/0.89 (~b(s(z), z)),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[1675, 118, 1607, 1603, 52, 1630])).
% 0.64/0.89 tff(1687,plain,
% 0.64/0.89 (r(s(z), z)),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[187, 1686])).
% 0.64/0.89 tff(1688,plain,
% 0.64/0.89 (~r(s(s(s(s(s(z))))), z)),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[1667, 1687, 1638])).
% 0.64/0.89 tff(1689,plain,
% 0.64/0.89 (b(s(s(s(s(s(z))))), z)),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[767, 1688])).
% 0.64/0.89 tff(1690,assumption,(b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 0.64/0.89 tff(1691,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)],[396, 391, 272])).
% 0.64/0.89 tff(1692,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)],[156, 1691])).
% 0.64/0.89 tff(1693,plain,
% 0.64/0.89 (~r(s(s(s(z))), z)),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[703, 391, 274])).
% 0.64/0.89 tff(1694,plain,
% 0.64/0.89 (b(s(s(s(z))), z)),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[649, 1693])).
% 0.64/0.89 tff(1695,assumption,(b(s(s(s(z))), z)), introduced(assumption)).
% 0.64/0.89 tff(1696,plain,
% 0.64/0.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 0.64/0.89 inference(rewrite,[status(thm)],[])).
% 0.64/0.89 tff(1697,plain,
% 0.64/0.89 (((~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(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 0.64/0.89 inference(rewrite,[status(thm)],[])).
% 0.64/0.89 tff(1698,plain,
% 0.64/0.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))))),
% 0.64/0.89 inference(monotonicity,[status(thm)],[1697])).
% 0.64/0.89 tff(1699,plain,
% 0.64/0.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 0.64/0.89 inference(transitivity,[status(thm)],[1698, 1696])).
% 0.64/0.89 tff(1700,plain,
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% 0.64/0.89 inference(quant_inst,[status(thm)],[])).
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% 0.64/0.89 inference(modus_ponens,[status(thm)],[1700, 1699])).
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% 0.64/0.89 inference(unit_resolution,[status(thm)],[1701, 118, 1695, 587, 73, 459, 1])).
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% 0.64/0.89 inference(unit_resolution,[status(thm)],[1703, 1694, 1, 459, 1692])).
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% 0.64/0.89 inference(unit_resolution,[status(thm)],[310, 1704])).
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% 0.64/0.90 inference(rewrite,[status(thm)],[])).
% 0.64/0.90 tff(1710,plain,
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% 0.64/0.90 inference(monotonicity,[status(thm)],[1709])).
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% 0.64/0.90 inference(transitivity,[status(thm)],[1710, 1708])).
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% 0.64/0.90 inference(quant_inst,[status(thm)],[])).
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% 0.64/0.90 inference(modus_ponens,[status(thm)],[1712, 1711])).
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% 0.64/0.90 inference(unit_resolution,[status(thm)],[1713, 118, 1692, 1, 1707, 1205, 1690])).
% 0.64/0.90 tff(1715,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.90 tff(1716,plain,
% 0.64/0.90 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 0.64/0.90 inference(unit_resolution,[status(thm)],[1715, 1689, 1, 1685, 1638, 1640, 272])).
% 0.64/0.90 tff(1717,plain,
% 0.64/0.90 (b(s(s(s(z))), s(s(s(s(z)))))),
% 0.64/0.90 inference(unit_resolution,[status(thm)],[402, 1716])).
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% 0.74/0.90 inference(unit_resolution,[status(thm)],[71, 1718])).
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% 0.74/0.90 inference(unit_resolution,[status(thm)],[631, 1719, 1630, 1717, 1])).
% 0.74/0.90 tff(1721,plain,
% 0.74/0.90 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[156, 1720])).
% 0.74/0.90 tff(1722,plain,
% 0.74/0.90 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[293, 1721, 272])).
% 0.74/0.90 tff(1723,plain,
% 0.74/0.90 (b(s(s(s(s(z)))), s(s(s(z))))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[310, 1722])).
% 0.74/0.90 tff(1724,plain,
% 0.74/0.90 (~b(s(z), s(s(s(z))))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[934, 1723, 1607, 52, 1630])).
% 0.74/0.90 tff(1725,plain,
% 0.74/0.90 (r(s(z), s(s(s(z))))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[668, 1724])).
% 0.74/0.90 tff(1726,plain,
% 0.74/0.90 ($false),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[194, 14, 1725, 1721, 2])).
% 0.74/0.90 tff(1727,plain,((~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.90 tff(1728,plain,
% 0.74/0.90 (~r(z, s(s(s(s(s(s(z)))))))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[1727, 2, 272, 1])).
% 0.74/0.90 tff(1729,plain,
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% 0.74/0.90 inference(unit_resolution,[status(thm)],[356, 1728])).
% 0.74/0.90 tff(1730,plain,
% 0.74/0.90 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[606, 274, 161])).
% 0.74/0.90 tff(1731,plain,
% 0.74/0.90 (b(s(s(s(s(z)))), s(s(s(z))))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[310, 1730])).
% 0.74/0.90 tff(1732,plain,
% 0.74/0.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 0.74/0.90 inference(rewrite,[status(thm)],[])).
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% 0.74/0.90 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 0.74/0.90 inference(rewrite,[status(thm)],[])).
% 0.74/0.90 tff(1734,plain,
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% 0.74/0.90 inference(monotonicity,[status(thm)],[1733])).
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% 0.74/0.90 inference(transitivity,[status(thm)],[1734, 1732])).
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% 0.74/0.90 inference(quant_inst,[status(thm)],[])).
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% 0.74/0.90 inference(modus_ponens,[status(thm)],[1736, 1735])).
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% 0.74/0.90 ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[1737, 118, 1607, 1603, 594])).
% 0.74/0.90 tff(1739,plain,
% 0.74/0.90 (~b(s(s(s(z))), s(z))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[1738, 1731])).
% 0.74/0.90 tff(1740,plain,
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% 0.74/0.90 inference(unit_resolution,[status(thm)],[105, 1739])).
% 0.74/0.90 tff(1741,plain,
% 0.74/0.90 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[79, 74, 2])).
% 0.74/0.90 tff(1742,plain,
% 0.74/0.90 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[581, 1741])).
% 0.74/0.90 tff(1743,plain,
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% 0.74/0.90 inference(unit_resolution,[status(thm)],[951, 74, 2])).
% 0.74/0.90 tff(1744,plain,
% 0.74/0.90 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[156, 1743])).
% 0.74/0.90 tff(1745,plain,
% 0.74/0.90 (~r(s(s(s(z))), z)),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[958, 74, 177])).
% 0.74/0.90 tff(1746,plain,
% 0.74/0.90 (b(s(s(s(z))), z)),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[649, 1745])).
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% 0.74/0.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 0.74/0.90 inference(rewrite,[status(thm)],[])).
% 0.74/0.90 tff(1748,plain,
% 0.74/0.90 (((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 0.74/0.90 inference(rewrite,[status(thm)],[])).
% 0.74/0.90 tff(1749,plain,
% 0.74/0.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))))),
% 0.74/0.90 inference(monotonicity,[status(thm)],[1748])).
% 0.74/0.90 tff(1750,plain,
% 0.74/0.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 0.74/0.90 inference(transitivity,[status(thm)],[1749, 1747])).
% 0.74/0.90 tff(1751,plain,
% 0.74/0.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 0.74/0.90 inference(quant_inst,[status(thm)],[])).
% 0.74/0.90 tff(1752,plain,
% 0.74/0.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 0.74/0.90 inference(modus_ponens,[status(thm)],[1751, 1750])).
% 0.74/0.90 tff(1753,plain,
% 0.74/0.90 ($false),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[1752, 118, 1746, 1744, 1742, 1, 235])).
% 0.74/0.90 tff(1754,plain,((~r(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.90 tff(1755,plain,
% 0.74/0.90 (~r(s(z), z)),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[1754, 1740, 1, 2, 1729])).
% 0.74/0.90 tff(1756,plain,
% 0.74/0.90 (b(s(z), z)),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[187, 1755])).
% 0.74/0.90 tff(1757,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(s(s(z))))) | (~r(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(z, s(s(s(z))))) | (~r(z, s(z))))),
% 0.74/0.90 inference(rewrite,[status(thm)],[])).
% 0.74/0.90 tff(1758,plain,
% 0.74/0.90 (((~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(z, s(z))))),
% 0.74/0.90 inference(rewrite,[status(thm)],[])).
% 0.74/0.90 tff(1759,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(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(z, s(z)))))),
% 0.74/0.90 inference(monotonicity,[status(thm)],[1758])).
% 0.74/0.90 tff(1760,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(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(z, s(z))))),
% 0.74/0.90 inference(transitivity,[status(thm)],[1759, 1757])).
% 0.74/0.90 tff(1761,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))))))),
% 0.74/0.90 inference(quant_inst,[status(thm)],[])).
% 0.74/0.90 tff(1762,plain,
% 0.74/0.90 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(z, s(z)))),
% 0.74/0.90 inference(modus_ponens,[status(thm)],[1761, 1760])).
% 0.74/0.90 tff(1763,plain,
% 0.74/0.90 ($false),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[1762, 14, 4, 74, 161])).
% 0.74/0.90 tff(1764,plain,((~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.90 tff(1765,plain,
% 0.74/0.90 (~r(z, s(s(s(z))))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[1764, 74, 4])).
% 0.74/0.90 tff(1766,plain,
% 0.74/0.90 (b(z, s(s(s(z))))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[71, 1765])).
% 0.74/0.90 tff(1767,plain,
% 0.74/0.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(z))))))),
% 0.74/0.90 inference(rewrite,[status(thm)],[])).
% 0.74/0.90 tff(1768,plain,
% 0.74/0.90 (((~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z))) <=> ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(z))))))),
% 0.74/0.90 inference(rewrite,[status(thm)],[])).
% 0.74/0.90 tff(1769,plain,
% 0.74/0.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(z)))))))),
% 0.74/0.90 inference(monotonicity,[status(thm)],[1768])).
% 0.74/0.90 tff(1770,plain,
% 0.74/0.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(z))))))),
% 0.74/0.90 inference(transitivity,[status(thm)],[1769, 1767])).
% 0.74/0.90 tff(1771,plain,
% 0.74/0.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 0.74/0.90 inference(quant_inst,[status(thm)],[])).
% 0.74/0.90 tff(1772,plain,
% 0.74/0.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(z)))))),
% 0.74/0.90 inference(modus_ponens,[status(thm)],[1771, 1770])).
% 0.74/0.90 tff(1773,plain,
% 0.74/0.90 ($false),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[1772, 118, 73, 1742, 1, 1766, 235])).
% 0.74/0.90 tff(1774,plain,((~r(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)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.90 tff(1775,plain,
% 0.74/0.90 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[1774, 74, 1, 235, 4, 2])).
% 0.74/0.90 tff(1776,plain,
% 0.74/0.90 ($false),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[156, 1775, 1743])).
% 0.74/0.90 tff(1777,plain,((~r(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.90 tff(1778,plain,
% 0.74/0.90 (~r(z, s(z))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[1777, 1740, 1729, 1, 2])).
% 0.74/0.90 tff(1779,plain,
% 0.74/0.90 (b(z, s(z))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[51, 1778])).
% 0.74/0.90 tff(1780,plain,
% 0.74/0.90 (~b(s(z), s(s(s(s(s(s(z)))))))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[1201, 118, 1779, 1756, 1, 1729])).
% 0.74/0.90 tff(1781,plain,
% 0.74/0.90 (r(s(z), s(s(s(s(s(s(z)))))))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[232, 1780])).
% 0.74/0.90 tff(1782,plain,
% 0.74/0.90 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[79, 1740, 2])).
% 0.74/0.90 tff(1783,plain,
% 0.74/0.90 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[581, 1782])).
% 0.74/0.90 tff(1784,plain,
% 0.74/0.90 (~b(s(s(s(z))), z)),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[1752, 118, 73, 1783, 1, 1729])).
% 0.74/0.90 tff(1785,plain,
% 0.74/0.90 (r(s(s(s(z))), z)),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[649, 1784])).
% 0.74/0.90 tff(1786,plain,
% 0.74/0.90 (~b(z, s(s(s(s(z)))))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[1675, 118, 1607, 1603, 1779, 1756])).
% 0.74/0.90 tff(1787,plain,
% 0.74/0.90 (r(z, s(s(s(s(z)))))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[389, 1786])).
% 0.74/0.90 tff(1788,assumption,(b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))), introduced(assumption)).
% 0.74/0.90 tff(1789,plain,
% 0.74/0.90 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[1682, 1253, 272])).
% 0.74/0.90 tff(1790,plain,
% 0.74/0.90 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[1684, 1789])).
% 0.74/0.90 tff(1791,plain,
% 0.74/0.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 0.74/0.90 inference(rewrite,[status(thm)],[])).
% 0.74/0.90 tff(1792,plain,
% 0.74/0.90 (((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(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(s(z)))))))) <=> ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 0.74/0.90 inference(rewrite,[status(thm)],[])).
% 0.74/0.90 tff(1793,plain,
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% 0.74/0.90 inference(monotonicity,[status(thm)],[1792])).
% 0.74/0.90 tff(1794,plain,
% 0.74/0.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(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(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 0.74/0.90 inference(transitivity,[status(thm)],[1793, 1791])).
% 0.74/0.90 tff(1795,plain,
% 0.74/0.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(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(s(z))))))))),
% 0.74/0.90 inference(quant_inst,[status(thm)],[])).
% 0.74/0.90 tff(1796,plain,
% 0.74/0.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))),
% 0.74/0.90 inference(modus_ponens,[status(thm)],[1795, 1794])).
% 0.74/0.90 tff(1797,plain,
% 0.74/0.90 (~b(s(s(s(s(s(z))))), z)),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[1796, 118, 1, 235, 1790, 1788])).
% 0.74/0.90 tff(1798,plain,
% 0.74/0.90 ($false),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[767, 1797, 1260])).
% 0.74/0.90 tff(1799,plain,((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.90 tff(1800,plain,
% 0.74/0.90 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[1799, 1787, 1729, 1628, 1, 272])).
% 0.74/0.90 tff(1801,plain,
% 0.74/0.90 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[1595, 1800])).
% 0.74/0.90 tff(1802,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))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(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(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(1803,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))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 0.74/0.91 inference(quant_inst,[status(thm)],[])).
% 0.74/0.91 tff(1804,plain,
% 0.74/0.91 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[1803, 1802])).
% 0.74/0.91 tff(1805,plain,
% 0.74/0.91 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[1804, 14, 175, 736])).
% 0.74/0.91 tff(1806,assumption,(s(s(s(s(s(z))))) = s(s(s(z)))), introduced(assumption)).
% 0.74/0.91 tff(1807,plain,
% 0.74/0.91 (s(s(s(z))) = s(s(s(s(s(z)))))),
% 0.74/0.91 inference(symmetry,[status(thm)],[1806])).
% 0.74/0.91 tff(1808,plain,
% 0.74/0.91 ($false),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[800, 1807])).
% 0.74/0.91 tff(1809,plain,(~(s(s(s(s(s(z))))) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.91 tff(1810,plain,
% 0.74/0.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(1811,plain,
% 0.74/0.91 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(1812,plain,
% 0.74/0.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[1811])).
% 0.74/0.91 tff(1813,plain,
% 0.74/0.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 0.74/0.91 inference(transitivity,[status(thm)],[1812, 1810])).
% 0.74/0.91 tff(1814,plain,
% 0.74/0.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 0.74/0.91 inference(quant_inst,[status(thm)],[])).
% 0.74/0.91 tff(1815,plain,
% 0.74/0.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[1814, 1813])).
% 0.74/0.91 tff(1816,plain,
% 0.74/0.91 ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[1815, 118, 594, 587, 1352])).
% 0.74/0.91 tff(1817,plain,
% 0.74/0.91 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[1816, 1652])).
% 0.74/0.91 tff(1818,plain,
% 0.74/0.91 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(z)))) | b(s(s(s(s(s(z))))), s(s(s(z)))) | r(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(s(z)))) | b(s(s(s(s(s(z))))), s(s(s(z)))) | r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(1819,plain,
% 0.74/0.91 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(z)))) | b(s(s(s(s(s(z))))), s(s(s(z)))) | r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 0.74/0.91 inference(quant_inst,[status(thm)],[])).
% 0.74/0.91 tff(1820,plain,
% 0.74/0.91 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(s(z)))) | b(s(s(s(s(s(z))))), s(s(s(z)))) | r(s(s(s(s(s(z))))), s(s(s(z))))),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[1819, 1818])).
% 0.74/0.91 tff(1821,plain,
% 0.74/0.91 ($false),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[1820, 46, 1817, 1809, 1805])).
% 0.74/0.91 tff(1822,plain,((~r(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.91 tff(1823,plain,
% 0.74/0.91 (~r(s(s(s(s(s(z))))), z)),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[1822, 1801, 594, 1731, 274, 1785])).
% 0.74/0.91 tff(1824,plain,
% 0.74/0.91 (b(s(s(s(s(s(z))))), z)),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[767, 1823])).
% 0.74/0.91 tff(1825,plain,
% 0.74/0.91 (~b(s(s(s(s(s(z))))), s(z))),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[1224, 1824, 1779, 1, 1781, 1756])).
% 0.74/0.91 tff(1826,plain,
% 0.74/0.91 (r(s(s(s(s(s(z))))), s(z))),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[829, 1825])).
% 0.74/0.91 tff(1827,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(s(s(s(s(s(z))))), s(z))) | (~r(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(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(1828,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(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 0.74/0.91 inference(quant_inst,[status(thm)],[])).
% 0.74/0.91 tff(1829,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(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[1828, 1827])).
% 0.74/0.91 tff(1830,plain,
% 0.74/0.91 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[1829, 14, 1740, 1826])).
% 0.74/0.91 tff(1831,plain,
% 0.74/0.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(1832,plain,
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% 0.74/0.91 inference(monotonicity,[status(thm)],[1832])).
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% 0.74/0.91 inference(transitivity,[status(thm)],[1833, 1831])).
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% 0.74/0.91 inference(modus_ponens,[status(thm)],[1835, 1834])).
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% 0.74/0.91 inference(unit_resolution,[status(thm)],[1836, 118, 594, 73, 1801, 1628])).
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% 0.74/0.91 tff(1840,plain,
% 0.74/0.91 (~r(s(s(s(s(z)))), z)),
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% 0.74/0.91 tff(1844,plain,
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% 0.74/0.91 inference(unit_resolution,[status(thm)],[356, 1844])).
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% 0.74/0.91 inference(unit_resolution,[status(thm)],[323, 1846])).
% 0.74/0.91 tff(1848,plain,
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% 0.74/0.91 inference(unit_resolution,[status(thm)],[538, 1847, 272, 234, 160])).
% 0.74/0.91 tff(1849,plain,
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% 0.74/0.91 inference(unit_resolution,[status(thm)],[402, 1850])).
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% 0.74/0.91 inference(unit_resolution,[status(thm)],[951, 160, 2])).
% 0.74/0.91 tff(1853,plain,
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% 0.74/0.91 inference(unit_resolution,[status(thm)],[105, 1852])).
% 0.74/0.91 tff(1854,plain,
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% 0.74/0.91 inference(unit_resolution,[status(thm)],[969, 1853, 1851, 1603, 1847])).
% 0.74/0.91 tff(1855,plain,
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% 0.74/0.91 inference(unit_resolution,[status(thm)],[668, 1854])).
% 0.74/0.91 tff(1856,plain,
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% 0.74/0.91 inference(unit_resolution,[status(thm)],[522, 1855, 1849, 234, 160])).
% 0.74/0.91 tff(1857,plain,((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.91 tff(1858,plain,
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% 0.74/0.91 inference(unit_resolution,[status(thm)],[1857, 234, 272, 2, 1])).
% 0.74/0.91 tff(1859,plain,
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% 0.74/0.91 inference(unit_resolution,[status(thm)],[156, 1858])).
% 0.74/0.91 tff(1860,plain,
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% 0.74/0.91 inference(unit_resolution,[status(thm)],[51, 1860])).
% 0.74/0.91 tff(1862,plain,
% 0.74/0.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(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(z)))), z)) | (~b(s(z), z)))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(1863,plain,
% 0.74/0.91 (((~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(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(z)))), z)) | (~b(s(z), z)))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
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% 0.74/0.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(z)))), z)) | (~b(s(z), z))))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[1863])).
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% 0.74/0.91 inference(transitivity,[status(thm)],[1864, 1862])).
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% 0.74/0.91 inference(quant_inst,[status(thm)],[])).
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% 0.74/0.91 inference(modus_ponens,[status(thm)],[1866, 1865])).
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% 0.74/0.91 inference(unit_resolution,[status(thm)],[1867, 118, 460, 961, 234, 721, 436])).
% 0.74/0.91 tff(1869,plain,((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.91 tff(1870,plain,
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% 0.74/0.91 tff(1871,plain,
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% 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(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, 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(z))), s(s(s(s(s(s(z)))))))))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
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% 0.74/0.91 inference(rewrite,[status(thm)],[])).
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% 0.74/0.91 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[1873])).
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% 0.74/0.91 inference(quant_inst,[status(thm)],[])).
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% 0.74/0.91 inference(modus_ponens,[status(thm)],[1876, 1875])).
% 0.74/0.91 tff(1878,plain,
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% 0.74/0.91 inference(unit_resolution,[status(thm)],[1877, 14, 272, 391, 53])).
% 0.74/0.91 tff(1879,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.91 tff(1880,plain,
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% 0.74/0.92 tff(1945,plain,
% 0.74/0.92 (b(s(z), s(s(s(z))))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[668, 1944])).
% 0.74/0.92 tff(1946,plain,
% 0.74/0.92 ($false),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[969, 1945, 1943, 460, 961, 1941])).
% 0.74/0.92 tff(1947,plain,((~r(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.92 tff(1948,plain,
% 0.74/0.92 (~r(z, s(s(s(z))))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[1947, 4, 1603, 1939, 339])).
% 0.74/0.92 tff(1949,plain,
% 0.74/0.92 (b(z, s(s(s(z))))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[71, 1948])).
% 0.74/0.92 tff(1950,plain,
% 0.74/0.92 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[581, 1880])).
% 0.74/0.92 tff(1951,plain,
% 0.74/0.92 ($false),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[1772, 118, 1692, 1950, 1, 271, 235])).
% 0.74/0.92 tff(1952,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.92 tff(1953,plain,
% 0.74/0.92 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[1952, 1949, 1, 357, 272])).
% 0.74/0.92 tff(1954,plain,
% 0.74/0.92 (b(s(s(s(z))), s(s(s(s(z)))))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[402, 1953])).
% 0.74/0.92 tff(1955,plain,
% 0.74/0.92 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[1737, 118, 460, 961, 594, 173])).
% 0.74/0.92 tff(1956,plain,
% 0.74/0.92 (r(s(s(s(s(z)))), s(s(s(z))))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[310, 1955])).
% 0.74/0.92 tff(1957,plain,
% 0.74/0.92 (~b(s(z), s(s(s(z))))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[969, 594, 460, 961, 173])).
% 0.74/0.92 tff(1958,plain,
% 0.74/0.92 (r(s(z), s(s(s(z))))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[668, 1957])).
% 0.74/0.92 tff(1959,plain,
% 0.74/0.92 (~r(s(s(s(z))), z)),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[182, 1958, 177])).
% 0.74/0.92 tff(1960,plain,
% 0.74/0.92 (b(s(s(s(z))), z)),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[649, 1959])).
% 0.74/0.92 tff(1961,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)],[293, 1956, 272])).
% 0.74/0.92 tff(1962,plain,
% 0.74/0.92 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[156, 1961])).
% 0.74/0.92 tff(1963,plain,
% 0.74/0.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(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(s(s(z)))))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(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(s(s(z)))))))) | (~b(z, s(s(s(z))))))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(1964,plain,
% 0.74/0.92 (((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(z))))))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(1965,plain,
% 0.74/0.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(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(s(s(z)))))))) | (~b(z, s(s(s(z)))))))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[1964])).
% 0.74/0.92 tff(1966,plain,
% 0.74/0.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(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(s(s(z)))))))) | (~b(z, s(s(s(z))))))),
% 0.74/0.92 inference(transitivity,[status(thm)],[1965, 1963])).
% 0.74/0.92 tff(1967,plain,
% 0.74/0.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), z)))),
% 0.74/0.92 inference(quant_inst,[status(thm)],[])).
% 0.74/0.92 tff(1968,plain,
% 0.74/0.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(z)))))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[1967, 1966])).
% 0.74/0.92 tff(1969,plain,
% 0.74/0.92 ($false),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[1968, 118, 1695, 73, 609, 271, 235])).
% 0.74/0.92 tff(1970,plain,((~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.92 tff(1971,plain,
% 0.74/0.92 (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[1970, 1962, 271, 1960, 235])).
% 0.74/0.92 tff(1972,plain,
% 0.74/0.92 (r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[581, 1971])).
% 0.74/0.92 tff(1973,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(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(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(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(1974,plain,
% 0.74/0.92 (((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(1975,plain,
% 0.74/0.92 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(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(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[1974])).
% 0.74/0.92 tff(1976,plain,
% 0.74/0.92 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(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(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 0.74/0.92 inference(transitivity,[status(thm)],[1975, 1973])).
% 0.74/0.92 tff(1977,plain,
% 0.74/0.92 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 0.74/0.92 inference(quant_inst,[status(thm)],[])).
% 0.74/0.92 tff(1978,plain,
% 0.74/0.92 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[1977, 1976])).
% 0.74/0.92 tff(1979,plain,
% 0.74/0.92 ($false),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[1978, 14, 288, 53, 543])).
% 0.74/0.92 tff(1980,plain,((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.92 tff(1981,plain,
% 0.74/0.92 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[1980, 1972, 1956])).
% 0.74/0.92 tff(1982,plain,
% 0.74/0.92 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[480, 1981])).
