%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRA163-1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n018.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 06:34:20 PM UTC 2026
% Result : Unsatisfiable 0.39s 0.57s
% Output : Proof 0.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRA163-1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.15/0.33 % Computer : n018.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 00:32:48 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.39/0.57 % SZS status Unsatisfiable
% 0.39/0.57 % SZS output start Proof
% 0.39/0.57 tff(b_type, type, (
% 0.39/0.57 b: ( $i * $i ) > $o)).
% 0.39/0.57 tff(z_type, type, (
% 0.39/0.57 z: $i)).
% 0.39/0.57 tff(s_type, type, (
% 0.39/0.57 s: $i > $i)).
% 0.39/0.57 tff(r_type, type, (
% 0.39/0.57 r: ( $i * $i ) > $o)).
% 0.39/0.57 tff(inj_0_type, type, (
% 0.39/0.57 inj_0: $i > $i)).
% 0.39/0.57 tff(1,assumption,(s(s(s(s(s(s(z)))))) = s(z)), introduced(assumption)).
% 0.39/0.57 tff(2,plain,
% 0.39/0.57 (s(z) = s(s(s(s(s(s(z))))))),
% 0.39/0.57 inference(symmetry,[status(thm)],[1])).
% 0.39/0.57 tff(3,plain,
% 0.39/0.57 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0) <=> ![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 0.39/0.57 inference(rewrite,[status(thm)],[])).
% 0.39/0.57 tff(4,plain,
% 0.39/0.57 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y)) <=> ![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 0.39/0.57 inference(rewrite,[status(thm)],[])).
% 0.39/0.57 tff(5,plain,
% 0.39/0.57 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y)) <=> ![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 0.39/0.57 inference(rewrite,[status(thm)],[])).
% 0.39/0.57 tff(6,axiom,(![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','sinj')).
% 0.39/0.57 tff(7,plain,
% 0.39/0.57 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 0.39/0.57 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.39/0.57 tff(8,plain,(
% 0.39/0.57 ![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 0.39/0.57 inference(skolemize,[status(sab)],[7])).
% 0.39/0.57 tff(9,plain,
% 0.39/0.57 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 0.39/0.57 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.39/0.57 tff(10,plain,
% 0.39/0.57 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 0.39/0.57 inference(modus_ponens,[status(thm)],[9, 3])).
% 0.39/0.57 tff(11,plain,
% 0.39/0.57 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(z)) = z)),
% 0.39/0.57 inference(quant_inst,[status(thm)],[])).
% 0.39/0.57 tff(12,plain,
% 0.39/0.57 (inj_0(s(z)) = z),
% 0.39/0.57 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.39/0.57 tff(13,assumption,(s(z) = s(s(s(s(s(s(z))))))), introduced(assumption)).
% 0.39/0.57 tff(14,plain,
% 0.39/0.57 (s(s(s(s(s(s(z)))))) = s(z)),
% 0.39/0.57 inference(symmetry,[status(thm)],[13])).
% 0.39/0.57 tff(15,plain,
% 0.39/0.57 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(z))),
% 0.39/0.57 inference(monotonicity,[status(thm)],[14])).
% 0.39/0.57 tff(16,plain,
% 0.39/0.57 ((~![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))))))),
% 0.39/0.57 inference(quant_inst,[status(thm)],[])).
% 0.39/0.57 tff(17,plain,
% 0.39/0.57 (inj_0(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))),
% 0.39/0.57 inference(unit_resolution,[status(thm)],[16, 10])).
% 0.39/0.57 tff(18,plain,
% 0.39/0.57 (s(s(s(s(s(z))))) = inj_0(s(s(s(s(s(s(z)))))))),
% 0.39/0.57 inference(symmetry,[status(thm)],[17])).
% 0.39/0.57 tff(19,plain,
% 0.39/0.57 (s(s(s(s(s(z))))) = z),
% 0.39/0.57 inference(transitivity,[status(thm)],[18, 15, 12])).
% 0.39/0.57 tff(20,plain,
% 0.39/0.57 (^[X: $i] : refl((~(s(X) = z)) <=> (~(s(X) = z)))),
% 0.39/0.57 inference(bind,[status(th)],[])).
% 0.39/0.57 tff(21,plain,
% 0.39/0.57 (![X: $i] : (~(s(X) = z)) <=> ![X: $i] : (~(s(X) = z))),
% 0.39/0.57 inference(quant_intro,[status(thm)],[20])).
% 0.39/0.57 tff(22,plain,
% 0.39/0.57 (![X: $i] : (~(s(X) = z)) <=> ![X: $i] : (~(s(X) = z))),
% 0.39/0.57 inference(rewrite,[status(thm)],[])).
% 0.39/0.57 tff(23,axiom,(![X: $i] : (~(s(X) = z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','snz')).
% 0.39/0.57 tff(24,plain,
% 0.39/0.57 (![X: $i] : (~(s(X) = z))),
% 0.39/0.57 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.39/0.57 tff(25,plain,(
% 0.39/0.57 ![X: $i] : (~(s(X) = z))),
% 0.39/0.57 inference(skolemize,[status(sab)],[24])).
% 0.39/0.57 tff(26,plain,
% 0.39/0.57 (![X: $i] : (~(s(X) = z))),
% 0.39/0.57 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.39/0.57 tff(27,plain,
% 0.39/0.57 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(z))))) = z))),
% 0.39/0.57 inference(quant_inst,[status(thm)],[])).
% 0.39/0.57 tff(28,plain,
% 0.39/0.57 (~(s(s(s(s(s(z))))) = z)),
% 0.39/0.57 inference(unit_resolution,[status(thm)],[27, 26])).
% 0.39/0.57 tff(29,plain,
% 0.39/0.57 ($false),
% 0.39/0.57 inference(unit_resolution,[status(thm)],[28, 19])).
% 0.39/0.57 tff(30,plain,(~(s(z) = s(s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 0.39/0.57 tff(31,plain,
% 0.39/0.57 ($false),
% 0.39/0.57 inference(unit_resolution,[status(thm)],[30, 2])).
% 0.39/0.57 tff(32,plain,(~(s(s(s(s(s(s(z)))))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 0.39/0.57 tff(33,assumption,(b(s(s(s(z))), s(z))), introduced(assumption)).
% 0.39/0.57 tff(34,assumption,(r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))), introduced(assumption)).
% 0.39/0.57 tff(35,assumption,(r(s(s(s(s(s(z))))), s(s(s(z))))), introduced(assumption)).
% 0.39/0.57 tff(36,plain,
% 0.39/0.57 ((z = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = z)),
% 0.39/0.57 inference(commutativity,[status(thm)],[])).
% 0.39/0.58 tff(37,plain,
% 0.39/0.58 ((s(s(s(s(s(s(s(z))))))) = z) <=> (z = s(s(s(s(s(s(s(z))))))))),
% 0.39/0.58 inference(symmetry,[status(thm)],[36])).
% 0.39/0.58 tff(38,plain,
% 0.39/0.58 ((~(s(s(s(s(s(s(s(z))))))) = z)) <=> (~(z = s(s(s(s(s(s(s(z)))))))))),
% 0.39/0.58 inference(monotonicity,[status(thm)],[37])).
% 0.39/0.58 tff(39,plain,
% 0.39/0.58 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(s(s(z))))))) = z))),
% 0.39/0.58 inference(quant_inst,[status(thm)],[])).
% 0.39/0.58 tff(40,plain,
% 0.39/0.58 (~(s(s(s(s(s(s(s(z))))))) = z)),
% 0.39/0.58 inference(unit_resolution,[status(thm)],[39, 26])).
% 0.39/0.58 tff(41,plain,
% 0.39/0.58 (~(z = s(s(s(s(s(s(s(z))))))))),
% 0.39/0.58 inference(modus_ponens,[status(thm)],[40, 38])).
% 0.39/0.58 tff(42,assumption,(r(z, s(s(s(z))))), introduced(assumption)).
% 0.39/0.58 tff(43,plain,
% 0.39/0.58 (^[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))))),
% 0.39/0.58 inference(bind,[status(th)],[])).
% 0.39/0.58 tff(44,plain,
% 0.39/0.58 (![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)))),
% 0.39/0.58 inference(quant_intro,[status(thm)],[43])).
% 0.39/0.58 tff(45,plain,
% 0.39/0.58 (![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)))),
% 0.39/0.58 inference(rewrite,[status(thm)],[])).
% 0.39/0.58 tff(46,plain,
% 0.39/0.58 (^[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))))),
% 0.39/0.58 inference(bind,[status(th)],[])).
% 0.39/0.58 tff(47,plain,
% 0.39/0.58 (![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)))),
% 0.39/0.58 inference(quant_intro,[status(thm)],[46])).
% 0.39/0.58 tff(48,axiom,(![X0: $i, X2: $i, X1: $i] : (((~r(X0, X1)) | (~r(X0, X2))) | (~r(X1, X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axr')).
% 0.39/0.58 tff(49,plain,
% 0.39/0.58 (![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 0.39/0.58 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.39/0.58 tff(50,plain,
% 0.39/0.58 (![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 0.39/0.58 inference(modus_ponens,[status(thm)],[49, 45])).
% 0.39/0.58 tff(51,plain,(
% 0.39/0.58 ![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 0.39/0.58 inference(skolemize,[status(sab)],[50])).
% 0.39/0.58 tff(52,plain,
% 0.39/0.58 (![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 0.39/0.58 inference(modus_ponens,[status(thm)],[51, 44])).
% 0.39/0.58 tff(53,plain,
% 0.39/0.58 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(z))))) | (~r(s(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(s(z))))))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 0.39/0.58 inference(rewrite,[status(thm)],[])).
% 0.39/0.58 tff(54,plain,
% 0.39/0.58 (((~r(s(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(s(z)))))))))) <=> ((~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 0.39/0.58 inference(rewrite,[status(thm)],[])).
% 0.39/0.58 tff(55,plain,
% 0.39/0.58 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(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(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(s(z))))))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))))),
% 0.39/0.58 inference(monotonicity,[status(thm)],[54])).
% 0.39/0.58 tff(56,plain,
% 0.39/0.58 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(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(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(s(z))))))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 0.39/0.58 inference(transitivity,[status(thm)],[55, 53])).
% 0.39/0.58 tff(57,plain,
% 0.39/0.58 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(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(s(z))))))))))),
% 0.39/0.58 inference(quant_inst,[status(thm)],[])).
% 0.39/0.58 tff(58,plain,
% 0.39/0.58 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(s(s(z))))))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 0.39/0.58 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.39/0.58 tff(59,plain,
% 0.39/0.58 (~r(z, s(s(s(s(s(s(s(z))))))))),
% 0.39/0.58 inference(unit_resolution,[status(thm)],[58, 52, 34, 42])).
% 0.39/0.58 tff(60,plain,
% 0.39/0.58 (^[Y: $i, X: $i] : refl(((X = Y) | b(X, Y) | r(X, Y)) <=> ((X = Y) | b(X, Y) | r(X, Y)))),
% 0.39/0.58 inference(bind,[status(th)],[])).
% 0.39/0.58 tff(61,plain,
% 0.39/0.58 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.39/0.58 inference(quant_intro,[status(thm)],[60])).
% 0.39/0.58 tff(62,plain,
% 0.39/0.58 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.39/0.58 inference(rewrite,[status(thm)],[])).
% 0.39/0.58 tff(63,plain,
% 0.39/0.58 (^[Y: $i, X: $i] : rewrite((((X = Y) | r(X, Y)) | b(X, Y)) <=> ((X = Y) | b(X, Y) | r(X, Y)))),
% 0.39/0.58 inference(bind,[status(th)],[])).
% 0.39/0.58 tff(64,plain,
% 0.39/0.58 (![Y: $i, X: $i] : (((X = Y) | r(X, Y)) | b(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.39/0.58 inference(quant_intro,[status(thm)],[63])).
% 0.39/0.58 tff(65,axiom,(![Y: $i, X: $i] : (((X = Y) | r(X, Y)) | b(X, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rb')).
% 0.39/0.58 tff(66,plain,
% 0.39/0.58 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.39/0.58 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.39/0.58 tff(67,plain,
% 0.39/0.58 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.39/0.58 inference(modus_ponens,[status(thm)],[66, 62])).
% 0.39/0.58 tff(68,plain,(
% 0.39/0.58 ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.39/0.58 inference(skolemize,[status(sab)],[67])).
% 0.39/0.58 tff(69,plain,
% 0.39/0.58 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.39/0.58 inference(modus_ponens,[status(thm)],[68, 61])).
% 0.39/0.58 tff(70,plain,
% 0.39/0.58 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(s(s(s(z)))))))) | b(z, s(s(s(s(s(s(s(z)))))))) | r(z, s(s(s(s(s(s(s(z)))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(s(s(s(z)))))))) | b(z, s(s(s(s(s(s(s(z)))))))) | r(z, s(s(s(s(s(s(s(z)))))))))),
% 0.39/0.58 inference(rewrite,[status(thm)],[])).
% 0.39/0.58 tff(71,plain,
% 0.39/0.58 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(s(s(s(z)))))))) | b(z, s(s(s(s(s(s(s(z)))))))) | r(z, s(s(s(s(s(s(s(z)))))))))),
% 0.39/0.58 inference(quant_inst,[status(thm)],[])).
% 0.39/0.58 tff(72,plain,
% 0.39/0.58 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(s(s(s(z)))))))) | b(z, s(s(s(s(s(s(s(z)))))))) | r(z, s(s(s(s(s(s(s(z))))))))),
% 0.39/0.58 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.39/0.58 tff(73,plain,
% 0.39/0.58 ((z = s(s(s(s(s(s(s(z)))))))) | b(z, s(s(s(s(s(s(s(z))))))))),
% 0.39/0.58 inference(unit_resolution,[status(thm)],[72, 69, 59])).
% 0.39/0.58 tff(74,plain,
% 0.39/0.58 (b(z, s(s(s(s(s(s(s(z))))))))),
% 0.39/0.58 inference(unit_resolution,[status(thm)],[73, 41])).
% 0.39/0.58 tff(75,plain,
% 0.39/0.58 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(z))))) | (~r(s(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(s(s(s(z))))))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 0.39/0.58 inference(rewrite,[status(thm)],[])).
% 0.39/0.58 tff(76,plain,
% 0.39/0.58 (((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), z))) <=> ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 0.39/0.58 inference(rewrite,[status(thm)],[])).
% 0.39/0.58 tff(77,plain,
% 0.39/0.58 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(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(s(z))))))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))))),
% 0.39/0.58 inference(monotonicity,[status(thm)],[76])).
% 0.39/0.58 tff(78,plain,
% 0.39/0.58 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(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(s(z))))))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 0.39/0.58 inference(transitivity,[status(thm)],[77, 75])).
% 0.39/0.58 tff(79,plain,
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% 0.39/0.58 inference(quant_inst,[status(thm)],[])).
% 0.39/0.58 tff(80,plain,
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% 0.39/0.58 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.39/0.58 tff(81,plain,
% 0.39/0.58 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 0.39/0.58 inference(unit_resolution,[status(thm)],[80, 52, 34, 42])).
% 0.39/0.58 tff(82,assumption,(~r(s(s(s(s(s(s(s(z))))))), z)), introduced(assumption)).
% 0.39/0.58 tff(83,assumption,(~b(s(s(s(s(s(s(s(z))))))), z)), introduced(assumption)).
% 0.39/0.58 tff(84,plain,
% 0.39/0.58 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = z) | b(s(s(s(s(s(s(s(z))))))), z) | r(s(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(s(z))))))) = z) | b(s(s(s(s(s(s(s(z))))))), z) | r(s(s(s(s(s(s(s(z))))))), z))),
% 0.39/0.58 inference(rewrite,[status(thm)],[])).
% 0.39/0.58 tff(85,plain,
% 0.39/0.58 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(z))))))) = z) | b(s(s(s(s(s(s(s(z))))))), z) | r(s(s(s(s(s(s(s(z))))))), z))),
% 0.39/0.58 inference(quant_inst,[status(thm)],[])).
