%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRA164-1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n029.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 0.38s 0.58s
% Output : Proof 0.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRA164-1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.11 % Command : run_E %s %d THM
% 0.15/0.32 % Computer : n029.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 00:36:01 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.38/0.58 % SZS status Unsatisfiable
% 0.38/0.58 % SZS output start Proof
% 0.38/0.58 tff(b_type, type, (
% 0.38/0.58 b: ( $i * $i ) > $o)).
% 0.38/0.58 tff(s_type, type, (
% 0.38/0.58 s: $i > $i)).
% 0.38/0.58 tff(z_type, type, (
% 0.38/0.58 z: $i)).
% 0.38/0.58 tff(r_type, type, (
% 0.38/0.58 r: ( $i * $i ) > $o)).
% 0.38/0.58 tff(inj_0_type, type, (
% 0.38/0.58 inj_0: $i > $i)).
% 0.38/0.58 tff(1,assumption,(r(z, s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 0.38/0.58 tff(2,assumption,(r(s(s(s(z))), z)), introduced(assumption)).
% 0.38/0.58 tff(3,assumption,(r(s(z), z)), introduced(assumption)).
% 0.38/0.58 tff(4,assumption,(r(s(z), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 0.38/0.58 tff(5,plain,
% 0.38/0.58 (^[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))))),
% 0.38/0.58 inference(bind,[status(th)],[])).
% 0.38/0.58 tff(6,plain,
% 0.38/0.58 (![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)))),
% 0.38/0.58 inference(quant_intro,[status(thm)],[5])).
% 0.38/0.58 tff(7,plain,
% 0.38/0.58 (![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)))),
% 0.38/0.58 inference(rewrite,[status(thm)],[])).
% 0.38/0.58 tff(8,plain,
% 0.38/0.58 (^[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))))),
% 0.38/0.58 inference(bind,[status(th)],[])).
% 0.38/0.58 tff(9,plain,
% 0.38/0.58 (![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)))),
% 0.38/0.58 inference(quant_intro,[status(thm)],[8])).
% 0.38/0.58 tff(10,axiom,(![X0: $i, X2: $i, X1: $i] : (((~r(X0, X1)) | (~r(X0, X2))) | (~r(X1, X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axr')).
% 0.38/0.58 tff(11,plain,
% 0.38/0.58 (![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 0.38/0.58 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.38/0.58 tff(12,plain,
% 0.38/0.58 (![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 0.38/0.58 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.38/0.58 tff(13,plain,(
% 0.38/0.58 ![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 0.38/0.58 inference(skolemize,[status(sab)],[12])).
% 0.38/0.58 tff(14,plain,
% 0.38/0.58 (![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 0.38/0.58 inference(modus_ponens,[status(thm)],[13, 6])).
% 0.38/0.58 tff(15,plain,
% 0.38/0.58 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 0.38/0.58 inference(rewrite,[status(thm)],[])).
% 0.38/0.58 tff(16,plain,
% 0.38/0.58 (((~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 0.38/0.58 inference(rewrite,[status(thm)],[])).
% 0.38/0.58 tff(17,plain,
% 0.38/0.58 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z))))))))))),
% 0.38/0.58 inference(monotonicity,[status(thm)],[16])).
% 0.38/0.58 tff(18,plain,
% 0.38/0.58 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 0.38/0.58 inference(transitivity,[status(thm)],[17, 15])).
% 0.38/0.58 tff(19,plain,
% 0.38/0.58 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(z), z)))),
% 0.38/0.58 inference(quant_inst,[status(thm)],[])).
% 0.38/0.58 tff(20,plain,
% 0.38/0.58 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z))))))))),
% 0.38/0.58 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.38/0.58 tff(21,plain,
% 0.38/0.58 ($false),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[20, 14, 3, 1, 4])).
% 0.38/0.58 tff(22,plain,((~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 0.38/0.58 tff(23,plain,
% 0.38/0.58 (~r(s(z), s(s(s(s(s(s(z)))))))),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[22, 3, 1])).
% 0.38/0.58 tff(24,assumption,(r(s(s(s(z))), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 0.38/0.58 tff(25,assumption,(r(s(s(z)), z)), introduced(assumption)).
% 0.38/0.58 tff(26,assumption,(r(s(z), s(s(s(z))))), introduced(assumption)).
% 0.38/0.58 tff(27,assumption,(b(z, s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 0.38/0.58 tff(28,plain,
% 0.38/0.58 (((~![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(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 0.38/0.58 inference(rewrite,[status(thm)],[])).
% 0.38/0.58 tff(29,plain,
% 0.38/0.58 (((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 0.38/0.58 inference(rewrite,[status(thm)],[])).
% 0.38/0.58 tff(30,plain,
% 0.38/0.58 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(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(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z))))))))))),
% 0.38/0.58 inference(monotonicity,[status(thm)],[29])).
% 0.38/0.58 tff(31,plain,
% 0.38/0.58 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(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(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 0.38/0.58 inference(transitivity,[status(thm)],[30, 28])).
% 0.38/0.58 tff(32,plain,
% 0.38/0.58 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(z))))))),
% 0.38/0.58 inference(quant_inst,[status(thm)],[])).
% 0.38/0.58 tff(33,plain,
% 0.38/0.58 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z))))))))),
% 0.38/0.58 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.38/0.58 tff(34,plain,
% 0.38/0.58 ($false),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[33, 14, 26, 24, 4])).
% 0.38/0.58 tff(35,plain,((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 0.38/0.58 tff(36,plain,
% 0.38/0.58 (~r(s(z), s(s(s(s(s(s(z)))))))),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[35, 26, 24])).
% 0.38/0.58 tff(37,assumption,(~b(s(z), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 0.38/0.58 tff(38,assumption,(s(z) = s(s(s(s(s(s(z))))))), introduced(assumption)).
% 0.38/0.58 tff(39,plain,
% 0.38/0.58 (s(s(s(s(s(s(z)))))) = s(z)),
% 0.38/0.58 inference(symmetry,[status(thm)],[38])).
% 0.38/0.58 tff(40,plain,
% 0.38/0.58 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0) <=> ![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 0.38/0.58 inference(rewrite,[status(thm)],[])).
% 0.38/0.58 tff(41,plain,
% 0.38/0.58 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y)) <=> ![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 0.38/0.58 inference(rewrite,[status(thm)],[])).
% 0.38/0.58 tff(42,plain,
% 0.38/0.58 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y)) <=> ![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 0.38/0.58 inference(rewrite,[status(thm)],[])).
% 0.38/0.58 tff(43,axiom,(![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sinj')).
% 0.38/0.58 tff(44,plain,
% 0.38/0.58 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 0.38/0.58 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.38/0.58 tff(45,plain,(
% 0.38/0.58 ![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 0.38/0.58 inference(skolemize,[status(sab)],[44])).
% 0.38/0.58 tff(46,plain,
% 0.38/0.58 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 0.38/0.58 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.38/0.58 tff(47,plain,
% 0.38/0.58 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 0.38/0.58 inference(modus_ponens,[status(thm)],[46, 40])).
% 0.38/0.58 tff(48,plain,
% 0.38/0.58 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(z)) = z)),
% 0.38/0.58 inference(quant_inst,[status(thm)],[])).
% 0.38/0.58 tff(49,plain,
% 0.38/0.58 (inj_0(s(z)) = z),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.38/0.58 tff(50,assumption,(s(s(s(s(s(s(z)))))) = s(z)), introduced(assumption)).
% 0.38/0.58 tff(51,plain,
% 0.38/0.58 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(z))),
% 0.38/0.58 inference(monotonicity,[status(thm)],[50])).
% 0.38/0.58 tff(52,plain,
% 0.38/0.58 ((~![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))))))),
% 0.38/0.58 inference(quant_inst,[status(thm)],[])).
% 0.38/0.58 tff(53,plain,
% 0.38/0.58 (inj_0(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[52, 47])).
% 0.38/0.58 tff(54,plain,
% 0.38/0.58 (s(s(s(s(s(z))))) = inj_0(s(s(s(s(s(s(z)))))))),
% 0.38/0.58 inference(symmetry,[status(thm)],[53])).
% 0.38/0.58 tff(55,plain,
% 0.38/0.58 (s(s(s(s(s(z))))) = z),
% 0.38/0.58 inference(transitivity,[status(thm)],[54, 51, 49])).
% 0.38/0.58 tff(56,plain,
% 0.38/0.58 (^[X: $i] : refl((~(s(X) = z)) <=> (~(s(X) = z)))),
% 0.38/0.58 inference(bind,[status(th)],[])).
% 0.38/0.58 tff(57,plain,
% 0.38/0.58 (![X: $i] : (~(s(X) = z)) <=> ![X: $i] : (~(s(X) = z))),
% 0.38/0.58 inference(quant_intro,[status(thm)],[56])).
% 0.38/0.58 tff(58,plain,
% 0.38/0.58 (![X: $i] : (~(s(X) = z)) <=> ![X: $i] : (~(s(X) = z))),
% 0.38/0.58 inference(rewrite,[status(thm)],[])).
% 0.38/0.58 tff(59,axiom,(![X: $i] : (~(s(X) = z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','snz')).
% 0.38/0.58 tff(60,plain,
% 0.38/0.58 (![X: $i] : (~(s(X) = z))),
% 0.38/0.58 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.38/0.58 tff(61,plain,(
% 0.38/0.58 ![X: $i] : (~(s(X) = z))),
% 0.38/0.58 inference(skolemize,[status(sab)],[60])).
% 0.38/0.58 tff(62,plain,
% 0.38/0.58 (![X: $i] : (~(s(X) = z))),
% 0.38/0.58 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.38/0.58 tff(63,plain,
% 0.38/0.58 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(z))))) = z))),
% 0.38/0.58 inference(quant_inst,[status(thm)],[])).
% 0.38/0.58 tff(64,plain,
% 0.38/0.58 (~(s(s(s(s(s(z))))) = z)),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[63, 62])).
% 0.38/0.58 tff(65,plain,
% 0.38/0.58 ($false),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[64, 55])).
% 0.38/0.58 tff(66,plain,(~(s(s(s(s(s(s(z)))))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 0.38/0.58 tff(67,plain,
% 0.38/0.58 ($false),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[66, 39])).