% 0.74/0.92 tff(1983,plain,
% 0.74/0.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), 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(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(z))))))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(1984,plain,
% 0.74/0.92 (((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(z))))))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(1985,plain,
% 0.74/0.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), 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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(z)))))))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[1984])).
% 0.74/0.92 tff(1986,plain,
% 0.74/0.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), 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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(z))))))),
% 0.74/0.92 inference(transitivity,[status(thm)],[1985, 1983])).
% 0.74/0.92 tff(1987,plain,
% 0.74/0.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), 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)))))))))),
% 0.74/0.92 inference(quant_inst,[status(thm)],[])).
% 0.74/0.92 tff(1988,plain,
% 0.74/0.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(z)))))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[1987, 1986])).
% 0.74/0.92 tff(1989,plain,
% 0.74/0.92 ($false),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[1988, 118, 1962, 1982, 721, 1, 271])).
% 0.74/0.92 tff(1990,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.92 tff(1991,plain,
% 0.74/0.92 (~b(s(s(s(z))), s(z))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[1990, 1954, 1, 1949, 357, 272, 1939, 1603, 721, 1935])).
% 0.74/0.92 tff(1992,plain,
% 0.74/0.92 (r(s(s(s(z))), s(z))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[105, 1991])).
% 0.74/0.92 tff(1993,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)],[951, 1992, 2])).
% 0.74/0.92 tff(1994,plain,
% 0.74/0.92 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[1774, 1992, 1, 357, 4, 2])).
% 0.74/0.92 tff(1995,plain,
% 0.74/0.92 ($false),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[156, 1994, 1993])).
% 0.74/0.92 tff(1996,plain,((~r(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.92 tff(1997,plain,
% 0.74/0.92 (~r(z, s(z))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[1996, 339, 2, 272, 721, 1])).
% 0.74/0.92 tff(1998,plain,
% 0.74/0.92 (b(z, s(z))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[51, 1997])).
% 0.74/0.92 tff(1999,plain,
% 0.74/0.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(2000,plain,
% 0.74/0.92 (((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(2001,plain,
% 0.74/0.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z)))))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[2000])).
% 0.74/0.92 tff(2002,plain,
% 0.74/0.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))))),
% 0.74/0.92 inference(transitivity,[status(thm)],[2001, 1999])).
% 0.74/0.92 tff(2003,plain,
% 0.74/0.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 0.74/0.92 inference(quant_inst,[status(thm)],[])).
% 0.74/0.92 tff(2004,plain,
% 0.74/0.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z)))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[2003, 2002])).
% 0.74/0.92 tff(2005,plain,
% 0.74/0.92 ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[2004, 118, 174, 173, 721])).
% 0.74/0.92 tff(2006,plain,
% 0.74/0.92 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[2005, 1695])).
% 0.74/0.92 tff(2007,plain,
% 0.74/0.92 (r(s(s(s(s(z)))), s(s(s(z))))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[310, 2006])).
% 0.74/0.92 tff(2008,plain,
% 0.74/0.92 ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[1554, 118, 174, 173, 1])).
% 0.74/0.92 tff(2009,plain,
% 0.74/0.92 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[2008, 1695])).
% 0.74/0.92 tff(2010,plain,
% 0.74/0.92 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[156, 2009])).
% 0.74/0.92 tff(2011,plain,
% 0.74/0.92 ($false),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[293, 2010, 2007, 272])).
% 0.74/0.92 tff(2012,plain,((~b(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.92 tff(2013,plain,
% 0.74/0.92 (~b(s(s(s(z))), z)),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[2012, 1998, 272, 1937, 1, 721])).
% 0.74/0.92 tff(2014,plain,
% 0.74/0.92 (r(s(s(s(z))), z)),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[649, 2013])).
% 0.74/0.92 tff(2015,plain,
% 0.74/0.92 (~r(s(z), s(s(s(z))))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[182, 2014, 1935])).
% 0.74/0.92 tff(2016,plain,
% 0.74/0.92 (b(s(z), s(s(s(z))))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[668, 2015])).
% 0.74/0.92 tff(2017,plain,
% 0.74/0.92 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[969, 2016, 1939, 1603, 1937])).
% 0.74/0.92 tff(2018,plain,
% 0.74/0.92 (r(s(s(s(z))), s(s(s(s(z)))))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[402, 2017])).
% 0.74/0.92 tff(2019,plain,
% 0.74/0.92 (~r(z, s(s(s(z))))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[1530, 2018, 339])).
% 0.74/0.92 tff(2020,plain,
% 0.74/0.92 (~b(z, s(s(s(z))))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[1952, 2018, 1, 357, 272])).
% 0.74/0.92 tff(2021,plain,
% 0.74/0.92 ($false),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[71, 2020, 2019])).
% 0.74/0.92 tff(2022,plain,((~r(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.93 tff(2023,plain,
% 0.74/0.93 (~r(z, s(s(s(s(z)))))),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[2022, 1841, 272, 1, 2])).
% 0.74/0.93 tff(2024,plain,
% 0.74/0.93 (b(z, s(s(s(s(z)))))),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[389, 2023])).
% 0.74/0.93 tff(2025,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(z), s(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(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(2026,plain,
% 0.74/0.93 (((~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(2027,plain,
% 0.74/0.93 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(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(z))))) | (~r(z, s(s(s(z)))))))),
% 0.74/0.93 inference(monotonicity,[status(thm)],[2026])).
% 0.74/0.93 tff(2028,plain,
% 0.74/0.93 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(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(z))))) | (~r(z, s(s(s(z))))))),
% 0.74/0.93 inference(transitivity,[status(thm)],[2027, 2025])).
% 0.74/0.93 tff(2029,plain,
% 0.74/0.93 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)))),
% 0.74/0.93 inference(quant_inst,[status(thm)],[])).
% 0.74/0.93 tff(2030,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(z), s(s(s(z))))) | (~r(z, s(s(s(z)))))),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[2029, 2028])).
% 0.74/0.93 tff(2031,plain,
% 0.74/0.93 (~r(s(z), z)),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[2030, 14, 176, 161])).
% 0.74/0.93 tff(2032,plain,
% 0.74/0.93 (b(s(z), z)),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[187, 2031])).
% 0.74/0.93 tff(2033,plain,
% 0.74/0.93 (~r(z, s(z))),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[266, 14, 176, 161])).
% 0.74/0.93 tff(2034,plain,
% 0.74/0.93 (b(z, s(z))),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[51, 2033])).
% 0.74/0.93 tff(2035,plain,
% 0.74/0.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(z), z)))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(2036,plain,
% 0.74/0.93 (((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z)))) <=> ((~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(z), z)))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(2037,plain,
% 0.74/0.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(z), z))))),
% 0.74/0.93 inference(monotonicity,[status(thm)],[2036])).
% 0.74/0.93 tff(2038,plain,
% 0.74/0.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(z), z)))),
% 0.74/0.93 inference(transitivity,[status(thm)],[2037, 2035])).
% 0.74/0.93 tff(2039,plain,
% 0.74/0.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))),
% 0.74/0.93 inference(quant_inst,[status(thm)],[])).
% 0.74/0.93 tff(2040,plain,
% 0.74/0.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(z), z))),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[2039, 2038])).
% 0.74/0.93 tff(2041,plain,
% 0.74/0.93 ($false),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[2040, 118, 460, 2034, 2032, 721, 436])).
% 0.74/0.93 tff(2042,plain,((~r(s(z), 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)))))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.93 tff(2043,plain,
% 0.74/0.93 (~r(s(z), s(s(s(z))))),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[2042, 2024, 1607, 1841, 161])).
% 0.74/0.93 tff(2044,plain,
% 0.74/0.93 (b(s(z), s(s(s(z))))),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[668, 2043])).
% 0.74/0.93 tff(2045,plain,
% 0.74/0.93 ($false),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[969, 2044, 1933, 1607, 1603, 594])).
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% 0.74/0.94 (((~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
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% 0.74/0.94 inference(unit_resolution,[status(thm)],[182, 2210, 2206])).
% 0.74/0.94 tff(2212,plain,
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% 0.74/0.94 inference(unit_resolution,[status(thm)],[187, 2211])).
% 0.74/0.94 tff(2213,plain,
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% 0.74/0.94 tff(2214,plain,
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% 0.74/0.94 inference(unit_resolution,[status(thm)],[71, 2213])).
% 0.74/0.94 tff(2215,plain,
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% 0.74/0.94 inference(unit_resolution,[status(thm)],[268, 2210, 2214])).
% 0.74/0.94 tff(2216,plain,
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% 0.74/0.94 inference(unit_resolution,[status(thm)],[51, 2215])).
% 0.74/0.94 tff(2217,plain,
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% 0.74/0.94 tff(2219,plain,
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% 0.74/0.94 inference(unit_resolution,[status(thm)],[2218, 2187, 3, 1, 272])).
% 0.74/0.94 tff(2220,plain,
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% 0.74/0.94 inference(unit_resolution,[status(thm)],[323, 2219])).
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% 0.74/0.94 inference(unit_resolution,[status(thm)],[2154, 118, 2220, 1, 1630, 2146])).
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% 0.74/0.94 tff(2224,plain,((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.94 tff(2225,plain,
% 0.74/0.94 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[2224, 2187, 3, 272])).
% 0.74/0.94 tff(2226,plain,
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% 0.74/0.94 inference(unit_resolution,[status(thm)],[156, 2225])).
% 0.74/0.94 tff(2227,plain,
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% 0.74/0.94 inference(unit_resolution,[status(thm)],[631, 2226, 1630, 2187, 1])).
% 0.74/0.94 tff(2228,plain,
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% 0.74/0.94 inference(unit_resolution,[status(thm)],[71, 2227])).
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% 0.74/0.94 inference(rewrite,[status(thm)],[])).
% 0.74/0.94 tff(2231,plain,
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% 0.74/0.94 inference(monotonicity,[status(thm)],[2230])).
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% 0.74/0.94 inference(transitivity,[status(thm)],[2231, 2229])).
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% 0.74/0.94 inference(quant_inst,[status(thm)],[])).
% 0.74/0.94 tff(2234,plain,
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% 0.74/0.94 inference(modus_ponens,[status(thm)],[2233, 2232])).
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% 0.74/0.94 ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[2234, 118, 2220, 2187, 2146])).
% 0.74/0.94 tff(2236,plain,
% 0.74/0.94 (~b(s(s(s(z))), s(z))),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[2235, 2226])).
% 0.74/0.94 tff(2237,plain,
% 0.74/0.94 (r(s(s(s(z))), s(z))),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[105, 2236])).
% 0.74/0.94 tff(2238,plain,
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% 0.74/0.94 inference(unit_resolution,[status(thm)],[1764, 2237, 2228, 2222])).
% 0.74/0.94 tff(2239,plain,((~r(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.94 tff(2240,plain,
% 0.74/0.94 (~r(z, s(s(s(s(s(s(z)))))))),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[2239, 272, 1])).
% 0.74/0.94 tff(2241,plain,
% 0.74/0.94 (b(z, s(s(s(s(s(s(z)))))))),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[356, 2240])).
% 0.74/0.94 tff(2242,plain,
% 0.74/0.94 (~b(z, s(s(s(z))))),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[1952, 391, 1, 2241, 272])).
% 0.74/0.94 tff(2243,plain,
% 0.74/0.94 (~r(z, s(s(s(z))))),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[1530, 391, 339])).
% 0.74/0.94 tff(2244,plain,
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% 0.74/0.94 inference(unit_resolution,[status(thm)],[71, 2243, 2242])).
% 0.74/0.94 tff(2245,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.94 tff(2246,plain,
% 0.74/0.94 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[2245, 339, 1, 272])).
% 0.74/0.94 tff(2247,plain,
% 0.74/0.94 (b(s(s(s(z))), s(s(s(s(z)))))),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[402, 2246])).
% 0.74/0.94 tff(2248,plain,
% 0.74/0.94 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[1593, 1253, 272])).
% 0.74/0.94 tff(2249,plain,
% 0.74/0.94 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[1799, 1253, 2241, 339, 1, 272])).
% 0.74/0.94 tff(2250,plain,
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% 0.74/0.94 tff(2251,plain,((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.94 tff(2252,plain,
% 0.74/0.94 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[2251, 339, 1, 272])).
% 0.74/0.94 tff(2253,plain,
% 0.74/0.94 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[1595, 2252])).
% 0.74/0.94 tff(2254,plain,
% 0.74/0.94 (~r(s(z), s(s(s(s(z)))))),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[1151, 274, 177])).
% 0.74/0.94 tff(2255,plain,
% 0.74/0.94 (b(s(z), s(s(s(s(z)))))),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[323, 2254])).
% 0.74/0.94 tff(2256,plain,
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% 0.74/0.94 inference(unit_resolution,[status(thm)],[922, 118, 2255, 594, 587, 172])).
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% 0.74/0.94 inference(unit_resolution,[status(thm)],[513, 2256, 1658])).
% 0.74/0.94 tff(2258,plain,((~r(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.94 tff(2259,plain,
% 0.74/0.94 (~b(s(z), s(s(s(z))))),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[2258, 608, 1943, 274, 177])).
% 0.74/0.94 tff(2260,plain,
% 0.74/0.94 (r(s(z), s(s(s(z))))),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[668, 2259])).
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% 0.74/0.94 tff(2262,plain,((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.94 tff(2263,plain,
% 0.74/0.94 (~r(s(s(s(s(z)))), z)),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[2262, 177, 339, 161])).
% 0.74/0.94 tff(2264,plain,
% 0.74/0.94 (b(s(s(s(s(z)))), z)),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[286, 2263])).
% 0.74/0.94 tff(2265,plain,
% 0.74/0.94 (~b(s(s(s(s(z)))), s(z))),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[2081, 173, 2253, 2247, 1939])).
% 0.74/0.94 tff(2266,plain,
% 0.74/0.94 (r(s(s(s(s(z)))), s(z))),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[513, 2265])).
% 0.74/0.94 tff(2267,plain,
% 0.74/0.94 (~b(z, s(z))),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[2012, 173, 272, 1695, 1, 721])).
% 0.74/0.94 tff(2268,plain,
% 0.74/0.94 (r(z, s(z))),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[51, 2267])).
% 0.74/0.94 tff(2269,plain,
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% 0.74/0.94 inference(unit_resolution,[status(thm)],[1074, 14, 495, 4, 339])).
% 0.74/0.95 tff(2270,plain,((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.95 tff(2271,plain,
% 0.74/0.95 ($false),
% 0.74/0.95 inference(unit_resolution,[status(thm)],[2270, 2268, 2266, 339])).
% 0.74/0.95 tff(2272,plain,((~b(s(s(s(z))), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.95 tff(2273,plain,
% 0.74/0.95 (~b(s(s(s(z))), s(z))),
% 0.74/0.95 inference(unit_resolution,[status(thm)],[2272, 2264, 272, 1695, 1, 339])).
% 0.74/0.95 tff(2274,plain,
% 0.74/0.95 (r(s(s(s(z))), s(z))),
% 0.74/0.95 inference(unit_resolution,[status(thm)],[105, 2273])).
% 0.74/0.95 tff(2275,plain,
% 0.74/0.95 (~r(z, s(z))),
% 0.74/0.95 inference(unit_resolution,[status(thm)],[1764, 2274, 161])).
% 0.74/0.95 tff(2276,plain,
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% 0.74/0.95 inference(unit_resolution,[status(thm)],[51, 2275])).
% 0.74/0.95 tff(2277,plain,
% 0.74/0.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 0.74/0.95 inference(rewrite,[status(thm)],[])).
% 0.74/0.95 tff(2278,plain,
% 0.74/0.95 (((~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 0.74/0.95 inference(rewrite,[status(thm)],[])).
% 0.74/0.95 tff(2279,plain,
% 0.74/0.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), 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, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))))),
% 0.74/0.95 inference(monotonicity,[status(thm)],[2278])).
% 0.74/0.95 tff(2280,plain,
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% 0.74/0.95 inference(transitivity,[status(thm)],[2279, 2277])).
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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)],[2281, 2280])).
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% 0.74/0.95 (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.74/0.95 inference(unit_resolution,[status(thm)],[2282, 118, 2276, 2264, 1, 2146])).
% 0.74/0.95 tff(2284,plain,
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% 0.74/0.95 inference(unit_resolution,[status(thm)],[480, 2283])).
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% 0.74/0.95 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
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% 0.74/0.95 inference(monotonicity,[status(thm)],[2286])).
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% 0.74/0.95 inference(transitivity,[status(thm)],[2287, 2285])).
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% 0.74/0.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(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(s(z))))))))),
% 0.74/0.95 inference(quant_inst,[status(thm)],[])).
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% 0.74/0.95 inference(modus_ponens,[status(thm)],[2289, 2288])).
% 0.74/0.95 tff(2291,plain,
% 0.74/0.95 ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 0.74/0.95 inference(unit_resolution,[status(thm)],[2290, 118, 460, 236, 1352])).
% 0.74/0.95 tff(2292,plain,
% 0.74/0.95 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 0.74/0.95 inference(unit_resolution,[status(thm)],[2291, 1318])).
% 0.74/0.95 tff(2293,plain,
% 0.74/0.95 (r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 0.74/0.95 inference(unit_resolution,[status(thm)],[1627, 2292])).
% 0.74/0.95 tff(2294,assumption,(r(s(s(s(s(z)))), s(s(s(s(s(z))))))), introduced(assumption)).
% 0.74/0.95 tff(2295,plain,
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% 0.74/0.95 inference(rewrite,[status(thm)],[])).
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% 0.74/0.95 (((~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(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(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 0.74/0.95 inference(rewrite,[status(thm)],[])).
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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(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(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(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 0.74/0.95 inference(monotonicity,[status(thm)],[2296])).
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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(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(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(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 0.74/0.95 inference(transitivity,[status(thm)],[2297, 2295])).
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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(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 0.74/0.95 inference(quant_inst,[status(thm)],[])).
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% 0.74/0.95 inference(modus_ponens,[status(thm)],[2299, 2298])).
% 0.74/0.95 tff(2301,plain,
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% 0.74/0.95 inference(unit_resolution,[status(thm)],[2300, 14, 543, 2294, 1584])).
% 0.74/0.95 tff(2302,plain,((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.95 tff(2303,plain,
% 0.74/0.95 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 0.74/0.95 inference(unit_resolution,[status(thm)],[2302, 2293, 543])).
% 0.74/0.95 tff(2304,plain,
% 0.74/0.95 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 0.74/0.95 inference(unit_resolution,[status(thm)],[1616, 2303])).
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% 0.74/0.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 0.74/0.95 inference(rewrite,[status(thm)],[])).
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% 0.74/0.95 (((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 0.74/0.95 inference(rewrite,[status(thm)],[])).
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% 0.74/0.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 0.74/0.95 inference(monotonicity,[status(thm)],[2306])).
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% 0.74/0.96 (((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
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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)],[2351, 2350])).
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% 0.74/0.96 tff(2355,plain,
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% 0.74/0.96 inference(unit_resolution,[status(thm)],[2354, 2344, 2274, 1695, 587, 2314])).
% 0.74/0.96 tff(2356,plain,
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% 0.74/0.96 tff(2366,plain,
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% 0.74/0.96 tff(2367,plain,
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% 0.74/0.96 inference(unit_resolution,[status(thm)],[51, 2366])).
% 0.74/0.96 tff(2368,plain,
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% 0.74/0.96 inference(unit_resolution,[status(thm)],[1764, 2367, 161])).
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% 0.74/0.96 tff(2370,plain,((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.96 tff(2371,plain,
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% 0.74/0.96 inference(unit_resolution,[status(thm)],[2234, 118, 1939, 2247, 2146])).
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% 0.74/0.96 inference(unit_resolution,[status(thm)],[2373, 2372])).
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% 0.74/0.96 tff(2379,plain,
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% 0.74/0.96 inference(unit_resolution,[status(thm)],[187, 2378])).
% 0.74/0.96 tff(2380,plain,
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% 0.74/0.96 inference(unit_resolution,[status(thm)],[958, 2379, 2375])).
% 0.74/0.96 tff(2381,plain,
% 0.74/0.96 (b(s(s(s(z))), z)),
% 0.74/0.96 inference(unit_resolution,[status(thm)],[649, 2380])).
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% 0.74/0.96 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 0.74/0.96 inference(unit_resolution,[status(thm)],[2358, 2381, 2379, 1, 161, 272, 339])).
% 0.74/0.96 tff(2383,plain,
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% 0.74/0.96 inference(unit_resolution,[status(thm)],[310, 2382])).
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% 0.74/0.96 inference(monotonicity,[status(thm)],[2385])).
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% 0.74/0.96 inference(transitivity,[status(thm)],[2386, 2384])).
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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)],[2388, 2387])).
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% 0.74/0.96 tff(2392,plain,
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% 0.74/0.96 inference(unit_resolution,[status(thm)],[51, 2397])).
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% 0.74/0.96 tff(2400,plain,
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% 0.74/0.96 inference(unit_resolution,[status(thm)],[649, 2399])).
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% 0.74/0.96 inference(rewrite,[status(thm)],[])).
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% 0.74/0.96 inference(monotonicity,[status(thm)],[2403])).
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% 0.74/0.96 inference(transitivity,[status(thm)],[2404, 2402])).
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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)],[2406, 2405])).
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% 0.74/0.96 tff(2410,plain,
% 0.74/0.96 (~b(s(z), s(s(s(s(s(s(z)))))))),
% 0.74/0.96 inference(unit_resolution,[status(thm)],[2409, 234, 73, 1, 271])).
% 0.74/0.96 tff(2411,plain,
% 0.74/0.96 (r(s(z), s(s(s(s(s(s(z)))))))),
% 0.74/0.96 inference(unit_resolution,[status(thm)],[232, 2410])).
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% 0.74/0.96 inference(rewrite,[status(thm)],[])).
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% 0.74/0.97 inference(rewrite,[status(thm)],[])).
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% 0.74/0.97 inference(monotonicity,[status(thm)],[2455])).
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% 0.74/0.97 inference(transitivity,[status(thm)],[2456, 2454])).
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% 0.74/0.97 inference(modus_ponens,[status(thm)],[2458, 2457])).
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% 0.74/0.97 (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
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% 0.74/0.97 tff(2461,plain,
% 0.74/0.97 (r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.74/0.97 inference(unit_resolution,[status(thm)],[480, 2460])).
% 0.74/0.97 tff(2462,plain,
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% 0.74/0.97 inference(unit_resolution,[status(thm)],[522, 2451, 235, 2448])).
% 0.74/0.97 tff(2463,plain,
% 0.74/0.97 (r(s(z), z)),
% 0.74/0.97 inference(unit_resolution,[status(thm)],[187, 2462])).
% 0.74/0.97 tff(2464,plain,
% 0.74/0.97 (~r(s(s(s(z))), z)),
% 0.74/0.97 inference(unit_resolution,[status(thm)],[1507, 2448])).
% 0.74/0.97 tff(2465,plain,
% 0.74/0.97 (b(s(s(s(z))), z)),
% 0.74/0.97 inference(unit_resolution,[status(thm)],[649, 2464])).
% 0.74/0.97 tff(2466,plain,
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% 0.74/0.97 inference(rewrite,[status(thm)],[])).
% 0.74/0.97 tff(2467,plain,
% 0.74/0.97 (((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))))),
% 0.74/0.97 inference(rewrite,[status(thm)],[])).
% 0.74/0.97 tff(2468,plain,
% 0.74/0.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z)))))))),
% 0.74/0.97 inference(monotonicity,[status(thm)],[2467])).
% 0.74/0.97 tff(2469,plain,
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% 0.74/0.97 inference(transitivity,[status(thm)],[2468, 2466])).
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% 0.74/0.97 inference(quant_inst,[status(thm)],[])).
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% 0.74/0.97 inference(modus_ponens,[status(thm)],[2470, 2469])).
% 0.74/0.97 tff(2472,plain,
% 0.74/0.97 (~b(s(s(s(s(z)))), z)),
% 0.74/0.97 inference(unit_resolution,[status(thm)],[2471, 118, 2465, 594, 587, 271])).
% 0.74/0.97 tff(2473,plain,
% 0.74/0.97 (r(s(s(s(s(z)))), z)),
% 0.74/0.97 inference(unit_resolution,[status(thm)],[286, 2472])).
% 0.74/0.97 tff(2474,plain,
% 0.74/0.97 (~r(s(s(s(s(s(z))))), z)),
% 0.74/0.97 inference(unit_resolution,[status(thm)],[1667, 2473, 2463])).
% 0.74/0.97 tff(2475,plain,
% 0.74/0.97 (b(s(s(s(s(s(z))))), z)),
% 0.74/0.97 inference(unit_resolution,[status(thm)],[767, 2474])).
% 0.74/0.97 tff(2476,plain,
% 0.74/0.97 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 0.74/0.97 inference(unit_resolution,[status(thm)],[2326, 2475, 235, 1, 2461])).
% 0.74/0.97 tff(2477,plain,
% 0.74/0.97 (~b(s(s(s(z))), s(z))),
% 0.74/0.97 inference(unit_resolution,[status(thm)],[2081, 961, 1352, 594, 460])).
% 0.74/0.97 tff(2478,plain,
% 0.74/0.97 (r(s(s(s(z))), s(z))),
% 0.74/0.97 inference(unit_resolution,[status(thm)],[105, 2477])).
% 0.74/0.97 tff(2479,plain,
% 0.74/0.97 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 0.74/0.97 inference(unit_resolution,[status(thm)],[2342, 2475, 460, 1352, 961, 2465, 587, 2478])).
% 0.74/0.97 tff(2480,plain,
% 0.74/0.97 ($false),
% 0.74/0.97 inference(unit_resolution,[status(thm)],[1616, 2479, 2476])).
% 0.74/0.97 tff(2481,plain,((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.97 tff(2482,plain,
% 0.74/0.97 (~b(s(s(s(s(z)))), s(z))),
% 0.74/0.97 inference(unit_resolution,[status(thm)],[2481, 1939, 2253, 2446, 2241, 1, 2146, 2247, 2393])).