% 0.39/0.58 tff(86,plain,
% 0.39/0.58 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(z))))))) = z) | b(s(s(s(s(s(s(s(z))))))), z) | r(s(s(s(s(s(s(s(z))))))), z)),
% 0.39/0.58 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.39/0.58 tff(87,plain,
% 0.39/0.58 ($false),
% 0.39/0.58 inference(unit_resolution,[status(thm)],[86, 69, 40, 83, 82])).
% 0.39/0.58 tff(88,plain,(b(s(s(s(s(s(s(s(z))))))), z) | r(s(s(s(s(s(s(s(z))))))), z)), inference(lemma,lemma(discharge,[]))).
% 0.39/0.58 tff(89,plain,
% 0.39/0.58 (b(s(s(s(s(s(s(s(z))))))), z)),
% 0.39/0.58 inference(unit_resolution,[status(thm)],[88, 81])).
% 0.39/0.58 tff(90,assumption,(r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 0.39/0.58 tff(91,plain,
% 0.39/0.58 (((~![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(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(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(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 0.39/0.58 inference(rewrite,[status(thm)],[])).
% 0.39/0.58 tff(92,plain,
% 0.39/0.58 (((~r(s(s(s(s(s(s(s(z))))))), 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(s(z)))))))))) <=> ((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 0.39/0.58 inference(rewrite,[status(thm)],[])).
% 0.39/0.58 tff(93,plain,
% 0.39/0.58 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), 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(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(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))))),
% 0.39/0.58 inference(monotonicity,[status(thm)],[92])).
% 0.39/0.58 tff(94,plain,
% 0.39/0.58 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), 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(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(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 0.39/0.58 inference(transitivity,[status(thm)],[93, 91])).
% 0.39/0.58 tff(95,plain,
% 0.39/0.58 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), 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(s(z))))))))))),
% 0.39/0.58 inference(quant_inst,[status(thm)],[])).
% 0.39/0.58 tff(96,plain,
% 0.39/0.58 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 0.39/0.58 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.39/0.58 tff(97,plain,
% 0.39/0.58 ($false),
% 0.39/0.58 inference(unit_resolution,[status(thm)],[96, 52, 35, 34, 90])).
% 0.39/0.58 tff(98,plain,((~r(s(s(s(s(s(s(s(z))))))), 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(s(z)))))))))), inference(lemma,lemma(discharge,[]))).
% 0.39/0.58 tff(99,plain,
% 0.39/0.58 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 0.39/0.58 inference(unit_resolution,[status(thm)],[98, 35, 34])).
% 0.39/0.58 tff(100,plain,
% 0.39/0.58 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(z))) = s(z))),
% 0.39/0.58 inference(quant_inst,[status(thm)],[])).
% 0.39/0.58 tff(101,plain,
% 0.39/0.58 (inj_0(s(s(z))) = s(z)),
% 0.39/0.58 inference(unit_resolution,[status(thm)],[100, 10])).
% 0.39/0.58 tff(102,plain,
% 0.39/0.58 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(s(s(z)))))))) = s(s(s(s(s(s(z)))))))),
% 0.39/0.58 inference(quant_inst,[status(thm)],[])).
% 0.39/0.58 tff(103,plain,
% 0.39/0.58 (inj_0(s(s(s(s(s(s(s(z)))))))) = s(s(s(s(s(s(z))))))),
% 0.39/0.58 inference(unit_resolution,[status(thm)],[102, 10])).
% 0.39/0.58 tff(104,assumption,(s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 0.39/0.58 tff(105,plain,
% 0.39/0.58 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(s(s(s(s(s(z))))))))),
% 0.39/0.58 inference(monotonicity,[status(thm)],[104])).
% 0.39/0.58 tff(106,plain,
% 0.39/0.58 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(z)))))) = s(s(s(s(z)))))),
% 0.39/0.58 inference(quant_inst,[status(thm)],[])).
% 0.39/0.58 tff(107,plain,
% 0.39/0.58 (inj_0(s(s(s(s(s(z)))))) = s(s(s(s(z))))),
% 0.39/0.58 inference(unit_resolution,[status(thm)],[106, 10])).
% 0.39/0.58 tff(108,plain,
% 0.39/0.58 (s(s(s(s(z)))) = inj_0(s(s(s(s(s(z))))))),
% 0.39/0.58 inference(symmetry,[status(thm)],[107])).
% 0.39/0.58 tff(109,plain,
% 0.39/0.58 (s(s(s(s(z)))) = s(s(s(s(s(s(z))))))),
% 0.39/0.58 inference(transitivity,[status(thm)],[108, 105, 103])).
% 0.39/0.58 tff(110,plain,
% 0.39/0.58 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(s(s(z)))))))),
% 0.39/0.58 inference(monotonicity,[status(thm)],[109])).
% 0.39/0.58 tff(111,plain,
% 0.39/0.58 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(z))))) = s(s(s(z))))),
% 0.39/0.58 inference(quant_inst,[status(thm)],[])).
% 0.39/0.58 tff(112,plain,
% 0.39/0.58 (inj_0(s(s(s(s(z))))) = s(s(s(z)))),
% 0.39/0.58 inference(unit_resolution,[status(thm)],[111, 10])).
% 0.39/0.58 tff(113,plain,
% 0.39/0.58 (s(s(s(z))) = inj_0(s(s(s(s(z)))))),
% 0.39/0.58 inference(symmetry,[status(thm)],[112])).
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% 0.39/0.58 (s(s(s(z))) = s(s(s(s(s(s(s(z)))))))),
% 0.39/0.58 inference(transitivity,[status(thm)],[113, 110, 17, 104])).
% 0.39/0.58 tff(115,plain,
% 0.39/0.58 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(s(s(s(z))))))))),
% 0.39/0.58 inference(monotonicity,[status(thm)],[114])).
% 0.39/0.58 tff(116,plain,
% 0.39/0.58 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(z)))) = s(s(z)))),
% 0.39/0.58 inference(quant_inst,[status(thm)],[])).
% 0.39/0.58 tff(117,plain,
% 0.39/0.58 (inj_0(s(s(s(z)))) = s(s(z))),
% 0.39/0.58 inference(unit_resolution,[status(thm)],[116, 10])).
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% 0.39/0.58 (s(s(z)) = inj_0(s(s(s(z))))),
% 0.39/0.58 inference(symmetry,[status(thm)],[117])).
% 0.39/0.58 tff(119,plain,
% 0.39/0.58 (s(s(z)) = s(s(s(s(s(s(z))))))),
% 0.39/0.58 inference(transitivity,[status(thm)],[118, 115, 103])).
% 0.39/0.58 tff(120,plain,
% 0.39/0.58 (inj_0(s(s(z))) = inj_0(s(s(s(s(s(s(z)))))))),
% 0.39/0.58 inference(monotonicity,[status(thm)],[119])).
% 0.39/0.58 tff(121,plain,
% 0.39/0.58 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(s(z)))),
% 0.39/0.58 inference(symmetry,[status(thm)],[120])).
% 0.39/0.58 tff(122,plain,
% 0.39/0.58 (s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))),
% 0.39/0.58 inference(symmetry,[status(thm)],[104])).
% 0.39/0.58 tff(123,plain,
% 0.39/0.58 (s(s(s(s(s(s(s(z))))))) = s(z)),
% 0.39/0.58 inference(transitivity,[status(thm)],[122, 18, 121, 101])).
% 0.39/0.58 tff(124,assumption,(s(s(s(s(s(s(s(z))))))) = s(z)), introduced(assumption)).
% 0.39/0.58 tff(125,plain,
% 0.39/0.58 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(z))),
% 0.39/0.58 inference(monotonicity,[status(thm)],[124])).
% 0.39/0.58 tff(126,plain,
% 0.39/0.58 (s(s(s(s(s(s(z)))))) = inj_0(s(s(s(s(s(s(s(z))))))))),
% 0.39/0.58 inference(symmetry,[status(thm)],[103])).
% 0.39/0.58 tff(127,plain,
% 0.39/0.58 (s(s(s(s(s(s(z)))))) = z),
% 0.39/0.58 inference(transitivity,[status(thm)],[126, 125, 12])).
% 0.39/0.58 tff(128,plain,
% 0.39/0.58 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(s(z)))))) = z))),
% 0.39/0.58 inference(quant_inst,[status(thm)],[])).
% 0.39/0.58 tff(129,plain,
% 0.39/0.58 (~(s(s(s(s(s(s(z)))))) = z)),
% 0.39/0.58 inference(unit_resolution,[status(thm)],[128, 26])).
% 0.39/0.58 tff(130,plain,
% 0.39/0.58 ($false),
% 0.39/0.58 inference(unit_resolution,[status(thm)],[129, 127])).
% 0.39/0.58 tff(131,plain,(~(s(s(s(s(s(s(s(z))))))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 0.39/0.58 tff(132,plain,
% 0.39/0.58 ($false),
% 0.39/0.58 inference(unit_resolution,[status(thm)],[131, 123])).
% 0.39/0.58 tff(133,plain,(~(s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 0.39/0.58 tff(134,plain,
% 0.39/0.58 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))),
% 0.39/0.58 inference(rewrite,[status(thm)],[])).
% 0.39/0.58 tff(135,plain,
% 0.39/0.58 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))),
% 0.39/0.58 inference(quant_inst,[status(thm)],[])).
% 0.39/0.58 tff(136,plain,
% 0.39/0.58 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 0.39/0.58 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.39/0.58 tff(137,plain,
% 0.39/0.58 ((s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 0.39/0.58 inference(unit_resolution,[status(thm)],[136, 69])).
% 0.39/0.58 tff(138,plain,
% 0.39/0.58 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))) | r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 0.39/0.58 inference(unit_resolution,[status(thm)],[137, 133])).
% 0.39/0.58 tff(139,plain,
% 0.39/0.58 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 0.39/0.58 inference(unit_resolution,[status(thm)],[138, 99])).
% 0.39/0.58 tff(140,plain,
% 0.39/0.58 (^[X0: $i, X3: $i, X2: $i, X1: $i] : refl(((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) <=> ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))))),
% 0.39/0.58 inference(bind,[status(th)],[])).
% 0.39/0.58 tff(141,plain,
% 0.39/0.58 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 0.39/0.58 inference(quant_intro,[status(thm)],[140])).
% 0.39/0.58 tff(142,plain,
% 0.39/0.58 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 0.39/0.58 inference(rewrite,[status(thm)],[])).
% 0.39/0.58 tff(143,plain,
% 0.39/0.58 (^[X0: $i, X3: $i, X2: $i, X1: $i] : trans(monotonicity(rewrite((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) <=> ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))), (((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) <=> (((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X2, X3))))), rewrite((((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X2, X3))) <=> ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))), (((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) <=> ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))))),
% 0.39/0.58 inference(bind,[status(th)],[])).
% 0.39/0.58 tff(144,plain,
% 0.39/0.58 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 0.39/0.58 inference(quant_intro,[status(thm)],[143])).
% 0.39/0.58 tff(145,axiom,(![X0: $i, X3: $i, X2: $i, X1: $i] : ((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axb')).
% 0.39/0.59 tff(146,plain,
% 0.39/0.59 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 0.39/0.59 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.39/0.59 tff(147,plain,
% 0.39/0.59 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 0.39/0.59 inference(modus_ponens,[status(thm)],[146, 142])).
% 0.39/0.59 tff(148,plain,(
% 0.39/0.59 ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 0.39/0.59 inference(skolemize,[status(sab)],[147])).
% 0.39/0.59 tff(149,plain,
% 0.39/0.59 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 0.39/0.59 inference(modus_ponens,[status(thm)],[148, 141])).
% 0.39/0.59 tff(150,plain,
% 0.39/0.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 0.39/0.59 inference(rewrite,[status(thm)],[])).
% 0.39/0.59 tff(151,plain,
% 0.39/0.59 (((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 0.39/0.59 inference(rewrite,[status(thm)],[])).
% 0.39/0.59 tff(152,plain,
% 0.39/0.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(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, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))))),
% 0.39/0.59 inference(monotonicity,[status(thm)],[151])).
% 0.39/0.59 tff(153,plain,
% 0.39/0.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(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, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))))),
% 0.39/0.59 inference(transitivity,[status(thm)],[152, 150])).
% 0.39/0.59 tff(154,plain,
% 0.39/0.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 0.39/0.59 inference(quant_inst,[status(thm)],[])).
% 0.39/0.59 tff(155,plain,
% 0.39/0.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z)))))))))),
% 0.39/0.59 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.39/0.59 tff(156,plain,
% 0.39/0.59 (~b(s(s(s(s(s(z))))), z)),
% 0.39/0.59 inference(unit_resolution,[status(thm)],[155, 149, 139, 89, 74])).
% 0.39/0.59 tff(157,assumption,(~r(s(s(s(s(s(z))))), z)), introduced(assumption)).
% 0.39/0.59 tff(158,assumption,(~b(s(s(s(s(s(z))))), z)), introduced(assumption)).
% 0.39/0.59 tff(159,plain,
% 0.39/0.59 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = z) | b(s(s(s(s(s(z))))), z) | r(s(s(s(s(s(z))))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = z) | b(s(s(s(s(s(z))))), z) | r(s(s(s(s(s(z))))), z))),
% 0.39/0.59 inference(rewrite,[status(thm)],[])).
% 0.39/0.59 tff(160,plain,
% 0.39/0.59 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = z) | b(s(s(s(s(s(z))))), z) | r(s(s(s(s(s(z))))), z))),
% 0.39/0.59 inference(quant_inst,[status(thm)],[])).
% 0.39/0.59 tff(161,plain,
% 0.39/0.59 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = z) | b(s(s(s(s(s(z))))), z) | r(s(s(s(s(s(z))))), z)),
% 0.39/0.59 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.39/0.59 tff(162,plain,
% 0.39/0.59 ($false),
% 0.39/0.59 inference(unit_resolution,[status(thm)],[161, 69, 28, 158, 157])).
% 0.39/0.59 tff(163,plain,(b(s(s(s(s(s(z))))), z) | r(s(s(s(s(s(z))))), z)), inference(lemma,lemma(discharge,[]))).
% 0.39/0.59 tff(164,plain,
% 0.39/0.59 (r(s(s(s(s(s(z))))), z)),
% 0.39/0.59 inference(unit_resolution,[status(thm)],[163, 156])).
% 0.39/0.59 tff(165,assumption,(b(s(s(s(s(s(z))))), s(z))), introduced(assumption)).
% 0.39/0.59 tff(166,assumption,(b(z, s(s(s(z))))), introduced(assumption)).
% 0.39/0.59 tff(167,assumption,(b(s(s(s(s(s(s(s(z))))))), s(z))), introduced(assumption)).
% 0.39/0.59 tff(168,plain,
% 0.39/0.59 ((s(z) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(z))),
% 0.39/0.59 inference(commutativity,[status(thm)],[])).
% 0.39/0.59 tff(169,plain,
% 0.39/0.59 ((s(s(s(s(s(z))))) = s(z)) <=> (s(z) = s(s(s(s(s(z))))))),
% 0.39/0.59 inference(symmetry,[status(thm)],[168])).
% 0.39/0.59 tff(170,plain,
% 0.39/0.59 ((~(s(s(s(s(s(z))))) = s(z))) <=> (~(s(z) = s(s(s(s(s(z)))))))),
% 0.39/0.59 inference(monotonicity,[status(thm)],[169])).
% 0.39/0.59 tff(171,assumption,(s(s(s(s(s(z))))) = s(z)), introduced(assumption)).
% 0.39/0.59 tff(172,plain,
% 0.39/0.59 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(z))),
% 0.39/0.59 inference(monotonicity,[status(thm)],[171])).
% 0.39/0.59 tff(173,plain,
% 0.39/0.59 (s(s(s(s(z)))) = z),
% 0.39/0.59 inference(transitivity,[status(thm)],[108, 172, 12])).
% 0.39/0.59 tff(174,plain,
% 0.39/0.59 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(z)))) = z))),
% 0.39/0.59 inference(quant_inst,[status(thm)],[])).