% 0.38/0.58 tff(68,plain,(~(s(z) = s(s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 0.38/0.58 tff(69,assumption,(~r(s(z), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 0.38/0.58 tff(70,plain,
% 0.38/0.58 (^[Y: $i, X: $i] : refl(((X = Y) | b(X, Y) | r(X, Y)) <=> ((X = Y) | b(X, Y) | r(X, Y)))),
% 0.38/0.58 inference(bind,[status(th)],[])).
% 0.38/0.58 tff(71,plain,
% 0.38/0.58 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.38/0.58 inference(quant_intro,[status(thm)],[70])).
% 0.38/0.58 tff(72,plain,
% 0.38/0.58 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.38/0.58 inference(rewrite,[status(thm)],[])).
% 0.38/0.58 tff(73,plain,
% 0.38/0.58 (^[Y: $i, X: $i] : rewrite((((X = Y) | r(X, Y)) | b(X, Y)) <=> ((X = Y) | b(X, Y) | r(X, Y)))),
% 0.38/0.58 inference(bind,[status(th)],[])).
% 0.38/0.58 tff(74,plain,
% 0.38/0.58 (![Y: $i, X: $i] : (((X = Y) | r(X, Y)) | b(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.38/0.58 inference(quant_intro,[status(thm)],[73])).
% 0.38/0.58 tff(75,axiom,(![Y: $i, X: $i] : (((X = Y) | r(X, Y)) | b(X, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','rb')).
% 0.38/0.58 tff(76,plain,
% 0.38/0.58 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.38/0.58 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.38/0.58 tff(77,plain,
% 0.38/0.58 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.38/0.58 inference(modus_ponens,[status(thm)],[76, 72])).
% 0.38/0.58 tff(78,plain,(
% 0.38/0.58 ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.38/0.58 inference(skolemize,[status(sab)],[77])).
% 0.38/0.58 tff(79,plain,
% 0.38/0.58 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.38/0.58 inference(modus_ponens,[status(thm)],[78, 71])).
% 0.38/0.58 tff(80,plain,
% 0.38/0.58 (((~![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))))))))),
% 0.38/0.58 inference(rewrite,[status(thm)],[])).
% 0.38/0.58 tff(81,plain,
% 0.38/0.58 ((~![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))))))))),
% 0.38/0.58 inference(quant_inst,[status(thm)],[])).
% 0.38/0.58 tff(82,plain,
% 0.38/0.58 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(s(s(z))))))) | b(s(z), s(s(s(s(s(s(z))))))) | r(s(z), s(s(s(s(s(s(z)))))))),
% 0.38/0.58 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.38/0.58 tff(83,plain,
% 0.38/0.58 ($false),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[82, 79, 69, 68, 37])).
% 0.38/0.58 tff(84,plain,(b(s(z), s(s(s(s(s(s(z))))))) | r(s(z), s(s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 0.38/0.58 tff(85,plain,
% 0.38/0.58 (b(s(z), s(s(s(s(s(s(z)))))))),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[84, 36])).
% 0.38/0.58 tff(86,assumption,(b(s(z), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 0.38/0.58 tff(87,assumption,(b(s(s(s(s(s(s(z)))))), s(z))), introduced(assumption)).
% 0.38/0.58 tff(88,assumption,(r(s(s(z)), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 0.38/0.58 tff(89,assumption,(b(s(s(s(s(s(s(z)))))), z)), introduced(assumption)).
% 0.38/0.58 tff(90,assumption,(z = s(s(z))), introduced(assumption)).
% 0.38/0.58 tff(91,plain,
% 0.38/0.58 (s(s(z)) = z),
% 0.38/0.58 inference(symmetry,[status(thm)],[90])).
% 0.38/0.58 tff(92,plain,
% 0.38/0.58 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(z)) = z))),
% 0.38/0.58 inference(quant_inst,[status(thm)],[])).
% 0.38/0.58 tff(93,plain,
% 0.38/0.58 (~(s(s(z)) = z)),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[92, 62])).
% 0.38/0.58 tff(94,plain,
% 0.38/0.58 ($false),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[93, 91])).
% 0.38/0.58 tff(95,plain,(~(z = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.38/0.58 tff(96,assumption,(b(s(s(z)), s(s(s(z))))), introduced(assumption)).
% 0.38/0.58 tff(97,plain,
% 0.38/0.58 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(z), 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(z)), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 0.38/0.58 inference(rewrite,[status(thm)],[])).
% 0.38/0.58 tff(98,plain,
% 0.38/0.58 (((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(z))))) <=> ((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 0.38/0.58 inference(rewrite,[status(thm)],[])).
% 0.38/0.58 tff(99,plain,
% 0.38/0.58 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(z))))))))))),
% 0.38/0.58 inference(monotonicity,[status(thm)],[98])).
% 0.38/0.58 tff(100,plain,
% 0.38/0.58 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 0.38/0.58 inference(transitivity,[status(thm)],[99, 97])).
% 0.38/0.58 tff(101,plain,
% 0.38/0.58 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(z)))))),
% 0.38/0.58 inference(quant_inst,[status(thm)],[])).
% 0.38/0.58 tff(102,plain,
% 0.38/0.58 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(z))))))))),
% 0.38/0.58 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.38/0.58 tff(103,plain,
% 0.38/0.58 (~r(s(z), s(s(z)))),
% 0.38/0.58 inference(unit_resolution,[status(thm)],[102, 14, 88, 4])).
% 0.38/0.58 tff(104,assumption,(s(z) = s(s(z))), introduced(assumption)).
% 0.38/0.58 tff(105,plain,
% 0.38/0.58 (inj_0(s(z)) = inj_0(s(s(z)))),
% 0.38/0.58 inference(monotonicity,[status(thm)],[104])).
% 0.38/0.58 tff(106,plain,
% 0.38/0.59 (inj_0(s(s(z))) = inj_0(s(z))),
% 0.38/0.59 inference(symmetry,[status(thm)],[105])).
% 0.38/0.59 tff(107,plain,
% 0.38/0.59 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(z))) = s(z))),
% 0.38/0.59 inference(quant_inst,[status(thm)],[])).
% 0.38/0.59 tff(108,plain,
% 0.38/0.59 (inj_0(s(s(z))) = s(z)),
% 0.38/0.59 inference(unit_resolution,[status(thm)],[107, 47])).
% 0.38/0.59 tff(109,plain,
% 0.38/0.59 (s(z) = inj_0(s(s(z)))),
% 0.38/0.59 inference(symmetry,[status(thm)],[108])).
% 0.38/0.59 tff(110,plain,
% 0.38/0.59 (s(z) = z),
% 0.38/0.59 inference(transitivity,[status(thm)],[109, 106, 49])).
% 0.38/0.59 tff(111,plain,
% 0.38/0.59 ((~![X: $i] : (~(s(X) = z))) | (~(s(z) = z))),
% 0.38/0.59 inference(quant_inst,[status(thm)],[])).
% 0.38/0.59 tff(112,plain,
% 0.38/0.59 (~(s(z) = z)),
% 0.38/0.59 inference(unit_resolution,[status(thm)],[111, 62])).
% 0.38/0.59 tff(113,plain,
% 0.38/0.59 ($false),
% 0.38/0.59 inference(unit_resolution,[status(thm)],[112, 110])).
% 0.38/0.59 tff(114,plain,(~(s(z) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.38/0.59 tff(115,plain,
% 0.38/0.59 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z))))),
% 0.38/0.59 inference(rewrite,[status(thm)],[])).
% 0.38/0.59 tff(116,plain,
% 0.38/0.59 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z))))),
% 0.38/0.59 inference(quant_inst,[status(thm)],[])).
% 0.38/0.59 tff(117,plain,
% 0.38/0.59 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z)))),
% 0.38/0.59 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.38/0.59 tff(118,plain,
% 0.38/0.59 (b(s(z), s(s(z)))),
% 0.38/0.59 inference(unit_resolution,[status(thm)],[117, 79, 114, 103])).
% 0.38/0.59 tff(119,assumption,(r(s(s(z)), s(z))), introduced(assumption)).
% 0.38/0.59 tff(120,plain,
% 0.38/0.59 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), 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(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 0.38/0.59 inference(rewrite,[status(thm)],[])).
% 0.38/0.59 tff(121,plain,
% 0.38/0.59 (((~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(z)))) <=> ((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 0.38/0.59 inference(rewrite,[status(thm)],[])).
% 0.38/0.59 tff(122,plain,
% 0.38/0.59 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(s(s(z))))))))))),
% 0.38/0.59 inference(monotonicity,[status(thm)],[121])).
% 0.38/0.59 tff(123,plain,
% 0.38/0.59 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 0.38/0.59 inference(transitivity,[status(thm)],[122, 120])).
% 0.38/0.59 tff(124,plain,
% 0.38/0.59 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(z))))),
% 0.38/0.59 inference(quant_inst,[status(thm)],[])).
% 0.38/0.59 tff(125,plain,
% 0.38/0.59 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(s(s(z))))))))),
% 0.38/0.59 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.38/0.59 tff(126,plain,
% 0.38/0.59 ($false),
% 0.38/0.59 inference(unit_resolution,[status(thm)],[125, 14, 88, 4, 119])).
% 0.38/0.59 tff(127,plain,((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.38/0.59 tff(128,plain,
% 0.38/0.59 (~r(s(s(z)), s(z))),
% 0.38/0.59 inference(unit_resolution,[status(thm)],[127, 4, 88])).
% 0.38/0.59 tff(129,plain,
% 0.38/0.59 ((s(s(z)) = s(z)) <=> (s(z) = s(s(z)))),
% 0.38/0.59 inference(commutativity,[status(thm)],[])).
% 0.38/0.59 tff(130,plain,
% 0.38/0.59 ((s(z) = s(s(z))) <=> (s(s(z)) = s(z))),
% 0.38/0.59 inference(symmetry,[status(thm)],[129])).
% 0.38/0.59 tff(131,plain,
% 0.38/0.59 ((~(s(z) = s(s(z)))) <=> (~(s(s(z)) = s(z)))),
% 0.38/0.59 inference(monotonicity,[status(thm)],[130])).
% 0.38/0.59 tff(132,plain,
% 0.38/0.59 (~(s(s(z)) = s(z))),
% 0.38/0.59 inference(modus_ponens,[status(thm)],[114, 131])).
% 0.38/0.59 tff(133,plain,
% 0.38/0.59 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z)))),
% 0.38/0.59 inference(rewrite,[status(thm)],[])).
% 0.38/0.59 tff(134,plain,
% 0.38/0.59 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z)))),
% 0.38/0.59 inference(quant_inst,[status(thm)],[])).