% 0.74/0.97 tff(2483,plain,
% 0.74/0.97 (r(s(s(s(s(z)))), s(z))),
% 0.74/0.97 inference(unit_resolution,[status(thm)],[513, 2482])).
% 0.74/0.97 tff(2484,plain,
% 0.74/0.97 (~r(z, s(z))),
% 0.74/0.97 inference(unit_resolution,[status(thm)],[2270, 2483, 339])).
% 0.74/0.97 tff(2485,plain,
% 0.74/0.97 (b(z, s(z))),
% 0.74/0.97 inference(unit_resolution,[status(thm)],[51, 2484])).
% 0.74/0.97 tff(2486,plain,
% 0.74/0.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))),
% 0.74/0.97 inference(rewrite,[status(thm)],[])).
% 0.74/0.97 tff(2487,plain,
% 0.74/0.97 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z)))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))),
% 0.74/0.97 inference(rewrite,[status(thm)],[])).
% 0.74/0.97 tff(2488,plain,
% 0.74/0.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(z, s(s(s(z)))))))),
% 0.74/0.97 inference(monotonicity,[status(thm)],[2487])).
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% 0.74/0.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))),
% 0.74/0.97 inference(transitivity,[status(thm)],[2488, 2486])).
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% 0.74/0.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))))),
% 0.74/0.97 inference(quant_inst,[status(thm)],[])).
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% 0.74/0.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(z, s(s(s(z)))))),
% 0.74/0.97 inference(modus_ponens,[status(thm)],[2490, 2489])).
% 0.74/0.97 tff(2492,plain,
% 0.74/0.97 ((~b(s(z), s(s(s(z))))) | (~b(z, s(z)))),
% 0.74/0.97 inference(unit_resolution,[status(thm)],[2491, 118, 1939, 2247, 2393])).
% 0.74/0.97 tff(2493,plain,
% 0.74/0.97 (~b(s(z), s(s(s(z))))),
% 0.74/0.97 inference(unit_resolution,[status(thm)],[2492, 2485])).
% 0.74/0.97 tff(2494,plain,
% 0.74/0.97 (r(s(z), s(s(s(z))))),
% 0.74/0.97 inference(unit_resolution,[status(thm)],[668, 2493])).
% 0.74/0.97 tff(2495,plain,
% 0.74/0.97 (~r(s(z), s(s(s(s(s(s(z)))))))),
% 0.74/0.97 inference(unit_resolution,[status(thm)],[220, 2494, 2444])).
% 0.74/0.97 tff(2496,plain,
% 0.74/0.97 (b(s(z), s(s(s(s(s(s(z)))))))),
% 0.74/0.97 inference(unit_resolution,[status(thm)],[232, 2495])).
% 0.74/0.97 tff(2497,plain,
% 0.74/0.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 0.74/0.97 inference(rewrite,[status(thm)],[])).
% 0.74/0.97 tff(2498,plain,
% 0.74/0.97 (((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 0.74/0.97 inference(rewrite,[status(thm)],[])).
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% 0.74/0.98 inference(monotonicity,[status(thm)],[2656])).
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% 0.74/0.98 inference(transitivity,[status(thm)],[2657, 2655])).
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% 0.74/0.98 tff(2667,plain,
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% 0.74/0.98 tff(2675,plain,
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% 0.74/0.98 tff(2679,plain,
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% 0.74/0.98 tff(2695,plain,
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% 0.74/0.98 inference(rewrite,[status(thm)],[])).
% 0.74/0.98 tff(2716,plain,
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% 0.74/0.98 inference(quant_inst,[status(thm)],[])).
% 0.74/0.98 tff(2717,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(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z)))),
% 0.74/0.98 inference(modus_ponens,[status(thm)],[2716, 2715])).
% 0.74/0.98 tff(2718,plain,
% 0.74/0.98 (~r(s(s(s(s(s(z))))), s(z))),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[2717, 14, 329, 1253])).
% 0.74/0.98 tff(2719,plain,
% 0.74/0.98 (b(s(s(s(s(s(z))))), s(z))),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[829, 2718])).
% 0.74/0.98 tff(2720,plain,
% 0.74/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 0.74/0.98 inference(rewrite,[status(thm)],[])).
% 0.74/0.98 tff(2721,plain,
% 0.74/0.98 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 0.74/0.98 inference(rewrite,[status(thm)],[])).
% 0.74/0.98 tff(2722,plain,
% 0.74/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 0.74/0.98 inference(monotonicity,[status(thm)],[2721])).
% 0.74/0.98 tff(2723,plain,
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% 0.74/0.98 inference(transitivity,[status(thm)],[2722, 2720])).
% 0.74/0.98 tff(2724,plain,
% 0.74/0.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 0.74/0.98 inference(quant_inst,[status(thm)],[])).
% 0.74/0.98 tff(2725,plain,
% 0.74/0.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 0.74/0.98 inference(modus_ponens,[status(thm)],[2724, 2723])).
% 0.74/0.98 tff(2726,plain,
% 0.74/0.98 ($false),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[2725, 118, 173, 172, 1269, 2719, 2714])).
% 0.74/0.98 tff(2727,plain,((~r(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))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.98 tff(2728,plain,
% 0.74/0.98 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[2727, 2702, 1853, 2706, 391])).
% 0.74/0.98 tff(2729,plain,
% 0.74/0.98 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[1595, 2728])).
% 0.74/0.98 tff(2730,plain,
% 0.74/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 0.74/0.99 inference(rewrite,[status(thm)],[])).
% 0.74/0.99 tff(2731,plain,
% 0.74/0.99 (((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 0.74/0.99 inference(rewrite,[status(thm)],[])).
% 0.74/0.99 tff(2732,plain,
% 0.74/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 0.74/0.99 inference(monotonicity,[status(thm)],[2731])).
% 0.74/0.99 tff(2733,plain,
% 0.74/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 0.74/0.99 inference(transitivity,[status(thm)],[2732, 2730])).
% 0.74/0.99 tff(2734,plain,
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% 0.74/0.99 inference(quant_inst,[status(thm)],[])).
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% 0.74/0.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 0.74/0.99 inference(modus_ponens,[status(thm)],[2734, 2733])).
% 0.74/0.99 tff(2736,plain,
% 0.74/0.99 ($false),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[2735, 118, 961, 587, 172, 1352, 724])).
% 0.74/0.99 tff(2737,plain,((~b(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(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.99 tff(2738,plain,
% 0.74/0.99 (~b(s(s(s(s(s(z))))), s(z))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[2737, 2704, 2700, 2702, 2729])).
% 0.74/0.99 tff(2739,plain,
% 0.74/0.99 (r(s(s(s(s(s(z))))), s(z))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[829, 2738])).
% 0.74/0.99 tff(2740,plain,
% 0.74/0.99 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[1586, 2739, 2])).
% 0.74/0.99 tff(2741,plain,
% 0.74/0.99 (b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[1627, 2740])).
% 0.74/0.99 tff(2742,plain,
% 0.74/0.99 ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[1367, 118, 1, 1532, 2729])).
% 0.74/0.99 tff(2743,plain,
% 0.74/0.99 (~b(s(s(s(s(s(z))))), z)),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[2742, 2741])).
% 0.74/0.99 tff(2744,plain,
% 0.74/0.99 (r(s(s(s(s(s(z))))), z)),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[767, 2743])).
% 0.74/0.99 tff(2745,plain,
% 0.74/0.99 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 0.74/0.99 inference(rewrite,[status(thm)],[])).
% 0.74/0.99 tff(2746,plain,
% 0.74/0.99 (((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z))) <=> ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 0.74/0.99 inference(rewrite,[status(thm)],[])).
% 0.74/0.99 tff(2747,plain,
% 0.74/0.99 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(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(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z)))))),
% 0.74/0.99 inference(monotonicity,[status(thm)],[2746])).
% 0.74/0.99 tff(2748,plain,
% 0.74/0.99 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(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(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 0.74/0.99 inference(transitivity,[status(thm)],[2747, 2745])).
% 0.74/0.99 tff(2749,plain,
% 0.74/0.99 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)))),
% 0.74/0.99 inference(quant_inst,[status(thm)],[])).
% 0.74/0.99 tff(2750,plain,
% 0.74/0.99 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z)))),
% 0.74/0.99 inference(modus_ponens,[status(thm)],[2749, 2748])).
% 0.74/0.99 tff(2751,plain,
% 0.74/0.99 ($false),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[2750, 14, 4, 2744, 2739])).
% 0.74/0.99 tff(2752,plain,((~r(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.99 tff(2753,plain,
% 0.74/0.99 (~r(z, s(z))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[2752, 161, 2, 391, 160, 1])).
% 0.74/0.99 tff(2754,plain,
% 0.74/0.99 (b(z, s(z))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[51, 2753])).
% 0.74/0.99 tff(2755,plain,
% 0.74/0.99 (~b(s(z), s(s(s(s(z)))))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[934, 2696, 1532, 2754, 2700])).
% 0.74/0.99 tff(2756,plain,
% 0.74/0.99 (r(s(z), s(s(s(s(z)))))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[323, 2755])).
% 0.74/0.99 tff(2757,plain,
% 0.74/0.99 (~r(s(z), z)),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[1151, 2756, 2698])).
% 0.74/0.99 tff(2758,plain,
% 0.74/0.99 (b(s(z), z)),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[187, 2757])).
% 0.74/0.99 tff(2759,plain,
% 0.74/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(z), z)))),
% 0.74/0.99 inference(rewrite,[status(thm)],[])).
% 0.74/0.99 tff(2760,plain,
% 0.74/0.99 (((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(z), z)))),
% 0.74/0.99 inference(rewrite,[status(thm)],[])).
% 0.74/0.99 tff(2761,plain,
% 0.74/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(z), z))))),
% 0.74/0.99 inference(monotonicity,[status(thm)],[2760])).
% 0.74/0.99 tff(2762,plain,
% 0.74/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(z), z)))),
% 0.74/0.99 inference(transitivity,[status(thm)],[2761, 2759])).
% 0.74/0.99 tff(2763,plain,
% 0.74/0.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))),
% 0.74/0.99 inference(quant_inst,[status(thm)],[])).
% 0.74/0.99 tff(2764,plain,
% 0.74/0.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(z), z))),
% 0.74/0.99 inference(modus_ponens,[status(thm)],[2763, 2762])).
% 0.74/0.99 tff(2765,plain,
% 0.74/0.99 ($false),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[2764, 118, 1509, 2754, 2758, 1853, 2696])).
% 0.74/0.99 tff(2766,plain,((~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)))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.99 tff(2767,plain,
% 0.74/0.99 (~r(z, s(s(s(z))))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[2766, 160, 2, 391, 1])).
% 0.74/0.99 tff(2768,plain,
% 0.74/0.99 (b(z, s(s(s(z))))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[71, 2767])).
% 0.74/0.99 tff(2769,plain,
% 0.74/0.99 (~r(s(z), s(s(s(z))))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[1520, 160, 2])).
% 0.74/0.99 tff(2770,plain,
% 0.74/0.99 (b(s(z), s(s(s(z))))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[668, 2769])).
% 0.74/0.99 tff(2771,plain,
% 0.74/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(z, s(s(s(z))))))),
% 0.74/0.99 inference(rewrite,[status(thm)],[])).
% 0.74/0.99 tff(2772,plain,
% 0.74/0.99 (((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(z, s(s(s(z))))))),
% 0.74/0.99 inference(rewrite,[status(thm)],[])).
% 0.74/0.99 tff(2773,plain,
% 0.74/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(z, s(s(s(z)))))))),
% 0.74/0.99 inference(monotonicity,[status(thm)],[2772])).
% 0.74/0.99 tff(2774,plain,
% 0.74/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(z, s(s(s(z))))))),
% 0.74/0.99 inference(transitivity,[status(thm)],[2773, 2771])).
% 0.74/0.99 tff(2775,plain,
% 0.74/0.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 0.74/0.99 inference(quant_inst,[status(thm)],[])).
% 0.74/0.99 tff(2776,plain,
% 0.74/0.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(z, s(s(s(z)))))),
% 0.74/0.99 inference(modus_ponens,[status(thm)],[2775, 2774])).
% 0.74/0.99 tff(2777,plain,
% 0.74/0.99 ($false),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[2776, 118, 1695, 234, 173, 172, 271])).
% 0.74/0.99 tff(2778,plain,((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.99 tff(2779,plain,
% 0.74/0.99 (~b(s(z), z)),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[2778, 1509, 1853, 2770, 2768])).
% 0.74/0.99 tff(2780,plain,
% 0.74/0.99 (r(s(z), z)),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[187, 2779])).
% 0.74/0.99 tff(2781,plain,
% 0.74/0.99 (~b(z, s(z))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[1515, 118, 1509, 1853, 2770, 2768])).
% 0.74/0.99 tff(2782,plain,
% 0.74/0.99 (r(z, s(z))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[51, 2781])).
% 0.74/0.99 tff(2783,plain,
% 0.74/0.99 (~r(z, s(s(s(s(z)))))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[449, 329, 4])).
% 0.74/0.99 tff(2784,plain,
% 0.74/0.99 (b(z, s(s(s(s(z)))))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[389, 2783])).
% 0.74/0.99 tff(2785,plain,
% 0.74/0.99 (~b(s(s(s(s(z)))), z)),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[1413, 2784, 1, 2590, 235])).
% 0.74/0.99 tff(2786,plain,
% 0.74/0.99 (r(s(s(s(s(z)))), z)),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[286, 2785])).
% 0.74/0.99 tff(2787,plain,
% 0.74/0.99 (~r(s(z), z)),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[1151, 2786, 329])).
% 0.74/0.99 tff(2788,plain,
% 0.74/0.99 (b(s(z), z)),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[187, 2787])).
% 0.74/0.99 tff(2789,plain,
% 0.74/0.99 (~b(s(z), s(s(s(s(s(s(z)))))))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[445, 2788, 2590, 2784, 235])).
% 0.74/0.99 tff(2790,plain,
% 0.74/0.99 (r(s(z), s(s(s(s(s(s(z)))))))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[232, 2789])).
% 0.74/0.99 tff(2791,plain,
% 0.74/0.99 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[2097, 274, 235, 609, 391])).
% 0.74/0.99 tff(2792,plain,
% 0.74/0.99 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[434, 2791])).
% 0.74/0.99 tff(2793,plain,
% 0.74/0.99 (((~![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(s(s(s(s(z)))))), 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(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), z)))),
% 0.74/0.99 inference(rewrite,[status(thm)],[])).
% 0.74/0.99 tff(2794,plain,
% 0.74/0.99 (((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), z)))),
% 0.74/0.99 inference(rewrite,[status(thm)],[])).
% 0.74/0.99 tff(2795,plain,
% 0.74/0.99 (((~![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(s(s(s(z)))), z)) | (~r(s(s(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(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), z))))),
% 0.74/0.99 inference(monotonicity,[status(thm)],[2794])).
% 0.74/0.99 tff(2796,plain,
% 0.74/0.99 (((~![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(s(s(s(z)))), z)) | (~r(s(s(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(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), z)))),
% 0.74/0.99 inference(transitivity,[status(thm)],[2795, 2793])).
% 0.74/0.99 tff(2797,plain,
% 0.74/0.99 ((~![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(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 0.74/0.99 inference(quant_inst,[status(thm)],[])).
% 0.74/0.99 tff(2798,plain,
% 0.74/0.99 ((~![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(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), z))),
% 0.74/0.99 inference(modus_ponens,[status(thm)],[2797, 2796])).
% 0.74/0.99 tff(2799,plain,
% 0.74/0.99 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[2798, 14, 274, 273])).
% 0.74/0.99 tff(2800,plain,
% 0.74/0.99 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[480, 2799])).
% 0.74/0.99 tff(2801,plain,
% 0.74/0.99 (((~![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)))))))))),
% 0.74/0.99 inference(rewrite,[status(thm)],[])).
% 0.74/0.99 tff(2802,plain,
% 0.74/0.99 (((~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)))))))))),
% 0.74/0.99 inference(rewrite,[status(thm)],[])).
% 0.74/0.99 tff(2803,plain,
% 0.74/0.99 (((~![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))))))))))),
% 0.74/0.99 inference(monotonicity,[status(thm)],[2802])).
% 0.74/0.99 tff(2804,plain,
% 0.74/0.99 (((~![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)))))))))),
% 0.74/0.99 inference(transitivity,[status(thm)],[2803, 2801])).
% 0.74/0.99 tff(2805,plain,
% 0.74/0.99 ((~![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)))))))))),
% 0.74/0.99 inference(quant_inst,[status(thm)],[])).
% 0.74/0.99 tff(2806,plain,
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% 0.74/0.99 tff(2809,plain,
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% 0.74/0.99 inference(unit_resolution,[status(thm)],[2808, 273, 212])).
% 0.74/0.99 tff(2810,plain,
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% 0.74/0.99 inference(unit_resolution,[status(thm)],[187, 2809])).
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% 0.74/0.99 inference(rewrite,[status(thm)],[])).
% 0.74/0.99 tff(2812,plain,
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% 0.74/0.99 inference(unit_resolution,[status(thm)],[668, 2817])).
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% 0.74/0.99 inference(unit_resolution,[status(thm)],[220, 2818, 212])).
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% 0.74/0.99 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[156, 2819])).
% 0.74/0.99 tff(2821,plain,
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% 0.74/0.99 inference(unit_resolution,[status(thm)],[2650, 2820, 609, 437, 2800])).
% 0.74/0.99 tff(2822,plain,
% 0.74/0.99 (r(s(s(s(s(z)))), s(s(s(z))))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[310, 2821])).
% 0.74/0.99 tff(2823,plain,
% 0.74/0.99 (~r(z, s(s(s(z))))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[606, 2822, 274])).
% 0.74/0.99 tff(2824,plain,
% 0.74/0.99 (b(z, s(s(s(z))))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[71, 2823])).
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% 0.74/0.99 inference(unit_resolution,[status(thm)],[1968, 118, 1695, 2820, 609, 2824, 235])).
% 0.74/0.99 tff(2826,plain,((~r(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.99 tff(2827,plain,
% 0.74/0.99 (~r(s(s(s(s(s(s(z)))))), z)),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[2826, 2095, 609, 235, 274, 2792, 212])).
% 0.74/0.99 tff(2828,plain,
% 0.74/0.99 (b(s(s(s(s(s(s(z)))))), z)),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[252, 2827])).
% 0.74/0.99 tff(2829,plain,
% 0.74/0.99 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
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% 0.74/0.99 tff(2830,plain,
% 0.74/0.99 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[156, 2829])).
% 0.74/0.99 tff(2831,plain,
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% 0.74/0.99 inference(unit_resolution,[status(thm)],[169, 161, 160])).
% 0.74/0.99 tff(2832,plain,
% 0.74/0.99 (b(z, s(s(s(s(s(s(z)))))))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[356, 2831])).
% 0.74/0.99 tff(2833,plain,
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% 0.74/0.99 inference(unit_resolution,[status(thm)],[396, 160, 391])).
% 0.74/0.99 tff(2834,plain,
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% 0.74/0.99 inference(unit_resolution,[status(thm)],[434, 2833])).
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% 0.74/1.00 inference(unit_resolution,[status(thm)],[703, 2851, 391])).
% 0.74/1.00 tff(2853,plain,
% 0.74/1.00 ($false),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[286, 2852, 2843])).
% 0.74/1.00 tff(2854,plain,((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.74/1.00 tff(2855,plain,
% 0.74/1.00 (~r(z, s(s(s(z))))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[2854, 2830, 609, 391])).
% 0.74/1.00 tff(2856,plain,
% 0.74/1.00 (b(z, s(s(s(z))))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[71, 2855])).
% 0.74/1.00 tff(2857,plain,
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% 0.74/1.00 inference(rewrite,[status(thm)],[])).
% 0.74/1.00 tff(2858,plain,
% 0.74/1.00 (((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(z)))))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(z))))))),
% 0.74/1.00 inference(rewrite,[status(thm)],[])).
% 0.74/1.00 tff(2859,plain,
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% 0.74/1.00 inference(monotonicity,[status(thm)],[2858])).
% 0.74/1.00 tff(2860,plain,
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% 0.74/1.00 inference(transitivity,[status(thm)],[2859, 2857])).
% 0.74/1.00 tff(2861,plain,
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% 0.74/1.00 inference(quant_inst,[status(thm)],[])).
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% 0.74/1.00 inference(modus_ponens,[status(thm)],[2861, 2860])).
% 0.74/1.00 tff(2863,plain,
% 0.74/1.00 ($false),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[2862, 118, 2095, 609, 2828, 2856, 235])).
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% 0.74/1.00 tff(2865,plain,
% 0.74/1.00 (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[2864, 2790, 391, 235, 2786])).
% 0.74/1.00 tff(2866,plain,
% 0.74/1.00 (r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[581, 2865])).
% 0.74/1.00 tff(2867,plain,
% 0.74/1.00 (~r(s(s(s(s(z)))), s(z))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[503, 2786, 4])).
% 0.74/1.00 tff(2868,plain,
% 0.74/1.00 (b(s(s(s(s(z)))), s(z))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[513, 2867])).
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% 0.74/1.00 inference(rewrite,[status(thm)],[])).
% 0.74/1.00 tff(2870,plain,
% 0.74/1.00 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(z))))))),
% 0.74/1.00 inference(rewrite,[status(thm)],[])).
% 0.74/1.00 tff(2871,plain,
% 0.74/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(z)))))))),
% 0.74/1.00 inference(monotonicity,[status(thm)],[2870])).
% 0.74/1.00 tff(2872,plain,
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% 0.74/1.00 inference(transitivity,[status(thm)],[2871, 2869])).
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% 0.74/1.00 inference(quant_inst,[status(thm)],[])).
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% 0.74/1.00 inference(modus_ponens,[status(thm)],[2873, 2872])).
% 0.74/1.00 tff(2875,plain,
% 0.74/1.00 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[2874, 118, 2868, 173, 2784, 271])).
% 0.74/1.00 tff(2876,plain,
% 0.74/1.00 (r(s(s(s(s(z)))), s(s(s(z))))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[310, 2875])).
% 0.74/1.00 tff(2877,plain,
% 0.74/1.00 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[1980, 2876, 2866])).
% 0.74/1.00 tff(2878,plain,
% 0.74/1.00 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[480, 2877])).
% 0.74/1.00 tff(2879,plain,
% 0.74/1.00 ($false),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[1250, 118, 2590, 2878, 1, 2784, 235])).
% 0.74/1.00 tff(2880,plain,((~r(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.74/1.00 tff(2881,plain,
% 0.74/1.00 (~r(s(z), s(s(s(s(z)))))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[2880, 1853, 2690, 1, 2768, 391, 2782])).
% 0.74/1.00 tff(2882,plain,
% 0.74/1.00 (b(s(z), s(s(s(s(z)))))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[323, 2881])).
% 0.74/1.00 tff(2883,plain,
% 0.74/1.00 (~r(s(s(s(s(z)))), s(z))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[2270, 339, 2782])).
% 0.74/1.00 tff(2884,plain,
% 0.74/1.00 (b(s(s(s(s(z)))), s(z))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[513, 2883])).
% 0.74/1.00 tff(2885,plain,
% 0.74/1.00 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[1115, 2884, 2590, 2770, 2882, 160])).
% 0.74/1.00 tff(2886,plain,
% 0.74/1.00 (r(s(s(s(s(z)))), s(s(s(z))))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[310, 2885])).
% 0.74/1.00 tff(2887,plain,
% 0.74/1.00 (~b(s(s(s(s(z)))), z)),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[1006, 2886, 1, 2690, 160])).
% 0.74/1.00 tff(2888,plain,
% 0.74/1.00 (r(s(s(s(s(z)))), z)),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[286, 2887])).
% 0.74/1.00 tff(2889,plain,
% 0.74/1.00 (~r(s(s(s(s(s(z))))), z)),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[1667, 2888, 2780])).
% 0.74/1.00 tff(2890,plain,
% 0.74/1.00 (b(s(s(s(s(s(z))))), z)),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[767, 2889])).
% 0.74/1.00 tff(2891,plain,
% 0.74/1.00 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[1586, 1164, 2])).
% 0.74/1.00 tff(2892,plain,
% 0.74/1.00 (b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[1627, 2891])).
% 0.74/1.00 tff(2893,plain,
% 0.74/1.00 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[2112, 2892, 235, 1, 1205])).
% 0.74/1.00 tff(2894,plain,
% 0.74/1.00 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[1684, 2893])).
% 0.74/1.00 tff(2895,plain,
% 0.74/1.00 ($false),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[1175, 14, 2, 2894, 1164])).
% 0.74/1.00 tff(2896,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 0.74/1.00 tff(2897,plain,
% 0.74/1.00 (~r(s(s(s(s(s(z))))), s(z))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[2896, 2890, 2690, 1, 2])).
% 0.74/1.00 tff(2898,plain,
% 0.74/1.00 (b(s(s(s(s(s(z))))), s(z))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[829, 2897])).
% 0.74/1.00 tff(2899,plain,
% 0.74/1.00 (((~![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(z))))), s(s(s(s(z)))))) | (~r(z, s(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(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))))),
% 0.74/1.00 inference(rewrite,[status(thm)],[])).
% 0.74/1.00 tff(2900,plain,
% 0.74/1.00 (((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z)))))))) <=> ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))))),
% 0.74/1.00 inference(rewrite,[status(thm)],[])).
% 0.74/1.00 tff(2901,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(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(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(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z)))))))))),
% 0.74/1.00 inference(monotonicity,[status(thm)],[2900])).
% 0.74/1.00 tff(2902,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(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(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(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))))),
% 0.74/1.00 inference(transitivity,[status(thm)],[2901, 2899])).
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% 0.74/1.00 inference(quant_inst,[status(thm)],[])).
% 0.74/1.00 tff(2904,plain,
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% 0.74/1.00 inference(modus_ponens,[status(thm)],[2903, 2902])).