% 0.39/0.59 tff(175,plain,
% 0.39/0.59 (~(s(s(s(s(z)))) = z)),
% 0.39/0.59 inference(unit_resolution,[status(thm)],[174, 26])).
% 0.39/0.59 tff(176,plain,
% 0.39/0.59 ($false),
% 0.39/0.59 inference(unit_resolution,[status(thm)],[175, 173])).
% 0.39/0.59 tff(177,plain,(~(s(s(s(s(s(z))))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 0.39/0.59 tff(178,plain,
% 0.39/0.59 (~(s(z) = s(s(s(s(s(z))))))),
% 0.39/0.59 inference(modus_ponens,[status(thm)],[177, 170])).
% 0.39/0.59 tff(179,assumption,(b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 0.39/0.59 tff(180,assumption,(b(s(z), s(s(s(z))))), introduced(assumption)).
% 0.39/0.59 tff(181,plain,
% 0.39/0.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 0.39/0.59 inference(rewrite,[status(thm)],[])).
% 0.39/0.59 tff(182,plain,
% 0.39/0.59 (((~b(s(z), s(s(s(z))))) | (~b(s(s(s(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(s(s(s(z)))))))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 0.39/0.59 inference(rewrite,[status(thm)],[])).
% 0.39/0.59 tff(183,plain,
% 0.39/0.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(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(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))))),
% 0.39/0.59 inference(monotonicity,[status(thm)],[182])).
% 0.39/0.59 tff(184,plain,
% 0.39/0.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(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(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 0.39/0.59 inference(transitivity,[status(thm)],[183, 181])).
% 0.39/0.59 tff(185,plain,
% 0.39/0.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(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(s(s(s(z))))))))))),
% 0.39/0.59 inference(quant_inst,[status(thm)],[])).
% 0.39/0.59 tff(186,plain,
% 0.39/0.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))),
% 0.39/0.59 inference(modus_ponens,[status(thm)],[185, 184])).
% 0.39/0.59 tff(187,plain,
% 0.39/0.59 ($false),
% 0.39/0.59 inference(unit_resolution,[status(thm)],[186, 149, 180, 179, 167, 165])).
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% 0.39/0.60 inference(modus_ponens,[status(thm)],[235, 234])).
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% 0.39/0.60 tff(251,plain,
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% 0.39/0.60 inference(unit_resolution,[status(thm)],[250, 241])).
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% 0.39/0.60 tff(253,assumption,(~b(s(s(s(s(s(z))))), s(s(s(z))))), introduced(assumption)).
% 0.39/0.60 tff(254,assumption,(~r(s(s(s(s(s(z))))), s(s(s(z))))), introduced(assumption)).
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% 0.39/0.60 tff(266,assumption,(~b(s(s(s(z))), z)), introduced(assumption)).
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% 0.39/0.60 inference(quant_inst,[status(thm)],[])).
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% 0.39/0.60 inference(unit_resolution,[status(thm)],[267, 26])).
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% 0.39/0.60 inference(monotonicity,[status(thm)],[274])).
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% 0.39/0.60 (~(s(s(s(s(s(z))))) = s(s(s(z))))),
% 0.39/0.60 inference(modus_ponens,[status(thm)],[250, 275])).
% 0.39/0.60 tff(277,assumption,(b(z, s(z))), introduced(assumption)).
% 0.39/0.60 tff(278,plain,
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% 0.39/0.60 inference(unit_resolution,[status(thm)],[283, 149, 277, 261, 165])).
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% 0.39/0.60 inference(unit_resolution,[status(thm)],[161, 69, 28, 284])).
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% 0.39/0.60 inference(unit_resolution,[status(thm)],[288, 52, 272, 285])).
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% 0.39/0.60 ((s(s(s(s(s(z))))) = s(s(s(z)))) | b(s(s(s(s(s(z))))), s(s(s(z))))),
% 0.39/0.60 inference(unit_resolution,[status(thm)],[257, 69, 289])).
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% 0.39/0.60 inference(monotonicity,[status(thm)],[294])).
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% 0.39/0.60 inference(transitivity,[status(thm)],[295, 293])).
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% 0.39/0.60 inference(quant_inst,[status(thm)],[])).
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% 0.39/0.60 inference(modus_ponens,[status(thm)],[297, 296])).
% 0.39/0.60 tff(299,plain,
% 0.39/0.60 ($false),
% 0.39/0.60 inference(unit_resolution,[status(thm)],[298, 149, 277, 261, 165, 292])).
% 0.39/0.60 tff(300,plain,((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 0.39/0.60 tff(301,plain,
% 0.39/0.60 (~b(z, s(s(s(s(s(z))))))),
% 0.39/0.60 inference(unit_resolution,[status(thm)],[300, 277, 261, 165])).
% 0.39/0.60 tff(302,assumption,(z = s(s(s(s(s(z)))))), introduced(assumption)).
% 0.39/0.60 tff(303,plain,
% 0.39/0.60 (s(s(s(s(s(z))))) = z),
% 0.39/0.60 inference(symmetry,[status(thm)],[302])).
% 0.39/0.60 tff(304,plain,
% 0.39/0.60 ($false),
% 0.39/0.60 inference(unit_resolution,[status(thm)],[28, 303])).
% 0.39/0.60 tff(305,plain,(~(z = s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.39/0.60 tff(306,assumption,(~r(z, s(s(s(s(s(z))))))), introduced(assumption)).
% 0.39/0.60 tff(307,assumption,(~b(z, s(s(s(s(s(z))))))), introduced(assumption)).
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% 0.39/0.60 tff(315,assumption,(r(s(s(s(z))), s(s(s(s(s(z))))))), introduced(assumption)).
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% 0.39/0.60 inference(quant_inst,[status(thm)],[])).
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% 0.39/0.60 tff(324,plain,
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% 0.39/0.60 inference(unit_resolution,[status(thm)],[323, 313, 266])).
% 0.39/0.60 tff(325,assumption,(~b(s(s(s(z))), s(s(s(s(s(z))))))), introduced(assumption)).
% 0.39/0.60 tff(326,assumption,(~r(s(s(s(z))), s(s(s(s(s(z))))))), introduced(assumption)).
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% 0.39/0.61 inference(unit_resolution,[status(thm)],[329, 69, 326, 250, 325])).
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% 0.39/0.61 tff(332,plain,
% 0.39/0.61 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 0.39/0.61 inference(unit_resolution,[status(thm)],[331, 324])).
% 0.39/0.61 tff(333,assumption,(r(s(z), s(s(s(z))))), introduced(assumption)).
% 0.39/0.61 tff(334,assumption,(r(s(s(s(z))), z)), introduced(assumption)).
% 0.39/0.61 tff(335,assumption,(r(z, s(z))), introduced(assumption)).
% 0.39/0.61 tff(336,plain,
% 0.39/0.61 (r(s(s(s(s(s(s(s(z))))))), z)),
% 0.39/0.61 inference(unit_resolution,[status(thm)],[88, 83])).
% 0.39/0.61 tff(337,assumption,(r(s(s(s(z))), s(z))), introduced(assumption)).
% 0.39/0.61 tff(338,plain,
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% 0.39/0.61 inference(unit_resolution,[status(thm)],[340, 52, 335, 337, 334])).
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% 0.39/0.61 inference(modus_ponens,[status(thm)],[345, 344])).
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% 0.39/0.61 inference(unit_resolution,[status(thm)],[346, 69])).
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% 0.39/0.61 inference(unit_resolution,[status(thm)],[347, 198])).
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% 0.39/0.61 inference(unit_resolution,[status(thm)],[348, 343])).
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% 0.39/0.61 inference(unit_resolution,[status(thm)],[86, 69, 40, 83])).
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% 0.47/0.62 inference(monotonicity,[status(thm)],[480])).
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% 0.47/0.62 inference(transitivity,[status(thm)],[481, 479])).
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% 0.47/0.62 tff(486,plain,
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% 0.47/0.62 inference(unit_resolution,[status(thm)],[138, 485])).
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% 0.47/0.62 (((~r(s(s(s(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(s(s(s(z)))))))))) <=> ((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(z))))), z)))),
% 0.47/0.62 inference(rewrite,[status(thm)],[])).
% 0.47/0.62 tff(489,plain,
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% 0.47/0.62 inference(monotonicity,[status(thm)],[488])).
% 0.47/0.62 tff(490,plain,
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% 0.47/0.62 inference(transitivity,[status(thm)],[489, 487])).
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% 0.47/0.62 tff(492,plain,
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% 0.47/0.62 tff(493,plain,
% 0.47/0.62 ($false),
% 0.47/0.62 inference(unit_resolution,[status(thm)],[492, 52, 90, 477, 365])).
% 0.47/0.62 tff(494,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
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% 0.47/0.62 (b(s(s(s(s(s(s(s(z))))))), z)),
% 0.47/0.62 inference(unit_resolution,[status(thm)],[88, 495])).
% 0.47/0.62 tff(497,assumption,(s(s(s(s(s(z))))) = s(s(s(s(s(s(z))))))), introduced(assumption)).
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% 0.47/0.62 inference(symmetry,[status(thm)],[497])).
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% 0.47/0.62 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z))))))),
% 0.47/0.62 inference(monotonicity,[status(thm)],[498])).
% 0.47/0.62 tff(500,plain,
% 0.47/0.62 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(z))))) = s(s(s(s(s(s(s(z))))))))),
% 0.47/0.62 inference(transitivity,[status(thm)],[499, 218])).
% 0.47/0.62 tff(501,plain,
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% 0.47/0.62 tff(502,plain,
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% 0.47/0.62 inference(monotonicity,[status(thm)],[501])).
% 0.47/0.62 tff(503,plain,
% 0.47/0.62 (~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(z)))))))),
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% 0.47/0.62 tff(504,plain,
% 0.47/0.62 (s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(z))))))),
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% 0.47/0.62 tff(505,plain,
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% 0.47/0.62 inference(unit_resolution,[status(thm)],[504, 503])).
% 0.47/0.62 tff(506,plain,(~(s(s(s(s(s(z))))) = s(s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.62 tff(507,assumption,(b(s(s(s(s(s(s(z)))))), s(s(s(z))))), introduced(assumption)).
% 0.47/0.62 tff(508,plain,
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% 0.47/0.62 tff(509,plain,
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% 0.47/0.62 inference(quant_inst,[status(thm)],[])).
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% 0.47/0.63 inference(monotonicity,[status(thm)],[513])).
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% 0.47/0.63 inference(transitivity,[status(thm)],[514, 512])).
% 0.47/0.63 tff(516,plain,
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% 0.47/0.63 inference(quant_inst,[status(thm)],[])).
% 0.47/0.63 tff(517,plain,
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% 0.47/0.63 inference(modus_ponens,[status(thm)],[516, 515])).
% 0.47/0.63 tff(518,plain,
% 0.47/0.63 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[517, 149, 507, 476, 478])).
% 0.47/0.63 tff(519,assumption,(~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 0.47/0.63 tff(520,assumption,(~(s(s(s(s(s(z))))) = s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 0.47/0.63 tff(521,plain,
% 0.47/0.63 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(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))))))) | r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(s(s(s(s(z))))))) | 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))))))))),
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% 0.47/0.63 inference(unit_resolution,[status(thm)],[524, 520, 519])).
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% 0.47/0.63 tff(527,assumption,(s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(z))))))), introduced(assumption)).
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% 0.47/0.63 tff(540,assumption,(r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))), introduced(assumption)).
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% 0.47/0.63 tff(573,plain,
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% 0.47/0.63 inference(transitivity,[status(thm)],[576, 574])).
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% 0.47/0.63 inference(quant_inst,[status(thm)],[])).
% 0.47/0.63 tff(579,plain,
% 0.47/0.63 ((~![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)))))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[578, 577])).
% 0.47/0.63 tff(580,plain,
% 0.47/0.63 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[579, 52, 569, 333])).
% 0.47/0.63 tff(581,plain,
% 0.47/0.63 (((~![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)))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(582,plain,
% 0.47/0.64 ((~![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)))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(583,plain,
% 0.47/0.64 ((~![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))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[582, 581])).
% 0.47/0.64 tff(584,plain,
% 0.47/0.64 ((s(s(s(s(s(s(z)))))) = s(z)) | b(s(s(s(s(s(s(z)))))), s(z))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[583, 69, 580])).
% 0.47/0.64 tff(585,plain,
% 0.47/0.64 (b(s(s(s(s(s(s(z)))))), s(z))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[584, 573])).
% 0.47/0.64 tff(586,plain,
% 0.47/0.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(587,plain,
% 0.47/0.64 (((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(588,plain,
% 0.47/0.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z))))),
% 0.47/0.64 inference(monotonicity,[status(thm)],[587])).
% 0.47/0.64 tff(589,plain,
% 0.47/0.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 0.47/0.64 inference(transitivity,[status(thm)],[588, 586])).
% 0.47/0.64 tff(590,plain,
% 0.47/0.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(591,plain,
% 0.47/0.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[590, 589])).
% 0.47/0.64 tff(592,plain,
% 0.47/0.64 (~b(s(s(s(s(s(s(z)))))), z)),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[591, 149, 277, 261, 585])).
% 0.47/0.64 tff(593,assumption,(~r(s(s(s(s(s(s(z)))))), z)), introduced(assumption)).
% 0.47/0.64 tff(594,assumption,(~b(s(s(s(s(s(s(z)))))), z)), introduced(assumption)).
% 0.47/0.64 tff(595,plain,
% 0.47/0.64 (((~![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))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(596,plain,
% 0.47/0.64 ((~![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))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(597,plain,
% 0.47/0.64 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = z) | b(s(s(s(s(s(s(z)))))), z) | r(s(s(s(s(s(s(z)))))), z)),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[596, 595])).
% 0.47/0.64 tff(598,plain,
% 0.47/0.64 ($false),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[597, 69, 129, 594, 593])).
% 0.47/0.64 tff(599,plain,(r(s(s(s(s(s(s(z)))))), z) | b(s(s(s(s(s(s(z)))))), z)), inference(lemma,lemma(discharge,[]))).
% 0.47/0.64 tff(600,plain,
% 0.47/0.64 (r(s(s(s(s(s(s(z)))))), z)),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[599, 592])).
% 0.47/0.64 tff(601,assumption,(r(s(s(s(s(s(s(z)))))), z)), introduced(assumption)).
% 0.47/0.64 tff(602,assumption,(r(s(s(s(s(s(s(z)))))), s(s(s(z))))), introduced(assumption)).
% 0.47/0.64 tff(603,plain,
% 0.47/0.64 (((~![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(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(s(s(z)))))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(604,plain,
% 0.47/0.64 (((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), z))) <=> ((~r(s(s(s(s(s(s(z)))))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(605,plain,
% 0.47/0.64 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))))),
% 0.47/0.64 inference(monotonicity,[status(thm)],[604])).
% 0.47/0.64 tff(606,plain,
% 0.47/0.64 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 0.47/0.64 inference(transitivity,[status(thm)],[605, 603])).
% 0.47/0.64 tff(607,plain,
% 0.47/0.64 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), z)))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(608,plain,
% 0.47/0.64 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[607, 606])).
% 0.47/0.64 tff(609,plain,
% 0.47/0.64 ($false),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[608, 52, 602, 42, 601])).
% 0.47/0.64 tff(610,plain,((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), z))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.64 tff(611,plain,
% 0.47/0.64 (~r(z, s(s(s(z))))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[610, 600, 569])).
% 0.47/0.64 tff(612,plain,
% 0.47/0.64 (b(z, s(s(s(z))))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[413, 611])).
% 0.47/0.64 tff(613,plain,
% 0.47/0.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), 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, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(614,plain,
% 0.47/0.64 (((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), z))) <=> ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(615,plain,
% 0.47/0.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 0.47/0.64 inference(monotonicity,[status(thm)],[614])).
% 0.47/0.64 tff(616,plain,
% 0.47/0.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 0.47/0.64 inference(transitivity,[status(thm)],[615, 613])).
% 0.47/0.64 tff(617,plain,
% 0.47/0.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(618,plain,
% 0.47/0.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[617, 616])).