% 0.38/0.59 tff(135,plain,
% 0.38/0.59 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z))),
% 0.38/0.59 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.38/0.59 tff(136,plain,
% 0.38/0.59 ((s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z))),
% 0.38/0.59 inference(unit_resolution,[status(thm)],[135, 79])).
% 0.38/0.59 tff(137,plain,
% 0.38/0.59 (b(s(s(z)), s(z)) | r(s(s(z)), s(z))),
% 0.38/0.59 inference(unit_resolution,[status(thm)],[136, 132])).
% 0.38/0.59 tff(138,plain,
% 0.38/0.59 (b(s(s(z)), s(z))),
% 0.38/0.59 inference(unit_resolution,[status(thm)],[137, 128])).
% 0.38/0.59 tff(139,assumption,(b(s(s(z)), s(z))), introduced(assumption)).
% 0.38/0.59 tff(140,assumption,(r(s(s(s(z))), s(z))), introduced(assumption)).
% 0.38/0.59 tff(141,plain,
% 0.38/0.59 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(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(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 0.38/0.59 inference(rewrite,[status(thm)],[])).
% 0.38/0.59 tff(142,plain,
% 0.38/0.59 (((~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 0.38/0.59 inference(rewrite,[status(thm)],[])).
% 0.38/0.59 tff(143,plain,
% 0.38/0.59 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z))))))))))),
% 0.38/0.59 inference(monotonicity,[status(thm)],[142])).
% 0.38/0.59 tff(144,plain,
% 0.38/0.59 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 0.38/0.59 inference(transitivity,[status(thm)],[143, 141])).
% 0.38/0.59 tff(145,plain,
% 0.38/0.59 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(z))))),
% 0.38/0.59 inference(quant_inst,[status(thm)],[])).
% 0.38/0.59 tff(146,plain,
% 0.38/0.59 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z))))))))),
% 0.38/0.59 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.38/0.59 tff(147,plain,
% 0.38/0.59 ($false),
% 0.38/0.59 inference(unit_resolution,[status(thm)],[146, 14, 140, 24, 4])).
% 0.38/0.59 tff(148,plain,((~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 0.38/0.59 tff(149,plain,
% 0.38/0.59 (~r(s(s(s(z))), s(z))),
% 0.38/0.59 inference(unit_resolution,[status(thm)],[148, 24, 4])).
% 0.38/0.59 tff(150,assumption,(s(z) = s(s(s(z)))), introduced(assumption)).
% 0.38/0.59 tff(151,plain,
% 0.38/0.59 (inj_0(s(z)) = inj_0(s(s(s(z))))),
% 0.38/0.59 inference(monotonicity,[status(thm)],[150])).
% 0.38/0.59 tff(152,plain,
% 0.38/0.59 (inj_0(s(s(s(z)))) = inj_0(s(z))),
% 0.38/0.59 inference(symmetry,[status(thm)],[151])).
% 0.38/0.59 tff(153,plain,
% 0.38/0.59 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(z)))) = s(s(z)))),
% 0.38/0.59 inference(quant_inst,[status(thm)],[])).
% 0.38/0.59 tff(154,plain,
% 0.38/0.59 (inj_0(s(s(s(z)))) = s(s(z))),
% 0.38/0.59 inference(unit_resolution,[status(thm)],[153, 47])).
% 0.38/0.59 tff(155,plain,
% 0.38/0.59 (s(s(z)) = inj_0(s(s(s(z))))),
% 0.38/0.59 inference(symmetry,[status(thm)],[154])).
% 0.38/0.59 tff(156,plain,
% 0.38/0.59 (s(s(z)) = z),
% 0.38/0.59 inference(transitivity,[status(thm)],[155, 152, 49])).
% 0.38/0.59 tff(157,plain,
% 0.38/0.59 ($false),
% 0.38/0.59 inference(unit_resolution,[status(thm)],[93, 156])).
% 0.38/0.59 tff(158,plain,(~(s(z) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.38/0.59 tff(159,plain,
% 0.38/0.59 ((s(s(s(z))) = s(z)) <=> (s(z) = s(s(s(z))))),
% 0.38/0.59 inference(commutativity,[status(thm)],[])).
% 0.38/0.59 tff(160,assumption,(s(s(s(z))) = s(z)), introduced(assumption)).
% 0.38/0.59 tff(161,plain,
% 0.38/0.59 (s(z) = s(s(s(z)))),
% 0.38/0.59 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.38/0.59 tff(162,assumption,(~(s(z) = s(s(s(z))))), introduced(assumption)).
% 0.38/0.59 tff(163,plain,
% 0.38/0.59 ($false),
% 0.38/0.59 inference(unit_resolution,[status(thm)],[162, 161])).
% 0.38/0.59 tff(164,plain,((~(s(s(s(z))) = s(z))) | (s(z) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.38/0.59 tff(165,plain,
% 0.38/0.59 (~(s(s(s(z))) = s(z))),
% 0.38/0.59 inference(unit_resolution,[status(thm)],[164, 158])).
% 0.38/0.59 tff(166,plain,
% 0.38/0.59 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z)))),
% 0.38/0.59 inference(rewrite,[status(thm)],[])).
% 0.38/0.59 tff(167,plain,
% 0.38/0.59 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z)))),
% 0.38/0.59 inference(quant_inst,[status(thm)],[])).
% 0.38/0.59 tff(168,plain,
% 0.38/0.59 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z))),
% 0.38/0.59 inference(modus_ponens,[status(thm)],[167, 166])).
% 0.38/0.59 tff(169,plain,
% 0.38/0.59 ((s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z))),
% 0.38/0.59 inference(unit_resolution,[status(thm)],[168, 79])).
% 0.38/0.59 tff(170,plain,
% 0.38/0.59 (b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z))),
% 0.38/0.59 inference(unit_resolution,[status(thm)],[169, 165])).
% 0.38/0.59 tff(171,plain,
% 0.38/0.59 (b(s(s(s(z))), s(z))),
% 0.38/0.59 inference(unit_resolution,[status(thm)],[170, 149])).
% 0.38/0.59 tff(172,plain,
% 0.38/0.59 (~r(s(z), s(s(s(z))))),
% 0.38/0.59 inference(unit_resolution,[status(thm)],[35, 24, 4])).
% 0.38/0.59 tff(173,plain,
% 0.38/0.59 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z)))))),
% 0.38/0.59 inference(rewrite,[status(thm)],[])).
% 0.38/0.59 tff(174,plain,
% 0.38/0.59 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z)))))),
% 0.38/0.59 inference(quant_inst,[status(thm)],[])).
% 0.38/0.59 tff(175,plain,
% 0.38/0.59 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z))))),
% 0.38/0.59 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.38/0.59 tff(176,plain,
% 0.38/0.59 ((s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z))))),
% 0.38/0.59 inference(unit_resolution,[status(thm)],[175, 79])).
% 0.38/0.59 tff(177,plain,
% 0.38/0.59 (b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z))))),
% 0.38/0.59 inference(unit_resolution,[status(thm)],[176, 158])).
% 0.38/0.59 tff(178,plain,
% 0.38/0.59 (b(s(z), s(s(s(z))))),
% 0.38/0.59 inference(unit_resolution,[status(thm)],[177, 172])).
% 0.38/0.59 tff(179,plain,
% 0.38/0.59 (^[X0: $i, X3: $i, X2: $i, X1: $i] : refl(((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) <=> ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))))),
% 0.38/0.59 inference(bind,[status(th)],[])).
% 0.38/0.59 tff(180,plain,
% 0.38/0.59 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 0.38/0.59 inference(quant_intro,[status(thm)],[179])).
% 0.38/0.59 tff(181,plain,
% 0.38/0.59 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 0.38/0.59 inference(rewrite,[status(thm)],[])).
% 0.38/0.59 tff(182,plain,
% 0.38/0.59 (^[X0: $i, X3: $i, X2: $i, X1: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) <=> ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))), (((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X0, X3))) <=> (((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X0, X3))))), rewrite((((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X0, X3))) <=> ((~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))), (((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X0, X3))) <=> ((~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))))), ((((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X0, X3))) | (~b(X2, X3))) <=> (((~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X2, X3))))), rewrite((((~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X2, X3))) <=> ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))), ((((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X0, X3))) | (~b(X2, X3))) <=> ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))))),
% 0.38/0.59 inference(bind,[status(th)],[])).
% 0.38/0.59 tff(183,plain,
% 0.38/0.59 (![X0: $i, X3: $i, X2: $i, X1: $i] : (((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X0, X3))) | (~b(X2, X3))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 0.38/0.59 inference(quant_intro,[status(thm)],[182])).
% 0.38/0.59 tff(184,axiom,(![X0: $i, X3: $i, X2: $i, X1: $i] : (((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X0, X3))) | (~b(X2, X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axb')).
% 0.38/0.59 tff(185,plain,
% 0.38/0.59 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 0.38/0.59 inference(modus_ponens,[status(thm)],[184, 183])).
% 0.38/0.59 tff(186,plain,
% 0.38/0.59 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 0.38/0.59 inference(modus_ponens,[status(thm)],[185, 181])).
% 0.38/0.59 tff(187,plain,(
% 0.38/0.59 ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 0.38/0.59 inference(skolemize,[status(sab)],[186])).
% 0.38/0.59 tff(188,plain,
% 0.38/0.59 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 0.38/0.59 inference(modus_ponens,[status(thm)],[187, 180])).
% 0.38/0.59 tff(189,plain,
% 0.38/0.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 0.38/0.59 inference(rewrite,[status(thm)],[])).
% 0.38/0.59 tff(190,plain,
% 0.38/0.59 (((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z)))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 0.38/0.59 inference(rewrite,[status(thm)],[])).
% 0.38/0.59 tff(191,plain,
% 0.38/0.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z)))))),
% 0.38/0.59 inference(monotonicity,[status(thm)],[190])).
% 0.38/0.59 tff(192,plain,
% 0.38/0.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 0.38/0.59 inference(transitivity,[status(thm)],[191, 189])).
% 0.38/0.59 tff(193,plain,
% 0.38/0.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 0.38/0.59 inference(quant_inst,[status(thm)],[])).
% 0.38/0.59 tff(194,plain,
% 0.38/0.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z)))),
% 0.38/0.59 inference(modus_ponens,[status(thm)],[193, 192])).