% 0.74/1.00 tff(2905,plain,
% 0.74/1.00 (~r(z, s(s(s(s(s(z))))))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[2904, 14, 339, 1253])).
% 0.74/1.00 tff(2906,plain,
% 0.74/1.00 (b(z, s(s(s(s(s(z))))))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[1431, 2905])).
% 0.74/1.00 tff(2907,plain,
% 0.74/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))))),
% 0.74/1.00 inference(rewrite,[status(thm)],[])).
% 0.74/1.00 tff(2908,plain,
% 0.74/1.00 (((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))))),
% 0.74/1.00 inference(rewrite,[status(thm)],[])).
% 0.74/1.00 tff(2909,plain,
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% 0.74/1.00 inference(transitivity,[status(thm)],[2909, 2907])).
% 0.74/1.00 tff(2911,plain,
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% 0.74/1.00 inference(quant_inst,[status(thm)],[])).
% 0.74/1.00 tff(2912,plain,
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% 0.74/1.00 inference(modus_ponens,[status(thm)],[2911, 2910])).
% 0.74/1.00 tff(2913,plain,
% 0.74/1.00 ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z)))))))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[2912, 118, 1695, 271, 1205])).
% 0.74/1.00 tff(2914,plain,
% 0.74/1.00 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[2913, 2906])).
% 0.74/1.00 tff(2915,plain,
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% 0.74/1.00 inference(unit_resolution,[status(thm)],[1820, 46, 2914, 1809, 2713])).
% 0.74/1.00 tff(2916,plain,((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.74/1.00 tff(2917,plain,
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% 0.74/1.00 inference(unit_resolution,[status(thm)],[2916, 2890, 2768, 1509, 339, 391])).
% 0.74/1.00 tff(2918,plain,
% 0.74/1.00 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[1595, 2917])).
% 0.74/1.00 tff(2919,plain,
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% 0.74/1.00 inference(rewrite,[status(thm)],[])).
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% 0.74/1.00 inference(transitivity,[status(thm)],[2921, 2919])).
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% 0.74/1.00 inference(quant_inst,[status(thm)],[])).
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% 0.74/1.01 inference(modus_ponens,[status(thm)],[2923, 2922])).
% 0.74/1.01 tff(2925,plain,
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% 0.74/1.01 inference(unit_resolution,[status(thm)],[2924, 118, 2882, 1853, 2918])).
% 0.74/1.01 tff(2926,plain,
% 0.74/1.01 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[2925, 2898])).
% 0.74/1.01 tff(2927,plain,
% 0.74/1.01 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[848, 46, 800, 2926])).
% 0.74/1.01 tff(2928,plain,
% 0.74/1.01 ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[1613, 118, 2882, 2884, 2918])).
% 0.74/1.01 tff(2929,plain,
% 0.74/1.01 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[2928, 2898])).
% 0.74/1.01 tff(2930,plain,
% 0.74/1.01 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[1616, 2929])).
% 0.74/1.01 tff(2931,plain,
% 0.74/1.01 (((~![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(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), 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(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 0.74/1.01 inference(rewrite,[status(thm)],[])).
% 0.74/1.01 tff(2932,plain,
% 0.74/1.01 (((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 0.74/1.01 inference(rewrite,[status(thm)],[])).
% 0.74/1.01 tff(2933,plain,
% 0.74/1.01 (((~![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(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
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% 0.74/1.01 tff(2934,plain,
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% 0.74/1.01 inference(transitivity,[status(thm)],[2933, 2931])).
% 0.74/1.01 tff(2935,plain,
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% 0.74/1.01 inference(quant_inst,[status(thm)],[])).
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% 0.74/1.01 inference(modus_ponens,[status(thm)],[2935, 2934])).
% 0.74/1.01 tff(2937,plain,
% 0.74/1.01 ($false),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[2936, 14, 391, 2930, 2927])).
% 0.74/1.01 tff(2938,plain,((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.74/1.01 tff(2939,plain,
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% 0.74/1.01 tff(2940,plain,
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% 0.74/1.01 inference(unit_resolution,[status(thm)],[389, 2939])).
% 0.74/1.01 tff(2941,plain,
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% 0.74/1.01 inference(unit_resolution,[status(thm)],[2862, 118, 1509, 1, 2768, 2690])).
% 0.74/1.01 tff(2942,plain,
% 0.74/1.01 (r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
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% 0.74/1.01 tff(2943,plain,
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% 0.74/1.01 inference(unit_resolution,[status(thm)],[1413, 2940, 1, 2590, 2690])).
% 0.74/1.01 tff(2944,plain,
% 0.74/1.01 (r(s(s(s(s(z)))), z)),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[286, 2943])).
% 0.74/1.01 tff(2945,plain,
% 0.74/1.01 (~r(s(s(s(s(z)))), s(z))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[503, 2944, 2782])).
% 0.74/1.01 tff(2946,plain,
% 0.74/1.01 (b(s(s(s(s(z)))), s(z))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[513, 2945])).
% 0.74/1.01 tff(2947,plain,
% 0.74/1.01 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[1115, 2946, 2590, 2770, 2882, 160])).
% 0.74/1.01 tff(2948,plain,
% 0.74/1.01 (r(s(s(s(s(z)))), s(s(s(z))))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[310, 2947])).
% 0.74/1.01 tff(2949,plain,
% 0.74/1.01 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[1980, 2948, 2942])).
% 0.74/1.01 tff(2950,plain,
% 0.74/1.01 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[480, 2949])).
% 0.74/1.01 tff(2951,plain,
% 0.74/1.01 ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[1250, 118, 437, 459, 235])).
% 0.74/1.01 tff(2952,plain,
% 0.74/1.01 (~b(s(s(s(s(s(s(z)))))), z)),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[2951, 436])).
% 0.74/1.01 tff(2953,plain,
% 0.74/1.01 (r(s(s(s(s(s(s(z)))))), z)),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[252, 2952])).
% 0.74/1.01 tff(2954,plain,
% 0.74/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 0.74/1.01 inference(rewrite,[status(thm)],[])).
% 0.74/1.01 tff(2955,plain,
% 0.74/1.01 (((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(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(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 0.74/1.01 inference(rewrite,[status(thm)],[])).
% 0.74/1.01 tff(2956,plain,
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% 0.74/1.01 inference(monotonicity,[status(thm)],[2955])).
% 0.74/1.01 tff(2957,plain,
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% 0.74/1.01 inference(transitivity,[status(thm)],[2956, 2954])).
% 0.74/1.01 tff(2958,plain,
% 0.74/1.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))),
% 0.74/1.01 inference(quant_inst,[status(thm)],[])).
% 0.74/1.01 tff(2959,plain,
% 0.74/1.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 0.74/1.01 inference(modus_ponens,[status(thm)],[2958, 2957])).
% 0.74/1.01 tff(2960,plain,
% 0.74/1.01 ((~b(z, s(s(s(s(z)))))) | (~b(s(z), z))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[2959, 118, 460, 459, 235])).
% 0.74/1.01 tff(2961,plain,
% 0.74/1.01 (~b(s(z), z)),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[2960, 436])).
% 0.74/1.01 tff(2962,plain,
% 0.74/1.01 (r(s(z), z)),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[187, 2961])).
% 0.74/1.01 tff(2963,plain,
% 0.74/1.01 ($false),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[2806, 14, 2962, 2953, 212])).
% 0.74/1.01 tff(2964,plain,((~b(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.74/1.01 tff(2965,plain,
% 0.74/1.01 (~r(s(z), s(s(s(s(s(s(z)))))))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[2964, 2950, 2590, 2690, 2882, 2940])).
% 0.74/1.01 tff(2966,plain,
% 0.74/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 0.74/1.01 inference(rewrite,[status(thm)],[])).
% 0.74/1.01 tff(2967,plain,
% 0.74/1.01 (((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(z)))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 0.74/1.01 inference(rewrite,[status(thm)],[])).
% 0.74/1.01 tff(2968,plain,
% 0.74/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z))))))))))),
% 0.74/1.01 inference(monotonicity,[status(thm)],[2967])).
% 0.74/1.01 tff(2969,plain,
% 0.74/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 0.74/1.01 inference(transitivity,[status(thm)],[2968, 2966])).
% 0.74/1.01 tff(2970,plain,
% 0.74/1.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(z))))),
% 0.74/1.01 inference(quant_inst,[status(thm)],[])).
% 0.74/1.01 tff(2971,plain,
% 0.74/1.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z))))))))),
% 0.74/1.01 inference(modus_ponens,[status(thm)],[2970, 2969])).
% 0.74/1.01 tff(2972,plain,
% 0.74/1.01 ((~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(z))))))))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[2971, 118, 460, 437, 235])).
% 0.74/1.01 tff(2973,plain,
% 0.74/1.01 (~b(z, s(z))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[2972, 237])).
% 0.74/1.01 tff(2974,plain,
% 0.74/1.01 (r(z, s(z))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[51, 2973])).
% 0.74/1.01 tff(2975,plain,
% 0.74/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(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(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(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(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 0.74/1.01 inference(rewrite,[status(thm)],[])).
% 0.74/1.01 tff(2976,plain,
% 0.74/1.01 (((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(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(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 0.74/1.01 inference(rewrite,[status(thm)],[])).
% 0.74/1.01 tff(2977,plain,
% 0.74/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))))),
% 0.74/1.01 inference(monotonicity,[status(thm)],[2976])).
% 0.74/1.01 tff(2978,plain,
% 0.74/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 0.74/1.01 inference(transitivity,[status(thm)],[2977, 2975])).
% 0.74/1.01 tff(2979,plain,
% 0.74/1.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(z))))),
% 0.74/1.01 inference(quant_inst,[status(thm)],[])).
% 0.74/1.01 tff(2980,plain,
% 0.74/1.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 0.74/1.01 inference(modus_ponens,[status(thm)],[2979, 2978])).
% 0.74/1.01 tff(2981,plain,
% 0.74/1.01 ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(s(z))))))))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[2980, 118, 460, 437, 459])).
% 0.74/1.01 tff(2982,plain,
% 0.74/1.01 (~b(s(s(s(s(z)))), s(z))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[2981, 237])).
% 0.74/1.01 tff(2983,plain,
% 0.74/1.01 (r(s(s(s(s(z)))), s(z))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[513, 2982])).
% 0.74/1.01 tff(2984,plain,
% 0.74/1.01 ($false),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[503, 2983, 2974, 274])).
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% 0.74/1.02 (b(s(z), z)),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[187, 3039])).
% 0.74/1.02 tff(3041,plain,
% 0.74/1.02 (~b(s(z), s(s(s(s(s(s(z)))))))),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[2409, 234, 1, 73, 271])).
% 0.74/1.02 tff(3042,plain,
% 0.74/1.02 (r(s(z), s(s(s(s(s(s(z)))))))),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[232, 3041])).
% 0.74/1.02 tff(3043,plain,
% 0.74/1.02 (~b(s(s(s(s(s(z))))), s(z))),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[1224, 1205, 174, 1, 3042, 234])).
% 0.74/1.02 tff(3044,plain,
% 0.74/1.02 (r(s(s(s(s(s(z))))), s(z))),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[829, 3043])).
% 0.74/1.02 tff(3045,plain,
% 0.74/1.02 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[1175, 14, 2, 3044])).
% 0.74/1.02 tff(3046,plain,
% 0.74/1.02 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[1713, 118, 73, 1, 271, 1205])).
% 0.74/1.02 tff(3047,plain,
% 0.74/1.02 ($false),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[1684, 3046, 3045])).
% 0.74/1.02 tff(3048,plain,((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 0.74/1.02 tff(3049,plain,
% 0.74/1.02 (~b(s(s(s(s(s(z))))), z)),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[3048, 3040, 1, 271, 2, 174, 73])).
% 0.74/1.02 tff(3050,plain,
% 0.74/1.02 (r(s(s(s(s(s(z))))), z)),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[767, 3049])).
% 0.74/1.02 tff(3051,plain,
% 0.74/1.02 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[1240, 14, 274, 3050])).
% 0.74/1.02 tff(3052,plain,
% 0.74/1.02 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[1616, 3051])).
% 0.74/1.02 tff(3053,plain,
% 0.74/1.02 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[1655, 14, 274, 3050])).
% 0.74/1.02 tff(3054,plain,
% 0.74/1.02 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[1595, 3053])).
% 0.74/1.02 tff(3055,plain,
% 0.74/1.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))),
% 0.74/1.02 inference(rewrite,[status(thm)],[])).
% 0.74/1.02 tff(3056,plain,
% 0.74/1.02 (((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))),
% 0.74/1.02 inference(rewrite,[status(thm)],[])).
% 0.74/1.02 tff(3057,plain,
% 0.74/1.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))))))),
% 0.74/1.02 inference(monotonicity,[status(thm)],[3056])).
% 0.74/1.02 tff(3058,plain,
% 0.74/1.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))),
% 0.74/1.02 inference(transitivity,[status(thm)],[3057, 3055])).
% 0.74/1.02 tff(3059,plain,
% 0.74/1.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 0.74/1.02 inference(quant_inst,[status(thm)],[])).
% 0.74/1.02 tff(3060,plain,
% 0.74/1.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))))),
% 0.74/1.02 inference(modus_ponens,[status(thm)],[3059, 3058])).
% 0.74/1.02 tff(3061,plain,
% 0.74/1.02 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[3060, 118, 2590, 459, 3054, 3052])).
% 0.74/1.02 tff(3062,plain,
% 0.74/1.02 (r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[1627, 3061])).
% 0.74/1.02 tff(3063,plain,
% 0.74/1.02 (~r(s(s(s(s(s(z))))), s(z))),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[1586, 3062, 2])).
% 0.74/1.02 tff(3064,plain,
% 0.74/1.02 (b(s(s(s(s(s(z))))), s(z))),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[829, 3063])).
% 0.74/1.02 tff(3065,plain,
% 0.74/1.02 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[2662, 73, 2590, 3016, 459])).
% 0.74/1.02 tff(3066,plain,
% 0.74/1.02 (r(s(s(s(s(z)))), s(s(s(z))))),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[310, 3065])).
% 0.74/1.02 tff(3067,plain,
% 0.74/1.02 ($false),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[1066, 14, 495, 74, 288])).
% 0.74/1.02 tff(3068,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.74/1.02 tff(3069,plain,
% 0.74/1.02 (~r(s(s(s(s(z)))), s(z))),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[3068, 74, 3066])).
% 0.74/1.02 tff(3070,plain,
% 0.74/1.02 (b(s(s(s(s(z)))), s(z))),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[513, 3069])).
% 0.74/1.02 tff(3071,assumption,(b(s(z), s(s(s(s(s(z))))))), introduced(assumption)).
% 0.74/1.02 tff(3072,plain,
% 0.74/1.02 ($false),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[1665, 118, 961, 1352, 2329, 3071, 724])).
% 0.74/1.02 tff(3073,plain,((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.74/1.02 tff(3074,plain,
% 0.74/1.02 (~b(s(z), s(s(s(s(s(z))))))),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[3073, 3070, 3054, 3052, 3064])).
% 0.74/1.02 tff(3075,plain,
% 0.74/1.02 (r(s(z), s(s(s(s(s(z))))))),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[791, 3074])).
% 0.74/1.02 tff(3076,plain,
% 0.74/1.02 (~b(s(z), s(s(s(s(s(s(z)))))))),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[2409, 3040, 1, 73, 271])).
% 0.74/1.02 tff(3077,plain,
% 0.74/1.02 (r(s(z), s(s(s(s(s(s(z)))))))),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[232, 3076])).
% 0.74/1.02 tff(3078,plain,
% 0.74/1.02 ($false),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[1222, 14, 3077, 3075, 3062])).
% 0.74/1.02 tff(3079,plain,((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 0.74/1.02 tff(3080,plain,
% 0.74/1.02 (~r(s(s(s(z))), s(z))),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[3079, 73, 459, 3038, 1, 271, 174, 2, 3036])).
% 0.74/1.02 tff(3081,plain,
% 0.74/1.02 (b(s(s(s(z))), s(z))),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[105, 3080])).
% 0.74/1.02 tff(3082,plain,
% 0.74/1.02 ($false),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[124, 118, 174, 3081, 73, 1, 271])).
% 0.74/1.02 tff(3083,plain,((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 0.74/1.02 tff(3084,plain,
% 0.74/1.02 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[3083, 52, 1, 3034, 3028, 2, 1525])).
% 0.74/1.02 tff(3085,plain,
% 0.74/1.02 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[156, 3084])).
% 0.74/1.02 tff(3086,plain,
% 0.74/1.02 (~r(s(s(s(z))), s(z))),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[951, 3085, 2])).
% 0.74/1.02 tff(3087,plain,
% 0.74/1.02 (b(s(s(s(z))), s(z))),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[105, 3086])).
% 0.74/1.02 tff(3088,plain,
% 0.74/1.02 (~r(s(z), s(s(s(z))))),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[1520, 3085, 2])).
% 0.74/1.02 tff(3089,plain,
% 0.74/1.02 (b(s(z), s(s(s(z))))),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[668, 3088])).
% 0.74/1.02 tff(3090,plain,
% 0.74/1.02 ($false),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[1517, 3089, 3087, 3, 3085, 52])).
% 0.74/1.02 tff(3091,plain,((~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z))), inference(lemma,lemma(discharge,[]))).
% 0.74/1.02 tff(3092,plain,
% 0.74/1.02 (~r(z, s(s(s(s(s(s(z)))))))),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[3091, 2, 1])).
% 0.74/1.02 tff(3093,plain,
% 0.74/1.02 (b(z, s(s(s(s(s(s(z)))))))),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[356, 3092])).
% 0.74/1.02 tff(3094,plain,
% 0.74/1.02 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[1006, 721, 1, 235, 160])).
% 0.74/1.02 tff(3095,plain,
% 0.74/1.02 (b(s(s(s(s(z)))), s(s(s(z))))),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[310, 3094])).
% 0.74/1.02 tff(3096,plain,
% 0.74/1.02 (~b(z, s(s(s(s(z)))))),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[1413, 721, 1, 2590, 235])).
% 0.74/1.02 tff(3097,plain,
% 0.74/1.02 (r(z, s(s(s(s(z)))))),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[389, 3096])).
% 0.74/1.02 tff(3098,plain,
% 0.74/1.02 (~b(s(z), s(s(s(s(z)))))),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[944, 3095, 594, 173, 172])).
% 0.74/1.02 tff(3099,plain,
% 0.74/1.02 (r(s(z), s(s(s(s(z)))))),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[323, 3098])).
% 0.74/1.02 tff(3100,plain,
% 0.74/1.02 (~r(z, s(z))),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[449, 3099, 3097])).
% 0.74/1.02 tff(3101,plain,
% 0.74/1.02 (b(z, s(z))),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[51, 3100])).
% 0.74/1.02 tff(3102,plain,
% 0.74/1.02 ($false),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[2004, 118, 1509, 3101, 173, 3095, 721])).
% 0.74/1.02 tff(3103,plain,((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.74/1.02 tff(3104,plain,
% 0.74/1.02 (~b(s(s(s(s(z)))), z)),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[3103, 1853, 3016, 2770, 1, 3093, 160])).
% 0.74/1.02 tff(3105,plain,
% 0.74/1.02 (r(s(s(s(s(z)))), z)),
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% 0.74/1.02 inference(unit_resolution,[status(thm)],[2258, 587, 594, 274, 172])).
% 0.74/1.02 tff(3107,plain,
% 0.74/1.02 (b(s(z), z)),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[187, 3106])).
% 0.74/1.02 tff(3108,plain,
% 0.74/1.02 (~b(s(s(s(s(z)))), s(z))),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[1161, 118, 594, 173, 587, 172])).
% 0.74/1.02 tff(3109,plain,
% 0.74/1.02 (r(s(s(s(s(z)))), s(z))),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[513, 3108])).
% 0.74/1.02 tff(3110,plain,
% 0.74/1.02 (~r(z, s(z))),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[503, 3109, 274])).
% 0.74/1.02 tff(3111,plain,
% 0.74/1.02 (b(z, s(z))),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[51, 3110])).
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% 0.86/1.03 inference(rewrite,[status(thm)],[])).
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% 0.86/1.03 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(3167,plain,
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% 0.86/1.03 inference(monotonicity,[status(thm)],[3166])).
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% 0.86/1.03 inference(unit_resolution,[status(thm)],[3170, 118, 3164, 3016, 3160, 2590, 3156])).
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% 0.86/1.03 inference(unit_resolution,[status(thm)],[286, 3173])).
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% 0.86/1.03 inference(unit_resolution,[status(thm)],[3123, 118, 594, 437, 235])).
% 0.86/1.03 tff(3176,plain,
% 0.86/1.03 (~b(z, s(s(s(z))))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[3175, 609])).
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% 0.86/1.03 inference(unit_resolution,[status(thm)],[71, 3176])).
% 0.86/1.03 tff(3178,plain,
% 0.86/1.03 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[606, 3177, 274])).
% 0.86/1.03 tff(3179,plain,
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% 0.86/1.03 inference(unit_resolution,[status(thm)],[310, 3178])).
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% 0.86/1.03 inference(rewrite,[status(thm)],[])).
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% 0.86/1.03 inference(monotonicity,[status(thm)],[3181])).
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% 0.86/1.03 inference(modus_ponens,[status(thm)],[3184, 3183])).
% 0.86/1.03 tff(3186,plain,
% 0.86/1.03 ($false),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[3185, 118, 594, 3179, 437, 73, 609])).
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% 0.86/1.03 tff(3194,plain,
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% 0.86/1.03 inference(unit_resolution,[status(thm)],[1125, 3193, 2])).
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% 0.86/1.03 inference(unit_resolution,[status(thm)],[71, 3203])).
% 0.86/1.03 tff(3205,plain,
% 0.86/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(3206,plain,
% 0.86/1.03 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(3207,plain,
% 0.86/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z)))))))),
% 0.86/1.03 inference(monotonicity,[status(thm)],[3206])).
% 0.86/1.03 tff(3208,plain,
% 0.86/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 0.86/1.03 inference(transitivity,[status(thm)],[3207, 3205])).
% 0.86/1.03 tff(3209,plain,
% 0.86/1.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 0.86/1.03 inference(quant_inst,[status(thm)],[])).
% 0.86/1.03 tff(3210,plain,
% 0.86/1.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z)))))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[3209, 3208])).
% 0.86/1.03 tff(3211,plain,
% 0.86/1.03 ($false),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[3210, 118, 3016, 2590, 3156, 3204, 3093])).
% 0.86/1.03 tff(3212,plain,((~r(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.03 tff(3213,plain,
% 0.86/1.03 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[3212, 1])).
% 0.86/1.03 tff(3214,plain,
% 0.86/1.03 (b(s(s(s(s(s(s(z)))))), s(z))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[210, 3213])).
% 0.86/1.03 tff(3215,plain,
% 0.86/1.03 (~r(z, s(z))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[1764, 161, 74])).
% 0.86/1.03 tff(3216,plain,
% 0.86/1.03 (b(z, s(z))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[51, 3215])).
% 0.86/1.03 tff(3217,plain,
% 0.86/1.03 (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[2282, 118, 174, 721, 1, 3214])).
% 0.86/1.03 tff(3218,plain,
% 0.86/1.03 (r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[480, 3217])).
% 0.86/1.03 tff(3219,plain,
% 0.86/1.03 (((~![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(z, s(s(s(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(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(z)))))))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(3220,plain,
% 0.86/1.03 ((~![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(z, s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(z)))))))),
% 0.86/1.03 inference(quant_inst,[status(thm)],[])).
% 0.86/1.03 tff(3221,plain,
% 0.86/1.03 ((~![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(z, s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(z))))))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[3220, 3219])).
% 0.86/1.03 tff(3222,plain,
% 0.86/1.03 (~r(z, s(s(s(s(z)))))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[3221, 14, 3, 3218])).
% 0.86/1.03 tff(3223,plain,
% 0.86/1.03 (b(z, s(s(s(s(z)))))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[389, 3222])).
% 0.86/1.03 tff(3224,plain,
% 0.86/1.03 (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[3024, 594, 721, 1])).
% 0.86/1.03 tff(3225,plain,
% 0.86/1.03 (~r(s(s(s(z))), z)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[571, 53, 3])).
% 0.86/1.03 tff(3226,plain,
% 0.86/1.03 (b(s(s(s(z))), z)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[649, 3225])).
% 0.86/1.03 tff(3227,plain,
% 0.86/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(3228,plain,
% 0.86/1.03 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(3229,plain,
% 0.86/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z)))))))),
% 0.86/1.03 inference(monotonicity,[status(thm)],[3228])).
% 0.86/1.03 tff(3230,plain,
% 0.86/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))))),
% 0.86/1.03 inference(transitivity,[status(thm)],[3229, 3227])).
% 0.86/1.03 tff(3231,plain,
% 0.86/1.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))),
% 0.86/1.03 inference(quant_inst,[status(thm)],[])).
% 0.86/1.03 tff(3232,plain,
% 0.86/1.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z)))))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[3231, 3230])).
% 0.86/1.03 tff(3233,plain,
% 0.86/1.03 ($false),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[3232, 118, 3226, 594, 721, 436, 72])).
% 0.86/1.03 tff(3234,plain,((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.03 tff(3235,plain,
% 0.86/1.03 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[3234, 594, 3, 436, 721])).
% 0.86/1.03 tff(3236,plain,
% 0.86/1.03 ($false),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[581, 3235, 3224])).
% 0.86/1.03 tff(3237,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.03 tff(3238,plain,
% 0.86/1.03 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[3237, 3, 3223, 721, 1])).
% 0.86/1.03 tff(3239,plain,
% 0.86/1.03 (r(s(s(s(z))), s(s(s(s(z)))))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[402, 3238])).
% 0.86/1.03 tff(3240,plain,
% 0.86/1.03 ($false),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[1540, 14, 329, 391, 74])).
% 0.86/1.03 tff(3241,plain,((~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)))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.04 tff(3242,plain,
% 0.86/1.04 (~r(s(z), s(s(s(s(z)))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[3241, 3239, 74])).