% 0.47/0.64 tff(619,plain,
% 0.47/0.64 ($false),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[618, 149, 374, 612, 496, 476])).
% 0.47/0.64 tff(620,plain,((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.64 tff(621,plain,
% 0.47/0.64 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[620, 475, 466, 261, 468, 471, 333])).
% 0.47/0.64 tff(622,plain,
% 0.47/0.64 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[363, 621])).
% 0.47/0.64 tff(623,plain,
% 0.47/0.64 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[443, 622, 333])).
% 0.47/0.64 tff(624,plain,
% 0.47/0.64 (b(s(s(s(s(s(s(s(z))))))), z)),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[372, 621, 272])).
% 0.47/0.64 tff(625,assumption,(b(s(s(s(s(s(s(s(z))))))), z)), introduced(assumption)).
% 0.47/0.64 tff(626,plain,
% 0.47/0.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
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% 0.47/0.67 inference(rewrite,[status(thm)],[])).
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% 0.47/0.67 inference(monotonicity,[status(thm)],[859])).
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% 0.47/0.67 tff(864,plain,
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% 0.47/0.67 inference(unit_resolution,[status(thm)],[863, 52, 35, 602])).
% 0.47/0.67 tff(865,plain,
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% 0.47/0.68 inference(monotonicity,[status(thm)],[867])).
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% 0.47/0.68 inference(quant_inst,[status(thm)],[])).
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% 0.47/0.68 inference(unit_resolution,[status(thm)],[871, 149, 865, 857, 854, 851])).
% 0.47/0.68 tff(873,plain,((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.68 tff(874,plain,
% 0.47/0.68 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.47/0.68 inference(unit_resolution,[status(thm)],[873, 838, 829])).
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% 0.47/0.68 inference(unit_resolution,[status(thm)],[568, 874])).
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% 0.47/0.68 tff(877,plain,
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% 0.47/0.68 inference(quant_inst,[status(thm)],[])).
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% 0.47/0.68 inference(quant_inst,[status(thm)],[])).
% 0.47/0.68 tff(892,plain,
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% 0.47/0.68 inference(modus_ponens,[status(thm)],[891, 890])).
% 0.47/0.68 tff(893,plain,
% 0.47/0.68 ($false),
% 0.47/0.68 inference(unit_resolution,[status(thm)],[892, 52, 889, 883, 365])).
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% 0.47/0.69 inference(monotonicity,[status(thm)],[946])).
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% 0.47/0.69 inference(transitivity,[status(thm)],[947, 945])).
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% 0.47/0.69 inference(quant_inst,[status(thm)],[])).
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% 0.47/0.69 inference(unit_resolution,[status(thm)],[950, 52, 936, 933])).
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% 0.47/0.69 inference(unit_resolution,[status(thm)],[312, 951])).
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% 0.47/0.69 inference(unit_resolution,[status(thm)],[954, 165])).
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% 0.47/0.69 inference(modus_ponens,[status(thm)],[957, 956])).
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% 0.47/0.69 inference(unit_resolution,[status(thm)],[958, 69, 459])).
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% 0.47/0.69 inference(unit_resolution,[status(thm)],[959, 955])).
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% 0.47/0.69 inference(rewrite,[status(thm)],[])).
% 0.47/0.69 tff(962,plain,
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% 0.47/0.69 inference(rewrite,[status(thm)],[])).
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% 0.47/0.69 inference(unit_resolution,[status(thm)],[972, 69])).
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% 0.47/0.69 inference(unit_resolution,[status(thm)],[973, 177])).
% 0.47/0.69 tff(975,plain,
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% 0.47/0.69 inference(unit_resolution,[status(thm)],[974, 969])).
% 0.47/0.69 tff(976,plain,
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% 0.47/0.69 inference(unit_resolution,[status(thm)],[633, 167, 261, 277])).
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% 0.47/0.69 inference(rewrite,[status(thm)],[])).
% 0.47/0.69 tff(1004,plain,
% 0.47/0.69 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 0.47/0.69 inference(rewrite,[status(thm)],[])).
% 0.47/0.69 tff(1005,plain,
% 0.47/0.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(z), 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, 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)))))))),
% 0.47/0.69 inference(monotonicity,[status(thm)],[1004])).
% 0.47/0.69 tff(1006,plain,
% 0.47/0.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(z), 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, 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))))))),
% 0.47/0.69 inference(transitivity,[status(thm)],[1005, 1003])).
% 0.47/0.69 tff(1007,plain,
% 0.47/0.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(z)))))))))),
% 0.47/0.69 inference(quant_inst,[status(thm)],[])).
% 0.47/0.69 tff(1008,plain,
% 0.47/0.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 0.47/0.69 inference(modus_ponens,[status(thm)],[1007, 1006])).
% 0.47/0.69 tff(1009,plain,
% 0.47/0.69 (~b(s(z), s(s(s(s(s(s(z)))))))),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[1008, 149, 33, 180, 507])).
% 0.47/0.69 tff(1010,plain,
% 0.47/0.69 (((~![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))))))))),
% 0.47/0.69 inference(rewrite,[status(thm)],[])).
% 0.47/0.69 tff(1011,plain,
% 0.47/0.69 ((~![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))))))))),
% 0.47/0.69 inference(quant_inst,[status(thm)],[])).
% 0.47/0.69 tff(1012,plain,
% 0.47/0.69 ((~![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)))))))),
% 0.47/0.69 inference(modus_ponens,[status(thm)],[1011, 1010])).
% 0.47/0.69 tff(1013,plain,
% 0.47/0.69 (r(s(z), s(s(s(s(s(s(z)))))))),
% 0.47/0.69 inference(unit_resolution,[status(thm)],[1012, 69, 30, 1009])).
% 0.47/0.69 tff(1014,plain,
% 0.47/0.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), 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, 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(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 0.47/0.69 inference(rewrite,[status(thm)],[])).
% 0.47/0.69 tff(1015,plain,
% 0.47/0.69 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 0.47/0.69 inference(rewrite,[status(thm)],[])).
% 0.47/0.69 tff(1016,plain,
% 0.47/0.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(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, 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(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 0.47/0.69 inference(monotonicity,[status(thm)],[1015])).
% 0.47/0.69 tff(1017,plain,
% 0.47/0.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(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, 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(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 0.47/0.70 inference(transitivity,[status(thm)],[1016, 1014])).
% 0.47/0.70 tff(1018,plain,
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% 0.47/0.70 inference(quant_inst,[status(thm)],[])).
% 0.47/0.70 tff(1019,plain,
% 0.47/0.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 0.47/0.70 inference(modus_ponens,[status(thm)],[1018, 1017])).
% 0.47/0.70 tff(1020,plain,
% 0.47/0.70 (~b(s(z), s(s(s(s(s(z))))))),
% 0.47/0.70 inference(unit_resolution,[status(thm)],[1019, 149, 33, 180, 478])).
% 0.47/0.70 tff(1021,plain,
% 0.47/0.70 ((s(z) = s(s(s(s(s(z)))))) | r(s(z), s(s(s(s(s(z))))))),
% 0.47/0.70 inference(unit_resolution,[status(thm)],[215, 69, 1020])).
% 0.47/0.70 tff(1022,plain,
% 0.47/0.70 (r(s(z), s(s(s(s(s(z))))))),
% 0.47/0.70 inference(unit_resolution,[status(thm)],[1021, 178])).
% 0.47/0.70 tff(1023,plain,
% 0.47/0.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(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(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(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(s(z)))))), s(s(s(z))))))),
% 0.47/0.70 inference(rewrite,[status(thm)],[])).
% 0.47/0.70 tff(1024,plain,
% 0.47/0.70 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(z))), 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(s(s(s(z)))))), s(s(s(z))))))),
% 0.47/0.70 inference(rewrite,[status(thm)],[])).
% 0.47/0.70 tff(1025,plain,
% 0.47/0.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(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(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(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(s(z)))))), s(s(s(z)))))))),
% 0.47/0.70 inference(monotonicity,[status(thm)],[1024])).
% 0.47/0.70 tff(1026,plain,
% 0.47/0.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(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(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(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(s(z)))))), s(s(s(z))))))),
% 0.47/0.70 inference(transitivity,[status(thm)],[1025, 1023])).
% 0.47/0.70 tff(1027,plain,
% 0.47/0.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 0.47/0.70 inference(quant_inst,[status(thm)],[])).
% 0.47/0.70 tff(1028,plain,
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% 0.47/0.70 inference(modus_ponens,[status(thm)],[1027, 1026])).
% 0.47/0.70 tff(1029,plain,
% 0.47/0.70 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 0.47/0.70 inference(unit_resolution,[status(thm)],[1028, 149, 33, 507, 478])).
% 0.47/0.70 tff(1030,plain,
% 0.47/0.70 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 0.54/0.70 inference(unit_resolution,[status(thm)],[524, 1029, 506])).
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% 0.54/0.70 inference(quant_inst,[status(thm)],[])).
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% 0.54/0.70 inference(modus_ponens,[status(thm)],[1032, 1031])).
% 0.54/0.70 tff(1034,plain,
% 0.54/0.70 ($false),
% 0.54/0.70 inference(unit_resolution,[status(thm)],[1033, 52, 1030, 1022, 1013])).
% 0.54/0.70 tff(1035,plain,((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.70 tff(1036,plain,
% 0.54/0.70 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.54/0.70 inference(unit_resolution,[status(thm)],[1035, 1002, 33, 994])).
% 0.54/0.70 tff(1037,plain,
% 0.54/0.70 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.54/0.70 inference(unit_resolution,[status(thm)],[568, 1036])).
% 0.54/0.70 tff(1038,plain,
% 0.54/0.70 (~r(s(s(s(s(s(s(z)))))), z)),
% 0.54/0.70 inference(unit_resolution,[status(thm)],[610, 1037, 42])).
% 0.54/0.70 tff(1039,plain,
% 0.54/0.70 (b(s(s(s(s(s(s(z)))))), z)),
% 0.54/0.70 inference(unit_resolution,[status(thm)],[599, 1038])).
% 0.54/0.70 tff(1040,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(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(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(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))))),
% 0.54/0.70 inference(rewrite,[status(thm)],[])).
% 0.54/0.70 tff(1041,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(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))))),
% 0.54/0.70 inference(quant_inst,[status(thm)],[])).
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% 0.54/0.71 inference(quant_inst,[status(thm)],[])).
% 0.54/0.71 tff(1083,plain,
% 0.54/0.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z)))))))),
% 0.54/0.71 inference(modus_ponens,[status(thm)],[1082, 1081])).
% 0.54/0.71 tff(1084,plain,
% 0.54/0.71 (~b(s(z), s(s(s(s(s(z))))))),
% 0.54/0.71 inference(unit_resolution,[status(thm)],[1083, 149, 277, 261, 1077])).
% 0.54/0.71 tff(1085,plain,
% 0.54/0.71 ((s(z) = s(s(s(s(s(z)))))) | r(s(z), s(s(s(s(s(z))))))),
% 0.54/0.71 inference(unit_resolution,[status(thm)],[215, 69, 1084])).
% 0.54/0.71 tff(1086,plain,
% 0.54/0.71 (r(s(z), s(s(s(s(s(z))))))),
% 0.54/0.71 inference(unit_resolution,[status(thm)],[1085, 178])).
% 0.54/0.71 tff(1087,plain,
% 0.54/0.71 (((~![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(s(z))))))), s(z))) | (~r(s(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(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 0.54/0.71 inference(rewrite,[status(thm)],[])).
% 0.54/0.71 tff(1088,plain,
% 0.54/0.71 ((~![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(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))))),
% 0.54/0.71 inference(quant_inst,[status(thm)],[])).
% 0.54/0.71 tff(1089,plain,
% 0.54/0.71 ((~![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(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z)))))))),
% 0.54/0.71 inference(modus_ponens,[status(thm)],[1088, 1087])).
% 0.54/0.71 tff(1090,plain,
% 0.54/0.71 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 0.54/0.71 inference(unit_resolution,[status(thm)],[1089, 52, 980, 975])).
% 0.54/0.71 tff(1091,plain,
% 0.54/0.71 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))) | b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 0.54/0.71 inference(unit_resolution,[status(thm)],[228, 69, 1090])).
% 0.54/0.71 tff(1092,plain,
% 0.54/0.71 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 0.54/0.71 inference(unit_resolution,[status(thm)],[1091, 221])).
% 0.54/0.71 tff(1093,plain,
% 0.54/0.71 (~r(z, s(s(s(s(s(z))))))),
% 0.54/0.71 inference(unit_resolution,[status(thm)],[950, 52, 1061, 968])).
% 0.54/0.71 tff(1094,plain,
% 0.54/0.71 (b(z, s(s(s(s(s(z))))))),
% 0.54/0.71 inference(unit_resolution,[status(thm)],[312, 1093])).
% 0.54/0.71 tff(1095,plain,
% 0.54/0.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(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, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))))),
% 0.54/0.71 inference(rewrite,[status(thm)],[])).
% 0.54/0.71 tff(1096,plain,
% 0.54/0.71 (((~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))) <=> ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))))),
% 0.54/0.71 inference(rewrite,[status(thm)],[])).
% 0.54/0.71 tff(1097,plain,
% 0.54/0.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z)))))))))),
% 0.54/0.71 inference(monotonicity,[status(thm)],[1096])).
% 0.54/0.71 tff(1098,plain,
% 0.54/0.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))))),
% 0.54/0.71 inference(transitivity,[status(thm)],[1097, 1095])).
% 0.54/0.71 tff(1099,plain,
% 0.54/0.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 0.54/0.71 inference(quant_inst,[status(thm)],[])).
% 0.54/0.71 tff(1100,plain,
% 0.54/0.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z)))))))),
% 0.54/0.71 inference(modus_ponens,[status(thm)],[1099, 1098])).
% 0.54/0.71 tff(1101,plain,
% 0.54/0.71 (~b(s(s(s(s(s(s(s(z))))))), z)),
% 0.54/0.71 inference(unit_resolution,[status(thm)],[1100, 149, 1094, 1077, 1092])).
% 0.54/0.71 tff(1102,plain,
% 0.54/0.71 (r(s(s(s(s(s(s(s(z))))))), z)),
% 0.54/0.71 inference(unit_resolution,[status(thm)],[88, 1101])).
% 0.54/0.71 tff(1103,plain,
% 0.54/0.71 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(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(s(z))))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 0.54/0.71 inference(rewrite,[status(thm)],[])).
% 0.54/0.71 tff(1104,plain,
% 0.54/0.71 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))))),
% 0.54/0.71 inference(quant_inst,[status(thm)],[])).
% 0.54/0.71 tff(1105,plain,
% 0.54/0.71 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(z)))))))))),
% 0.54/0.71 inference(modus_ponens,[status(thm)],[1104, 1103])).
% 0.54/0.71 tff(1106,plain,
% 0.54/0.71 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 0.54/0.71 inference(unit_resolution,[status(thm)],[1105, 52, 334, 1102])).
% 0.54/0.71 tff(1107,plain,
% 0.54/0.71 ((s(s(s(z))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 0.54/0.71 inference(unit_resolution,[status(thm)],[806, 69, 1106])).
% 0.54/0.71 tff(1108,plain,
% 0.54/0.71 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 0.54/0.71 inference(unit_resolution,[status(thm)],[1107, 799])).
% 0.54/0.71 tff(1109,plain,
% 0.54/0.71 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 0.54/0.71 inference(unit_resolution,[status(thm)],[814, 149, 1050, 991, 1108])).
% 0.54/0.71 tff(1110,plain,
% 0.54/0.71 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 0.54/0.71 inference(unit_resolution,[status(thm)],[331, 1109])).
% 0.54/0.71 tff(1111,plain,
% 0.54/0.71 (((~![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(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(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 0.54/0.71 inference(rewrite,[status(thm)],[])).
% 0.54/0.71 tff(1112,plain,
% 0.54/0.71 (((~r(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(z)))))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 0.54/0.71 inference(rewrite,[status(thm)],[])).
% 0.54/0.71 tff(1113,plain,
% 0.54/0.71 (((~![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(z))))))) | (~r(s(z), s(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(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 0.54/0.71 inference(monotonicity,[status(thm)],[1112])).