% 0.38/0.59 tff(195,plain,
% 0.38/0.59 ($false),
% 0.38/0.59 inference(unit_resolution,[status(thm)],[194, 188, 178, 171, 96, 139])).
% 0.38/0.59 tff(196,plain,((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 0.38/0.59 tff(197,plain,
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% 0.38/0.59 inference(unit_resolution,[status(thm)],[196, 138, 96, 4])).
% 0.38/0.59 tff(198,assumption,(s(s(s(z))) = s(s(s(s(s(s(z))))))), introduced(assumption)).
% 0.38/0.59 tff(199,plain,
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% 0.38/0.59 inference(monotonicity,[status(thm)],[198])).
% 0.38/0.59 tff(200,plain,
% 0.38/0.59 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(z)))))) = s(s(s(s(z)))))),
% 0.38/0.59 inference(quant_inst,[status(thm)],[])).
% 0.38/0.59 tff(201,plain,
% 0.38/0.59 (inj_0(s(s(s(s(s(z)))))) = s(s(s(s(z))))),
% 0.38/0.59 inference(unit_resolution,[status(thm)],[200, 47])).
% 0.38/0.59 tff(202,plain,
% 0.38/0.59 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(s(s(z)))))))),
% 0.38/0.59 inference(monotonicity,[status(thm)],[198])).
% 0.38/0.59 tff(203,plain,
% 0.38/0.59 (s(s(z)) = s(s(s(s(s(z)))))),
% 0.38/0.59 inference(transitivity,[status(thm)],[155, 202, 53])).
% 0.38/0.59 tff(204,plain,
% 0.38/0.59 (inj_0(s(s(z))) = inj_0(s(s(s(s(s(z))))))),
% 0.38/0.59 inference(monotonicity,[status(thm)],[203])).
% 0.38/0.59 tff(205,plain,
% 0.38/0.59 (s(z) = s(s(s(s(s(s(s(z)))))))),
% 0.38/0.59 inference(transitivity,[status(thm)],[109, 204, 201, 199])).
% 0.38/0.59 tff(206,plain,
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% 0.38/0.59 inference(monotonicity,[status(thm)],[205])).
% 0.38/0.59 tff(207,plain,
% 0.38/0.59 (inj_0(s(s(s(s(s(s(s(z)))))))) = inj_0(s(z))),
% 0.38/0.59 inference(symmetry,[status(thm)],[206])).
% 0.38/0.59 tff(208,plain,
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% 0.38/0.59 inference(quant_inst,[status(thm)],[])).
% 0.38/0.59 tff(209,plain,
% 0.38/0.59 (inj_0(s(s(s(s(s(s(s(z)))))))) = s(s(s(s(s(s(z))))))),
% 0.38/0.59 inference(unit_resolution,[status(thm)],[208, 47])).
% 0.38/0.59 tff(210,plain,
% 0.38/0.59 (s(s(s(s(s(s(z)))))) = inj_0(s(s(s(s(s(s(s(z))))))))),
% 0.38/0.59 inference(symmetry,[status(thm)],[209])).
% 0.38/0.59 tff(211,plain,
% 0.38/0.59 (s(s(s(s(s(s(z)))))) = z),
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% 0.38/0.59 tff(212,plain,
% 0.38/0.59 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(s(z)))))) = z))),
% 0.38/0.59 inference(quant_inst,[status(thm)],[])).
% 0.38/0.59 tff(213,plain,
% 0.38/0.59 (~(s(s(s(s(s(s(z)))))) = z)),
% 0.38/0.59 inference(unit_resolution,[status(thm)],[212, 62])).
% 0.38/0.59 tff(214,plain,
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% 0.38/0.59 inference(unit_resolution,[status(thm)],[213, 211])).
% 0.38/0.59 tff(215,plain,(~(s(s(s(z))) = s(s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 0.38/0.59 tff(216,plain,
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% 0.38/0.59 inference(quant_inst,[status(thm)],[])).
% 0.38/0.60 tff(218,plain,
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% 0.38/0.60 inference(modus_ponens,[status(thm)],[217, 216])).
% 0.38/0.60 tff(219,plain,
% 0.38/0.60 ((s(s(s(z))) = s(s(s(s(s(s(z))))))) | b(s(s(s(z))), s(s(s(s(s(s(z))))))) | r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 0.38/0.60 inference(unit_resolution,[status(thm)],[218, 79])).
% 0.38/0.60 tff(220,plain,
% 0.38/0.60 (b(s(s(s(z))), s(s(s(s(s(s(z))))))) | r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 0.38/0.60 inference(unit_resolution,[status(thm)],[219, 215])).
% 0.38/0.60 tff(221,plain,
% 0.38/0.60 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 0.38/0.60 inference(unit_resolution,[status(thm)],[220, 197])).
% 0.38/0.60 tff(222,assumption,(r(s(s(s(s(s(s(z)))))), s(s(s(z))))), introduced(assumption)).
% 0.38/0.60 tff(223,plain,
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% 0.38/0.60 inference(rewrite,[status(thm)],[])).
% 0.38/0.60 tff(224,plain,
% 0.38/0.60 (((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(z))))))))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 0.38/0.60 inference(rewrite,[status(thm)],[])).
% 0.38/0.60 tff(225,plain,
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% 0.38/0.60 inference(monotonicity,[status(thm)],[224])).
% 0.38/0.60 tff(226,plain,
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% 0.38/0.60 inference(transitivity,[status(thm)],[225, 223])).
% 0.38/0.60 tff(227,plain,
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% 0.38/0.60 inference(quant_inst,[status(thm)],[])).
% 0.38/0.60 tff(228,plain,
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% 0.38/0.60 inference(modus_ponens,[status(thm)],[227, 226])).
% 0.38/0.60 tff(229,plain,
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% 0.38/0.60 inference(unit_resolution,[status(thm)],[228, 14, 26, 222, 4])).
% 0.38/0.60 tff(230,plain,((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 0.38/0.60 tff(231,plain,
% 0.38/0.60 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.38/0.60 inference(unit_resolution,[status(thm)],[230, 26, 4])).
% 0.38/0.60 tff(232,plain,
% 0.38/0.60 ((s(s(s(s(s(s(z)))))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(s(s(s(z)))))))),
% 0.38/0.60 inference(commutativity,[status(thm)],[])).
% 0.38/0.60 tff(233,assumption,(s(s(s(s(s(s(z)))))) = s(s(s(z)))), introduced(assumption)).
% 0.38/0.60 tff(234,plain,
% 0.38/0.60 (s(s(s(z))) = s(s(s(s(s(s(z))))))),
% 0.38/0.60 inference(modus_ponens,[status(thm)],[233, 232])).
% 0.38/0.60 tff(235,assumption,(~(s(s(s(z))) = s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 0.38/0.60 tff(236,plain,
% 0.38/0.60 ($false),
% 0.38/0.60 inference(unit_resolution,[status(thm)],[235, 234])).
% 0.38/0.60 tff(237,plain,((~(s(s(s(s(s(s(z)))))) = s(s(s(z))))) | (s(s(s(z))) = s(s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 0.38/0.60 tff(238,plain,
% 0.38/0.60 (~(s(s(s(s(s(s(z)))))) = s(s(s(z))))),
% 0.38/0.60 inference(unit_resolution,[status(thm)],[237, 215])).
% 0.38/0.60 tff(239,plain,
% 0.38/0.60 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(s(s(z)))) | b(s(s(s(s(s(s(z)))))), s(s(s(z)))) | r(s(s(s(s(s(s(z)))))), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(s(s(z)))) | b(s(s(s(s(s(s(z)))))), s(s(s(z)))) | r(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 0.38/0.60 inference(rewrite,[status(thm)],[])).
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% 0.38/0.60 inference(quant_inst,[status(thm)],[])).
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% 0.38/0.60 inference(modus_ponens,[status(thm)],[240, 239])).
% 0.38/0.60 tff(242,plain,
% 0.38/0.60 ((s(s(s(s(s(s(z)))))) = s(s(s(z)))) | b(s(s(s(s(s(s(z)))))), s(s(s(z)))) | r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.38/0.60 inference(unit_resolution,[status(thm)],[241, 79])).
% 0.38/0.60 tff(243,plain,
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% 0.38/0.60 inference(unit_resolution,[status(thm)],[242, 238])).
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% 0.38/0.60 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.38/0.60 inference(unit_resolution,[status(thm)],[243, 231])).
% 0.38/0.60 tff(245,assumption,(b(s(s(s(z))), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 0.38/0.60 tff(246,assumption,(b(s(s(s(z))), s(z))), introduced(assumption)).
% 0.38/0.60 tff(247,plain,
% 0.38/0.60 (~r(z, s(s(s(s(s(s(z)))))))),
% 0.38/0.60 inference(unit_resolution,[status(thm)],[22, 3, 4])).
% 0.38/0.60 tff(248,plain,
% 0.38/0.60 ((z = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(z)))))) = z)),
% 0.38/0.60 inference(commutativity,[status(thm)],[])).
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% 0.38/0.60 ((s(s(s(s(s(s(z)))))) = z) <=> (z = s(s(s(s(s(s(z)))))))),
% 0.38/0.60 inference(symmetry,[status(thm)],[248])).
% 0.38/0.60 tff(250,plain,
% 0.38/0.60 ((~(s(s(s(s(s(s(z)))))) = z)) <=> (~(z = s(s(s(s(s(s(z))))))))),
% 0.38/0.60 inference(monotonicity,[status(thm)],[249])).
% 0.38/0.60 tff(251,plain,
% 0.38/0.60 (~(z = s(s(s(s(s(s(z)))))))),
% 0.38/0.60 inference(modus_ponens,[status(thm)],[213, 250])).
% 0.38/0.60 tff(252,plain,
% 0.38/0.60 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(s(s(z))))))) | b(z, s(s(s(s(s(s(z))))))) | r(z, s(s(s(s(s(s(z))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(s(s(z))))))) | b(z, s(s(s(s(s(s(z))))))) | r(z, s(s(s(s(s(s(z))))))))),
% 0.38/0.60 inference(rewrite,[status(thm)],[])).
% 0.38/0.60 tff(253,plain,
% 0.38/0.60 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(s(s(z))))))) | b(z, s(s(s(s(s(s(z))))))) | r(z, s(s(s(s(s(s(z))))))))),
% 0.38/0.60 inference(quant_inst,[status(thm)],[])).