% 0.86/1.04 tff(3243,plain,
% 0.86/1.04 (b(s(z), s(s(s(s(z)))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[323, 3242])).
% 0.86/1.04 tff(3244,plain,
% 0.86/1.04 ($false),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[876, 14, 495, 391, 74])).
% 0.86/1.04 tff(3245,plain,((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.04 tff(3246,plain,
% 0.86/1.04 (~r(s(s(s(s(z)))), s(z))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[3245, 3239, 74])).
% 0.86/1.04 tff(3247,plain,
% 0.86/1.04 (b(s(s(s(s(z)))), s(z))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[513, 3246])).
% 0.86/1.04 tff(3248,plain,
% 0.86/1.04 (~b(s(z), z)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[1917, 3247, 174, 721, 3243])).
% 0.86/1.04 tff(3249,plain,
% 0.86/1.04 (~r(s(s(s(s(z)))), s(z))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[3245, 391, 74])).
% 0.86/1.04 tff(3250,plain,
% 0.86/1.04 (b(s(s(s(s(z)))), s(z))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[513, 3249])).
% 0.86/1.04 tff(3251,plain,
% 0.86/1.04 (~r(s(z), s(s(s(s(z)))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[3241, 391, 74])).
% 0.86/1.04 tff(3252,plain,
% 0.86/1.04 (b(s(z), s(s(s(s(z)))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[323, 3251])).
% 0.86/1.04 tff(3253,plain,
% 0.86/1.04 ($false),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[520, 118, 460, 961, 437, 237, 236])).
% 0.86/1.04 tff(3254,plain,((~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(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.04 tff(3255,plain,
% 0.86/1.04 ($false),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[3254, 3252, 3250, 437, 236, 237])).
% 0.86/1.04 tff(3256,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.04 tff(3257,plain,
% 0.86/1.04 (~b(s(z), s(s(s(s(s(s(z)))))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[3256, 3239, 3214, 2590, 74])).
% 0.86/1.04 tff(3258,plain,
% 0.86/1.04 (r(s(z), s(s(s(s(s(s(z)))))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[232, 3257])).
% 0.86/1.04 tff(3259,plain,
% 0.86/1.04 (~r(s(z), z)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[1027, 3258, 3])).
% 0.86/1.04 tff(3260,plain,
% 0.86/1.04 ($false),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[187, 3259, 3248])).
% 0.86/1.04 tff(3261,plain,((~r(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.04 tff(3262,plain,
% 0.86/1.04 (~r(z, s(s(s(s(s(s(z)))))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[3261, 721, 174, 74, 1])).
% 0.86/1.04 tff(3263,plain,
% 0.86/1.04 (b(z, s(s(s(s(s(s(z)))))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[356, 3262])).
% 0.86/1.04 tff(3264,plain,
% 0.86/1.04 (~b(s(z), z)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[2365, 3263, 1, 3214, 174])).
% 0.86/1.04 tff(3265,plain,
% 0.86/1.04 (r(s(z), z)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[187, 3264])).
% 0.86/1.04 tff(3266,plain,
% 0.86/1.04 (~b(z, s(s(s(s(z)))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[1413, 3263, 1, 2590, 721])).
% 0.86/1.04 tff(3267,plain,
% 0.86/1.04 (r(z, s(s(s(s(z)))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[389, 3266])).
% 0.86/1.04 tff(3268,plain,
% 0.86/1.04 (~r(s(z), s(s(s(s(z)))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[1340, 3267, 3265])).
% 0.86/1.04 tff(3269,plain,
% 0.86/1.04 (b(s(z), s(s(s(s(z)))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[323, 3268])).
% 0.86/1.04 tff(3270,plain,
% 0.86/1.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(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(z))) | (~b(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(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(z))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(3271,plain,
% 0.86/1.04 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(s(z))))))))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(3272,plain,
% 0.86/1.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(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(z))) | (~b(z, s(s(s(s(s(s(z))))))))))),
% 0.86/1.04 inference(monotonicity,[status(thm)],[3271])).
% 0.86/1.04 tff(3273,plain,
% 0.86/1.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(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(z))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 0.86/1.04 inference(transitivity,[status(thm)],[3272, 3270])).
% 0.86/1.04 tff(3274,plain,
% 0.86/1.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 0.86/1.04 inference(quant_inst,[status(thm)],[])).
% 0.86/1.04 tff(3275,plain,
% 0.86/1.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z))))))))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[3274, 3273])).
% 0.86/1.04 tff(3276,plain,
% 0.86/1.04 ($false),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[3275, 118, 3269, 174, 2590, 3263, 3214])).
% 0.86/1.04 tff(3277,plain,((~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.04 tff(3278,plain,
% 0.86/1.04 (~b(s(s(s(s(z)))), z)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[3277, 3216, 1, 74])).
% 0.86/1.04 tff(3279,plain,
% 0.86/1.04 (r(s(s(s(s(z)))), z)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[286, 3278])).
% 0.86/1.04 tff(3280,plain,
% 0.86/1.04 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[606, 3279, 161])).
% 0.86/1.04 tff(3281,plain,
% 0.86/1.04 (b(s(s(s(s(z)))), s(s(s(z))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[310, 3280])).
% 0.86/1.04 tff(3282,plain,
% 0.86/1.04 (~b(z, s(s(s(s(z)))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[1413, 2832, 1, 2590, 721])).
% 0.86/1.04 tff(3283,plain,
% 0.86/1.04 (r(z, s(s(s(s(z)))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[389, 3282])).
% 0.86/1.04 tff(3284,plain,
% 0.86/1.04 (~b(s(z), z)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[2365, 2832, 1, 3214, 3216])).
% 0.86/1.04 tff(3285,plain,
% 0.86/1.04 (r(s(z), z)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[187, 3284])).
% 0.86/1.04 tff(3286,plain,
% 0.86/1.04 (~r(s(z), s(s(s(s(z)))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[1340, 3285, 3283])).
% 0.86/1.04 tff(3287,plain,
% 0.86/1.04 (b(s(z), s(s(s(s(z)))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[323, 3286])).
% 0.86/1.04 tff(3288,plain,
% 0.86/1.04 ($false),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[3275, 118, 3287, 3216, 2590, 2832, 3214])).
% 0.86/1.04 tff(3289,plain,((~r(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.04 tff(3290,plain,
% 0.86/1.04 (~r(z, s(s(s(z))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[3289, 721, 1, 74, 160])).
% 0.86/1.04 tff(3291,plain,
% 0.86/1.04 (b(z, s(s(s(z))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[71, 3290])).
% 0.86/1.04 tff(3292,plain,
% 0.86/1.04 (~r(s(z), z)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[1027, 212, 3])).
% 0.86/1.04 tff(3293,plain,
% 0.86/1.04 (b(s(z), z)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[187, 3292])).
% 0.86/1.04 tff(3294,plain,
% 0.86/1.04 (~r(s(z), s(s(s(z))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[220, 212, 160])).
% 0.86/1.04 tff(3295,plain,
% 0.86/1.04 (b(s(z), s(s(s(z))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[668, 3294])).
% 0.86/1.04 tff(3296,plain,
% 0.86/1.04 ($false),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[1464, 3295, 3293, 1, 3214, 271])).
% 0.86/1.04 tff(3297,plain,((~r(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.04 tff(3298,plain,
% 0.86/1.04 (~r(s(z), s(s(s(s(s(s(z)))))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[3297, 3, 3291, 160, 1])).
% 0.86/1.04 tff(3299,plain,
% 0.86/1.04 (b(s(z), s(s(s(s(s(s(z)))))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[232, 3298])).
% 0.86/1.04 tff(3300,plain,
% 0.86/1.04 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[3256, 3299, 3214, 2590, 74])).
% 0.86/1.04 tff(3301,plain,
% 0.86/1.04 (b(s(s(s(z))), s(s(s(s(z)))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[402, 3300])).
% 0.86/1.04 tff(3302,plain,
% 0.86/1.04 (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[3024, 3301, 721, 1])).
% 0.86/1.04 tff(3303,plain,
% 0.86/1.04 (r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[581, 3302])).
% 0.86/1.04 tff(3304,plain,
% 0.86/1.04 (~b(z, s(s(s(s(z)))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[3234, 3303, 3, 3301, 721])).
% 0.86/1.04 tff(3305,plain,
% 0.86/1.04 (r(z, s(s(s(s(z)))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[389, 3304])).
% 0.86/1.04 tff(3306,plain,
% 0.86/1.04 (~r(s(s(s(s(z)))), s(z))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[3068, 288, 74])).
% 0.86/1.04 tff(3307,plain,
% 0.86/1.04 (b(s(s(s(s(z)))), s(z))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[513, 3306])).
% 0.86/1.04 tff(3308,plain,
% 0.86/1.04 (~b(s(z), s(s(s(s(z)))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[3254, 3307, 2590, 3214, 237])).
% 0.86/1.04 tff(3309,plain,
% 0.86/1.04 (r(s(z), s(s(s(s(z)))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[323, 3308])).
% 0.86/1.04 tff(3310,plain,
% 0.86/1.04 (~r(s(z), s(s(s(z))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[489, 288, 2590, 160])).
% 0.86/1.04 tff(3311,plain,
% 0.86/1.04 (b(s(z), s(s(s(z))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[668, 3310])).
% 0.86/1.04 tff(3312,plain,
% 0.86/1.04 (~b(s(z), z)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[1464, 3311, 1, 3214, 271])).
% 0.86/1.04 tff(3313,plain,
% 0.86/1.04 (r(s(z), z)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[187, 3312])).
% 0.86/1.04 tff(3314,plain,
% 0.86/1.04 ($false),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[1340, 3313, 3309, 339])).
% 0.86/1.04 tff(3315,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.04 tff(3316,plain,
% 0.86/1.04 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[3315, 3305, 1, 3291, 3299, 160, 74])).
% 0.86/1.04 tff(3317,plain,
% 0.86/1.04 (b(s(s(s(s(z)))), s(s(s(z))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[310, 3316])).
% 0.86/1.04 tff(3318,plain,
% 0.86/1.04 ($false),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[2471, 118, 1509, 3301, 3317, 721, 3291])).
% 0.86/1.04 tff(3319,plain,((~r(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.04 tff(3320,plain,
% 0.86/1.04 (~r(z, s(s(s(s(s(s(z)))))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[3319, 721, 1, 160, 74])).
% 0.86/1.04 tff(3321,plain,
% 0.86/1.04 (b(z, s(s(s(s(s(s(z)))))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[356, 3320])).
% 0.86/1.04 tff(3322,plain,
% 0.86/1.04 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[1006, 3321, 1, 160, 721])).
% 0.86/1.04 tff(3323,plain,
% 0.86/1.04 (b(s(s(s(s(z)))), s(s(s(z))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[310, 3322])).
% 0.86/1.04 tff(3324,plain,
% 0.86/1.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(z))))))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(3325,plain,
% 0.86/1.04 (((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(z))))))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(3326,plain,
% 0.86/1.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(z)))))))),
% 0.86/1.04 inference(monotonicity,[status(thm)],[3325])).
% 0.86/1.04 tff(3327,plain,
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% 0.86/1.04 inference(transitivity,[status(thm)],[3326, 3324])).
% 0.86/1.04 tff(3328,plain,
% 0.86/1.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 0.86/1.04 inference(quant_inst,[status(thm)],[])).
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% 0.86/1.04 inference(modus_ponens,[status(thm)],[3328, 3327])).
% 0.86/1.04 tff(3330,plain,
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% 0.86/1.04 inference(unit_resolution,[status(thm)],[3329, 118, 3323, 2590, 721, 1, 3291])).
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% 0.86/1.04 tff(3332,plain,
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% 0.86/1.04 inference(unit_resolution,[status(thm)],[3331, 160, 1, 74])).
% 0.86/1.04 tff(3333,plain,
% 0.86/1.04 (r(s(s(s(s(z)))), z)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[286, 3332])).
% 0.86/1.04 tff(3334,plain,
% 0.86/1.04 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[606, 161, 3333])).
% 0.86/1.04 tff(3335,plain,
% 0.86/1.04 (b(s(s(s(s(z)))), s(s(s(z))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[310, 3334])).
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% 0.86/1.04 inference(unit_resolution,[status(thm)],[2694, 2832, 160, 161])).
% 0.86/1.04 tff(3337,plain,
% 0.86/1.04 (b(s(z), s(s(s(z))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[668, 3336])).
% 0.86/1.04 tff(3338,plain,
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% 0.86/1.04 inference(unit_resolution,[status(thm)],[2365, 3216, 1, 3214, 2832])).
% 0.86/1.04 tff(3339,plain,
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% 0.86/1.04 inference(unit_resolution,[status(thm)],[187, 3338])).
% 0.86/1.04 tff(3340,plain,
% 0.86/1.04 (~r(z, s(s(s(s(z)))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[2262, 3339, 3333, 161])).
% 0.86/1.04 tff(3341,plain,
% 0.86/1.04 (b(z, s(s(s(s(z)))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[389, 3340])).
% 0.86/1.04 tff(3342,plain,
% 0.86/1.04 (~r(s(z), s(s(s(s(z)))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[1151, 3339, 3333])).
% 0.86/1.04 tff(3343,plain,
% 0.86/1.04 (b(s(z), s(s(s(s(z)))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[323, 3342])).
% 0.86/1.04 tff(3344,plain,
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% 0.86/1.04 inference(unit_resolution,[status(thm)],[934, 3343, 3341, 3216, 3337, 3335])).
% 0.86/1.04 tff(3345,plain,((~r(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.04 tff(3346,plain,
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% 0.86/1.04 inference(unit_resolution,[status(thm)],[3345, 160, 1, 74])).
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% 0.86/1.04 inference(unit_resolution,[status(thm)],[71, 3346])).
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% 0.86/1.04 inference(unit_resolution,[status(thm)],[232, 3348])).
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% 0.86/1.04 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[551, 3, 3333])).
% 0.86/1.04 tff(3351,plain,
% 0.86/1.04 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[480, 3350])).
% 0.86/1.04 tff(3352,plain,
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% 0.86/1.04 inference(unit_resolution,[status(thm)],[468, 3351, 2590, 3214, 3349])).
% 0.86/1.04 tff(3353,plain,
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% 0.86/1.04 inference(unit_resolution,[status(thm)],[323, 3352])).
% 0.86/1.04 tff(3354,plain,
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% 0.86/1.04 inference(unit_resolution,[status(thm)],[1151, 3353, 3333])).
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% 0.86/1.04 inference(unit_resolution,[status(thm)],[187, 3354])).
% 0.86/1.04 tff(3356,plain,
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% 0.86/1.04 inference(unit_resolution,[status(thm)],[1464, 3355, 1, 3214, 3347])).
% 0.86/1.04 tff(3357,plain,
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% 0.86/1.04 inference(unit_resolution,[status(thm)],[668, 3356])).
% 0.86/1.04 tff(3358,plain,
% 0.86/1.04 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[456, 3357, 3353])).
% 0.86/1.04 tff(3359,plain,
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% 0.86/1.04 inference(unit_resolution,[status(thm)],[310, 3358])).
% 0.86/1.04 tff(3360,plain,
% 0.86/1.04 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[3256, 3349, 3214, 2590, 74])).
% 0.86/1.04 tff(3361,plain,
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% 0.86/1.04 inference(unit_resolution,[status(thm)],[402, 3360])).
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% 0.86/1.04 inference(unit_resolution,[status(thm)],[641, 118, 1509, 3361, 3359, 3347])).
% 0.86/1.04 tff(3363,plain,
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% 0.86/1.04 inference(unit_resolution,[status(thm)],[389, 3362])).
% 0.86/1.04 tff(3364,plain,
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% 0.86/1.04 inference(unit_resolution,[status(thm)],[449, 3363, 3353])).
% 0.86/1.04 tff(3365,plain,
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% 0.86/1.04 inference(unit_resolution,[status(thm)],[51, 3364])).
% 0.86/1.04 tff(3366,plain,
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% 0.86/1.04 tff(3367,plain,((~r(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.04 tff(3368,plain,
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% 0.86/1.04 inference(unit_resolution,[status(thm)],[3367, 160, 74, 1])).
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% 0.86/1.04 inference(unit_resolution,[status(thm)],[356, 3368])).
% 0.86/1.04 tff(3370,plain,
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% 0.86/1.04 inference(unit_resolution,[status(thm)],[522, 176, 160, 235])).
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% 0.86/1.04 inference(unit_resolution,[status(thm)],[187, 3370])).
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% 0.86/1.04 inference(unit_resolution,[status(thm)],[1340, 329, 177])).
% 0.86/1.04 tff(3373,plain,
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% 0.86/1.04 inference(unit_resolution,[status(thm)],[389, 3372])).
% 0.86/1.04 tff(3374,plain,
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% 0.86/1.04 inference(unit_resolution,[status(thm)],[1151, 329, 177])).
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% 0.86/1.04 inference(unit_resolution,[status(thm)],[456, 329, 176])).
% 0.86/1.04 tff(3377,plain,
% 0.86/1.04 (b(s(s(s(s(z)))), s(s(s(z))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[310, 3376])).
% 0.86/1.04 tff(3378,plain,
% 0.86/1.04 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[898, 329, 176])).
% 0.86/1.04 tff(3379,plain,
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% 0.86/1.04 inference(unit_resolution,[status(thm)],[402, 3378])).
% 0.86/1.04 tff(3380,plain,
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% 0.86/1.04 tff(3381,plain,((~r(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.04 tff(3382,plain,
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% 0.86/1.04 inference(unit_resolution,[status(thm)],[3381, 3371, 1509, 176])).
% 0.86/1.04 tff(3383,plain,
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% 0.86/1.04 inference(unit_resolution,[status(thm)],[323, 3382])).
% 0.86/1.04 tff(3384,plain,
% 0.86/1.04 (~b(s(s(s(s(z)))), s(z))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[3254, 3383, 437, 236, 233])).
% 0.86/1.04 tff(3385,plain,
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% 0.86/1.04 tff(3386,plain,
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% 0.86/1.04 tff(3388,plain,
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% 0.86/1.04 inference(unit_resolution,[status(thm)],[668, 3388])).
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% 0.86/1.04 inference(unit_resolution,[status(thm)],[187, 3390])).
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% 0.86/1.04 inference(unit_resolution,[status(thm)],[1151, 3391, 3333])).
% 0.86/1.04 tff(3393,plain,
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% 0.86/1.04 inference(unit_resolution,[status(thm)],[323, 3392])).
% 0.86/1.04 tff(3394,plain,
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% 0.86/1.04 inference(unit_resolution,[status(thm)],[974, 14, 3391, 3333])).
% 0.86/1.04 tff(3395,plain,
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% 0.86/1.04 inference(unit_resolution,[status(thm)],[513, 3394])).
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% 0.86/1.04 inference(unit_resolution,[status(thm)],[1115, 3395, 2590, 3393, 3389, 160])).
% 0.86/1.04 tff(3397,plain,
% 0.86/1.04 (r(s(s(s(s(z)))), s(s(s(z))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[310, 3396])).
% 0.86/1.04 tff(3398,plain,
% 0.86/1.04 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[487, 14, 160, 3397])).
% 0.86/1.04 tff(3399,plain,
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% 0.86/1.04 tff(3402,plain,
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% 0.86/1.04 inference(unit_resolution,[status(thm)],[3401, 74, 1])).
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% 0.86/1.04 inference(unit_resolution,[status(thm)],[156, 3402])).
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% 0.86/1.04 inference(unit_resolution,[status(thm)],[402, 3404])).
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% 0.86/1.04 inference(unit_resolution,[status(thm)],[2365, 235, 1, 3214, 174])).
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% 0.86/1.04 inference(unit_resolution,[status(thm)],[187, 3406])).
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% 0.86/1.04 (~r(z, s(s(s(s(z)))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[2262, 3407, 161, 274])).
% 0.86/1.04 tff(3409,plain,
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% 0.86/1.04 inference(unit_resolution,[status(thm)],[389, 3408])).
% 0.86/1.04 tff(3410,plain,
% 0.86/1.04 (~r(s(z), s(s(s(s(z)))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[1151, 3407, 274])).
% 0.86/1.04 tff(3411,plain,
% 0.86/1.04 (b(s(z), s(s(s(s(z)))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[323, 3410])).
% 0.86/1.04 tff(3412,plain,
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% 0.86/1.04 tff(3414,plain,
% 0.86/1.04 (~b(z, s(s(s(s(s(s(z)))))))),
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% 0.86/1.04 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
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% 0.86/1.04 tff(3417,plain,
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% 0.86/1.04 inference(unit_resolution,[status(thm)],[480, 3416])).
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% 0.86/1.04 inference(unit_resolution,[status(thm)],[713, 3415, 2590, 3279, 3281])).
% 0.86/1.04 tff(3419,plain,
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% 0.86/1.04 inference(unit_resolution,[status(thm)],[649, 3418])).
% 0.86/1.04 tff(3420,plain,
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% 0.86/1.04 inference(unit_resolution,[status(thm)],[1703, 3419, 3417, 1, 3403, 3281])).
% 0.86/1.04 tff(3421,plain,((~r(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.04 tff(3422,plain,
% 0.86/1.04 (~r(z, s(s(s(z))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[3421, 74, 1])).
% 0.86/1.04 tff(3423,plain,
% 0.86/1.04 (b(z, s(s(s(z))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[71, 3422])).
% 0.86/1.04 tff(3424,plain,
% 0.86/1.04 (~r(s(z), z)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[1151, 329, 274])).
% 0.86/1.04 tff(3425,plain,
% 0.86/1.04 (b(s(z), z)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[187, 3424])).
% 0.86/1.04 tff(3426,plain,
% 0.86/1.04 (~r(s(z), s(s(s(z))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[2666, 329, 2590, 73, 459])).
% 0.86/1.04 tff(3427,plain,
% 0.86/1.04 (b(s(z), s(s(s(z))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[668, 3426])).
% 0.86/1.04 tff(3428,plain,
% 0.86/1.04 ($false),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[1464, 3427, 3425, 1, 3214, 271])).
% 0.86/1.04 tff(3429,plain,((~r(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.04 tff(3430,plain,
% 0.86/1.04 (~r(s(z), s(s(s(s(z)))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[3429, 596, 3423, 3403, 1, 274])).
% 0.86/1.04 tff(3431,plain,
% 0.86/1.04 (b(s(z), s(s(s(s(z)))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[323, 3430])).
% 0.86/1.04 tff(3432,plain,
% 0.86/1.04 (~b(s(z), s(s(s(s(s(s(z)))))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[468, 3431, 2590, 3214, 596])).
% 0.86/1.04 tff(3433,plain,
% 0.86/1.04 (r(s(z), s(s(s(s(s(s(z)))))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[232, 3432])).
% 0.86/1.04 tff(3434,plain,
% 0.86/1.04 (~r(s(z), z)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[1027, 3433, 3])).
% 0.86/1.04 tff(3435,plain,
% 0.86/1.04 (b(s(z), z)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[187, 3434])).
% 0.86/1.04 tff(3436,plain,
% 0.86/1.04 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(z, s(z))))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(3437,plain,
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% 0.86/1.04 tff(3438,plain,
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% 0.86/1.04 inference(monotonicity,[status(thm)],[3437])).
% 0.86/1.04 tff(3439,plain,
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% 0.86/1.05 inference(transitivity,[status(thm)],[3438, 3436])).
% 0.86/1.05 tff(3440,plain,
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% 0.86/1.05 inference(quant_inst,[status(thm)],[])).
% 0.86/1.05 tff(3441,plain,
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% 0.86/1.05 inference(modus_ponens,[status(thm)],[3440, 3439])).
% 0.86/1.05 tff(3442,plain,
% 0.86/1.05 (~r(z, s(z))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[3441, 14, 3, 3433])).
% 0.86/1.05 tff(3443,plain,
% 0.86/1.05 (b(z, s(z))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[51, 3442])).
% 0.86/1.05 tff(3444,plain,
% 0.86/1.05 (~r(s(z), s(s(s(z))))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[2425, 14, 53, 212])).
% 0.86/1.05 tff(3445,plain,
% 0.86/1.05 (b(s(z), s(s(s(z))))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[668, 3444])).
% 0.86/1.05 tff(3446,plain,
% 0.86/1.05 (((~![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(s(s(z)))))))) | (~r(s(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(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(3447,plain,
% 0.86/1.05 (((~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(3448,plain,
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% 0.86/1.05 inference(monotonicity,[status(thm)],[3447])).
% 0.86/1.05 tff(3449,plain,
% 0.86/1.05 (((~![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(z))), s(s(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(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 0.86/1.05 inference(transitivity,[status(thm)],[3448, 3446])).
% 0.86/1.05 tff(3450,plain,
% 0.86/1.05 ((~![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(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(z))))),
% 0.86/1.05 inference(quant_inst,[status(thm)],[])).
% 0.86/1.05 tff(3451,plain,
% 0.86/1.05 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[3450, 3449])).
% 0.86/1.05 tff(3452,plain,
% 0.86/1.05 (~r(s(s(s(z))), s(z))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[3451, 14, 53, 212])).
% 0.86/1.05 tff(3453,plain,
% 0.86/1.05 (b(s(s(s(z))), s(z))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[105, 3452])).
% 0.86/1.05 tff(3454,plain,
% 0.86/1.05 ($false),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[1041, 118, 174, 234, 3453, 3445, 271])).
% 0.86/1.05 tff(3455,plain,((~r(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.05 tff(3456,plain,
% 0.86/1.05 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[3455, 3443, 3423, 3433, 3435])).
% 0.86/1.05 tff(3457,plain,
% 0.86/1.05 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[581, 3456])).
% 0.86/1.05 tff(3458,plain,
% 0.86/1.05 (~b(s(s(s(z))), z)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[2612, 3457, 3403, 1, 3423])).
% 0.86/1.05 tff(3459,plain,
% 0.86/1.05 (r(s(s(s(z))), z)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[649, 3458])).
% 0.86/1.05 tff(3460,plain,
% 0.86/1.05 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[703, 3459, 274])).