% 0.54/0.71 tff(1114,plain,
% 0.54/0.71 (((~![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(z))))))) | (~r(s(z), s(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(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 0.54/0.71 inference(transitivity,[status(thm)],[1113, 1111])).
% 0.54/0.71 tff(1115,plain,
% 0.54/0.71 ((~![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(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(z))))))),
% 0.54/0.71 inference(quant_inst,[status(thm)],[])).
% 0.54/0.71 tff(1116,plain,
% 0.54/0.71 ((~![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(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 0.54/0.71 inference(modus_ponens,[status(thm)],[1115, 1114])).
% 0.54/0.71 tff(1117,plain,
% 0.54/0.71 (~r(s(z), s(s(s(z))))),
% 0.54/0.71 inference(unit_resolution,[status(thm)],[1116, 52, 1110, 1086])).
% 0.54/0.71 tff(1118,plain,
% 0.54/0.71 (b(s(z), s(s(s(z))))),
% 0.54/0.71 inference(unit_resolution,[status(thm)],[204, 1117])).
% 0.54/0.71 tff(1119,plain,
% 0.54/0.71 (~b(s(z), s(s(s(s(s(s(z)))))))),
% 0.54/0.71 inference(unit_resolution,[status(thm)],[1008, 149, 33, 1118, 1075])).
% 0.54/0.71 tff(1120,plain,
% 0.54/0.71 (r(s(z), s(s(s(s(s(s(z)))))))),
% 0.54/0.71 inference(unit_resolution,[status(thm)],[1012, 69, 30, 1119])).
% 0.54/0.71 tff(1121,plain,
% 0.54/0.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 0.54/0.71 inference(rewrite,[status(thm)],[])).
% 0.54/0.71 tff(1122,plain,
% 0.54/0.71 (((~b(s(s(s(z))), s(z))) | (~b(s(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(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(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 0.54/0.71 inference(rewrite,[status(thm)],[])).
% 0.54/0.71 tff(1123,plain,
% 0.54/0.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))))),
% 0.54/0.71 inference(monotonicity,[status(thm)],[1122])).
% 0.54/0.71 tff(1124,plain,
% 0.54/0.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 0.54/0.71 inference(transitivity,[status(thm)],[1123, 1121])).
% 0.54/0.71 tff(1125,plain,
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% 0.54/0.71 inference(quant_inst,[status(thm)],[])).
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% 0.54/0.71 tff(1128,plain,
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% 0.54/0.71 inference(unit_resolution,[status(thm)],[672, 69, 1127])).
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% 0.54/0.71 inference(quant_inst,[status(thm)],[])).
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% 0.54/0.71 inference(monotonicity,[status(thm)],[1136])).
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% 0.54/0.71 inference(transitivity,[status(thm)],[1137, 1135])).
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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)],[1139, 1138])).
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% 0.54/0.71 inference(unit_resolution,[status(thm)],[1140, 52, 1134, 1129, 1120])).
% 0.54/0.71 tff(1142,plain,((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.71 tff(1143,plain,
% 0.54/0.71 (~b(z, s(z))),
% 0.54/0.71 inference(unit_resolution,[status(thm)],[1142, 334, 33, 261])).
% 0.54/0.71 tff(1144,plain,
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% 0.54/0.71 inference(unit_resolution,[status(thm)],[465, 1143])).
% 0.54/0.71 tff(1145,plain,
% 0.54/0.71 (b(s(s(s(s(s(s(s(z))))))), z)),
% 0.54/0.71 inference(unit_resolution,[status(thm)],[394, 1144, 261, 334])).
% 0.54/0.71 tff(1146,plain,
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% 0.54/0.71 inference(rewrite,[status(thm)],[])).
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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)],[1147, 1146])).
% 0.54/0.71 tff(1149,plain,
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% 0.54/0.71 tff(1153,plain,
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% 0.54/0.71 inference(monotonicity,[status(thm)],[1152])).
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% 0.54/0.72 inference(transitivity,[status(thm)],[1153, 1151])).
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% 0.54/0.72 tff(1160,plain,
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% 0.54/0.72 tff(1161,plain,
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% 0.54/0.72 inference(unit_resolution,[status(thm)],[392, 52, 335, 435])).
% 0.54/0.72 tff(1162,plain,
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% 0.54/0.72 inference(unit_resolution,[status(thm)],[86, 69, 40, 1161])).
% 0.54/0.72 tff(1163,plain,
% 0.54/0.72 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[987, 52, 435, 981])).
% 0.54/0.72 tff(1164,plain,
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% 0.54/0.72 tff(1165,plain,
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% 0.54/0.72 tff(1166,plain,
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% 0.54/0.72 inference(rewrite,[status(thm)],[])).
% 0.54/0.72 tff(1167,plain,
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% 0.54/0.72 inference(monotonicity,[status(thm)],[1166])).
% 0.54/0.72 tff(1168,plain,
% 0.54/0.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(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(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(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(s(z))))))))) | (~b(z, s(s(s(s(s(z))))))))),
% 0.54/0.72 inference(transitivity,[status(thm)],[1167, 1165])).
% 0.54/0.72 tff(1169,plain,
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% 0.54/0.72 inference(quant_inst,[status(thm)],[])).
% 0.54/0.72 tff(1170,plain,
% 0.54/0.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(z)))))))),
% 0.54/0.72 inference(modus_ponens,[status(thm)],[1169, 1168])).
% 0.54/0.72 tff(1171,plain,
% 0.54/0.72 ($false),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[1170, 149, 1164, 292, 1162, 1160])).
% 0.54/0.72 tff(1172,plain,((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.72 tff(1173,plain,
% 0.54/0.72 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[1172, 1158, 975, 1144])).
% 0.54/0.72 tff(1174,plain,
% 0.54/0.72 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[385, 1173])).
% 0.54/0.72 tff(1175,plain,
% 0.54/0.72 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[379, 1174, 33, 261])).
% 0.54/0.72 tff(1176,plain,
% 0.54/0.72 (r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[363, 1175])).
% 0.54/0.72 tff(1177,plain,
% 0.54/0.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(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(s(z))))))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(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(s(z))))))))) | (~b(z, s(s(s(s(s(z))))))))),
% 0.54/0.72 inference(rewrite,[status(thm)],[])).
% 0.54/0.72 tff(1178,plain,
% 0.54/0.72 (((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), z))) <=> ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(z))))))))),
% 0.54/0.72 inference(rewrite,[status(thm)],[])).
% 0.54/0.72 tff(1179,plain,
% 0.54/0.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(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(s(z))))))))) | (~b(z, s(s(s(s(s(z)))))))))),
% 0.54/0.72 inference(monotonicity,[status(thm)],[1178])).
% 0.54/0.72 tff(1180,plain,
% 0.54/0.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(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(s(z))))))))) | (~b(z, s(s(s(s(s(z))))))))),
% 0.54/0.72 inference(transitivity,[status(thm)],[1179, 1177])).
% 0.54/0.72 tff(1181,plain,
% 0.54/0.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)))),
% 0.54/0.72 inference(quant_inst,[status(thm)],[])).
% 0.54/0.72 tff(1182,plain,
% 0.54/0.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(z, s(s(s(s(s(z)))))))),
% 0.54/0.72 inference(modus_ponens,[status(thm)],[1181, 1180])).
% 0.54/0.72 tff(1183,plain,
% 0.54/0.72 ($false),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[1182, 149, 139, 292, 625, 230])).
% 0.54/0.72 tff(1184,plain,((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.72 tff(1185,plain,
% 0.54/0.72 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[1184, 1158, 1145, 1176])).
% 0.54/0.72 tff(1186,plain,
% 0.54/0.72 ((s(s(s(s(s(z))))) = s(s(s(z)))) | b(s(s(s(s(s(z))))), s(s(s(z))))),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[257, 69, 1185])).
% 0.54/0.72 tff(1187,plain,
% 0.54/0.72 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[1186, 276])).
% 0.54/0.72 tff(1188,plain,
% 0.54/0.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), 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(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), 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(z))))))),
% 0.54/0.72 inference(rewrite,[status(thm)],[])).
% 0.54/0.72 tff(1189,plain,
% 0.54/0.72 (((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(s(s(s(z))), 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(z))))))),
% 0.54/0.72 inference(rewrite,[status(thm)],[])).
% 0.54/0.72 tff(1190,plain,
% 0.54/0.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), 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(z)))))))),
% 0.54/0.72 inference(monotonicity,[status(thm)],[1189])).
% 0.54/0.72 tff(1191,plain,
% 0.54/0.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), 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(z))))))),
% 0.54/0.72 inference(transitivity,[status(thm)],[1190, 1188])).
% 0.54/0.72 tff(1192,plain,
% 0.54/0.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)))),
% 0.54/0.72 inference(quant_inst,[status(thm)],[])).
% 0.54/0.72 tff(1193,plain,
% 0.54/0.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 0.54/0.72 inference(modus_ponens,[status(thm)],[1192, 1191])).
% 0.54/0.72 tff(1194,plain,
% 0.54/0.72 ($false),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[1193, 149, 33, 166, 715, 478])).
% 0.54/0.72 tff(1195,plain,((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.72 tff(1196,plain,
% 0.54/0.72 (~b(z, s(s(s(z))))),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[1195, 1187, 33, 1150])).
% 0.54/0.72 tff(1197,plain,
% 0.54/0.72 (r(z, s(s(s(z))))),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[413, 1196])).
% 0.54/0.72 tff(1198,plain,
% 0.54/0.72 (~r(s(z), s(s(s(z))))),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[403, 1197, 1144])).
% 0.54/0.72 tff(1199,plain,
% 0.54/0.72 (b(s(z), s(s(s(z))))),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[204, 1198])).
% 0.54/0.72 tff(1200,plain,
% 0.54/0.72 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[1035, 1199, 33, 1187])).
% 0.54/0.72 tff(1201,plain,
% 0.54/0.72 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[568, 1200])).
% 0.54/0.72 tff(1202,plain,
% 0.54/0.72 (~r(s(s(s(s(s(s(z)))))), z)),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[610, 1201, 1197])).
% 0.54/0.72 tff(1203,plain,
% 0.54/0.72 (b(s(s(s(s(s(s(z)))))), z)),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[599, 1202])).
% 0.54/0.72 tff(1204,plain,
% 0.54/0.72 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[1042, 52, 1201, 1176])).
% 0.54/0.72 tff(1205,plain,
% 0.54/0.72 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[537, 1204, 884])).
% 0.54/0.72 tff(1206,plain,
% 0.54/0.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))))),
% 0.54/0.72 inference(rewrite,[status(thm)],[])).
% 0.54/0.72 tff(1207,plain,
% 0.54/0.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))))),
% 0.54/0.72 inference(quant_inst,[status(thm)],[])).
% 0.54/0.72 tff(1208,plain,
% 0.54/0.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z))))))))),
% 0.54/0.72 inference(modus_ponens,[status(thm)],[1207, 1206])).
% 0.54/0.72 tff(1209,plain,
% 0.54/0.72 ($false),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[1208, 149, 1205, 1158, 1203, 1145])).
% 0.54/0.72 tff(1210,plain,((~r(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.72 tff(1211,plain,
% 0.54/0.72 (~r(s(s(s(z))), z)),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[1210, 33, 261])).
% 0.54/0.72 tff(1212,plain,
% 0.54/0.72 (b(s(s(s(z))), z)),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[271, 69, 268, 1211])).
% 0.54/0.72 tff(1213,plain,
% 0.54/0.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))))),
% 0.54/0.72 inference(rewrite,[status(thm)],[])).
% 0.54/0.72 tff(1214,plain,
% 0.54/0.72 (((~b(z, s(s(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))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))))),
% 0.54/0.72 inference(rewrite,[status(thm)],[])).
% 0.54/0.72 tff(1215,plain,
% 0.54/0.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(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, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z)))))))))),
% 0.54/0.72 inference(monotonicity,[status(thm)],[1214])).
% 0.54/0.72 tff(1216,plain,
% 0.54/0.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(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, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))))),
% 0.54/0.72 inference(transitivity,[status(thm)],[1215, 1213])).
% 0.54/0.72 tff(1217,plain,
% 0.54/0.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 0.54/0.72 inference(quant_inst,[status(thm)],[])).
% 0.54/0.72 tff(1218,plain,
% 0.54/0.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z)))))))),
% 0.54/0.72 inference(modus_ponens,[status(thm)],[1217, 1216])).
% 0.54/0.72 tff(1219,plain,
% 0.54/0.72 ($false),
% 0.54/0.72 inference(unit_resolution,[status(thm)],[1218, 149, 261, 33, 1212, 292])).
% 0.54/0.72 tff(1220,plain,((~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.73 tff(1221,plain,
% 0.54/0.73 (~b(z, s(s(s(s(s(z))))))),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[1220, 33, 261])).
% 0.54/0.73 tff(1222,plain,
% 0.54/0.73 (r(z, s(s(s(s(s(z))))))),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[312, 1221])).
% 0.54/0.73 tff(1223,plain,
% 0.54/0.73 ($false),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[1156, 52, 335, 981, 314])).
% 0.54/0.73 tff(1224,plain,((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.73 tff(1225,plain,
% 0.54/0.73 (~r(z, s(z))),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[1224, 1222, 975])).
% 0.54/0.73 tff(1226,plain,
% 0.54/0.73 (b(z, s(z))),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[465, 1225])).
% 0.54/0.73 tff(1227,plain,
% 0.54/0.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(1228,plain,
% 0.54/0.73 (((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z))) <=> ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(1229,plain,
% 0.54/0.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z))))),
% 0.54/0.73 inference(monotonicity,[status(thm)],[1228])).
% 0.54/0.73 tff(1230,plain,
% 0.54/0.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)))),
% 0.54/0.73 inference(transitivity,[status(thm)],[1229, 1227])).
% 0.54/0.73 tff(1231,plain,
% 0.54/0.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 0.54/0.73 inference(quant_inst,[status(thm)],[])).
% 0.54/0.73 tff(1232,plain,
% 0.54/0.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[1231, 1230])).
% 0.54/0.73 tff(1233,plain,
% 0.54/0.73 ($false),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[1232, 149, 1226, 261, 33, 1212])).
% 0.54/0.73 tff(1234,plain,((~b(s(s(s(z))), s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.73 tff(1235,plain,
% 0.54/0.73 (~b(s(z), z)),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[1234, 33])).
% 0.54/0.73 tff(1236,plain,
% 0.54/0.73 (r(s(z), z)),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[959, 1235])).
% 0.54/0.73 tff(1237,assumption,(r(s(z), z)), introduced(assumption)).
% 0.54/0.73 tff(1238,plain,
% 0.54/0.73 (((~![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), 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), s(s(s(z))))) | (~r(s(z), z)) | (~r(z, s(s(s(z))))))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(1239,plain,
% 0.54/0.73 (((~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(z), z)) | (~r(z, s(s(s(z))))))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(1240,plain,
% 0.54/0.73 (((~![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), s(s(s(z))))) | (~r(s(z), z)) | (~r(z, s(s(s(z)))))))),
% 0.54/0.73 inference(monotonicity,[status(thm)],[1239])).
% 0.54/0.73 tff(1241,plain,
% 0.54/0.73 (((~![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), s(s(s(z))))) | (~r(s(z), z)) | (~r(z, s(s(s(z))))))),
% 0.54/0.73 inference(transitivity,[status(thm)],[1240, 1238])).
% 0.54/0.73 tff(1242,plain,
% 0.54/0.73 ((~![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)))),
% 0.54/0.73 inference(quant_inst,[status(thm)],[])).
% 0.54/0.73 tff(1243,plain,
% 0.54/0.73 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)) | (~r(z, s(s(s(z)))))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[1242, 1241])).
% 0.54/0.73 tff(1244,plain,
% 0.54/0.73 ($false),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[1243, 52, 1237, 42, 333])).
% 0.54/0.73 tff(1245,plain,((~r(s(z), s(s(s(z))))) | (~r(s(z), z)) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.73 tff(1246,plain,
% 0.54/0.73 (~r(s(z), s(s(s(z))))),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[1245, 42, 1236])).