% 0.38/0.60 tff(254,plain,
% 0.38/0.60 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(s(s(z))))))) | b(z, s(s(s(s(s(s(z))))))) | r(z, s(s(s(s(s(s(z)))))))),
% 0.38/0.60 inference(modus_ponens,[status(thm)],[253, 252])).
% 0.38/0.60 tff(255,plain,
% 0.38/0.60 ((z = s(s(s(s(s(s(z))))))) | b(z, s(s(s(s(s(s(z))))))) | r(z, s(s(s(s(s(s(z)))))))),
% 0.38/0.60 inference(unit_resolution,[status(thm)],[254, 79])).
% 0.38/0.60 tff(256,plain,
% 0.38/0.60 (b(z, s(s(s(s(s(s(z))))))) | r(z, s(s(s(s(s(s(z)))))))),
% 0.38/0.60 inference(unit_resolution,[status(thm)],[255, 251])).
% 0.38/0.60 tff(257,plain,
% 0.38/0.60 (b(z, s(s(s(s(s(s(z)))))))),
% 0.38/0.60 inference(unit_resolution,[status(thm)],[256, 247])).
% 0.38/0.60 tff(258,assumption,(b(z, s(s(s(z))))), introduced(assumption)).
% 0.38/0.60 tff(259,assumption,(b(s(s(s(s(s(s(z)))))), s(s(s(z))))), introduced(assumption)).
% 0.38/0.60 tff(260,plain,
% 0.38/0.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 0.38/0.60 inference(rewrite,[status(thm)],[])).
% 0.38/0.60 tff(261,plain,
% 0.38/0.60 (((~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z))))))))) <=> ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 0.38/0.60 inference(rewrite,[status(thm)],[])).
% 0.38/0.60 tff(262,plain,
% 0.38/0.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))))),
% 0.38/0.60 inference(monotonicity,[status(thm)],[261])).
% 0.38/0.60 tff(263,plain,
% 0.38/0.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 0.38/0.60 inference(transitivity,[status(thm)],[262, 260])).
% 0.38/0.60 tff(264,plain,
% 0.38/0.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 0.38/0.60 inference(quant_inst,[status(thm)],[])).
% 0.38/0.60 tff(265,plain,
% 0.38/0.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 0.38/0.60 inference(modus_ponens,[status(thm)],[264, 263])).
% 0.38/0.60 tff(266,plain,
% 0.38/0.60 ($false),
% 0.38/0.60 inference(unit_resolution,[status(thm)],[265, 188, 27, 245, 259, 258])).
% 0.38/0.60 tff(267,plain,((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.38/0.60 tff(268,plain,
% 0.38/0.60 (~b(z, s(s(s(z))))),
% 0.38/0.60 inference(unit_resolution,[status(thm)],[267, 257, 245, 244])).
% 0.38/0.60 tff(269,assumption,(~b(z, s(s(s(z))))), introduced(assumption)).
% 0.38/0.60 tff(270,assumption,(z = s(s(s(z)))), introduced(assumption)).
% 0.38/0.60 tff(271,plain,
% 0.38/0.60 (s(s(s(z))) = z),
% 0.38/0.60 inference(symmetry,[status(thm)],[270])).
% 0.38/0.60 tff(272,plain,
% 0.38/0.60 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(z))) = z))),
% 0.38/0.60 inference(quant_inst,[status(thm)],[])).
% 0.38/0.60 tff(273,plain,
% 0.38/0.60 (~(s(s(s(z))) = z)),
% 0.38/0.60 inference(unit_resolution,[status(thm)],[272, 62])).
% 0.38/0.60 tff(274,plain,
% 0.38/0.60 ($false),
% 0.38/0.60 inference(unit_resolution,[status(thm)],[273, 271])).
% 0.38/0.60 tff(275,plain,(~(z = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.38/0.60 tff(276,assumption,(~r(z, s(s(s(z))))), introduced(assumption)).
% 0.38/0.60 tff(277,plain,
% 0.38/0.60 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z)))))),
% 0.38/0.60 inference(rewrite,[status(thm)],[])).
% 0.38/0.60 tff(278,plain,
% 0.38/0.60 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z)))))),
% 0.38/0.60 inference(quant_inst,[status(thm)],[])).
% 0.38/0.60 tff(279,plain,
% 0.38/0.60 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z))))),
% 0.38/0.60 inference(modus_ponens,[status(thm)],[278, 277])).
% 0.38/0.60 tff(280,plain,
% 0.38/0.60 ($false),
% 0.38/0.60 inference(unit_resolution,[status(thm)],[279, 79, 276, 275, 269])).
% 0.38/0.60 tff(281,plain,(r(z, s(s(s(z)))) | b(z, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.38/0.60 tff(282,plain,
% 0.38/0.60 (r(z, s(s(s(z))))),
% 0.38/0.60 inference(unit_resolution,[status(thm)],[281, 268])).
% 0.38/0.60 tff(283,assumption,(b(s(s(s(z))), z)), introduced(assumption)).
% 0.38/0.60 tff(284,assumption,(r(z, s(s(s(z))))), introduced(assumption)).
% 0.38/0.60 tff(285,plain,
% 0.38/0.60 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 0.38/0.60 inference(rewrite,[status(thm)],[])).
% 0.38/0.60 tff(286,plain,
% 0.38/0.60 (((~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 0.38/0.60 inference(rewrite,[status(thm)],[])).
% 0.38/0.60 tff(287,plain,
% 0.38/0.60 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z)))))))),
% 0.38/0.60 inference(monotonicity,[status(thm)],[286])).
% 0.38/0.60 tff(288,plain,
% 0.38/0.60 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 0.38/0.60 inference(transitivity,[status(thm)],[287, 285])).
% 0.38/0.60 tff(289,plain,
% 0.38/0.60 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(z))))),
% 0.38/0.60 inference(quant_inst,[status(thm)],[])).
% 0.38/0.60 tff(290,plain,
% 0.38/0.60 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z)))))),
% 0.38/0.60 inference(modus_ponens,[status(thm)],[289, 288])).
% 0.38/0.60 tff(291,plain,
% 0.38/0.60 (~r(z, s(z))),
% 0.38/0.60 inference(unit_resolution,[status(thm)],[290, 14, 26, 284])).
% 0.38/0.60 tff(292,plain,
% 0.38/0.60 ((z = s(z)) <=> (s(z) = z)),
% 0.38/0.60 inference(commutativity,[status(thm)],[])).
% 0.38/0.60 tff(293,plain,
% 0.38/0.60 ((s(z) = z) <=> (z = s(z))),
% 0.38/0.60 inference(symmetry,[status(thm)],[292])).
% 0.38/0.60 tff(294,plain,
% 0.38/0.60 ((~(s(z) = z)) <=> (~(z = s(z)))),
% 0.38/0.60 inference(monotonicity,[status(thm)],[293])).
% 0.38/0.60 tff(295,plain,
% 0.38/0.60 (~(z = s(z))),
% 0.38/0.60 inference(modus_ponens,[status(thm)],[112, 294])).
% 0.38/0.60 tff(296,plain,
% 0.38/0.60 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(z)) | b(z, s(z)) | r(z, s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(z)) | b(z, s(z)) | r(z, s(z)))),
% 0.38/0.60 inference(rewrite,[status(thm)],[])).
% 0.38/0.60 tff(297,plain,
% 0.38/0.60 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(z)) | b(z, s(z)) | r(z, s(z)))),
% 0.38/0.60 inference(quant_inst,[status(thm)],[])).
% 0.38/0.60 tff(298,plain,
% 0.38/0.60 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(z)) | b(z, s(z)) | r(z, s(z))),
% 0.38/0.60 inference(modus_ponens,[status(thm)],[297, 296])).
% 0.38/0.60 tff(299,plain,
% 0.38/0.60 ((z = s(z)) | b(z, s(z)) | r(z, s(z))),
% 0.38/0.60 inference(unit_resolution,[status(thm)],[298, 79])).
% 0.38/0.60 tff(300,plain,
% 0.38/0.60 (b(z, s(z)) | r(z, s(z))),
% 0.38/0.60 inference(unit_resolution,[status(thm)],[299, 295])).
% 0.38/0.60 tff(301,plain,
% 0.38/0.60 (b(z, s(z))),
% 0.38/0.60 inference(unit_resolution,[status(thm)],[300, 291])).
% 0.38/0.60 tff(302,plain,
% 0.38/0.60 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 0.38/0.60 inference(rewrite,[status(thm)],[])).
% 0.38/0.60 tff(303,plain,
% 0.38/0.60 (((~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 0.38/0.60 inference(rewrite,[status(thm)],[])).
% 0.38/0.60 tff(304,plain,
% 0.38/0.60 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z)))))))),
% 0.38/0.60 inference(monotonicity,[status(thm)],[303])).
% 0.38/0.60 tff(305,plain,
% 0.38/0.60 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 0.38/0.60 inference(transitivity,[status(thm)],[304, 302])).
% 0.38/0.60 tff(306,plain,
% 0.38/0.60 ((~![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)))),
% 0.38/0.60 inference(quant_inst,[status(thm)],[])).
% 0.38/0.60 tff(307,plain,
% 0.38/0.60 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z)))))),
% 0.38/0.60 inference(modus_ponens,[status(thm)],[306, 305])).
% 0.38/0.60 tff(308,plain,
% 0.38/0.60 (~r(s(z), z)),
% 0.38/0.60 inference(unit_resolution,[status(thm)],[307, 14, 26, 284])).
% 0.38/0.60 tff(309,plain,
% 0.38/0.60 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = z) | b(s(z), z) | r(s(z), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = z) | b(s(z), z) | r(s(z), z))),
% 0.38/0.60 inference(rewrite,[status(thm)],[])).
% 0.38/0.60 tff(310,plain,
% 0.38/0.60 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = z) | b(s(z), z) | r(s(z), z))),
% 0.38/0.60 inference(quant_inst,[status(thm)],[])).
% 0.38/0.60 tff(311,plain,
% 0.38/0.60 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = z) | b(s(z), z) | r(s(z), z)),
% 0.38/0.60 inference(modus_ponens,[status(thm)],[310, 309])).
% 0.38/0.60 tff(312,plain,
% 0.38/0.60 (b(s(z), z) | r(s(z), z)),
% 0.38/0.60 inference(unit_resolution,[status(thm)],[311, 79, 112])).