% 0.86/1.05 tff(3461,plain,
% 0.86/1.05 (b(s(s(s(z))), s(s(s(s(z)))))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[402, 3460])).
% 0.86/1.05 tff(3462,plain,
% 0.86/1.05 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[2650, 3457, 2590, 3403, 596])).
% 0.86/1.05 tff(3463,plain,
% 0.86/1.05 (r(s(s(s(s(z)))), s(s(s(z))))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[310, 3462])).
% 0.86/1.05 tff(3464,plain,
% 0.86/1.05 (~r(s(s(s(s(z)))), s(z))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[3068, 3463, 74])).
% 0.86/1.05 tff(3465,plain,
% 0.86/1.05 (b(s(s(s(s(z)))), s(z))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[513, 3464])).
% 0.86/1.05 tff(3466,plain,
% 0.86/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(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(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(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(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(3467,plain,
% 0.86/1.05 (((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(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(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(3468,plain,
% 0.86/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))))),
% 0.86/1.05 inference(monotonicity,[status(thm)],[3467])).
% 0.86/1.05 tff(3469,plain,
% 0.86/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 0.86/1.05 inference(transitivity,[status(thm)],[3468, 3466])).
% 0.86/1.05 tff(3470,plain,
% 0.86/1.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 0.86/1.05 inference(quant_inst,[status(thm)],[])).
% 0.86/1.05 tff(3471,plain,
% 0.86/1.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[3470, 3469])).
% 0.86/1.05 tff(3472,plain,
% 0.86/1.05 ($false),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[3471, 118, 3465, 3461, 3457, 596, 3214])).
% 0.86/1.05 tff(3473,plain,((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~r(z, s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.05 tff(3474,plain,
% 0.86/1.05 (~r(s(s(s(s(z)))), z)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[3473, 3, 1, 74])).
% 0.86/1.05 tff(3475,plain,
% 0.86/1.05 (b(s(s(s(s(z)))), z)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[286, 3474])).
% 0.86/1.05 tff(3476,plain,
% 0.86/1.05 (~b(z, s(z))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[3261, 3475, 3, 74, 1])).
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% 0.86/1.05 inference(modus_ponens,[status(thm)],[3522, 3521])).
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% 0.86/1.05 ($false),
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% 0.86/1.05 tff(3532,plain,
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% 0.86/1.05 tff(3535,plain,
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% 0.86/1.05 tff(3546,plain,
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% 0.86/1.06 tff(3556,plain,
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% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(3564,plain,
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% 0.86/1.06 inference(monotonicity,[status(thm)],[3564])).
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% 0.86/1.06 inference(modus_ponens,[status(thm)],[3567, 3566])).
% 0.86/1.06 tff(3569,plain,
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% 0.86/1.06 inference(unit_resolution,[status(thm)],[3568, 118, 1695, 172, 73, 237, 1])).
% 0.86/1.06 tff(3570,plain,((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.06 tff(3571,plain,
% 0.86/1.06 (~b(s(z), s(s(s(z))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[3570, 3562, 73, 1695, 3554])).
% 0.86/1.06 tff(3572,plain,
% 0.86/1.06 (r(s(z), s(s(s(z))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[668, 3571])).
% 0.86/1.06 tff(3573,plain,
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% 0.86/1.06 inference(unit_resolution,[status(thm)],[468, 3562, 3558, 437, 3491])).
% 0.86/1.06 tff(3574,plain,
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% 0.86/1.06 tff(3577,plain,
% 0.86/1.06 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[3576, 3479, 2590, 3403, 3])).
% 0.86/1.06 tff(3578,plain,
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% 0.86/1.06 tff(3579,plain,((~r(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.06 tff(3580,plain,
% 0.86/1.06 (~r(z, s(s(s(s(s(s(z)))))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[3579, 74, 1])).
% 0.86/1.06 tff(3581,plain,
% 0.86/1.06 (b(z, s(s(s(s(s(s(z)))))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[356, 3580])).
% 0.86/1.06 tff(3582,plain,
% 0.86/1.06 (~b(s(z), z)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[2430, 3581, 3214, 1, 3403, 3423, 74])).
% 0.86/1.06 tff(3583,plain,
% 0.86/1.06 (r(s(z), z)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[187, 3582])).
% 0.86/1.06 tff(3584,plain,
% 0.86/1.06 (~r(s(s(s(z))), z)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[958, 3583, 74])).
% 0.86/1.06 tff(3585,plain,
% 0.86/1.06 (b(s(s(s(z))), z)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[649, 3584])).
% 0.86/1.06 tff(3586,plain,
% 0.86/1.06 (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[2612, 3585, 3403, 1, 3423])).
% 0.86/1.06 tff(3587,plain,
% 0.86/1.06 (r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[581, 3586])).
% 0.86/1.06 tff(3588,plain,
% 0.86/1.06 (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[1002, 721, 1, 2590, 235])).
% 0.86/1.06 tff(3589,plain,
% 0.86/1.06 (r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[480, 3588])).
% 0.86/1.06 tff(3590,plain,
% 0.86/1.06 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[1980, 3589, 53])).
% 0.86/1.06 tff(3591,plain,
% 0.86/1.06 (b(s(s(s(s(z)))), s(s(s(z))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[310, 3590])).
% 0.86/1.06 tff(3592,plain,
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% 0.86/1.06 inference(unit_resolution,[status(thm)],[3329, 118, 3591, 2590, 721, 1, 271])).
% 0.86/1.06 tff(3593,plain,((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.06 tff(3594,plain,
% 0.86/1.06 (~b(s(s(s(s(z)))), z)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[3593, 3423, 1, 3587, 3581])).
% 0.86/1.06 tff(3595,plain,
% 0.86/1.06 (r(s(s(s(s(z)))), z)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[286, 3594])).
% 0.86/1.06 tff(3596,plain,
% 0.86/1.06 (~r(s(z), s(s(s(s(z)))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[1151, 3595, 3583])).
% 0.86/1.06 tff(3597,plain,
% 0.86/1.06 (b(s(z), s(s(s(s(z)))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[323, 3596])).
% 0.86/1.06 tff(3598,plain,
% 0.86/1.06 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[2442, 3597, 1, 3214, 3403, 3423, 3581])).
% 0.86/1.06 tff(3599,plain,
% 0.86/1.06 (r(s(s(s(z))), s(s(s(s(z)))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[402, 3598])).
% 0.86/1.06 tff(3600,plain,
% 0.86/1.06 (~r(s(s(s(s(s(z))))), z)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[1667, 3595, 3583])).
% 0.86/1.06 tff(3601,plain,
% 0.86/1.06 (b(s(s(s(s(s(z))))), z)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[767, 3600])).
% 0.86/1.06 tff(3602,plain,
% 0.86/1.06 (~r(s(s(s(s(z)))), s(z))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[3245, 3599, 74])).
% 0.86/1.06 tff(3603,plain,
% 0.86/1.06 (b(s(s(s(s(z)))), s(z))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[513, 3602])).
% 0.86/1.06 tff(3604,plain,
% 0.86/1.06 (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[3141, 118, 3597, 3603, 2590, 3214])).
% 0.86/1.06 tff(3605,plain,
% 0.86/1.06 (r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[480, 3604])).
% 0.86/1.06 tff(3606,plain,
% 0.86/1.06 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[1980, 3605, 3587])).
% 0.86/1.06 tff(3607,plain,
% 0.86/1.06 (b(s(s(s(s(z)))), s(s(s(z))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[310, 3606])).
% 0.86/1.06 tff(3608,plain,
% 0.86/1.06 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[2326, 3605, 3601, 1, 3581])).
% 0.86/1.06 tff(3609,plain,
% 0.86/1.06 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[1616, 3608])).
% 0.86/1.06 tff(3610,plain,
% 0.86/1.06 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[2342, 3609, 3601, 3597, 3603, 3585, 3607, 74])).
% 0.86/1.06 tff(3611,plain,
% 0.86/1.06 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[1595, 3610])).
% 0.86/1.06 tff(3612,plain,
% 0.86/1.06 (~r(z, s(s(s(s(z)))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[2916, 3611, 3423, 3585, 3601, 3599])).
% 0.86/1.06 tff(3613,plain,
% 0.86/1.06 (b(z, s(s(s(s(z)))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[389, 3612])).
% 0.86/1.06 tff(3614,plain,
% 0.86/1.06 ($false),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[3000, 118, 3607, 2590, 3403, 3613, 3581])).
% 0.86/1.06 tff(3615,plain,((~r(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.06 tff(3616,plain,
% 0.86/1.06 (~r(s(s(s(z))), s(z))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[3615, 1])).
% 0.86/1.06 tff(3617,plain,
% 0.86/1.06 (b(s(s(s(z))), s(z))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[105, 3616])).
% 0.86/1.06 tff(3618,plain,
% 0.86/1.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(3619,plain,
% 0.86/1.06 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(3620,plain,
% 0.86/1.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[3619])).
% 0.86/1.06 tff(3621,plain,
% 0.86/1.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 0.86/1.06 inference(transitivity,[status(thm)],[3620, 3618])).
% 0.86/1.06 tff(3622,plain,
% 0.86/1.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 0.86/1.06 inference(quant_inst,[status(thm)],[])).
% 0.86/1.06 tff(3623,plain,
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% 0.86/1.06 inference(modus_ponens,[status(thm)],[3622, 3621])).
% 0.86/1.06 tff(3624,plain,
% 0.86/1.06 (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[3623, 118, 460, 3617, 2590, 3214])).
% 0.86/1.06 tff(3625,plain,
% 0.86/1.06 (r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[581, 3624])).
% 0.86/1.06 tff(3626,plain,
% 0.86/1.06 (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[1002, 235, 1, 2590, 721])).
% 0.86/1.06 tff(3627,plain,
% 0.86/1.06 (r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[480, 3626])).
% 0.86/1.06 tff(3628,plain,
% 0.86/1.06 (~b(z, s(s(s(s(z)))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[1413, 235, 1, 2590, 721])).
% 0.86/1.06 tff(3629,plain,
% 0.86/1.06 (r(z, s(s(s(s(z)))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[389, 3628])).
% 0.86/1.06 tff(3630,plain,
% 0.86/1.06 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[1530, 3629, 161])).
% 0.86/1.06 tff(3631,plain,
% 0.86/1.06 (b(s(s(s(z))), s(s(s(s(z)))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[402, 3630])).
% 0.86/1.06 tff(3632,plain,
% 0.86/1.06 (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[3024, 3631, 721, 1])).
% 0.86/1.06 tff(3633,plain,
% 0.86/1.06 (r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[581, 3632])).
% 0.86/1.06 tff(3634,plain,
% 0.86/1.06 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[1980, 3633, 3627])).
% 0.86/1.06 tff(3635,plain,
% 0.86/1.06 (b(s(s(s(s(z)))), s(s(s(z))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[310, 3634])).
% 0.86/1.06 tff(3636,plain,
% 0.86/1.06 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[1530, 339, 161])).
% 0.86/1.06 tff(3637,plain,
% 0.86/1.06 (b(s(s(s(z))), s(s(s(s(z)))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[402, 3636])).
% 0.86/1.06 tff(3638,plain,
% 0.86/1.06 (~r(s(z), s(s(s(s(z)))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[1340, 177, 339])).
% 0.86/1.06 tff(3639,plain,
% 0.86/1.06 (b(s(z), s(s(s(s(z)))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[323, 3638])).
% 0.86/1.06 tff(3640,plain,
% 0.86/1.06 (~b(s(z), s(s(s(z))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[944, 3639, 173, 3637, 587])).
% 0.86/1.06 tff(3641,plain,
% 0.86/1.06 (r(s(z), s(s(s(z))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[668, 3640])).
% 0.86/1.06 tff(3642,plain,
% 0.86/1.06 ($false),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[2030, 14, 177, 3641, 161])).
% 0.86/1.06 tff(3643,plain,((~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.06 tff(3644,plain,
% 0.86/1.06 (~r(s(z), z)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[3643, 3635, 3617, 161, 3629])).
% 0.86/1.06 tff(3645,plain,
% 0.86/1.06 (b(s(z), z)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[187, 3644])).
% 0.86/1.06 tff(3646,plain,
% 0.86/1.06 (~b(z, s(z))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[2365, 3645, 1, 3214, 235])).
% 0.86/1.06 tff(3647,plain,
% 0.86/1.06 (r(z, s(z))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[51, 3646])).
% 0.86/1.06 tff(3648,plain,
% 0.86/1.06 (~r(s(z), s(s(s(z))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[268, 3647, 161])).
% 0.86/1.06 tff(3649,plain,
% 0.86/1.06 (b(s(z), s(s(s(z))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[668, 3648])).
% 0.86/1.06 tff(3650,plain,
% 0.86/1.06 (~r(s(z), s(s(s(s(z)))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[449, 3647, 3629])).
% 0.86/1.06 tff(3651,plain,
% 0.86/1.06 (b(s(z), s(s(s(s(z)))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[323, 3650])).
% 0.86/1.06 tff(3652,plain,
% 0.86/1.06 ($false),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[944, 3651, 3649, 3617, 3631, 3635])).
% 0.86/1.06 tff(3653,plain,((~b(z, s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.06 tff(3654,plain,
% 0.86/1.06 (~b(z, s(s(s(s(s(s(z)))))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[3653, 161, 1, 721])).
% 0.86/1.06 tff(3655,plain,
% 0.86/1.06 (r(z, s(s(s(s(s(s(z)))))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[356, 3654])).
% 0.86/1.06 tff(3656,plain,
% 0.86/1.06 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[169, 3655, 161])).
% 0.86/1.06 tff(3657,plain,
% 0.86/1.06 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[156, 3656])).
% 0.86/1.06 tff(3658,plain,
% 0.86/1.06 (~b(s(z), s(s(s(z))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[1892, 609, 3214, 3617, 3657])).
% 0.86/1.06 tff(3659,plain,
% 0.86/1.06 (r(s(z), s(s(s(z))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[668, 3658])).
% 0.86/1.06 tff(3660,plain,
% 0.86/1.06 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[3024, 609, 721, 1])).
% 0.86/1.06 tff(3661,plain,
% 0.86/1.06 (r(s(s(s(z))), s(s(s(s(z)))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[402, 3660])).
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% 0.86/1.06 tff(3704,plain,
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% 0.86/1.07 inference(transitivity,[status(thm)],[3726, 3724])).
% 0.86/1.07 tff(3728,plain,
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% 0.86/1.07 inference(quant_inst,[status(thm)],[])).
% 0.86/1.07 tff(3729,plain,
% 0.86/1.07 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[3728, 3727])).
% 0.86/1.07 tff(3730,plain,
% 0.86/1.07 ($false),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[3729, 14, 3, 1680, 736])).
% 0.86/1.07 tff(3731,plain,((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.07 tff(3732,plain,
% 0.86/1.07 (~r(s(s(s(s(s(z))))), z)),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[3731, 3723, 3])).
% 0.86/1.07 tff(3733,plain,
% 0.86/1.07 (b(s(s(s(s(s(z))))), z)),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[767, 3732])).
% 0.86/1.07 tff(3734,plain,
% 0.86/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(3735,plain,
% 0.86/1.07 (((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(3736,plain,
% 0.86/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))))),
% 0.86/1.07 inference(monotonicity,[status(thm)],[3735])).
% 0.86/1.07 tff(3737,plain,
% 0.86/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 0.86/1.07 inference(transitivity,[status(thm)],[3736, 3734])).
% 0.86/1.07 tff(3738,plain,
% 0.86/1.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 0.86/1.07 inference(quant_inst,[status(thm)],[])).
% 0.86/1.07 tff(3739,plain,
% 0.86/1.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[3738, 3737])).
% 0.86/1.07 tff(3740,plain,
% 0.86/1.07 ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[3739, 118, 721, 3707, 3715])).
% 0.86/1.07 tff(3741,plain,
% 0.86/1.07 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[3740, 3733])).
% 0.86/1.07 tff(3742,plain,
% 0.86/1.07 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[1616, 3741])).
% 0.86/1.07 tff(3743,plain,
% 0.86/1.07 ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[1367, 118, 1, 3707, 3715])).
% 0.86/1.07 tff(3744,plain,
% 0.86/1.07 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[3743, 3733])).
% 0.86/1.07 tff(3745,plain,
% 0.86/1.07 (r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[1627, 3744])).
% 0.86/1.07 tff(3746,plain,
% 0.86/1.07 ($false),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[2302, 3745, 3742, 3709])).
% 0.86/1.07 tff(3747,plain,((~r(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.07 tff(3748,plain,
% 0.86/1.07 (~r(z, s(s(s(s(s(s(z)))))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[3747, 721, 1])).
% 0.86/1.07 tff(3749,plain,
% 0.86/1.07 (b(z, s(s(s(s(s(s(z)))))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[356, 3748])).
% 0.86/1.07 tff(3750,plain,
% 0.86/1.07 (~b(z, s(s(s(s(z)))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[1413, 3749, 1, 2590, 721])).
% 0.86/1.07 tff(3751,plain,
% 0.86/1.07 (r(z, s(s(s(s(z)))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[389, 3750])).
% 0.86/1.07 tff(3752,plain,
% 0.86/1.07 (~r(z, s(z))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[449, 3751, 3689])).
% 0.86/1.07 tff(3753,plain,
% 0.86/1.07 (b(z, s(z))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[51, 3752])).
% 0.86/1.07 tff(3754,plain,
% 0.86/1.07 (~r(s(z), z)),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[1340, 3751, 3689])).
% 0.86/1.07 tff(3755,plain,
% 0.86/1.07 (b(s(z), z)),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[187, 3754])).
% 0.86/1.07 tff(3756,plain,
% 0.86/1.07 ($false),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[2365, 3755, 3753, 1, 3214, 3749])).
% 0.86/1.07 tff(3757,plain,((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.07 tff(3758,plain,
% 0.86/1.07 (~b(s(s(s(s(z)))), z)),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[3757, 1])).
% 0.86/1.07 tff(3759,plain,
% 0.86/1.07 (r(s(s(s(s(z)))), z)),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[286, 3758])).
% 0.86/1.07 tff(3760,plain,
% 0.86/1.07 (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[3141, 118, 460, 1659, 437, 236])).
% 0.86/1.07 tff(3761,plain,
% 0.86/1.07 (r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[480, 3760])).
% 0.86/1.07 tff(3762,plain,
% 0.86/1.07 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[1980, 3761, 53])).
% 0.86/1.07 tff(3763,plain,
% 0.86/1.07 (b(s(s(s(s(z)))), s(s(s(z))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[310, 3762])).
% 0.86/1.07 tff(3764,plain,
% 0.86/1.07 (~b(s(z), s(s(s(s(s(s(z)))))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[3254, 1659, 437, 236, 460])).
% 0.86/1.07 tff(3765,plain,
% 0.86/1.07 (r(s(z), s(s(s(s(s(s(z)))))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[232, 3764])).
% 0.86/1.07 tff(3766,plain,
% 0.86/1.07 (~r(s(z), s(s(s(z))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[2425, 14, 53, 3765])).
% 0.86/1.07 tff(3767,plain,
% 0.86/1.07 (b(s(z), s(s(s(z))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[668, 3766])).
% 0.86/1.07 tff(3768,plain,
% 0.86/1.07 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[2258, 3767, 274, 3763, 177])).
% 0.86/1.07 tff(3769,plain,
% 0.86/1.07 (r(s(s(s(z))), s(s(s(s(z)))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[402, 3768])).
% 0.86/1.07 tff(3770,plain,
% 0.86/1.07 (((~![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(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(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(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(3771,plain,
% 0.86/1.07 (((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(3772,plain,
% 0.86/1.07 (((~![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(s(z))), s(s(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(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))))),
% 0.86/1.07 inference(monotonicity,[status(thm)],[3771])).
% 0.86/1.07 tff(3773,plain,
% 0.86/1.07 (((~![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(s(z))), s(s(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(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 0.86/1.07 inference(transitivity,[status(thm)],[3772, 3770])).
% 0.86/1.07 tff(3774,plain,
% 0.86/1.07 ((~![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(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 0.86/1.07 inference(quant_inst,[status(thm)],[])).
% 0.86/1.07 tff(3775,plain,
% 0.86/1.07 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[3774, 3773])).
% 0.86/1.07 tff(3776,plain,
% 0.86/1.07 ($false),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[3775, 14, 3769, 53, 3761])).
% 0.86/1.07 tff(3777,plain,((~r(s(z), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.07 tff(3778,plain,
% 0.86/1.07 (~r(s(z), z)),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[3777, 3625, 3759, 460, 2590, 3214])).
% 0.86/1.07 tff(3779,plain,
% 0.86/1.07 (b(s(z), z)),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[187, 3778])).
% 0.86/1.07 tff(3780,plain,
% 0.86/1.07 (~b(z, s(z))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[2365, 235, 1, 3214, 3779])).
% 0.86/1.07 tff(3781,plain,
% 0.86/1.07 (r(z, s(z))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[51, 3780])).
% 0.86/1.07 tff(3782,plain,
% 0.86/1.07 (~r(s(s(s(s(z)))), s(z))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[503, 3781, 3759])).
% 0.86/1.07 tff(3783,plain,
% 0.86/1.07 (b(s(s(s(s(z)))), s(z))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[513, 3782])).
% 0.86/1.07 tff(3784,plain,
% 0.86/1.07 (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[3141, 118, 460, 3783, 2590, 3214])).
% 0.86/1.07 tff(3785,plain,
% 0.86/1.07 (r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[480, 3784])).
% 0.86/1.07 tff(3786,plain,
% 0.86/1.07 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[1980, 3785, 3625])).
% 0.86/1.07 tff(3787,plain,
% 0.86/1.07 (b(s(s(s(s(z)))), s(s(s(z))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[310, 3786])).
% 0.86/1.07 tff(3788,plain,
% 0.86/1.07 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[3775, 14, 3625, 3785])).
% 0.86/1.07 tff(3789,plain,
% 0.86/1.07 (b(s(s(s(z))), s(s(s(s(z)))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[402, 3788])).
% 0.86/1.07 tff(3790,plain,
% 0.86/1.07 (~b(s(z), s(s(s(s(s(s(z)))))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[245, 235, 1, 3214, 3779])).
% 0.86/1.07 tff(3791,plain,
% 0.86/1.07 (r(s(z), s(s(s(s(s(s(z)))))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[232, 3790])).
% 0.86/1.07 tff(3792,plain,
% 0.86/1.07 (~r(s(z), s(s(s(z))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[2425, 14, 3625, 3791])).
% 0.86/1.07 tff(3793,plain,
% 0.86/1.07 (b(s(z), s(s(s(z))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[668, 3792])).
% 0.86/1.07 tff(3794,plain,
% 0.86/1.07 ($false),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[944, 3793, 3789, 3617, 460, 3787])).
% 0.86/1.07 tff(3795,plain,((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.07 tff(3796,plain,
% 0.86/1.07 (~b(z, s(s(s(s(s(s(z)))))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[3795, 460, 1])).
% 0.86/1.07 tff(3797,plain,
% 0.86/1.07 (r(z, s(s(s(s(s(s(z)))))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[356, 3796])).
% 0.86/1.07 tff(3798,plain,
% 0.86/1.07 (~r(s(s(s(z))), z)),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[571, 3797, 3625])).
% 0.86/1.07 tff(3799,plain,
% 0.86/1.07 (b(s(s(s(z))), z)),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[649, 3798])).
% 0.86/1.07 tff(3800,plain,
% 0.86/1.07 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[3576, 3799, 2590, 3625, 3797])).
% 0.86/1.07 tff(3801,plain,
% 0.86/1.07 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[156, 3800])).
% 0.86/1.07 tff(3802,plain,
% 0.86/1.07 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[551, 3797, 3759])).
% 0.86/1.07 tff(3803,plain,
% 0.86/1.07 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[480, 3802])).
% 0.86/1.07 tff(3804,plain,
% 0.86/1.07 (~b(s(z), s(s(s(s(s(s(z)))))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[468, 3803, 2590, 3214, 460])).
% 0.86/1.07 tff(3805,plain,
% 0.86/1.07 (r(s(z), s(s(s(s(s(s(z)))))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[232, 3804])).
% 0.86/1.07 tff(3806,plain,
% 0.86/1.07 (~b(z, s(s(s(z))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[3297, 3805, 3797, 3801, 1])).
% 0.86/1.07 tff(3807,plain,
% 0.86/1.07 (~r(z, s(s(s(z))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[169, 3801, 3797])).
% 0.86/1.07 tff(3808,plain,
% 0.86/1.07 ($false),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[71, 3807, 3806])).
% 0.86/1.07 tff(3809,plain,((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), z))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.07 tff(3810,plain,
% 0.86/1.07 (~b(s(z), s(s(s(s(z)))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[3809, 1])).
% 0.86/1.07 tff(3811,plain,
% 0.86/1.07 (r(s(z), s(s(s(s(z)))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[323, 3810])).
% 0.86/1.07 tff(3812,plain,
% 0.86/1.07 (~r(s(z), z)),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[1151, 3811, 3759])).
% 0.86/1.07 tff(3813,plain,
% 0.86/1.07 (b(s(z), z)),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[187, 3812])).
% 0.86/1.07 tff(3814,plain,
% 0.86/1.07 (~b(z, s(z))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[2365, 235, 1, 3214, 3813])).
% 0.86/1.07 tff(3815,plain,
% 0.86/1.07 (r(z, s(z))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[51, 3814])).
% 0.86/1.07 tff(3816,plain,
% 0.86/1.07 (~r(z, s(s(s(s(z)))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[449, 3815, 3811])).
% 0.86/1.07 tff(3817,plain,
% 0.86/1.07 (b(z, s(s(s(s(z)))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[389, 3816])).
% 0.86/1.07 tff(3818,plain,
% 0.86/1.07 (~r(s(s(s(s(z)))), s(z))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[503, 3815, 3759])).
% 0.86/1.07 tff(3819,plain,
% 0.86/1.07 (b(s(s(s(s(z)))), s(z))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[513, 3818])).