% 0.54/0.73 tff(1247,plain,
% 0.54/0.73 (b(s(z), s(s(s(z))))),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[204, 1246])).
% 0.54/0.73 tff(1248,plain,
% 0.54/0.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), 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, 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(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(1249,plain,
% 0.54/0.73 (((~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(s(s(s(s(z))))), s(z)))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(1250,plain,
% 0.54/0.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), 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, 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(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 0.54/0.73 inference(monotonicity,[status(thm)],[1249])).
% 0.54/0.73 tff(1251,plain,
% 0.54/0.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), 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, 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(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 0.54/0.73 inference(transitivity,[status(thm)],[1250, 1248])).
% 0.54/0.73 tff(1252,plain,
% 0.54/0.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 0.54/0.73 inference(quant_inst,[status(thm)],[])).
% 0.54/0.73 tff(1253,plain,
% 0.54/0.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[1252, 1251])).
% 0.54/0.73 tff(1254,plain,
% 0.54/0.73 (~b(s(s(s(s(s(z))))), s(z))),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[1253, 149, 33, 1247, 478])).
% 0.54/0.73 tff(1255,plain,
% 0.54/0.73 (r(s(s(s(s(s(z))))), s(z))),
% 0.54/0.73 inference(unit_resolution,[status(thm)],[974, 1254])).
% 0.54/0.73 tff(1256,plain,
% 0.54/0.73 ((s(s(s(s(s(s(z)))))) = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(z)))))))),
% 0.54/0.73 inference(commutativity,[status(thm)],[])).
% 0.54/0.73 tff(1257,plain,
% 0.54/0.73 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(z)))))) = s(s(s(s(s(s(s(z))))))))),
% 0.54/0.73 inference(symmetry,[status(thm)],[1256])).
% 0.54/0.73 tff(1258,plain,
% 0.54/0.73 ((~(s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(s(s(s(s(z)))))) = s(s(s(s(s(s(s(z)))))))))),
% 0.54/0.73 inference(monotonicity,[status(thm)],[1257])).
% 0.54/0.73 tff(1259,plain,
% 0.54/0.73 (~(s(s(s(s(s(s(z)))))) = s(s(s(s(s(s(s(z))))))))),
% 0.54/0.73 inference(modus_ponens,[status(thm)],[884, 1258])).
% 0.54/0.73 tff(1260,plain,
% 0.54/0.73 (((~![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(s(z))))))))) | (~r(s(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(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(1261,plain,
% 0.54/0.73 (((~r(s(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(s(z)))))))))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(1262,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(s(z))))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(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(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))))),
% 0.54/0.73 inference(monotonicity,[status(thm)],[1261])).
% 0.54/0.73 tff(1263,plain,
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% 0.54/0.74 tff(1329,plain,
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% 0.54/0.74 inference(unit_resolution,[status(thm)],[413, 1332])).
% 0.54/0.74 tff(1334,plain,
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% 0.54/0.74 tff(1335,plain,
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% 0.54/0.74 tff(1354,plain,
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% 0.54/0.74 tff(1360,plain,
% 0.54/0.74 (~r(z, s(z))),
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% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(1363,plain,
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% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(1364,plain,
% 0.54/0.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))))),
% 0.54/0.74 inference(monotonicity,[status(thm)],[1363])).
% 0.54/0.74 tff(1365,plain,
% 0.54/0.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 0.54/0.74 inference(transitivity,[status(thm)],[1364, 1362])).
% 0.54/0.74 tff(1366,plain,
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% 0.54/0.74 inference(quant_inst,[status(thm)],[])).
% 0.54/0.74 tff(1367,plain,
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% 0.54/0.74 inference(modus_ponens,[status(thm)],[1366, 1365])).
% 0.54/0.74 tff(1368,plain,
% 0.54/0.74 ($false),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[1367, 149, 277, 180, 167, 625])).
% 0.54/0.74 tff(1369,plain,((~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.74 tff(1370,plain,
% 0.54/0.74 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[1369, 992, 277, 1247])).
% 0.54/0.74 tff(1371,plain,
% 0.54/0.74 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[385, 1370])).
% 0.54/0.74 tff(1372,plain,
% 0.54/0.74 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[989, 1371, 981])).
% 0.54/0.74 tff(1373,plain,
% 0.54/0.74 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[1049, 1371, 33, 277, 42, 334, 351])).
% 0.54/0.74 tff(1374,plain,
% 0.54/0.74 ($false),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[138, 1373, 1372])).
% 0.54/0.74 tff(1375,plain,(b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.74 tff(1376,plain,
% 0.54/0.74 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[1375, 42, 1361, 33, 272, 1255])).
% 0.54/0.74 tff(1377,plain,
% 0.54/0.74 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[1058, 1376, 478, 33])).
% 0.54/0.74 tff(1378,plain,
% 0.54/0.74 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[138, 1377])).
% 0.54/0.74 tff(1379,plain,
% 0.54/0.74 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[989, 1378, 1255])).
% 0.54/0.74 tff(1380,plain,
% 0.54/0.74 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[385, 1379])).
% 0.54/0.74 tff(1381,plain,
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% 0.54/0.74 inference(unit_resolution,[status(thm)],[1341, 149, 33, 1247, 1376, 1380])).
% 0.54/0.74 tff(1382,plain,((~r(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | b(s(s(s(z))), z)), inference(lemma,lemma(discharge,[]))).
% 0.54/0.74 tff(1383,plain,
% 0.54/0.74 (~r(z, s(s(s(z))))),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[1382, 33, 478, 266])).
% 0.54/0.74 tff(1384,plain,
% 0.54/0.74 (b(z, s(s(s(z))))),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[413, 1383])).
% 0.54/0.74 tff(1385,plain,
% 0.54/0.74 (~b(z, s(s(s(s(s(z))))))),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[1276, 149, 33, 1384, 478])).
% 0.54/0.74 tff(1386,plain,
% 0.54/0.74 (r(z, s(s(s(s(s(z))))))),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[312, 1385])).
% 0.54/0.74 tff(1387,plain,
% 0.54/0.74 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[323, 1386, 266])).
% 0.54/0.75 tff(1388,plain,
% 0.54/0.75 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[331, 1387])).
% 0.54/0.75 tff(1389,plain,
% 0.54/0.75 (((~![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), z)) | (~r(s(s(s(z))), 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), z)) | (~r(s(s(s(z))), z)))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(1390,plain,
% 0.54/0.75 (((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(1391,plain,
% 0.54/0.75 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(z))), z))))),
% 0.54/0.75 inference(monotonicity,[status(thm)],[1390])).
% 0.54/0.75 tff(1392,plain,
% 0.54/0.75 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)))),
% 0.54/0.75 inference(transitivity,[status(thm)],[1391, 1389])).
% 0.54/0.75 tff(1393,plain,
% 0.54/0.75 ((~![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))))))),
% 0.54/0.75 inference(quant_inst,[status(thm)],[])).
% 0.54/0.75 tff(1394,plain,
% 0.54/0.75 ((~![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), z)) | (~r(s(s(s(z))), z))),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[1393, 1392])).
% 0.54/0.75 tff(1395,plain,
% 0.54/0.75 (~r(s(z), s(s(s(z))))),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[1394, 52, 1236, 272])).
% 0.54/0.75 tff(1396,plain,
% 0.54/0.75 (b(s(z), s(s(s(z))))),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[204, 1395])).
% 0.54/0.75 tff(1397,plain,
% 0.54/0.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, 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, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(1398,plain,
% 0.54/0.75 (((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(1399,plain,
% 0.54/0.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), 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, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 0.54/0.75 inference(monotonicity,[status(thm)],[1398])).
% 0.54/0.75 tff(1400,plain,
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% 0.54/0.75 inference(transitivity,[status(thm)],[1399, 1397])).
% 0.54/0.75 tff(1401,plain,
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% 0.54/0.75 inference(quant_inst,[status(thm)],[])).
% 0.54/0.75 tff(1402,plain,
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% 0.54/0.75 inference(modus_ponens,[status(thm)],[1401, 1400])).
% 0.54/0.75 tff(1403,plain,
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% 0.54/0.75 inference(unit_resolution,[status(thm)],[1402, 149, 1361, 1396, 1384, 1388])).
% 0.54/0.75 tff(1404,plain,((~b(s(s(s(z))), s(z))) | b(s(s(s(z))), z) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.75 tff(1405,plain,
% 0.54/0.75 (~b(s(s(s(z))), s(z))),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[1404, 478, 266])).
% 0.54/0.75 tff(1406,plain,
% 0.54/0.75 (r(s(s(s(z))), s(z))),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[348, 1405])).
% 0.54/0.75 tff(1407,plain,
% 0.54/0.75 (((~![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))))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(1408,plain,
% 0.54/0.75 ((~![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))))),
% 0.54/0.75 inference(quant_inst,[status(thm)],[])).
% 0.54/0.75 tff(1409,plain,
% 0.54/0.75 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[1408, 1407])).
% 0.54/0.75 tff(1410,plain,
% 0.54/0.75 ($false),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[1409, 52, 1237, 337, 334])).
% 0.54/0.75 tff(1411,plain,((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.75 tff(1412,plain,
% 0.54/0.75 (~r(s(z), z)),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[1411, 272, 1406])).
% 0.54/0.75 tff(1413,plain,
% 0.54/0.75 (b(s(z), z)),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[959, 1412])).
% 0.54/0.75 tff(1414,plain,
% 0.54/0.75 (~b(s(s(s(s(s(z))))), s(z))),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[954, 1413])).
% 0.54/0.75 tff(1415,plain,
% 0.54/0.75 (r(s(s(s(s(s(z))))), s(z))),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[974, 1414])).
% 0.54/0.75 tff(1416,plain,
% 0.54/0.75 (((~![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(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(1417,plain,
% 0.54/0.75 (((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
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% 0.54/0.75 inference(transitivity,[status(thm)],[1470, 1468])).
% 0.54/0.75 tff(1472,plain,
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% 0.54/0.75 inference(quant_inst,[status(thm)],[])).
% 0.54/0.75 tff(1473,plain,
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% 0.54/0.75 inference(modus_ponens,[status(thm)],[1472, 1471])).
% 0.54/0.75 tff(1474,plain,
% 0.54/0.75 ($false),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[1473, 149, 261, 1467, 1466, 292])).
% 0.54/0.75 tff(1475,plain,((~b(z, s(s(s(s(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))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.75 tff(1476,plain,
% 0.54/0.75 (~b(s(z), s(s(s(s(s(s(z)))))))),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[1475, 1465, 1413, 1449])).
% 0.54/0.76 tff(1477,plain,
% 0.54/0.76 (r(s(z), s(s(s(s(s(s(z)))))))),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[1012, 69, 30, 1476])).
% 0.54/0.76 tff(1478,plain,
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% 0.54/0.76 inference(rewrite,[status(thm)],[])).
% 0.54/0.76 tff(1479,plain,
% 0.54/0.76 (((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z)))))))) <=> ((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))))),
% 0.54/0.76 inference(rewrite,[status(thm)],[])).
% 0.54/0.76 tff(1480,plain,
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% 0.54/0.76 inference(monotonicity,[status(thm)],[1479])).
% 0.54/0.76 tff(1481,plain,
% 0.54/0.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))))),
% 0.54/0.76 inference(transitivity,[status(thm)],[1480, 1478])).
% 0.54/0.76 tff(1482,plain,
% 0.54/0.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))))),
% 0.54/0.76 inference(quant_inst,[status(thm)],[])).
% 0.54/0.76 tff(1483,plain,
% 0.54/0.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z)))))))),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[1482, 1481])).
% 0.54/0.76 tff(1484,plain,
% 0.54/0.76 (~b(s(z), s(s(s(s(s(z))))))),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[1483, 149, 1413, 1449, 1455])).
% 0.54/0.76 tff(1485,plain,
% 0.54/0.76 ((s(z) = s(s(s(s(s(z)))))) | r(s(z), s(s(s(s(s(z))))))),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[215, 69, 1484])).
% 0.54/0.76 tff(1486,plain,
% 0.54/0.76 (r(s(z), s(s(s(s(s(z))))))),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[1485, 178])).
% 0.54/0.76 tff(1487,plain,
% 0.54/0.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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))))))))),
% 0.54/0.76 inference(rewrite,[status(thm)],[])).
% 0.54/0.76 tff(1488,plain,
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% 0.54/0.76 inference(quant_inst,[status(thm)],[])).
% 0.54/0.76 tff(1489,plain,
% 0.54/0.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))))),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[1488, 1487])).
% 0.54/0.76 tff(1490,plain,
% 0.54/0.76 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[1489, 149, 1438, 1465, 1455])).
% 0.54/0.76 tff(1491,assumption,(s(s(s(s(s(s(z)))))) = s(s(s(s(s(z)))))), introduced(assumption)).
% 0.54/0.76 tff(1492,plain,
% 0.54/0.76 (s(s(s(s(s(z))))) = s(s(s(s(s(s(z))))))),
% 0.54/0.76 inference(symmetry,[status(thm)],[1491])).
% 0.54/0.76 tff(1493,plain,
% 0.54/0.76 ($false),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[506, 1492])).
% 0.54/0.76 tff(1494,plain,(~(s(s(s(s(s(s(z)))))) = s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.76 tff(1495,plain,
% 0.54/0.76 (r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[849, 69, 1494, 1490])).
% 0.54/0.76 tff(1496,plain,
% 0.54/0.76 (((~![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(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(s(s(s(s(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(z))))))))),
% 0.54/0.76 inference(rewrite,[status(thm)],[])).
% 0.54/0.76 tff(1497,plain,
% 0.54/0.76 (((~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(s(s(s(s(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(z))))))))),
% 0.54/0.76 inference(rewrite,[status(thm)],[])).
% 0.54/0.76 tff(1498,plain,
% 0.54/0.76 (((~![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(s(s(s(s(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(z)))))))))),
% 0.54/0.76 inference(monotonicity,[status(thm)],[1497])).
% 0.54/0.76 tff(1499,plain,
% 0.54/0.76 (((~![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(s(s(s(s(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(z))))))))),
% 0.54/0.76 inference(transitivity,[status(thm)],[1498, 1496])).
% 0.54/0.76 tff(1500,plain,
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% 0.54/0.76 inference(quant_inst,[status(thm)],[])).
% 0.54/0.76 tff(1501,plain,
% 0.54/0.76 ((~![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(s(z)))))))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[1500, 1499])).
% 0.54/0.76 tff(1502,plain,
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% 0.54/0.76 inference(unit_resolution,[status(thm)],[1501, 52, 1495, 1486, 1477])).
% 0.54/0.76 tff(1503,plain,((~b(s(s(s(s(s(z))))), s(s(s(z))))) | b(s(s(s(z))), z)), inference(lemma,lemma(discharge,[]))).
% 0.54/0.76 tff(1504,plain,
% 0.54/0.76 (b(s(s(s(z))), z)),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[1503, 260])).
% 0.54/0.76 tff(1505,plain,
% 0.54/0.76 (~b(s(s(s(s(s(z))))), z)),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[752, 1504, 166, 260])).
% 0.54/0.76 tff(1506,plain,
% 0.54/0.76 (r(s(s(s(s(s(z))))), z)),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[163, 1505])).
% 0.54/0.76 tff(1507,plain,
% 0.54/0.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))),
% 0.54/0.76 inference(rewrite,[status(thm)],[])).
% 0.54/0.76 tff(1508,plain,
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% 0.54/0.76 inference(quant_inst,[status(thm)],[])).
% 0.54/0.76 tff(1509,plain,
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% 0.54/0.76 inference(modus_ponens,[status(thm)],[1508, 1507])).
% 0.54/0.76 tff(1510,plain,
% 0.54/0.76 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[1509, 149, 744, 507, 478])).
% 0.54/0.76 tff(1511,plain,
% 0.54/0.76 (~b(s(s(s(s(s(s(z)))))), z)),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[881, 149, 744, 507, 166])).