% 0.38/0.60 tff(313,plain,
% 0.38/0.60 (b(s(z), z)),
% 0.38/0.60 inference(unit_resolution,[status(thm)],[312, 308])).
% 0.38/0.60 tff(314,plain,
% 0.38/0.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 0.38/0.60 inference(rewrite,[status(thm)],[])).
% 0.38/0.60 tff(315,plain,
% 0.38/0.60 (((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z)))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 0.38/0.60 inference(rewrite,[status(thm)],[])).
% 0.38/0.60 tff(316,plain,
% 0.38/0.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z))))),
% 0.38/0.60 inference(monotonicity,[status(thm)],[315])).
% 0.38/0.60 tff(317,plain,
% 0.38/0.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 0.38/0.60 inference(transitivity,[status(thm)],[316, 314])).
% 0.38/0.60 tff(318,plain,
% 0.38/0.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 0.38/0.60 inference(quant_inst,[status(thm)],[])).
% 0.38/0.60 tff(319,plain,
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% 0.38/0.61 inference(unit_resolution,[status(thm)],[281, 371])).
% 0.38/0.61 tff(373,assumption,(r(z, s(z))), introduced(assumption)).
% 0.38/0.61 tff(374,plain,
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% 0.38/0.61 inference(unit_resolution,[status(thm)],[290, 14, 373, 26, 284])).
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% 0.38/0.61 inference(unit_resolution,[status(thm)],[375, 372, 26])).
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% 0.38/0.61 inference(commutativity,[status(thm)],[])).
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% 0.38/0.61 inference(monotonicity,[status(thm)],[378])).
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% 0.38/0.61 inference(modus_ponens,[status(thm)],[93, 379])).
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% 0.38/0.61 tff(382,plain,
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% 0.38/0.61 tff(383,assumption,(s(s(z)) = s(s(s(s(s(s(z))))))), introduced(assumption)).
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% 0.38/0.61 tff(385,plain,
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% 0.38/0.61 inference(transitivity,[status(thm)],[54, 385, 108])).
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% 0.38/0.61 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(z))),
% 0.38/0.61 inference(monotonicity,[status(thm)],[386])).
% 0.38/0.61 tff(388,plain,
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% 0.38/0.61 inference(symmetry,[status(thm)],[201])).
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% 0.38/0.61 inference(quant_inst,[status(thm)],[])).
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% 0.38/0.61 inference(unit_resolution,[status(thm)],[390, 62])).
% 0.38/0.61 tff(392,plain,
% 0.38/0.61 ($false),
% 0.38/0.61 inference(unit_resolution,[status(thm)],[391, 389])).
% 0.38/0.61 tff(393,plain,(~(s(s(z)) = s(s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 0.38/0.61 tff(394,plain,
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% 0.38/0.61 inference(unit_resolution,[status(thm)],[393, 382])).
% 0.38/0.61 tff(395,plain,(~(s(s(s(s(s(s(z)))))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.38/0.61 tff(396,plain,
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% 0.38/0.61 inference(transitivity,[status(thm)],[398, 396])).
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% 0.38/0.61 (~b(s(z), s(s(s(s(s(s(z)))))))),
% 0.38/0.61 inference(unit_resolution,[status(thm)],[401, 188, 360, 27, 89])).
% 0.38/0.61 tff(403,plain,
% 0.38/0.61 (r(s(z), s(s(s(s(s(s(z)))))))),
% 0.38/0.61 inference(unit_resolution,[status(thm)],[84, 402])).
% 0.38/0.61 tff(404,plain,
% 0.38/0.61 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 0.38/0.61 inference(unit_resolution,[status(thm)],[35, 403, 26])).
% 0.38/0.61 tff(405,plain,
% 0.38/0.62 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 0.38/0.62 inference(unit_resolution,[status(thm)],[220, 404])).
% 0.38/0.62 tff(406,assumption,(b(s(s(z)), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 0.38/0.62 tff(407,plain,
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% 0.38/0.62 inference(rewrite,[status(thm)],[])).
% 0.38/0.62 tff(408,plain,
% 0.38/0.62 (((~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
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% 0.38/0.62 tff(409,plain,
% 0.38/0.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))))),
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% 0.38/0.62 inference(transitivity,[status(thm)],[409, 407])).
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% 0.38/0.62 (~b(s(s(z)), s(s(s(z))))),
% 0.38/0.62 inference(unit_resolution,[status(thm)],[412, 188, 406, 245, 259])).
% 0.38/0.62 tff(414,assumption,(~r(s(s(z)), s(s(s(z))))), introduced(assumption)).
% 0.38/0.62 tff(415,assumption,(~b(s(s(z)), s(s(s(z))))), introduced(assumption)).
% 0.38/0.62 tff(416,assumption,(s(s(z)) = s(s(s(z)))), introduced(assumption)).
% 0.38/0.62 tff(417,plain,
% 0.38/0.62 (inj_0(s(s(z))) = inj_0(s(s(s(z))))),
% 0.38/0.62 inference(monotonicity,[status(thm)],[416])).
% 0.38/0.62 tff(418,plain,
% 0.38/0.62 (s(z) = s(s(s(z)))),
% 0.38/0.62 inference(transitivity,[status(thm)],[109, 417, 154, 416])).
% 0.38/0.62 tff(419,plain,
% 0.38/0.62 ($false),
% 0.38/0.62 inference(unit_resolution,[status(thm)],[158, 418])).
% 0.38/0.62 tff(420,plain,(~(s(s(z)) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.38/0.62 tff(421,plain,
% 0.38/0.62 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z)))))),
% 0.38/0.62 inference(rewrite,[status(thm)],[])).
% 0.38/0.62 tff(422,plain,
% 0.38/0.62 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z)))))),
% 0.38/0.62 inference(quant_inst,[status(thm)],[])).
% 0.38/0.62 tff(423,plain,
% 0.38/0.62 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z))))),
% 0.38/0.62 inference(modus_ponens,[status(thm)],[422, 421])).
% 0.38/0.62 tff(424,plain,
% 0.38/0.62 ($false),
% 0.38/0.62 inference(unit_resolution,[status(thm)],[423, 79, 420, 415, 414])).
% 0.38/0.62 tff(425,plain,(r(s(s(z)), s(s(s(z)))) | b(s(s(z)), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.38/0.62 tff(426,plain,
% 0.38/0.62 (r(s(s(z)), s(s(s(z))))),
% 0.38/0.62 inference(unit_resolution,[status(thm)],[425, 413])).
% 0.38/0.62 tff(427,assumption,(b(s(s(z)), z)), introduced(assumption)).
% 0.38/0.62 tff(428,plain,
% 0.38/0.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 0.38/0.62 inference(rewrite,[status(thm)],[])).
% 0.38/0.62 tff(429,plain,
% 0.38/0.62 (((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), z))) <=> ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 0.38/0.62 inference(rewrite,[status(thm)],[])).
% 0.38/0.62 tff(430,plain,
% 0.38/0.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z))))),
% 0.38/0.62 inference(monotonicity,[status(thm)],[429])).
% 0.38/0.62 tff(431,plain,
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% 0.38/0.62 inference(transitivity,[status(thm)],[430, 428])).
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% 0.38/0.62 inference(quant_inst,[status(thm)],[])).
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% 0.38/0.62 inference(modus_ponens,[status(thm)],[432, 431])).
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% 0.38/0.62 tff(436,plain,
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% 0.38/0.62 inference(unit_resolution,[status(thm)],[265, 188, 27, 245, 259])).
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% 0.38/0.62 inference(unit_resolution,[status(thm)],[279, 79, 275, 438])).
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% 0.38/0.62 inference(rewrite,[status(thm)],[])).
% 0.38/0.62 tff(441,plain,
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% 0.38/0.62 inference(rewrite,[status(thm)],[])).
% 0.38/0.62 tff(442,plain,
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% 0.38/0.62 inference(monotonicity,[status(thm)],[441])).
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% 0.38/0.62 inference(transitivity,[status(thm)],[442, 440])).
% 0.38/0.62 tff(444,plain,
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% 0.38/0.62 inference(quant_inst,[status(thm)],[])).
% 0.38/0.62 tff(445,plain,
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% 0.38/0.62 inference(modus_ponens,[status(thm)],[444, 443])).
% 0.38/0.62 tff(446,plain,
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% 0.38/0.62 inference(unit_resolution,[status(thm)],[445, 14, 439, 437, 426])).
% 0.38/0.62 tff(447,plain,((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 0.38/0.62 tff(448,plain,
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% 0.38/0.62 inference(unit_resolution,[status(thm)],[447, 405, 259, 27, 89])).
% 0.38/0.62 tff(449,plain,
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% 0.38/0.62 inference(rewrite,[status(thm)],[])).
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% 0.38/0.62 inference(quant_inst,[status(thm)],[])).
% 0.38/0.62 tff(451,plain,
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% 0.38/0.62 inference(modus_ponens,[status(thm)],[450, 449])).
% 0.38/0.62 tff(452,plain,
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% 0.38/0.62 inference(unit_resolution,[status(thm)],[451, 79])).
% 0.38/0.62 tff(453,plain,
% 0.38/0.62 (b(s(s(z)), s(s(s(s(s(s(z))))))) | r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 0.38/0.62 inference(unit_resolution,[status(thm)],[452, 393])).
% 0.38/0.62 tff(454,plain,
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% 0.38/0.62 inference(unit_resolution,[status(thm)],[453, 448])).
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% 0.38/0.62 inference(unit_resolution,[status(thm)],[102, 14, 454, 403])).
% 0.38/0.62 tff(456,plain,
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% 0.38/0.62 inference(unit_resolution,[status(thm)],[117, 79, 114, 455])).
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% 0.38/0.62 inference(unit_resolution,[status(thm)],[267, 405, 259, 27])).
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% 0.38/0.62 inference(unit_resolution,[status(thm)],[281, 457])).
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% 0.38/0.62 inference(unit_resolution,[status(thm)],[321, 458, 26, 246])).
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% 0.38/0.62 inference(unit_resolution,[status(thm)],[326, 459])).
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% 0.38/0.62 inference(rewrite,[status(thm)],[])).
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% 0.38/0.62 inference(quant_inst,[status(thm)],[])).
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% 0.38/0.62 tff(471,plain,((~(s(s(s(z))) = s(s(z)))) | (s(s(z)) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.38/0.62 tff(472,plain,
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% 0.38/0.62 inference(unit_resolution,[status(thm)],[471, 420])).