% 0.86/1.07 tff(3820,plain,
% 0.86/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(z))) | (~b(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(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(z))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(3821,plain,
% 0.86/1.07 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(z))))))))) <=> ((~b(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(z))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(3822,plain,
% 0.86/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(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(z))) | (~b(z, s(s(s(s(s(s(z))))))))))),
% 0.86/1.07 inference(monotonicity,[status(thm)],[3821])).
% 0.86/1.07 tff(3823,plain,
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% 0.86/1.07 inference(transitivity,[status(thm)],[3822, 3820])).
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% 0.86/1.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 0.86/1.07 inference(quant_inst,[status(thm)],[])).
% 0.86/1.07 tff(3825,plain,
% 0.86/1.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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(z))) | (~b(z, s(s(s(s(s(s(z))))))))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[3824, 3823])).
% 0.86/1.07 tff(3826,plain,
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% 0.86/1.07 inference(unit_resolution,[status(thm)],[3825, 118, 3819, 2590, 3817, 235, 3214])).
% 0.86/1.07 tff(3827,plain,((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.07 tff(3828,plain,
% 0.86/1.07 (~b(z, s(s(s(s(s(s(z)))))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[3827, 1])).
% 0.86/1.07 tff(3829,plain,
% 0.86/1.07 (r(z, s(s(s(s(s(s(z)))))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[356, 3828])).
% 0.86/1.07 tff(3830,plain,
% 0.86/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), 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(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(3831,plain,
% 0.86/1.07 (((~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(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(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(3832,plain,
% 0.86/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))))),
% 0.86/1.07 inference(monotonicity,[status(thm)],[3831])).
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% 0.86/1.07 inference(transitivity,[status(thm)],[3832, 3830])).
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% 0.86/1.07 inference(quant_inst,[status(thm)],[])).
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% 0.86/1.07 inference(modus_ponens,[status(thm)],[3834, 3833])).
% 0.86/1.07 tff(3836,plain,
% 0.86/1.07 (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[3835, 118, 3813, 3617, 1, 3214])).
% 0.86/1.07 tff(3837,plain,
% 0.86/1.07 (r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[581, 3836])).
% 0.86/1.07 tff(3838,plain,
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% 0.86/1.07 inference(unit_resolution,[status(thm)],[571, 3829, 3837])).
% 0.86/1.07 tff(3839,plain,
% 0.86/1.07 (b(s(s(s(z))), z)),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[649, 3838])).
% 0.86/1.07 tff(3840,plain,
% 0.86/1.07 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[3576, 3839, 2590, 3837, 3829])).
% 0.86/1.07 tff(3841,plain,
% 0.86/1.07 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[156, 3840])).
% 0.86/1.07 tff(3842,plain,
% 0.86/1.07 (~r(z, s(s(s(z))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[169, 3841, 3829])).
% 0.86/1.07 tff(3843,plain,
% 0.86/1.07 (b(z, s(s(s(z))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[71, 3842])).
% 0.86/1.07 tff(3844,plain,
% 0.86/1.07 (~b(z, s(z))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[3545, 3843, 3617, 3813, 3839])).
% 0.86/1.07 tff(3845,plain,
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% 0.86/1.07 inference(unit_resolution,[status(thm)],[51, 3844])).
% 0.86/1.07 tff(3846,plain,
% 0.86/1.07 (~r(z, s(s(s(s(z)))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[449, 3845, 3811])).
% 0.86/1.07 tff(3847,plain,
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% 0.86/1.07 inference(unit_resolution,[status(thm)],[389, 3846])).
% 0.86/1.07 tff(3848,plain,
% 0.86/1.07 (~b(s(z), s(s(s(z))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[1464, 3843, 1, 3214, 3813])).
% 0.86/1.07 tff(3849,plain,
% 0.86/1.07 (r(s(z), s(s(s(z))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[668, 3848])).
% 0.86/1.07 tff(3850,plain,
% 0.86/1.07 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[456, 3849, 3811])).
% 0.86/1.07 tff(3851,plain,
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% 0.86/1.07 inference(unit_resolution,[status(thm)],[310, 3850])).
% 0.86/1.07 tff(3852,plain,
% 0.86/1.07 (~r(s(s(s(s(z)))), s(z))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[503, 3845, 3759])).
% 0.86/1.07 tff(3853,plain,
% 0.86/1.07 (b(s(s(s(s(z)))), s(z))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[513, 3852])).
% 0.86/1.07 tff(3854,plain,
% 0.86/1.07 ($false),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[2874, 118, 3853, 3617, 3851, 3847, 3843])).
% 0.86/1.07 tff(3855,plain,(~b(s(s(s(s(s(s(z)))))), z)), inference(lemma,lemma(discharge,[]))).
% 0.86/1.07 tff(3856,plain,
% 0.86/1.07 (r(s(s(s(s(s(s(z)))))), z)),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[252, 3855])).
% 0.86/1.07 tff(3857,plain,
% 0.86/1.07 ($false),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[2840, 14, 160, 161, 273])).
% 0.86/1.07 tff(3858,plain,((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), z))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.07 tff(3859,plain,
% 0.86/1.07 ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[3858, 3856])).
% 0.86/1.07 tff(3860,plain,
% 0.86/1.07 (~r(z, s(s(s(z))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[3859, 160])).
% 0.86/1.07 tff(3861,plain,
% 0.86/1.07 (b(z, s(s(s(z))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[71, 3860])).
% 0.86/1.07 tff(3862,plain,
% 0.86/1.07 ($false),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[2798, 14, 274, 273, 543])).
% 0.86/1.07 tff(3863,plain,((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.07 tff(3864,plain,
% 0.86/1.07 ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[3863, 3856])).
% 0.86/1.07 tff(3865,plain,
% 0.86/1.07 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[3864, 274])).
% 0.86/1.07 tff(3866,plain,
% 0.86/1.07 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[480, 3865])).
% 0.86/1.07 tff(3867,plain,
% 0.86/1.07 ((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[279, 3856])).
% 0.86/1.07 tff(3868,plain,
% 0.86/1.07 (~r(s(s(s(s(z)))), z)),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[3867, 272])).
% 0.86/1.07 tff(3869,plain,
% 0.86/1.07 (b(s(s(s(s(z)))), z)),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[286, 3868])).
% 0.86/1.07 tff(3870,plain,
% 0.86/1.07 (((~![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(z, s(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(s(s(z)))))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(3871,plain,
% 0.86/1.07 (((~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(s(s(s(s(s(s(z)))))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(3872,plain,
% 0.86/1.07 (((~![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(s(s(s(s(s(s(z)))))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))))),
% 0.86/1.07 inference(monotonicity,[status(thm)],[3871])).
% 0.86/1.07 tff(3873,plain,
% 0.86/1.07 (((~![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(s(s(s(s(s(s(z)))))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 0.86/1.07 inference(transitivity,[status(thm)],[3872, 3870])).
% 0.86/1.07 tff(3874,plain,
% 0.86/1.07 ((~![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)))),
% 0.86/1.07 inference(quant_inst,[status(thm)],[])).
% 0.86/1.07 tff(3875,plain,
% 0.86/1.07 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[3874, 3873])).
% 0.86/1.07 tff(3876,plain,
% 0.86/1.07 ($false),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[3875, 14, 272, 339, 273])).
% 0.86/1.07 tff(3877,plain,((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), z))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.07 tff(3878,plain,
% 0.86/1.07 ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[3877, 3856])).
% 0.86/1.08 tff(3879,plain,
% 0.86/1.08 (~r(z, s(s(s(s(z)))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[3878, 272])).
% 0.86/1.08 tff(3880,plain,
% 0.86/1.08 (b(z, s(s(s(s(z)))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[389, 3879])).
% 0.86/1.08 tff(3881,plain,
% 0.86/1.08 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(z, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(z, s(z))))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(3882,plain,
% 0.86/1.08 (((~r(z, s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), z))) <=> ((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(z, s(z))))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(3883,plain,
% 0.86/1.08 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(s(z)))))), 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(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(z, s(z)))))),
% 0.86/1.08 inference(monotonicity,[status(thm)],[3882])).
% 0.86/1.08 tff(3884,plain,
% 0.86/1.08 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(s(z)))))), 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(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(z, s(z))))),
% 0.86/1.08 inference(transitivity,[status(thm)],[3883, 3881])).
% 0.86/1.08 tff(3885,plain,
% 0.86/1.08 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), z)))),
% 0.86/1.08 inference(quant_inst,[status(thm)],[])).
% 0.86/1.08 tff(3886,plain,
% 0.86/1.08 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(z, s(z)))),
% 0.86/1.08 inference(modus_ponens,[status(thm)],[3885, 3884])).
% 0.86/1.08 tff(3887,plain,
% 0.86/1.08 ($false),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[3886, 14, 4, 273, 2])).
% 0.86/1.08 tff(3888,plain,((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(z)))))), z))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.08 tff(3889,plain,
% 0.86/1.08 ((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(z, s(z)))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[3888, 3856])).
% 0.86/1.08 tff(3890,plain,
% 0.86/1.08 (~r(z, s(z))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[3889, 2])).
% 0.86/1.08 tff(3891,plain,
% 0.86/1.08 (b(z, s(z))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[51, 3890])).
% 0.86/1.08 tff(3892,plain,
% 0.86/1.08 ($false),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[1636, 118, 1607, 1603, 3891, 3869, 3880])).
% 0.86/1.08 tff(3893,plain,((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.08 tff(3894,plain,
% 0.86/1.08 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[3893, 272])).
% 0.86/1.08 tff(3895,plain,
% 0.86/1.08 (b(s(s(s(s(s(s(z)))))), s(z))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[210, 3894])).
% 0.86/1.08 tff(3896,plain,
% 0.86/1.08 (~r(z, s(s(s(z))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[3858, 273, 160])).
% 0.86/1.08 tff(3897,plain,
% 0.86/1.08 (b(z, s(s(s(z))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[71, 3896])).
% 0.86/1.08 tff(3898,plain,
% 0.86/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(3899,plain,
% 0.86/1.08 (((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(3900,plain,
% 0.86/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z)))))))),
% 0.86/1.08 inference(monotonicity,[status(thm)],[3899])).
% 0.86/1.08 tff(3901,plain,
% 0.86/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))))),
% 0.86/1.08 inference(transitivity,[status(thm)],[3900, 3898])).
% 0.86/1.08 tff(3902,plain,
% 0.86/1.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))),
% 0.86/1.08 inference(quant_inst,[status(thm)],[])).
% 0.86/1.08 tff(3903,plain,
% 0.86/1.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z)))))),
% 0.86/1.08 inference(modus_ponens,[status(thm)],[3902, 3901])).
% 0.86/1.08 tff(3904,plain,
% 0.86/1.08 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[3903, 118, 1509, 721, 436, 3897])).
% 0.86/1.08 tff(3905,plain,
% 0.86/1.08 (r(s(s(s(s(z)))), s(s(s(z))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[310, 3904])).
% 0.86/1.08 tff(3906,plain,
% 0.86/1.08 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[293, 3905, 160])).
% 0.86/1.08 tff(3907,plain,
% 0.86/1.08 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[434, 3906])).
% 0.86/1.08 tff(3908,plain,
% 0.86/1.08 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[487, 14, 160, 3905])).
% 0.86/1.08 tff(3909,plain,
% 0.86/1.08 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[480, 3908])).
% 0.86/1.08 tff(3910,plain,
% 0.86/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(3911,plain,
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% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(3912,plain,
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% 0.86/1.08 inference(monotonicity,[status(thm)],[3911])).
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% 0.86/1.08 inference(transitivity,[status(thm)],[3912, 3910])).
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% 0.86/1.08 inference(quant_inst,[status(thm)],[])).
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% 0.86/1.08 inference(modus_ponens,[status(thm)],[3914, 3913])).
% 0.86/1.08 tff(3916,plain,
% 0.86/1.08 (~b(z, s(s(s(s(s(s(z)))))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[3915, 118, 3907, 3909, 721, 436])).
% 0.86/1.08 tff(3917,plain,
% 0.86/1.08 (r(z, s(s(s(s(s(s(z)))))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[356, 3916])).
% 0.86/1.08 tff(3918,plain,
% 0.86/1.08 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[3232, 118, 1509, 721, 436, 3897])).
% 0.86/1.08 tff(3919,plain,
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% 0.86/1.08 inference(unit_resolution,[status(thm)],[402, 3918])).
% 0.86/1.08 tff(3920,plain,
% 0.86/1.08 (~r(z, s(s(s(s(z)))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[3877, 272, 273])).
% 0.86/1.08 tff(3921,plain,
% 0.86/1.08 (b(z, s(s(s(s(z)))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[389, 3920])).
% 0.86/1.08 tff(3922,plain,
% 0.86/1.08 (~r(z, s(s(s(z))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[2042, 3921, 176, 287, 460])).
% 0.86/1.08 tff(3923,plain,
% 0.86/1.08 (b(z, s(s(s(z))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[71, 3922])).
% 0.86/1.08 tff(3924,plain,
% 0.86/1.08 ($false),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[3232, 118, 1509, 403, 287, 3921, 3923])).
% 0.86/1.08 tff(3925,plain,((~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))) | (~b(s(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(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.08 tff(3926,plain,
% 0.86/1.08 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[3925, 460, 176, 273, 160])).
% 0.86/1.08 tff(3927,plain,
% 0.86/1.08 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[434, 3926])).
% 0.86/1.08 tff(3928,plain,
% 0.86/1.08 (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[468, 3927, 233, 211, 460])).
% 0.86/1.08 tff(3929,plain,
% 0.86/1.08 (r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[480, 3928])).
% 0.86/1.08 tff(3930,plain,
% 0.86/1.08 (~r(s(s(s(s(z)))), z)),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[3863, 3929, 273])).
% 0.86/1.08 tff(3931,plain,
% 0.86/1.08 (b(s(s(s(s(z)))), z)),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[286, 3930])).
% 0.86/1.08 tff(3932,plain,
% 0.86/1.08 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[489, 3927, 160, 176])).
% 0.86/1.08 tff(3933,plain,
% 0.86/1.08 (b(s(s(s(s(z)))), s(s(s(z))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[310, 3932])).
% 0.86/1.08 tff(3934,plain,
% 0.86/1.08 (~b(z, s(z))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[2971, 118, 460, 3927, 233, 235])).
% 0.86/1.08 tff(3935,plain,
% 0.86/1.08 (r(z, s(z))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[51, 3934])).
% 0.86/1.08 tff(3936,plain,
% 0.86/1.08 (~r(z, s(s(s(z))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[268, 3935, 176])).
% 0.86/1.08 tff(3937,plain,
% 0.86/1.08 (b(z, s(s(s(z))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[71, 3936])).
% 0.86/1.08 tff(3938,plain,
% 0.86/1.08 (~b(z, s(s(s(s(z)))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[3903, 118, 1509, 3933, 3931, 3937])).
% 0.86/1.08 tff(3939,plain,
% 0.86/1.08 (r(z, s(s(s(s(z)))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[389, 3938])).
% 0.86/1.08 tff(3940,plain,
% 0.86/1.08 (~b(s(s(s(s(z)))), s(z))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[3254, 460, 3927, 233, 211])).
% 0.86/1.08 tff(3941,plain,
% 0.86/1.08 (r(s(s(s(s(z)))), s(z))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[513, 3940])).
% 0.86/1.08 tff(3942,plain,
% 0.86/1.08 ($false),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[1074, 14, 3941, 3935, 3939])).
% 0.86/1.08 tff(3943,plain,((~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(z), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.08 tff(3944,plain,
% 0.86/1.08 (~b(z, s(s(s(s(s(s(z)))))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[3943, 460, 176, 273, 160])).
% 0.86/1.08 tff(3945,plain,
% 0.86/1.08 (r(z, s(s(s(s(s(s(z)))))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[356, 3944])).
% 0.86/1.08 tff(3946,plain,
% 0.86/1.08 (~r(z, s(s(s(z))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[169, 3945, 160])).
% 0.86/1.08 tff(3947,plain,
% 0.86/1.08 (b(z, s(s(s(z))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[71, 3946])).
% 0.86/1.08 tff(3948,plain,
% 0.86/1.08 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[2471, 118, 1509, 3933, 3931, 3947])).
% 0.86/1.08 tff(3949,plain,
% 0.86/1.08 (r(s(s(s(z))), s(s(s(s(z)))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[402, 3948])).
% 0.86/1.08 tff(3950,plain,
% 0.86/1.08 (~b(s(s(s(s(z)))), s(z))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[3254, 3927, 460, 233, 211])).
% 0.86/1.08 tff(3951,plain,
% 0.86/1.08 (r(s(s(s(s(z)))), s(z))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[513, 3950])).
% 0.86/1.08 tff(3952,plain,
% 0.86/1.08 (~r(s(s(s(z))), s(z))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[3245, 3951, 3949])).
% 0.86/1.08 tff(3953,plain,
% 0.86/1.08 (b(s(s(s(z))), s(z))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[105, 3952])).
% 0.86/1.08 tff(3954,plain,
% 0.86/1.08 (~b(z, s(s(s(s(z)))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[3903, 118, 1509, 3933, 3931, 3947])).
% 0.86/1.08 tff(3955,plain,
% 0.86/1.08 (r(z, s(s(s(s(z)))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[389, 3954])).
% 0.86/1.08 tff(3956,plain,
% 0.86/1.08 (~r(z, s(z))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[2270, 3951, 3955])).
% 0.86/1.08 tff(3957,plain,
% 0.86/1.08 (b(z, s(z))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[51, 3956])).
% 0.86/1.08 tff(3958,plain,
% 0.86/1.08 ($false),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[2004, 118, 1509, 3957, 3953, 3933, 3931])).
% 0.86/1.08 tff(3959,plain,((~b(s(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(z))))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.08 tff(3960,plain,
% 0.86/1.08 (~b(s(z), s(s(s(s(z)))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[3959, 176, 160, 273])).
% 0.86/1.08 tff(3961,plain,
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% 0.86/1.08 inference(unit_resolution,[status(thm)],[323, 3960])).
% 0.86/1.08 tff(3962,plain,
% 0.86/1.08 (~r(s(z), z)),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[3381, 3961, 1509, 176])).
% 0.86/1.08 tff(3963,plain,
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% 0.86/1.08 inference(unit_resolution,[status(thm)],[187, 3962])).
% 0.86/1.08 tff(3964,plain,
% 0.86/1.08 (~b(z, s(s(s(s(s(s(z)))))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[522, 3963, 160, 176])).
% 0.86/1.08 tff(3965,plain,
% 0.86/1.08 (r(z, s(s(s(s(s(s(z)))))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[356, 3964])).
% 0.86/1.08 tff(3966,plain,
% 0.86/1.08 (~r(z, s(s(s(z))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[169, 3965, 160])).
% 0.86/1.08 tff(3967,plain,
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% 0.86/1.08 inference(unit_resolution,[status(thm)],[71, 3966])).
% 0.86/1.08 tff(3968,plain,
% 0.86/1.08 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[456, 3961, 176])).
% 0.86/1.08 tff(3969,plain,
% 0.86/1.08 (b(s(s(s(s(z)))), s(s(s(z))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[310, 3968])).
% 0.86/1.08 tff(3970,plain,
% 0.86/1.08 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[898, 3961, 176])).
% 0.86/1.08 tff(3971,plain,
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% 0.86/1.08 inference(unit_resolution,[status(thm)],[402, 3970])).
% 0.86/1.08 tff(3972,plain,
% 0.86/1.08 (~b(s(s(s(s(z)))), z)),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[2471, 118, 1509, 3971, 3969, 3967])).
% 0.86/1.08 tff(3973,plain,
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% 0.86/1.08 inference(unit_resolution,[status(thm)],[286, 3972])).
% 0.86/1.08 tff(3974,plain,
% 0.86/1.08 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[551, 3973, 3965])).
% 0.86/1.08 tff(3975,plain,
% 0.86/1.08 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[480, 3974])).
% 0.86/1.08 tff(3976,plain,
% 0.86/1.08 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[691, 3965, 3963, 211, 233, 3969, 160])).
% 0.86/1.08 tff(3977,plain,
% 0.86/1.08 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[434, 3976])).
% 0.86/1.08 tff(3978,plain,
% 0.86/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(3979,plain,
% 0.86/1.08 (((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(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(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(3980,plain,
% 0.86/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))))),
% 0.86/1.08 inference(monotonicity,[status(thm)],[3979])).
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% 0.86/1.10 tff(4177,plain,
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% 0.86/1.10 tff(4187,plain,
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% 0.86/1.10 inference(rewrite,[status(thm)],[])).
% 0.86/1.10 tff(4190,plain,
% 0.86/1.10 (((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 0.86/1.10 inference(rewrite,[status(thm)],[])).
% 0.86/1.10 tff(4191,plain,
% 0.86/1.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z))))))))))),
% 0.86/1.10 inference(monotonicity,[status(thm)],[4190])).
% 0.86/1.10 tff(4192,plain,
% 0.86/1.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 0.86/1.10 inference(transitivity,[status(thm)],[4191, 4189])).
% 0.86/1.10 tff(4193,plain,
% 0.86/1.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 0.86/1.10 inference(quant_inst,[status(thm)],[])).
% 0.86/1.10 tff(4194,plain,
% 0.86/1.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z))))))))),
% 0.86/1.10 inference(modus_ponens,[status(thm)],[4193, 4192])).
% 0.86/1.10 tff(4195,plain,
% 0.86/1.10 ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z))),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[4194, 118, 3869, 1343, 4143])).
% 0.86/1.10 tff(4196,plain,
% 0.86/1.10 (~b(s(s(s(s(z)))), s(z))),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[4195, 4182])).
% 0.86/1.10 tff(4197,plain,
% 0.86/1.10 (r(s(s(s(s(z)))), s(z))),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[513, 4196])).
% 0.86/1.10 tff(4198,plain,
% 0.86/1.10 (~r(s(s(s(z))), s(z))),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[1085, 4197, 2512, 3869, 4184])).
% 0.86/1.10 tff(4199,plain,
% 0.86/1.10 (b(s(s(s(z))), s(z))),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[105, 4198])).
% 0.86/1.10 tff(4200,plain,
% 0.86/1.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 0.86/1.10 inference(rewrite,[status(thm)],[])).
% 0.86/1.10 tff(4201,plain,
% 0.86/1.10 (((~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(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 0.86/1.10 inference(rewrite,[status(thm)],[])).
% 0.86/1.10 tff(4202,plain,
% 0.86/1.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z)))))))),
% 0.86/1.10 inference(monotonicity,[status(thm)],[4201])).
% 0.86/1.10 tff(4203,plain,
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% 0.86/1.10 inference(transitivity,[status(thm)],[4202, 4200])).
% 0.86/1.10 tff(4204,plain,
% 0.86/1.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 0.86/1.10 inference(quant_inst,[status(thm)],[])).
% 0.86/1.10 tff(4205,plain,
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% 0.86/1.10 inference(modus_ponens,[status(thm)],[4204, 4203])).
% 0.86/1.10 tff(4206,plain,
% 0.86/1.10 ($false),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[4205, 118, 4199, 4100, 4188, 4143, 3895])).
% 0.86/1.10 tff(4207,plain,((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.10 tff(4208,plain,
% 0.86/1.10 (~r(s(z), s(s(s(s(z)))))),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[4207, 272])).
% 0.86/1.10 tff(4209,plain,
% 0.86/1.10 (b(s(z), s(s(s(s(z)))))),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[323, 4208])).
% 0.86/1.10 tff(4210,plain,
% 0.86/1.10 (~b(z, s(z))),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[2040, 118, 4209, 234, 3869, 3880])).
% 0.86/1.10 tff(4211,plain,
% 0.86/1.10 (r(z, s(z))),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[51, 4210])).
% 0.86/1.10 tff(4212,plain,
% 0.86/1.10 (~b(s(s(s(s(z)))), s(z))),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[1869, 234, 3869, 3880, 4209])).
% 0.86/1.10 tff(4213,plain,
% 0.86/1.10 (r(s(s(s(s(z)))), s(z))),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[513, 4212])).
% 0.86/1.10 tff(4214,plain,
% 0.86/1.10 (~r(z, s(s(s(z))))),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[268, 176, 4])).
% 0.86/1.10 tff(4215,plain,
% 0.86/1.10 (b(z, s(s(s(z))))),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[71, 4214])).
% 0.86/1.10 tff(4216,plain,
% 0.86/1.10 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), 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(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(z))))))),
% 0.86/1.10 inference(rewrite,[status(thm)],[])).
% 0.86/1.10 tff(4217,plain,
% 0.86/1.10 (((~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)))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(z))))))),
% 0.86/1.10 inference(rewrite,[status(thm)],[])).
% 0.86/1.10 tff(4218,plain,
% 0.86/1.10 (((~![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(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(z)))))))),
% 0.86/1.10 inference(monotonicity,[status(thm)],[4217])).
% 0.86/1.10 tff(4219,plain,
% 0.86/1.10 (((~![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(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(z))))))),
% 0.86/1.10 inference(transitivity,[status(thm)],[4218, 4216])).
% 0.86/1.10 tff(4220,plain,
% 0.86/1.10 ((~![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))))),
% 0.86/1.10 inference(quant_inst,[status(thm)],[])).
% 0.86/1.10 tff(4221,plain,
% 0.86/1.10 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(z)))))),
% 0.86/1.10 inference(modus_ponens,[status(thm)],[4220, 4219])).
% 0.86/1.10 tff(4222,plain,
% 0.86/1.10 ($false),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[4221, 14, 495, 176, 288])).
% 0.86/1.11 tff(4223,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.11 tff(4224,plain,
% 0.86/1.11 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[4223, 176, 495])).
% 0.86/1.11 tff(4225,plain,
% 0.86/1.11 (b(s(s(s(s(z)))), s(s(s(z))))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[310, 4224])).
% 0.86/1.11 tff(4226,plain,
% 0.86/1.11 ($false),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[536, 118, 460, 234, 4225, 436, 4215])).