% 0.54/0.76 tff(1512,plain,
% 0.54/0.76 (r(s(s(s(s(s(s(z)))))), z)),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[599, 1511])).
% 0.54/0.76 tff(1513,assumption,(r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))), introduced(assumption)).
% 0.54/0.76 tff(1514,plain,
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% 0.54/0.76 inference(rewrite,[status(thm)],[])).
% 0.54/0.76 tff(1515,plain,
% 0.54/0.76 (((~r(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)))))), z))) <=> ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))),
% 0.54/0.76 inference(rewrite,[status(thm)],[])).
% 0.54/0.76 tff(1516,plain,
% 0.54/0.76 (((~![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(s(s(z)))))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))))))),
% 0.54/0.76 inference(monotonicity,[status(thm)],[1515])).
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% 0.54/0.77 inference(rewrite,[status(thm)],[])).
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% 0.54/0.77 inference(monotonicity,[status(thm)],[1559])).
% 0.54/0.77 tff(1561,plain,
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% 0.54/0.77 inference(transitivity,[status(thm)],[1560, 1558])).
% 0.54/0.77 tff(1562,plain,
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% 0.54/0.77 inference(modus_ponens,[status(thm)],[1562, 1561])).
% 0.54/0.77 tff(1564,plain,
% 0.54/0.77 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 0.54/0.77 inference(unit_resolution,[status(thm)],[1563, 52, 1546, 1557])).
% 0.54/0.77 tff(1565,plain,
% 0.54/0.77 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 0.54/0.77 inference(unit_resolution,[status(thm)],[331, 1564])).
% 0.54/0.77 tff(1566,plain,
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% 0.54/0.77 inference(rewrite,[status(thm)],[])).
% 0.54/0.77 tff(1567,plain,
% 0.54/0.77 (((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
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% 0.54/0.77 inference(monotonicity,[status(thm)],[1567])).
% 0.54/0.77 tff(1569,plain,
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% 0.54/0.77 inference(transitivity,[status(thm)],[1568, 1566])).
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% 0.54/0.77 inference(unit_resolution,[status(thm)],[1571, 149, 165, 1565, 1538])).
% 0.54/0.77 tff(1573,plain,
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% 0.54/0.77 inference(unit_resolution,[status(thm)],[204, 1572])).
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% 0.54/0.77 (~r(s(z), s(s(s(s(s(s(s(z))))))))),
% 0.54/0.77 inference(unit_resolution,[status(thm)],[1265, 52, 34, 1573])).
% 0.54/0.77 tff(1575,plain,
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% 0.54/0.77 inference(unit_resolution,[status(thm)],[672, 69, 1574])).
% 0.54/0.77 tff(1576,plain,
% 0.54/0.77 (b(s(z), s(s(s(s(s(s(s(z))))))))),
% 0.54/0.77 inference(unit_resolution,[status(thm)],[1575, 265])).
% 0.54/0.77 tff(1577,plain,
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% 0.54/0.77 inference(unit_resolution,[status(thm)],[579, 52, 1526, 1573])).
% 0.54/0.77 tff(1578,plain,
% 0.54/0.77 ((s(s(s(s(s(s(z)))))) = s(z)) | b(s(s(s(s(s(s(z)))))), s(z))),
% 0.54/0.77 inference(unit_resolution,[status(thm)],[583, 69, 1577])).
% 0.54/0.77 tff(1579,plain,
% 0.54/0.77 (b(s(s(s(s(s(s(z)))))), s(z))),
% 0.54/0.77 inference(unit_resolution,[status(thm)],[1578, 573])).
% 0.54/0.77 tff(1580,plain,
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% 0.54/0.77 inference(unit_resolution,[status(thm)],[1042, 52, 1526, 34])).
% 0.54/0.77 tff(1581,plain,
% 0.54/0.77 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))),
% 0.54/0.77 inference(unit_resolution,[status(thm)],[537, 884])).
% 0.54/0.77 tff(1582,plain,
% 0.54/0.77 (b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))),
% 0.54/0.77 inference(unit_resolution,[status(thm)],[1581, 1580])).
% 0.54/0.77 tff(1583,plain,
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% 0.54/0.77 tff(1584,plain,
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% 0.54/0.77 inference(monotonicity,[status(thm)],[1584])).
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% 0.54/0.77 inference(transitivity,[status(thm)],[1585, 1583])).
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% 0.54/0.77 inference(modus_ponens,[status(thm)],[1587, 1586])).
% 0.54/0.77 tff(1589,plain,
% 0.54/0.77 ($false),
% 0.54/0.77 inference(unit_resolution,[status(thm)],[1588, 149, 1582, 1579, 1576, 1529])).
% 0.54/0.77 tff(1590,plain,((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.77 tff(1591,plain,
% 0.54/0.77 (~r(z, s(s(s(s(s(z))))))),
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% 0.54/0.77 tff(1592,plain,
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% 0.54/0.77 tff(1594,plain,
% 0.54/0.77 (((~b(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(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 0.54/0.77 inference(rewrite,[status(thm)],[])).
% 0.54/0.77 tff(1595,plain,
% 0.54/0.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 0.54/0.77 inference(monotonicity,[status(thm)],[1594])).
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% 0.54/0.78 inference(unit_resolution,[status(thm)],[599, 1638])).
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% 0.54/0.78 inference(rewrite,[status(thm)],[])).
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% 0.54/0.78 (((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 0.54/0.78 inference(rewrite,[status(thm)],[])).
% 0.54/0.78 tff(1642,plain,
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% 0.54/0.78 inference(monotonicity,[status(thm)],[1641])).
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% 0.54/0.78 inference(transitivity,[status(thm)],[1642, 1640])).
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% 0.54/0.78 inference(quant_inst,[status(thm)],[])).
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% 0.54/0.78 inference(modus_ponens,[status(thm)],[1644, 1643])).
% 0.54/0.78 tff(1646,plain,
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% 0.54/0.78 inference(unit_resolution,[status(thm)],[1645, 149, 1606, 1604, 166])).
% 0.54/0.78 tff(1647,plain,
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% 0.54/0.78 inference(unit_resolution,[status(thm)],[465, 1646])).
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% 0.54/0.78 inference(rewrite,[status(thm)],[])).
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% 0.54/0.78 inference(quant_inst,[status(thm)],[])).
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% 0.54/0.78 inference(modus_ponens,[status(thm)],[1649, 1648])).
% 0.54/0.78 tff(1651,plain,
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% 0.54/0.78 inference(unit_resolution,[status(thm)],[1650, 52, 1647, 1639, 1631])).
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% 0.54/0.78 tff(1653,plain,
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% 0.54/0.78 inference(unit_resolution,[status(thm)],[1652, 165, 34])).
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% 0.54/0.78 (r(z, s(s(s(z))))),
% 0.54/0.78 inference(unit_resolution,[status(thm)],[413, 1653])).
% 0.54/0.78 tff(1655,plain,
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% 0.54/0.78 inference(unit_resolution,[status(thm)],[80, 52, 34, 1654])).
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% 0.54/0.78 inference(unit_resolution,[status(thm)],[88, 1655])).
% 0.54/0.78 tff(1657,plain,
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% 0.54/0.78 inference(unit_resolution,[status(thm)],[1245, 1654, 960])).
% 0.54/0.78 tff(1658,plain,
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% 0.54/0.78 inference(unit_resolution,[status(thm)],[204, 1657])).
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% 0.54/0.78 inference(unit_resolution,[status(thm)],[727, 42, 337])).
% 0.54/0.78 tff(1660,plain,
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% 0.54/0.78 inference(unit_resolution,[status(thm)],[465, 1659])).
% 0.54/0.78 tff(1661,plain,
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% 0.54/0.78 inference(unit_resolution,[status(thm)],[1411, 337, 1237])).
% 0.54/0.78 tff(1662,plain,
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% 0.54/0.78 inference(unit_resolution,[status(thm)],[271, 69, 268, 1661])).
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% 0.54/0.78 inference(rewrite,[status(thm)],[])).
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% 0.54/0.78 inference(quant_inst,[status(thm)],[])).
% 0.54/0.78 tff(1665,plain,
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% 0.54/0.78 inference(modus_ponens,[status(thm)],[1664, 1663])).
% 0.54/0.78 tff(1666,plain,
% 0.54/0.78 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 0.54/0.78 inference(unit_resolution,[status(thm)],[1665, 52, 337, 981])).
% 0.54/0.78 tff(1667,plain,
% 0.54/0.78 ((s(s(s(s(s(z))))) = s(s(s(z)))) | b(s(s(s(s(s(z))))), s(s(s(z))))),
% 0.54/0.78 inference(unit_resolution,[status(thm)],[257, 69, 1666])).
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% 0.54/0.78 inference(unit_resolution,[status(thm)],[1667, 276])).
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% 0.54/0.78 inference(quant_inst,[status(thm)],[])).
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% 0.54/0.78 inference(modus_ponens,[status(thm)],[1670, 1669])).
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% 0.54/0.78 tff(1673,plain,((~b(s(s(s(s(s(z))))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.78 tff(1674,plain,
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% 0.54/0.78 inference(unit_resolution,[status(thm)],[163, 1674])).
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% 0.54/0.78 inference(rewrite,[status(thm)],[])).
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% 0.54/0.78 inference(quant_inst,[status(thm)],[])).
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% 0.54/0.78 inference(modus_ponens,[status(thm)],[1677, 1676])).
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% 0.54/0.78 inference(unit_resolution,[status(thm)],[1678, 52, 1237, 981, 1675])).
% 0.54/0.78 tff(1680,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), z)) | (~b(z, s(z))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.78 tff(1681,plain,
% 0.54/0.78 (~r(s(s(s(s(s(z))))), s(z))),
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% 0.54/0.78 tff(1682,plain,
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% 0.54/0.78 tff(1683,plain,
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% 0.54/0.78 tff(1684,plain,
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% 0.54/0.78 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)],[1689, 1688])).
% 0.54/0.79 tff(1691,plain,
% 0.54/0.79 (~b(s(s(s(s(s(z))))), z)),
% 0.54/0.79 inference(unit_resolution,[status(thm)],[1690, 149, 1660, 1684, 1682])).
% 0.54/0.79 tff(1692,plain,
% 0.54/0.79 (r(s(s(s(s(s(z))))), z)),
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% 0.64/0.80 tff(1881,plain,
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% 0.64/0.80 inference(unit_resolution,[status(thm)],[88, 1880])).
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% 0.64/0.80 inference(quant_inst,[status(thm)],[])).
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% 0.64/0.80 inference(modus_ponens,[status(thm)],[1883, 1882])).
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% 0.64/0.80 tff(1887,plain,
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% 0.64/0.80 inference(unit_resolution,[status(thm)],[1886, 1881, 1237])).
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% 0.64/0.80 inference(unit_resolution,[status(thm)],[385, 1887])).
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% 0.64/0.80 inference(unit_resolution,[status(thm)],[494, 1881, 477])).
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% 0.64/0.80 inference(unit_resolution,[status(thm)],[138, 1889])).
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% 0.64/0.80 inference(unit_resolution,[status(thm)],[1544, 149, 1890, 1888, 165, 1538])).
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% 0.64/0.80 tff(1893,plain,
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% 0.64/0.80 inference(unit_resolution,[status(thm)],[312, 1893])).
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% 0.64/0.80 inference(unit_resolution,[status(thm)],[1598, 149, 1842, 1862, 1894, 478])).
% 0.64/0.80 tff(1896,plain,((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.80 tff(1897,plain,
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% 0.64/0.80 inference(unit_resolution,[status(thm)],[1896, 478])).
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% 0.64/0.80 inference(unit_resolution,[status(thm)],[974, 1897])).
% 0.64/0.80 tff(1899,plain,
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% 0.64/0.80 inference(unit_resolution,[status(thm)],[1421, 52, 1860, 1898])).
% 0.64/0.80 tff(1900,plain,
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% 0.64/0.80 inference(unit_resolution,[status(thm)],[331, 1899])).
% 0.64/0.80 tff(1901,plain,
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% 0.64/0.80 inference(unit_resolution,[status(thm)],[989, 435, 981])).
% 0.64/0.80 tff(1902,plain,
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% 0.64/0.80 inference(unit_resolution,[status(thm)],[138, 1901])).
% 0.64/0.80 tff(1903,plain,
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% 0.64/0.80 inference(unit_resolution,[status(thm)],[734, 435, 337])).
% 0.64/0.80 tff(1904,plain,
% 0.64/0.80 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 0.64/0.80 inference(unit_resolution,[status(thm)],[363, 1903])).
% 0.64/0.80 tff(1905,plain,
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% 0.64/0.81 inference(rewrite,[status(thm)],[])).
% 0.64/0.81 tff(1906,plain,
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% 0.64/0.81 inference(rewrite,[status(thm)],[])).
% 0.64/0.81 tff(1907,plain,
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% 0.64/0.81 inference(monotonicity,[status(thm)],[1906])).
% 0.64/0.81 tff(1908,plain,
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% 0.64/0.81 inference(transitivity,[status(thm)],[1907, 1905])).
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% 0.64/0.81 inference(quant_inst,[status(thm)],[])).
% 0.64/0.81 tff(1910,plain,
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% 0.64/0.81 inference(modus_ponens,[status(thm)],[1909, 1908])).
% 0.64/0.81 tff(1911,plain,
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% 0.64/0.81 inference(unit_resolution,[status(thm)],[1910, 149, 744, 1904, 1902, 1668])).
% 0.64/0.81 tff(1912,plain,((~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.81 tff(1913,plain,
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% 0.64/0.81 inference(unit_resolution,[status(thm)],[1912, 1898, 1860, 1842])).
% 0.64/0.81 tff(1914,plain,
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% 0.64/0.81 inference(unit_resolution,[status(thm)],[385, 1913])).
% 0.64/0.81 tff(1915,plain,
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% 0.64/0.81 inference(unit_resolution,[status(thm)],[1785, 1898, 1860])).
% 0.64/0.81 tff(1916,plain,
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% 0.64/0.81 inference(unit_resolution,[status(thm)],[465, 1915])).
% 0.64/0.81 tff(1917,plain,
% 0.64/0.81 (~b(s(s(s(s(s(z))))), z)),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[1673, 1916, 478, 1842])).
% 0.64/0.81 tff(1918,plain,
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% 0.64/0.81 inference(unit_resolution,[status(thm)],[163, 1917])).
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% 0.64/0.81 (~r(s(z), z)),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[1832, 1898, 1860])).
% 0.64/0.81 tff(1920,plain,
% 0.64/0.81 (b(s(z), z)),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[959, 1919])).
% 0.64/0.81 tff(1921,plain,
% 0.64/0.81 (~r(s(z), s(s(s(z))))),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[620, 1900, 1841, 1916, 1920, 478, 1918])).
% 0.64/0.81 tff(1922,plain,
% 0.64/0.81 (b(s(z), s(s(s(z))))),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[204, 1921])).
% 0.64/0.81 tff(1923,plain,
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% 0.64/0.81 inference(rewrite,[status(thm)],[])).
% 0.64/0.81 tff(1924,plain,
% 0.64/0.81 (((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 0.64/0.81 inference(rewrite,[status(thm)],[])).
% 0.64/0.81 tff(1925,plain,
% 0.64/0.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 0.64/0.81 inference(monotonicity,[status(thm)],[1924])).
% 0.64/0.81 tff(1926,plain,
% 0.64/0.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 0.64/0.81 inference(transitivity,[status(thm)],[1925, 1923])).
% 0.64/0.81 tff(1927,plain,
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% 0.64/0.81 inference(quant_inst,[status(thm)],[])).
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% 0.64/0.81 inference(modus_ponens,[status(thm)],[1927, 1926])).
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% 0.64/0.81 inference(unit_resolution,[status(thm)],[1928, 149, 1922, 1841, 1914, 1900])).
% 0.64/0.81 tff(1930,plain,(~b(s(s(s(s(s(z))))), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.81 tff(1931,plain,
% 0.64/0.81 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[259, 1930])).
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% 0.64/0.81 inference(unit_resolution,[status(thm)],[1737, 1769, 975, 1931])).