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% 0.38/0.62 inference(modus_ponens,[status(thm)],[474, 473])).
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% 0.38/0.62 inference(unit_resolution,[status(thm)],[476, 464])).
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% 0.38/0.62 inference(rewrite,[status(thm)],[])).
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% 0.46/0.63 inference(modus_ponens,[status(thm)],[484, 483])).
% 0.46/0.63 tff(486,plain,
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% 0.46/0.63 inference(unit_resolution,[status(thm)],[485, 188, 246, 479, 477, 456])).
% 0.46/0.63 tff(487,plain,((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(z))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 0.46/0.63 tff(488,plain,
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% 0.46/0.63 inference(unit_resolution,[status(thm)],[487, 246, 25, 26, 259, 27, 360])).
% 0.46/0.63 tff(489,plain,
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% 0.46/0.63 inference(rewrite,[status(thm)],[])).
% 0.46/0.63 tff(490,plain,
% 0.46/0.63 ((~![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))),
% 0.46/0.63 inference(quant_inst,[status(thm)],[])).
% 0.46/0.63 tff(491,plain,
% 0.46/0.63 ((~![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)),
% 0.46/0.63 inference(modus_ponens,[status(thm)],[490, 489])).
% 0.46/0.63 tff(492,plain,
% 0.46/0.63 (b(s(s(s(s(s(s(z)))))), z) | r(s(s(s(s(s(s(z)))))), z)),
% 0.46/0.63 inference(unit_resolution,[status(thm)],[491, 79, 213])).
% 0.46/0.63 tff(493,plain,
% 0.46/0.63 (r(s(s(s(s(s(s(z)))))), z)),
% 0.46/0.63 inference(unit_resolution,[status(thm)],[492, 488])).
% 0.46/0.63 tff(494,plain,
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% 0.46/0.63 inference(rewrite,[status(thm)],[])).
% 0.46/0.63 tff(495,plain,
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% 0.46/0.63 inference(quant_inst,[status(thm)],[])).
% 0.46/0.63 tff(496,plain,
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% 0.46/0.63 inference(modus_ponens,[status(thm)],[495, 494])).
% 0.46/0.63 tff(497,plain,
% 0.46/0.63 (~r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.46/0.63 inference(unit_resolution,[status(thm)],[496, 14, 493, 25])).
% 0.46/0.63 tff(498,plain,
% 0.46/0.63 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(s(z))) | b(s(s(s(s(s(s(z)))))), s(s(z))) | r(s(s(s(s(s(s(z)))))), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(s(z))) | b(s(s(s(s(s(s(z)))))), s(s(z))) | r(s(s(s(s(s(s(z)))))), s(s(z))))),
% 0.46/0.63 inference(rewrite,[status(thm)],[])).
% 0.46/0.63 tff(499,plain,
% 0.46/0.63 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(s(z))) | b(s(s(s(s(s(s(z)))))), s(s(z))) | r(s(s(s(s(s(s(z)))))), s(s(z))))),
% 0.46/0.63 inference(quant_inst,[status(thm)],[])).
% 0.46/0.63 tff(500,plain,
% 0.46/0.63 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(s(z))) | b(s(s(s(s(s(s(z)))))), s(s(z))) | r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.46/0.63 inference(modus_ponens,[status(thm)],[499, 498])).
% 0.46/0.63 tff(501,plain,
% 0.46/0.63 (b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.46/0.63 inference(unit_resolution,[status(thm)],[500, 79, 497, 395])).
% 0.46/0.63 tff(502,plain,
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% 0.46/0.63 inference(rewrite,[status(thm)],[])).
% 0.46/0.63 tff(503,plain,
% 0.46/0.63 (((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), z)))),
% 0.46/0.63 inference(rewrite,[status(thm)],[])).
% 0.46/0.63 tff(504,plain,
% 0.46/0.63 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), z))))),
% 0.46/0.63 inference(monotonicity,[status(thm)],[503])).
% 0.46/0.63 tff(505,plain,
% 0.46/0.63 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), z)))),
% 0.46/0.63 inference(transitivity,[status(thm)],[504, 502])).
% 0.46/0.63 tff(506,plain,
% 0.46/0.63 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 0.46/0.63 inference(quant_inst,[status(thm)],[])).
% 0.46/0.63 tff(507,plain,
% 0.46/0.63 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), z))),
% 0.46/0.63 inference(modus_ponens,[status(thm)],[506, 505])).
% 0.46/0.63 tff(508,plain,
% 0.46/0.63 (~r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 0.46/0.63 inference(unit_resolution,[status(thm)],[507, 14, 493, 25])).
% 0.46/0.63 tff(509,plain,
% 0.46/0.63 (b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 0.46/0.63 inference(unit_resolution,[status(thm)],[453, 508])).
% 0.46/0.63 tff(510,plain,
% 0.46/0.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 0.46/0.63 inference(rewrite,[status(thm)],[])).
% 0.46/0.63 tff(511,plain,
% 0.46/0.63 (((~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(s(z))))))))) <=> ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 0.46/0.63 inference(rewrite,[status(thm)],[])).
% 0.46/0.63 tff(512,plain,
% 0.46/0.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))))),
% 0.46/0.63 inference(monotonicity,[status(thm)],[511])).
% 0.46/0.63 tff(513,plain,
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% 0.46/0.63 inference(transitivity,[status(thm)],[512, 510])).
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% 0.46/0.63 inference(quant_inst,[status(thm)],[])).
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% 0.46/0.63 inference(modus_ponens,[status(thm)],[514, 513])).
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% 0.46/0.63 (~b(z, s(s(z)))),
% 0.46/0.63 inference(unit_resolution,[status(thm)],[515, 188, 509, 27, 501])).
% 0.46/0.63 tff(517,plain,
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% 0.46/0.63 inference(rewrite,[status(thm)],[])).
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% 0.46/0.63 inference(quant_inst,[status(thm)],[])).
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% 0.46/0.63 inference(modus_ponens,[status(thm)],[518, 517])).
% 0.46/0.63 tff(520,plain,
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% 0.46/0.63 inference(unit_resolution,[status(thm)],[519, 79, 516])).
% 0.46/0.63 tff(521,plain,
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% 0.46/0.63 inference(unit_resolution,[status(thm)],[520, 380])).
% 0.46/0.63 tff(522,assumption,(r(s(s(z)), s(s(s(z))))), introduced(assumption)).
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% 0.46/0.63 inference(rewrite,[status(thm)],[])).
% 0.46/0.63 tff(524,plain,
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% 0.46/0.63 inference(quant_inst,[status(thm)],[])).
% 0.46/0.63 tff(525,plain,
% 0.46/0.63 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z))))),
% 0.46/0.63 inference(modus_ponens,[status(thm)],[524, 523])).
% 0.46/0.63 tff(526,plain,
% 0.46/0.63 (~r(s(z), s(s(z)))),
% 0.46/0.63 inference(unit_resolution,[status(thm)],[525, 14, 26, 522])).
% 0.46/0.63 tff(527,plain,
% 0.46/0.63 (b(s(z), s(s(z)))),
% 0.46/0.63 inference(unit_resolution,[status(thm)],[117, 79, 114, 526])).
% 0.46/0.63 tff(528,plain,
% 0.46/0.63 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 0.46/0.63 inference(rewrite,[status(thm)],[])).
% 0.46/0.63 tff(529,plain,
% 0.46/0.63 (((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 0.46/0.63 inference(rewrite,[status(thm)],[])).
% 0.46/0.63 tff(530,plain,
% 0.46/0.63 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z))))),
% 0.46/0.63 inference(monotonicity,[status(thm)],[529])).
% 0.46/0.63 tff(531,plain,
% 0.46/0.63 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 0.46/0.63 inference(transitivity,[status(thm)],[530, 528])).
% 0.46/0.63 tff(532,plain,
% 0.46/0.63 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 0.46/0.63 inference(quant_inst,[status(thm)],[])).
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% 0.46/0.64 inference(monotonicity,[status(thm)],[576])).
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% 0.46/0.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)))),
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% 0.46/0.67 inference(monotonicity,[status(thm)],[817])).
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% 0.46/0.67 inference(quant_inst,[status(thm)],[])).
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% 0.46/0.67 tff(834,plain,
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% 0.46/0.67 inference(symmetry,[status(thm)],[835])).
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% 0.46/0.67 tff(845,assumption,(r(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 0.46/0.67 tff(846,assumption,(r(s(s(s(s(z)))), z)), introduced(assumption)).
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% 0.46/0.67 inference(quant_inst,[status(thm)],[])).
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% 0.46/0.67 tff(851,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 0.46/0.67 tff(852,plain,
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% 0.46/0.67 tff(854,assumption,(~b(s(s(s(s(z)))), z)), introduced(assumption)).
% 0.46/0.67 tff(855,plain,
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% 0.46/0.67 tff(860,plain,
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% 0.46/0.68 tff(878,plain,
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% 0.46/0.68 tff(885,plain,(~(s(s(s(s(z)))) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.46/0.68 tff(886,plain,
% 0.46/0.68 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z)))))),
% 0.46/0.68 inference(rewrite,[status(thm)],[])).
% 0.46/0.68 tff(887,plain,
% 0.46/0.68 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z)))))),
% 0.46/0.68 inference(quant_inst,[status(thm)],[])).
% 0.46/0.68 tff(888,plain,
% 0.46/0.68 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z))))),
% 0.46/0.68 inference(modus_ponens,[status(thm)],[887, 886])).
% 0.46/0.68 tff(889,plain,
% 0.46/0.68 ((s(s(s(s(z)))) = s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z))))),
% 0.46/0.68 inference(unit_resolution,[status(thm)],[888, 79])).
% 0.46/0.68 tff(890,plain,
% 0.46/0.68 (b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z))))),
% 0.46/0.68 inference(unit_resolution,[status(thm)],[889, 885])).
% 0.46/0.68 tff(891,plain,
% 0.46/0.68 (b(s(s(s(s(z)))), s(s(s(z))))),
% 0.46/0.68 inference(unit_resolution,[status(thm)],[890, 878])).
% 0.46/0.68 tff(892,assumption,(b(s(s(s(z))), s(s(z)))), introduced(assumption)).
% 0.46/0.68 tff(893,assumption,(b(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 0.46/0.68 tff(894,plain,
% 0.46/0.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 0.46/0.68 inference(rewrite,[status(thm)],[])).
% 0.46/0.68 tff(895,plain,
% 0.46/0.68 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 0.46/0.68 inference(rewrite,[status(thm)],[])).