% 0.86/1.11 tff(4227,plain,((~r(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.11 tff(4228,plain,
% 0.86/1.11 (~r(s(z), s(s(s(z))))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[4227, 234, 4209, 3880, 4213, 4211])).
% 0.86/1.11 tff(4229,plain,
% 0.86/1.11 (b(s(z), s(s(s(z))))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[668, 4228])).
% 0.86/1.11 tff(4230,plain,
% 0.86/1.11 (~r(s(s(s(z))), s(z))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[3245, 391, 495])).
% 0.86/1.11 tff(4231,plain,
% 0.86/1.11 (b(s(s(s(z))), s(z))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[105, 4230])).
% 0.86/1.11 tff(4232,plain,
% 0.86/1.11 ($false),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[1892, 4231, 1950, 4100, 3895, 172])).
% 0.86/1.11 tff(4233,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.11 tff(4234,plain,
% 0.86/1.11 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[4233, 4229, 4213, 272])).
% 0.86/1.11 tff(4235,plain,
% 0.86/1.11 (b(s(s(s(z))), s(s(s(s(z)))))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[402, 4234])).
% 0.86/1.11 tff(4236,plain,
% 0.86/1.11 (~r(s(s(s(z))), s(z))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[1085, 4235, 4213, 3869, 4211])).
% 0.86/1.11 tff(4237,plain,
% 0.86/1.11 (b(s(s(s(z))), s(z))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[105, 4236])).
% 0.86/1.11 tff(4238,plain,
% 0.86/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(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)))), z)) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(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)))), z)) | (~b(s(z), z)))),
% 0.86/1.11 inference(rewrite,[status(thm)],[])).
% 0.86/1.11 tff(4239,plain,
% 0.86/1.11 (((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(z))), s(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)))), z)) | (~b(s(z), z)))),
% 0.86/1.11 inference(rewrite,[status(thm)],[])).
% 0.86/1.11 tff(4240,plain,
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% 0.86/1.11 inference(monotonicity,[status(thm)],[4239])).
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% 0.86/1.11 inference(transitivity,[status(thm)],[4240, 4238])).
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% 0.86/1.11 inference(unit_resolution,[status(thm)],[4248, 4247])).
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% 0.86/1.11 inference(unit_resolution,[status(thm)],[4248, 177])).
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% 0.86/1.11 inference(unit_resolution,[status(thm)],[232, 4251])).
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% 0.86/1.11 inference(unit_resolution,[status(thm)],[4054, 3856])).
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% 0.86/1.11 inference(rewrite,[status(thm)],[])).
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% 0.86/1.11 inference(monotonicity,[status(thm)],[4260])).
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% 0.86/1.11 inference(unit_resolution,[status(thm)],[71, 4293])).
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% 0.86/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 0.86/1.11 inference(rewrite,[status(thm)],[])).
% 0.86/1.11 tff(4296,plain,
% 0.86/1.11 (((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 0.86/1.11 inference(rewrite,[status(thm)],[])).
% 0.86/1.11 tff(4297,plain,
% 0.86/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))))),
% 0.86/1.11 inference(monotonicity,[status(thm)],[4296])).
% 0.86/1.11 tff(4298,plain,
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% 0.86/1.11 inference(transitivity,[status(thm)],[4297, 4295])).
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% 0.86/1.11 inference(quant_inst,[status(thm)],[])).
% 0.86/1.11 tff(4300,plain,
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% 0.86/1.11 inference(modus_ponens,[status(thm)],[4299, 4298])).
% 0.86/1.11 tff(4301,plain,
% 0.86/1.11 (~b(z, s(s(s(s(s(s(z)))))))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[4300, 118, 4100, 4294, 4281, 4279])).
% 0.86/1.11 tff(4302,plain,
% 0.86/1.11 (r(z, s(s(s(s(s(s(z)))))))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[356, 4301])).
% 0.86/1.11 tff(4303,plain,
% 0.86/1.11 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[1593, 4277, 272])).
% 0.86/1.11 tff(4304,plain,
% 0.86/1.11 (b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[1627, 4303])).
% 0.86/1.11 tff(4305,plain,
% 0.86/1.11 (~b(s(s(s(s(s(z))))), s(z))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[760, 118, 4250, 3895, 4279, 4304])).
% 0.86/1.11 tff(4306,plain,
% 0.86/1.11 (r(s(s(s(s(s(z))))), s(z))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[829, 4305])).
% 0.86/1.11 tff(4307,plain,
% 0.86/1.11 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[1829, 14, 74, 1164])).
% 0.86/1.11 tff(4308,plain,
% 0.86/1.11 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[1820, 46, 1809, 4307])).
% 0.86/1.11 tff(4309,plain,
% 0.86/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 0.86/1.11 inference(rewrite,[status(thm)],[])).
% 0.86/1.11 tff(4310,plain,
% 0.86/1.11 (((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 0.86/1.11 inference(rewrite,[status(thm)],[])).
% 0.86/1.11 tff(4311,plain,
% 0.86/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 0.86/1.11 inference(monotonicity,[status(thm)],[4310])).
% 0.86/1.11 tff(4312,plain,
% 0.86/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 0.86/1.11 inference(transitivity,[status(thm)],[4311, 4309])).
% 0.86/1.11 tff(4313,plain,
% 0.86/1.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 0.86/1.12 inference(quant_inst,[status(thm)],[])).
% 0.86/1.12 tff(4314,plain,
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% 0.86/1.12 inference(modus_ponens,[status(thm)],[4313, 4312])).
% 0.86/1.12 tff(4315,plain,
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% 0.86/1.12 inference(unit_resolution,[status(thm)],[4314, 118, 1695, 271, 1205, 4308, 2346])).
% 0.86/1.12 tff(4316,plain,((~r(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.12 tff(4317,plain,
% 0.86/1.12 (~r(s(s(s(z))), s(z))),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[4316, 1695, 4294, 4281, 4306])).
% 0.86/1.12 tff(4318,plain,
% 0.86/1.12 (b(s(s(s(z))), s(z))),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[105, 4317])).
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% 0.86/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 0.86/1.12 inference(rewrite,[status(thm)],[])).
% 0.86/1.12 tff(4320,plain,
% 0.86/1.12 (((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 0.86/1.12 inference(rewrite,[status(thm)],[])).
% 0.86/1.12 tff(4321,plain,
% 0.86/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))))),
% 0.86/1.12 inference(monotonicity,[status(thm)],[4320])).
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% 0.86/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 0.86/1.12 inference(transitivity,[status(thm)],[4321, 4319])).
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% 0.86/1.12 inference(quant_inst,[status(thm)],[])).
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% 0.86/1.12 inference(modus_ponens,[status(thm)],[4323, 4322])).
% 0.86/1.12 tff(4325,plain,
% 0.86/1.12 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[4324, 118, 173, 1950, 236, 1790])).
% 0.86/1.12 tff(4326,plain,
% 0.86/1.12 ($false),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[1820, 46, 4325, 1809, 2713])).
% 0.86/1.12 tff(4327,plain,((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~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,[]))).
% 0.86/1.12 tff(4328,plain,
% 0.86/1.12 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[4327, 4318, 272, 3895, 4277])).
% 0.86/1.12 tff(4329,plain,
% 0.86/1.12 (b(s(s(s(z))), s(s(s(s(z)))))),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[402, 4328])).
% 0.86/1.12 tff(4330,plain,
% 0.86/1.12 ($false),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[3232, 118, 1695, 4329, 3869, 3880, 4294])).
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% 0.86/1.12 inference(rewrite,[status(thm)],[])).
% 0.86/1.12 tff(4399,plain,
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% 0.86/1.12 inference(monotonicity,[status(thm)],[4398])).
% 0.86/1.12 tff(4400,plain,
% 0.86/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(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(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 0.86/1.12 inference(transitivity,[status(thm)],[4399, 4397])).
% 0.86/1.12 tff(4401,plain,
% 0.86/1.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(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(z))))))))),
% 0.86/1.12 inference(quant_inst,[status(thm)],[])).
% 0.86/1.12 tff(4402,plain,
% 0.86/1.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z)))),
% 0.86/1.12 inference(modus_ponens,[status(thm)],[4401, 4400])).
% 0.86/1.12 tff(4403,plain,
% 0.86/1.12 ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[4402, 118, 4388, 4393, 4380])).
% 0.86/1.12 tff(4404,plain,
% 0.86/1.12 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[4403, 4386])).
% 0.86/1.12 tff(4405,plain,
% 0.86/1.12 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[1616, 4404])).
% 0.86/1.12 tff(4406,plain,
% 0.86/1.12 (((~![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(z)))), s(s(s(s(s(z))))))) | (~r(z, 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)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))))),
% 0.86/1.12 inference(rewrite,[status(thm)],[])).
% 0.86/1.12 tff(4407,plain,
% 0.86/1.12 (((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))))),
% 0.86/1.12 inference(rewrite,[status(thm)],[])).
% 0.86/1.12 tff(4408,plain,
% 0.86/1.12 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(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)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z)))))))))),
% 0.86/1.12 inference(monotonicity,[status(thm)],[4407])).
% 0.86/1.12 tff(4409,plain,
% 0.86/1.12 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(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)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))))),
% 0.86/1.12 inference(transitivity,[status(thm)],[4408, 4406])).
% 0.86/1.12 tff(4410,plain,
% 0.86/1.12 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)))),
% 0.86/1.12 inference(quant_inst,[status(thm)],[])).
% 0.86/1.12 tff(4411,plain,
% 0.96/1.12 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z)))))))),
% 0.96/1.12 inference(modus_ponens,[status(thm)],[4410, 4409])).
% 0.96/1.12 tff(4412,plain,
% 0.96/1.12 ($false),
% 0.96/1.12 inference(unit_resolution,[status(thm)],[4411, 14, 274, 4405, 4396])).
% 0.96/1.12 tff(4413,plain,((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(z)))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.12 tff(4414,plain,
% 0.96/1.12 (~r(s(s(s(z))), s(z))),
% 0.96/1.12 inference(unit_resolution,[status(thm)],[4413, 4373, 274, 2])).
% 0.96/1.12 tff(4415,plain,
% 0.96/1.12 (b(s(s(s(z))), s(z))),
% 0.96/1.12 inference(unit_resolution,[status(thm)],[105, 4414])).
% 0.96/1.12 tff(4416,plain,
% 0.96/1.12 (~r(z, s(s(s(z))))),
% 0.96/1.12 inference(unit_resolution,[status(thm)],[4344, 4415, 2, 274, 339])).
% 0.96/1.12 tff(4417,plain,
% 0.96/1.12 (b(z, s(s(s(z))))),
% 0.96/1.12 inference(unit_resolution,[status(thm)],[71, 4416])).
% 0.96/1.12 tff(4418,plain,
% 0.96/1.12 (~b(s(s(s(s(z)))), s(z))),
% 0.96/1.12 inference(unit_resolution,[status(thm)],[4389, 4252])).
% 0.96/1.12 tff(4419,plain,
% 0.96/1.12 (r(s(s(s(s(z)))), s(z))),
% 0.96/1.12 inference(unit_resolution,[status(thm)],[513, 4418])).
% 0.96/1.12 tff(4420,plain,
% 0.96/1.12 ($false),
% 0.96/1.12 inference(unit_resolution,[status(thm)],[974, 14, 4419, 177, 274])).
% 0.96/1.12 tff(4421,plain,((~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.12 tff(4422,plain,
% 0.96/1.12 (~r(s(z), z)),
% 0.96/1.12 inference(unit_resolution,[status(thm)],[4421, 4373, 274])).
% 0.96/1.12 tff(4423,plain,
% 0.96/1.12 (b(s(z), z)),
% 0.96/1.12 inference(unit_resolution,[status(thm)],[187, 4422])).
% 0.96/1.12 tff(4424,plain,
% 0.96/1.12 (~b(s(s(s(z))), z)),
% 0.96/1.12 inference(unit_resolution,[status(thm)],[3545, 4423, 3891, 4415, 4417])).
% 0.96/1.12 tff(4425,plain,
% 0.96/1.12 (r(s(s(s(z))), z)),
% 0.96/1.12 inference(unit_resolution,[status(thm)],[649, 4424])).
% 0.96/1.12 tff(4426,plain,
% 0.96/1.12 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 0.96/1.12 inference(unit_resolution,[status(thm)],[703, 4425, 274])).
% 0.96/1.12 tff(4427,plain,
% 0.96/1.12 (b(s(s(s(z))), s(s(s(s(z)))))),
% 0.96/1.12 inference(unit_resolution,[status(thm)],[402, 4426])).
% 0.96/1.12 tff(4428,plain,
% 0.96/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))),
% 0.96/1.12 inference(rewrite,[status(thm)],[])).
% 0.96/1.12 tff(4429,plain,
% 0.96/1.12 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))),
% 0.96/1.12 inference(rewrite,[status(thm)],[])).
% 0.96/1.12 tff(4430,plain,
% 0.96/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(z, s(s(s(z)))))))),
% 0.96/1.12 inference(monotonicity,[status(thm)],[4429])).
% 0.96/1.12 tff(4431,plain,
% 0.96/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))),
% 0.96/1.12 inference(transitivity,[status(thm)],[4430, 4428])).
% 0.96/1.12 tff(4432,plain,
% 0.96/1.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))),
% 0.96/1.12 inference(quant_inst,[status(thm)],[])).
% 0.96/1.12 tff(4433,plain,
% 0.96/1.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(z, s(s(s(z)))))),
% 0.96/1.12 inference(modus_ponens,[status(thm)],[4432, 4431])).
% 0.96/1.12 tff(4434,plain,
% 0.96/1.12 ($false),
% 0.96/1.12 inference(unit_resolution,[status(thm)],[4433, 118, 4373, 3891, 4427, 4415, 4417])).
% 0.96/1.12 tff(4435,plain,((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.12 tff(4436,plain,
% 0.96/1.12 (~r(z, s(s(s(s(z)))))),
% 0.96/1.12 inference(unit_resolution,[status(thm)],[4435, 2, 274])).
% 0.96/1.12 tff(4437,plain,
% 0.96/1.12 (b(z, s(s(s(s(z)))))),
% 0.96/1.12 inference(unit_resolution,[status(thm)],[389, 4436])).
% 0.96/1.12 tff(4438,plain,
% 0.96/1.12 (~r(z, s(z))),
% 0.96/1.12 inference(unit_resolution,[status(thm)],[3888, 2, 273])).
% 0.96/1.12 tff(4439,plain,
% 0.96/1.12 (b(z, s(z))),
% 0.96/1.12 inference(unit_resolution,[status(thm)],[51, 4438])).
% 0.96/1.12 tff(4440,plain,
% 0.96/1.12 (~b(s(s(s(s(z)))), z)),
% 0.96/1.12 inference(unit_resolution,[status(thm)],[4097, 436, 273, 160])).
% 0.96/1.12 tff(4441,plain,
% 0.96/1.12 (r(s(s(s(s(z)))), z)),
% 0.96/1.12 inference(unit_resolution,[status(thm)],[286, 4440])).
% 0.96/1.12 tff(4442,plain,
% 0.96/1.12 (~b(s(z), z)),
% 0.96/1.12 inference(unit_resolution,[status(thm)],[4044, 1155])).
% 0.96/1.12 tff(4443,plain,
% 0.96/1.12 (r(s(z), z)),
% 0.96/1.12 inference(unit_resolution,[status(thm)],[187, 4442])).
% 0.96/1.12 tff(4444,plain,
% 0.96/1.12 (~r(s(z), s(s(s(s(z)))))),
% 0.96/1.12 inference(unit_resolution,[status(thm)],[1151, 4443, 4441])).
% 0.96/1.12 tff(4445,plain,
% 0.96/1.12 (b(s(z), s(s(s(s(z)))))),
% 0.96/1.12 inference(unit_resolution,[status(thm)],[323, 4444])).
% 0.96/1.12 tff(4446,plain,
% 0.96/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))))),
% 0.96/1.12 inference(rewrite,[status(thm)],[])).
% 0.96/1.12 tff(4447,plain,
% 0.96/1.12 (((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z))) <=> ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))))),
% 0.96/1.12 inference(rewrite,[status(thm)],[])).
% 0.96/1.12 tff(4448,plain,
% 0.96/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z)))))),
% 0.96/1.12 inference(monotonicity,[status(thm)],[4447])).
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% 0.96/1.13 inference(monotonicity,[status(thm)],[4588])).
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% 0.96/1.13 inference(transitivity,[status(thm)],[4589, 4587])).
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% 0.96/1.13 inference(quant_inst,[status(thm)],[])).
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% 0.96/1.14 tff(4752,plain,
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% 0.96/1.14 inference(unit_resolution,[status(thm)],[581, 4751])).
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% 0.96/1.15 inference(modus_ponens,[status(thm)],[4780, 4779])).
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% 0.96/1.15 inference(unit_resolution,[status(thm)],[4781, 118, 460, 4775, 4340, 4746, 237])).
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% 0.96/1.15 tff(4784,plain,
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% 0.96/1.15 tff(4805,plain,
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% 0.96/1.15 tff(4806,plain,
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% 0.96/1.15 tff(4807,plain,
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% 0.96/1.15 inference(unit_resolution,[status(thm)],[105, 4806])).
% 0.96/1.15 tff(4808,plain,
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% 0.96/1.15 tff(4809,plain,
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% 0.96/1.15 tff(4810,plain,
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% 0.96/1.15 tff(4811,plain,
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% 0.96/1.15 tff(4812,plain,
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% 0.96/1.15 tff(4813,plain,
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% 0.96/1.15 inference(unit_resolution,[status(thm)],[323, 4815])).
% 0.96/1.15 tff(4817,plain,
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% 0.96/1.15 inference(unit_resolution,[status(thm)],[3241, 4816, 4807])).
% 0.96/1.15 tff(4818,plain,
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% 0.96/1.15 tff(4820,plain,(~r(s(s(s(s(s(s(z)))))), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.15 tff(4821,plain,
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% 0.96/1.15 tff(4822,plain,
% 0.96/1.15 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
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% 0.96/1.15 tff(4823,plain,
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% 0.96/1.15 tff(4824,plain,
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% 0.96/1.15 tff(4827,plain,((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.15 tff(4828,plain,
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% 0.96/1.15 tff(4829,plain,
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% 0.96/1.15 inference(unit_resolution,[status(thm)],[513, 4828])).
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% 0.96/1.15 inference(unit_resolution,[status(thm)],[513, 4832])).
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% 0.96/1.15 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.96/1.15 inference(unit_resolution,[status(thm)],[1125, 4833, 2])).
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% 0.96/1.15 inference(unit_resolution,[status(thm)],[4827, 4833, 2])).
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% 0.96/1.15 tff(4839,plain,
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% 0.96/1.15 tff(4840,plain,
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% 0.96/1.15 inference(unit_resolution,[status(thm)],[456, 3505, 176])).
% 0.96/1.15 tff(4841,plain,
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% 0.96/1.15 inference(unit_resolution,[status(thm)],[323, 4840])).
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% 0.96/1.15 tff(4844,plain,
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% 0.96/1.15 inference(unit_resolution,[status(thm)],[4843, 1695, 4340, 4720, 4805, 174, 4821])).
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% 0.96/1.15 tff(4848,plain,((~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
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% 0.96/1.15 tff(4858,plain,
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% 0.96/1.15 tff(4862,plain,
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% 0.96/1.15 inference(unit_resolution,[status(thm)],[668, 4861])).
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% 0.96/1.15 tff(4864,plain,
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% 0.96/1.16 inference(unit_resolution,[status(thm)],[649, 4968])).
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% 0.96/1.16 inference(unit_resolution,[status(thm)],[1892, 172, 4821, 4932, 173])).
% 0.96/1.16 tff(4971,plain,
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% 0.96/1.16 tff(4974,plain,
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% 0.96/1.16 tff(4984,plain,
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% 0.96/1.16 tff(4988,plain,
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% 0.96/1.16 inference(unit_resolution,[status(thm)],[356, 4994])).
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% 0.96/1.16 inference(rewrite,[status(thm)],[])).
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% 0.96/1.16 inference(monotonicity,[status(thm)],[4997])).
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% 0.96/1.16 inference(transitivity,[status(thm)],[4998, 4996])).
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% 0.96/1.16 inference(quant_inst,[status(thm)],[])).
% 0.96/1.16 tff(5001,plain,
% 0.96/1.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))),
% 0.96/1.16 inference(modus_ponens,[status(thm)],[5000, 4999])).
% 0.96/1.16 tff(5002,plain,
% 0.96/1.16 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[5001, 118, 587, 4340, 4821, 1352])).
% 0.96/1.16 tff(5003,plain,
% 0.96/1.16 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[1684, 5002])).
% 0.96/1.16 tff(5004,plain,
% 0.96/1.16 (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[4882, 587, 594])).
% 0.96/1.16 tff(5005,plain,
% 0.96/1.16 (r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[581, 5004])).
% 0.96/1.16 tff(5006,plain,
% 0.96/1.16 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(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(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 0.96/1.16 inference(rewrite,[status(thm)],[])).
% 0.96/1.16 tff(5007,plain,
% 0.96/1.16 (((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 0.96/1.16 inference(rewrite,[status(thm)],[])).
% 0.96/1.16 tff(5008,plain,
% 0.96/1.16 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(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(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))))),
% 0.96/1.16 inference(monotonicity,[status(thm)],[5007])).
% 0.96/1.16 tff(5009,plain,
% 0.96/1.16 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(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(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 0.96/1.16 inference(transitivity,[status(thm)],[5008, 5006])).
% 0.96/1.16 tff(5010,plain,
% 0.96/1.16 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 0.96/1.16 inference(quant_inst,[status(thm)],[])).
% 0.96/1.16 tff(5011,plain,
% 0.96/1.16 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))),
% 0.96/1.16 inference(modus_ponens,[status(thm)],[5010, 5009])).
% 0.96/1.16 tff(5012,plain,
% 0.96/1.16 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[5011, 14, 5005, 5003])).
% 0.96/1.16 tff(5013,plain,
% 0.96/1.16 (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[2662, 587, 4340, 4821, 594])).
% 0.96/1.16 tff(5014,plain,
% 0.96/1.16 (r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[480, 5013])).
% 0.96/1.16 tff(5015,plain,
% 0.96/1.16 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[2324, 14, 5014, 5003])).
% 0.96/1.16 tff(5016,plain,
% 0.96/1.16 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[1616, 5015])).
% 0.96/1.16 tff(5017,plain,
% 0.96/1.16 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[1816, 5016])).
% 0.96/1.16 tff(5018,plain,
% 0.96/1.16 ($false),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[1820, 46, 5017, 1809, 5012])).
% 0.96/1.16 tff(5019,plain,((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.16 tff(5020,plain,
% 0.96/1.16 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[5019, 4989, 4991])).
% 0.96/1.16 tff(5021,plain,
% 0.96/1.16 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[1595, 5020])).
% 0.96/1.16 tff(5022,plain,
% 0.96/1.16 (~r(z, s(z))),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[449, 339, 329])).
% 0.96/1.16 tff(5023,plain,
% 0.96/1.16 (b(z, s(z))),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[51, 5022])).
% 0.96/1.16 tff(5024,plain,
% 0.96/1.16 (~b(s(s(s(s(s(z))))), s(z))),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[1271, 1253, 234, 5023, 329, 339])).
% 0.96/1.16 tff(5025,plain,
% 0.96/1.16 (r(s(s(s(s(s(z))))), s(z))),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[829, 5024])).
% 0.96/1.16 tff(5026,plain,
% 0.96/1.16 ($false),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[2717, 14, 329, 1253, 5025])).
% 0.96/1.16 tff(5027,plain,((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(z), z)) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.16 tff(5028,plain,
% 0.96/1.16 (~r(z, s(s(s(s(z)))))),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[5027, 5021, 4938, 4805])).
% 0.96/1.16 tff(5029,plain,
% 0.96/1.16 (b(z, s(s(s(s(z)))))),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[389, 5028])).
% 0.96/1.16 tff(5030,plain,
% 0.96/1.16 ($false),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[3000, 118, 4991, 4340, 4821, 5029, 4995])).
% 0.96/1.16 tff(5031,plain,(~r(s(s(s(z))), s(z))), inference(lemma,lemma(discharge,[]))).
% 0.96/1.16 tff(5032,plain,
% 0.96/1.16 (b(s(s(s(z))), s(z))),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[105, 5031])).
% 0.96/1.16 tff(5033,plain,
% 0.96/1.16 (~b(s(s(s(z))), z)),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[4848, 5032, 4988])).
% 0.96/1.16 tff(5034,plain,
% 0.96/1.16 (r(s(s(s(z))), z)),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[649, 5033])).
% 0.96/1.16 tff(5035,plain,
% 0.96/1.16 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[4856, 14, 5034, 3856])).
% 0.96/1.16 tff(5036,plain,
% 0.96/1.16 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[581, 5035])).
% 0.96/1.16 tff(5037,plain,
% 0.96/1.16 (~b(s(z), s(s(s(z))))),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[1892, 5036, 4821, 4932, 5032])).
% 0.96/1.16 tff(5038,plain,
% 0.96/1.16 (r(s(z), s(s(s(z))))),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[668, 5037])).
% 0.96/1.16 tff(5039,plain,
% 0.96/1.16 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[4223, 5038, 4934])).
% 0.96/1.16 tff(5040,plain,
% 0.96/1.16 (b(s(s(s(s(z)))), s(s(s(z))))),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[310, 5039])).
% 0.96/1.16 tff(5041,plain,
% 0.96/1.16 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[898, 5038, 4938])).
% 0.96/1.16 tff(5042,plain,
% 0.96/1.16 (b(s(s(s(z))), s(s(s(s(z)))))),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[402, 5041])).
% 0.96/1.16 tff(5043,plain,
% 0.96/1.16 ($false),
% 0.96/1.16 inference(unit_resolution,[status(thm)],[4882, 5042, 5040, 5036])).
% 0.96/1.16 % SZS output end Proof
% 0.96/1.16 % E exiting
%------------------------------------------------------------------------------