% 0.64/0.81 tff(1933,plain,(~b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 0.64/0.81 tff(1934,plain,
% 0.64/0.81 (r(s(z), z)),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[959, 1933])).
% 0.64/0.81 tff(1935,plain,
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% 0.64/0.81 inference(rewrite,[status(thm)],[])).
% 0.64/0.81 tff(1936,plain,
% 0.64/0.81 (((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z)))))))))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 0.64/0.81 inference(rewrite,[status(thm)],[])).
% 0.64/0.81 tff(1937,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(s(s(s(z))))))), z)) | (~r(s(z), z)) | (~r(s(z), s(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(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z))))),
% 0.64/0.81 inference(monotonicity,[status(thm)],[1936])).
% 0.64/0.81 tff(1938,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(s(s(s(z))))))), z)) | (~r(s(z), z)) | (~r(s(z), s(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(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z)))),
% 0.64/0.81 inference(transitivity,[status(thm)],[1937, 1935])).
% 0.64/0.81 tff(1939,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(s(s(s(z))))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(s(z))))))))))),
% 0.64/0.81 inference(quant_inst,[status(thm)],[])).
% 0.64/0.81 tff(1940,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(s(z), s(s(s(s(s(s(s(z))))))))) | (~r(s(s(s(s(s(s(s(z))))))), z))),
% 0.64/0.81 inference(modus_ponens,[status(thm)],[1939, 1938])).
% 0.64/0.81 tff(1941,plain,
% 0.64/0.81 (~r(s(z), s(s(s(s(s(s(s(z))))))))),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[1940, 52, 1934, 365])).
% 0.64/0.81 tff(1942,plain,
% 0.64/0.81 ((s(z) = s(s(s(s(s(s(s(z)))))))) | b(s(z), s(s(s(s(s(s(s(z))))))))),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[672, 69, 1941])).
% 0.64/0.81 tff(1943,plain,
% 0.64/0.81 (b(s(z), s(s(s(s(s(s(s(z))))))))),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[1942, 265])).
% 0.64/0.81 tff(1944,plain,
% 0.64/0.81 ((~r(s(s(s(s(s(s(s(z))))))), z)) | (~r(s(s(s(s(s(s(s(z))))))), s(z)))),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[1886, 1934])).
% 0.64/0.81 tff(1945,plain,
% 0.64/0.81 (~r(s(s(s(s(s(s(s(z))))))), s(z))),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[1944, 365])).
% 0.64/0.81 tff(1946,plain,
% 0.64/0.81 (b(s(s(s(s(s(s(s(z))))))), s(z))),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[385, 1945])).
% 0.64/0.81 tff(1947,plain,
% 0.64/0.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 0.64/0.81 inference(rewrite,[status(thm)],[])).
% 0.64/0.81 tff(1948,plain,
% 0.64/0.81 (((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 0.64/0.81 inference(rewrite,[status(thm)],[])).
% 0.64/0.81 tff(1949,plain,
% 0.64/0.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))))),
% 0.64/0.81 inference(monotonicity,[status(thm)],[1948])).
% 0.64/0.81 tff(1950,plain,
% 0.64/0.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 0.64/0.81 inference(transitivity,[status(thm)],[1949, 1947])).
% 0.64/0.81 tff(1951,plain,
% 0.64/0.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 0.64/0.81 inference(quant_inst,[status(thm)],[])).
% 0.64/0.81 tff(1952,plain,
% 0.64/0.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 0.64/0.81 inference(modus_ponens,[status(thm)],[1951, 1950])).
% 0.64/0.81 tff(1953,plain,
% 0.64/0.81 ($false),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[1952, 149, 33, 1841, 1946, 1943])).
% 0.64/0.81 tff(1954,plain,((~r(s(s(s(s(s(s(s(z))))))), z)) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.81 tff(1955,plain,
% 0.64/0.81 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[1954, 33])).
% 0.64/0.81 tff(1956,plain,
% 0.64/0.81 (b(s(s(s(s(s(s(s(z))))))), z)),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[88, 1955])).
% 0.64/0.81 tff(1957,plain,
% 0.64/0.81 ($false),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[451, 149, 33, 1841, 166, 1956])).
% 0.64/0.81 tff(1958,plain,((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.81 tff(1959,plain,
% 0.64/0.81 (~b(z, s(s(s(z))))),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[1958, 33])).
% 0.64/0.81 tff(1960,plain,
% 0.64/0.81 (r(z, s(s(s(z))))),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[413, 1959])).
% 0.64/0.81 tff(1961,plain,
% 0.64/0.81 ((~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z)))))),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[1245, 1934])).
% 0.64/0.81 tff(1962,plain,
% 0.64/0.81 (~r(s(z), s(s(s(z))))),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[1961, 1960])).
% 0.64/0.81 tff(1963,plain,
% 0.64/0.81 (b(s(z), s(s(s(z))))),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[204, 1962])).
% 0.64/0.81 tff(1964,plain,
% 0.64/0.81 (~b(s(s(s(s(s(s(s(z))))))), s(z))),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[1341, 149, 33, 1963, 1841])).
% 0.64/0.81 tff(1965,plain,
% 0.64/0.81 (r(s(s(s(s(s(s(s(z))))))), s(z))),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[385, 1964])).
% 0.64/0.81 tff(1966,plain,
% 0.64/0.81 (~r(z, s(s(s(s(s(z))))))),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[950, 52, 1931, 1960])).
% 0.64/0.81 tff(1967,plain,
% 0.64/0.81 (b(z, s(s(s(s(s(z))))))),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[312, 1966])).
% 0.64/0.81 tff(1968,plain,
% 0.64/0.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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))))), s(s(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, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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))))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(z))))))))),
% 0.64/0.81 inference(rewrite,[status(thm)],[])).
% 0.64/0.81 tff(1969,plain,
% 0.64/0.81 (((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(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)))))), 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))))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(z))))))))),
% 0.64/0.81 inference(rewrite,[status(thm)],[])).
% 0.64/0.81 tff(1970,plain,
% 0.64/0.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(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)))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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))))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(z)))))))))),
% 0.64/0.81 inference(monotonicity,[status(thm)],[1969])).
% 0.64/0.81 tff(1971,plain,
% 0.64/0.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(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)))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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))))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(z))))))))),
% 0.64/0.81 inference(transitivity,[status(thm)],[1970, 1968])).
% 0.64/0.81 tff(1972,plain,
% 0.64/0.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(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)))))), z)))),
% 0.64/0.81 inference(quant_inst,[status(thm)],[])).
% 0.64/0.81 tff(1973,plain,
% 0.64/0.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(z)))))))),
% 0.64/0.81 inference(modus_ponens,[status(thm)],[1972, 1971])).
% 0.64/0.81 tff(1974,plain,
% 0.64/0.81 ($false),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[1973, 149, 1616, 292, 1065, 1612])).
% 0.64/0.81 tff(1975,plain,((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.81 tff(1976,plain,
% 0.64/0.81 ((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(z)))))),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[1975, 1931])).
% 0.64/0.81 tff(1977,plain,
% 0.64/0.81 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[1976, 1967, 1960])).
% 0.64/0.81 tff(1978,plain,
% 0.64/0.81 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.64/0.81 inference(unit_resolution,[status(thm)],[568, 1977])).
% 0.64/0.81 tff(1979,assumption,(r(s(s(s(s(s(s(z)))))), s(z))), introduced(assumption)).
% 0.64/0.81 tff(1980,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(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))))) <=> ((~![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(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))))),
% 0.64/0.81 inference(rewrite,[status(thm)],[])).
% 0.64/0.81 tff(1981,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(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))))),
% 0.64/0.82 inference(quant_inst,[status(thm)],[])).
% 0.64/0.82 tff(1982,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(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(z))) | (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z))))))))),
% 0.64/0.82 inference(modus_ponens,[status(thm)],[1981, 1980])).
% 0.64/0.82 tff(1983,plain,
% 0.64/0.82 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))),
% 0.64/0.82 inference(unit_resolution,[status(thm)],[1982, 52, 435, 1979])).
% 0.64/0.82 tff(1984,plain,
% 0.64/0.82 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 0.64/0.82 inference(unit_resolution,[status(thm)],[1886, 435, 1237])).
% 0.64/0.82 tff(1985,plain,
% 0.64/0.82 (b(s(s(s(s(s(s(s(z))))))), z)),
% 0.64/0.82 inference(unit_resolution,[status(thm)],[88, 1984])).
% 0.64/0.82 tff(1986,plain,
% 0.64/0.82 (~r(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 0.64/0.82 inference(unit_resolution,[status(thm)],[1184, 1985, 292, 35])).
% 0.64/0.82 tff(1987,plain,
% 0.64/0.82 (b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))),
% 0.64/0.82 inference(unit_resolution,[status(thm)],[363, 1986])).
% 0.64/0.82 tff(1988,plain,
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% 0.64/0.82 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 0.64/0.82 inference(unit_resolution,[status(thm)],[2032, 149, 2026, 2012, 1943])).
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% 0.64/0.82 ((s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))) | r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
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% 0.64/0.82 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(z))))))),
% 0.64/0.82 inference(unit_resolution,[status(thm)],[2034, 221])).
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% 0.64/0.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 0.64/0.82 inference(rewrite,[status(thm)],[])).
% 0.64/0.82 tff(2037,plain,
% 0.64/0.82 (((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(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(s(s(s(z)))))))))) <=> ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 0.64/0.82 inference(rewrite,[status(thm)],[])).
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% 0.64/0.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(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(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))))),
% 0.64/0.82 inference(monotonicity,[status(thm)],[2037])).
% 0.64/0.82 tff(2039,plain,
% 0.64/0.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(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(s(s(s(z))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z))))),
% 0.64/0.82 inference(transitivity,[status(thm)],[2038, 2036])).
% 0.64/0.82 tff(2040,plain,
% 0.64/0.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(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(s(s(s(z))))))))))),
% 0.64/0.82 inference(quant_inst,[status(thm)],[])).
% 0.64/0.82 tff(2041,plain,
% 0.64/0.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(z)))),
% 0.64/0.82 inference(modus_ponens,[status(thm)],[2040, 2039])).
% 0.64/0.82 tff(2042,plain,
% 0.64/0.82 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 0.64/0.82 inference(unit_resolution,[status(thm)],[2041, 149, 2026, 2012, 1943])).
% 0.64/0.82 tff(2043,plain,
% 0.64/0.82 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(z))))))))),
% 0.64/0.82 inference(unit_resolution,[status(thm)],[138, 2042])).
% 0.64/0.82 tff(2044,plain,
% 0.64/0.82 (~r(s(s(s(s(s(z))))), z)),
% 0.64/0.82 inference(unit_resolution,[status(thm)],[494, 2043, 365])).
% 0.64/0.82 tff(2045,plain,
% 0.64/0.82 (b(s(s(s(s(s(z))))), z)),
% 0.64/0.82 inference(unit_resolution,[status(thm)],[163, 2044])).
% 0.64/0.82 tff(2046,plain,
% 0.64/0.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(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, 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))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 0.64/0.82 inference(rewrite,[status(thm)],[])).
% 0.64/0.82 tff(2047,plain,
% 0.64/0.82 (((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 0.64/0.82 inference(rewrite,[status(thm)],[])).
% 0.64/0.82 tff(2048,plain,
% 0.64/0.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 0.64/0.82 inference(monotonicity,[status(thm)],[2047])).
% 0.64/0.82 tff(2049,plain,
% 0.64/0.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 0.64/0.82 inference(transitivity,[status(thm)],[2048, 2046])).
% 0.64/0.82 tff(2050,plain,
% 0.64/0.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 0.64/0.82 inference(quant_inst,[status(thm)],[])).
% 0.64/0.83 tff(2051,plain,
% 0.64/0.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 0.64/0.83 inference(modus_ponens,[status(thm)],[2050, 2049])).
% 0.64/0.83 tff(2052,plain,
% 0.64/0.83 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[2051, 149, 744, 2009, 2045])).
% 0.64/0.83 tff(2053,plain,
% 0.64/0.83 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[331, 2052])).
% 0.64/0.83 tff(2054,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(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(s(z))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(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(s(z))))))))))),
% 0.64/0.83 inference(rewrite,[status(thm)],[])).
% 0.64/0.83 tff(2055,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(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(s(z))))))))))),
% 0.64/0.83 inference(quant_inst,[status(thm)],[])).
% 0.64/0.83 tff(2056,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(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(s(z)))))))))),
% 0.64/0.83 inference(modus_ponens,[status(thm)],[2055, 2054])).
% 0.64/0.83 tff(2057,plain,
% 0.64/0.83 (~r(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[2056, 52, 2053, 2035])).
% 0.64/0.83 tff(2058,plain,
% 0.64/0.83 ((s(s(s(z))) = s(s(s(s(s(s(s(z)))))))) | b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[806, 69, 2057])).
% 0.64/0.83 tff(2059,plain,
% 0.64/0.83 (b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[2058, 799])).
% 0.64/0.83 tff(2060,plain,
% 0.64/0.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 0.64/0.83 inference(rewrite,[status(thm)],[])).
% 0.64/0.83 tff(2061,plain,
% 0.64/0.83 (((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 0.64/0.83 inference(rewrite,[status(thm)],[])).
% 0.64/0.83 tff(2062,plain,
% 0.64/0.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))))),
% 0.64/0.83 inference(monotonicity,[status(thm)],[2061])).
% 0.64/0.83 tff(2063,plain,
% 0.64/0.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))))),
% 0.64/0.83 inference(transitivity,[status(thm)],[2062, 2060])).
% 0.64/0.83 tff(2064,plain,
% 0.64/0.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(z))))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(z), s(s(s(z))))))),
% 0.64/0.83 inference(quant_inst,[status(thm)],[])).
% 0.64/0.83 tff(2065,plain,
% 0.64/0.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(z))))))))) | (~b(s(s(s(s(s(s(s(z))))))), s(s(s(z)))))),
% 0.64/0.83 inference(modus_ponens,[status(thm)],[2064, 2063])).
% 0.64/0.83 tff(2066,plain,
% 0.64/0.83 (~b(s(z), s(s(s(z))))),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[2065, 149, 1841, 1943, 2059])).
% 0.64/0.83 tff(2067,plain,
% 0.64/0.83 (r(s(z), s(s(s(z))))),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[204, 2066])).
% 0.64/0.83 tff(2068,plain,
% 0.64/0.83 ((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(z), s(s(s(z)))))),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[873, 1931])).
% 0.64/0.83 tff(2069,plain,
% 0.64/0.83 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[2068, 2067])).
% 0.64/0.83 tff(2070,plain,
% 0.64/0.83 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[568, 2069])).
% 0.64/0.83 tff(2071,plain,
% 0.64/0.83 (~b(s(s(s(s(s(s(z)))))), z)),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[881, 149, 744, 2070, 2009])).
% 0.64/0.83 tff(2072,plain,
% 0.64/0.83 (r(s(s(s(s(s(s(z)))))), z)),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[599, 2071])).
% 0.64/0.83 tff(2073,plain,
% 0.64/0.83 (~b(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[887, 149, 744, 2070, 1841])).
% 0.64/0.83 tff(2074,plain,
% 0.64/0.83 (r(s(s(s(s(s(s(s(z))))))), s(s(s(s(s(s(z)))))))),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[1581, 2073])).
% 0.64/0.83 tff(2075,plain,
% 0.64/0.83 ($false),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[892, 52, 2074, 2072, 365])).
% 0.64/0.83 tff(2076,plain,((~b(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(s(z))))))), z))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.83 tff(2077,plain,
% 0.64/0.83 (~r(s(s(s(s(s(s(s(z))))))), z)),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[2076, 2006])).
% 0.64/0.83 tff(2078,plain,
% 0.64/0.83 (b(s(s(s(s(s(s(s(z))))))), z)),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[88, 2077])).
% 0.64/0.83 tff(2079,plain,
% 0.64/0.83 ($false),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[1879, 149, 2006, 1841, 2009, 2078])).
% 0.64/0.83 % SZS output end Proof
% 0.64/0.83 % E exiting
%------------------------------------------------------------------------------