% 0.46/0.68 tff(896,plain,
% 0.46/0.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 0.46/0.68 inference(monotonicity,[status(thm)],[895])).
% 0.46/0.68 tff(897,plain,
% 0.46/0.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 0.46/0.68 inference(transitivity,[status(thm)],[896, 894])).
% 0.46/0.68 tff(898,plain,
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% 0.46/0.68 inference(quant_inst,[status(thm)],[])).
% 0.46/0.68 tff(899,plain,
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% 0.46/0.68 inference(modus_ponens,[status(thm)],[898, 897])).
% 0.46/0.68 tff(900,plain,
% 0.46/0.68 (~b(s(s(s(s(z)))), s(s(z)))),
% 0.46/0.68 inference(unit_resolution,[status(thm)],[899, 188, 96, 893, 892])).
% 0.46/0.68 tff(901,assumption,(s(s(s(s(z)))) = s(s(z))), introduced(assumption)).
% 0.46/0.68 tff(902,plain,
% 0.46/0.68 (s(s(z)) = s(s(s(s(z))))),
% 0.46/0.68 inference(symmetry,[status(thm)],[901])).
% 0.46/0.68 tff(903,plain,
% 0.46/0.68 (inj_0(s(s(z))) = inj_0(s(s(s(s(z)))))),
% 0.46/0.68 inference(monotonicity,[status(thm)],[902])).
% 0.46/0.68 tff(904,plain,
% 0.46/0.68 (s(z) = s(s(s(z)))),
% 0.46/0.68 inference(transitivity,[status(thm)],[109, 903, 839])).
% 0.46/0.68 tff(905,plain,
% 0.46/0.68 ($false),
% 0.46/0.68 inference(unit_resolution,[status(thm)],[158, 904])).
% 0.46/0.68 tff(906,plain,(~(s(s(s(s(z)))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.46/0.68 tff(907,plain,
% 0.46/0.68 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z))))),
% 0.46/0.68 inference(rewrite,[status(thm)],[])).
% 0.46/0.68 tff(908,plain,
% 0.46/0.68 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z))))),
% 0.46/0.68 inference(quant_inst,[status(thm)],[])).
% 0.46/0.68 tff(909,plain,
% 0.46/0.68 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z)))),
% 0.46/0.68 inference(modus_ponens,[status(thm)],[908, 907])).
% 0.46/0.68 tff(910,plain,
% 0.46/0.68 (r(s(s(s(s(z)))), s(s(z)))),
% 0.46/0.68 inference(unit_resolution,[status(thm)],[909, 79, 906, 900])).
% 0.46/0.68 tff(911,plain,
% 0.46/0.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 0.46/0.68 inference(rewrite,[status(thm)],[])).
% 0.46/0.68 tff(912,plain,
% 0.46/0.68 (((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 0.46/0.68 inference(rewrite,[status(thm)],[])).
% 0.46/0.68 tff(913,plain,
% 0.46/0.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 0.46/0.68 inference(monotonicity,[status(thm)],[912])).
% 0.46/0.68 tff(914,plain,
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% 0.46/0.68 inference(transitivity,[status(thm)],[913, 911])).
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% 0.46/0.68 inference(quant_inst,[status(thm)],[])).
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% 0.46/0.68 inference(modus_ponens,[status(thm)],[915, 914])).
% 0.46/0.68 tff(917,plain,
% 0.46/0.68 (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
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% 0.46/0.68 tff(918,assumption,(s(s(s(s(z)))) = s(s(s(s(s(s(z))))))), introduced(assumption)).
% 0.46/0.68 tff(919,plain,
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% 0.46/0.68 tff(922,plain,
% 0.46/0.68 (s(s(z)) = s(s(s(s(s(s(z))))))),
% 0.46/0.68 inference(transitivity,[status(thm)],[155, 921, 201, 918])).
% 0.46/0.68 tff(923,plain,
% 0.46/0.68 ($false),
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% 0.46/0.68 tff(924,plain,(~(s(s(s(s(z)))) = s(s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 0.46/0.68 tff(925,plain,
% 0.46/0.68 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 0.46/0.68 inference(rewrite,[status(thm)],[])).
% 0.46/0.68 tff(926,plain,
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% 0.46/0.68 inference(quant_inst,[status(thm)],[])).
% 0.46/0.68 tff(927,plain,
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% 0.46/0.68 inference(modus_ponens,[status(thm)],[926, 925])).
% 0.46/0.68 tff(928,plain,
% 0.46/0.68 (r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.46/0.68 inference(unit_resolution,[status(thm)],[927, 79, 924, 917])).
% 0.46/0.68 tff(929,plain,
% 0.46/0.68 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 0.46/0.68 inference(rewrite,[status(thm)],[])).
% 0.46/0.68 tff(930,plain,
% 0.46/0.68 (((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(z))))) <=> ((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 0.46/0.68 inference(rewrite,[status(thm)],[])).
% 0.46/0.68 tff(931,plain,
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% 0.46/0.69 inference(quant_inst,[status(thm)],[])).
% 0.46/0.69 tff(982,plain,
% 0.46/0.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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))),
% 0.46/0.69 inference(modus_ponens,[status(thm)],[981, 980])).
% 0.46/0.69 tff(983,plain,
% 0.46/0.69 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 0.46/0.69 inference(unit_resolution,[status(thm)],[982, 188, 968, 976, 89])).
% 0.46/0.69 tff(984,plain,
% 0.46/0.69 (r(s(s(s(s(s(s(z)))))), s(z))),
% 0.46/0.69 inference(unit_resolution,[status(thm)],[627, 983])).
% 0.46/0.69 tff(985,plain,
% 0.46/0.69 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 0.46/0.69 inference(rewrite,[status(thm)],[])).
% 0.46/0.69 tff(986,plain,
% 0.46/0.69 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 0.46/0.69 inference(quant_inst,[status(thm)],[])).
% 0.46/0.69 tff(987,plain,
% 0.46/0.69 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 0.46/0.69 inference(modus_ponens,[status(thm)],[986, 985])).
% 0.46/0.69 tff(988,plain,
% 0.46/0.69 ($false),
% 0.46/0.69 inference(unit_resolution,[status(thm)],[987, 14, 140, 222, 984])).
% 0.46/0.69 tff(989,plain,((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 0.46/0.69 tff(990,plain,
% 0.46/0.69 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.46/0.69 inference(unit_resolution,[status(thm)],[989, 960, 89, 221, 88, 4])).
% 0.46/0.69 tff(991,plain,
% 0.46/0.69 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.46/0.69 inference(unit_resolution,[status(thm)],[243, 990])).
% 0.46/0.69 tff(992,plain,
% 0.46/0.69 (~b(z, s(s(s(z))))),
% 0.46/0.69 inference(unit_resolution,[status(thm)],[267, 964, 221, 991])).
% 0.46/0.69 tff(993,plain,
% 0.46/0.69 (r(z, s(s(s(z))))),
% 0.46/0.69 inference(unit_resolution,[status(thm)],[281, 992])).
% 0.46/0.69 tff(994,plain,
% 0.46/0.69 (~r(z, s(z))),
% 0.46/0.69 inference(unit_resolution,[status(thm)],[644, 993, 960])).
% 0.46/0.69 tff(995,plain,
% 0.46/0.69 (b(z, s(z))),
% 0.46/0.69 inference(unit_resolution,[status(thm)],[300, 994])).
% 0.46/0.69 tff(996,plain,
% 0.46/0.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 0.46/0.69 inference(rewrite,[status(thm)],[])).
% 0.46/0.69 tff(997,plain,
% 0.46/0.69 (((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 0.46/0.69 inference(rewrite,[status(thm)],[])).
% 0.46/0.69 tff(998,plain,
% 0.46/0.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))))),
% 0.46/0.69 inference(monotonicity,[status(thm)],[997])).
% 0.46/0.69 tff(999,plain,
% 0.46/0.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 0.46/0.69 inference(transitivity,[status(thm)],[998, 996])).
% 0.46/0.69 tff(1000,plain,
% 0.46/0.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))))),
% 0.46/0.69 inference(quant_inst,[status(thm)],[])).
% 0.46/0.69 tff(1001,plain,
% 0.46/0.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))),
% 0.46/0.69 inference(modus_ponens,[status(thm)],[1000, 999])).
% 0.46/0.69 tff(1002,plain,
% 0.46/0.69 (~b(z, s(s(z)))),
% 0.46/0.69 inference(unit_resolution,[status(thm)],[1001, 188, 995, 138, 118])).
% 0.46/0.69 tff(1003,plain,
% 0.46/0.69 (r(z, s(s(z)))),
% 0.46/0.69 inference(unit_resolution,[status(thm)],[519, 79, 1002, 95])).
% 0.46/0.69 tff(1004,assumption,(r(z, s(s(z)))), introduced(assumption)).
% 0.46/0.69 tff(1005,assumption,(r(s(s(s(z))), s(s(z)))), introduced(assumption)).
% 0.46/0.69 tff(1006,plain,
% 0.46/0.69 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)))),
% 0.46/0.69 inference(rewrite,[status(thm)],[])).
% 0.46/0.69 tff(1007,plain,
% 0.46/0.69 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)))),
% 0.46/0.69 inference(quant_inst,[status(thm)],[])).
% 0.46/0.69 tff(1008,plain,
% 0.46/0.69 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z))),
% 0.46/0.69 inference(modus_ponens,[status(thm)],[1007, 1006])).
% 0.46/0.69 tff(1009,plain,
% 0.46/0.69 ($false),
% 0.46/0.69 inference(unit_resolution,[status(thm)],[1008, 14, 2, 1005, 1004])).
% 0.46/0.69 tff(1010,plain,((~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.46/0.69 tff(1011,plain,
% 0.46/0.69 (~r(s(s(s(z))), s(s(z)))),
% 0.46/0.69 inference(unit_resolution,[status(thm)],[1010, 1003, 966])).
% 0.46/0.69 tff(1012,plain,
% 0.46/0.69 (b(s(s(s(z))), s(s(z)))),
% 0.46/0.69 inference(unit_resolution,[status(thm)],[476, 1011])).
% 0.46/0.69 tff(1013,plain,
% 0.46/0.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))))),
% 0.46/0.69 inference(rewrite,[status(thm)],[])).
% 0.46/0.69 tff(1014,plain,
% 0.46/0.69 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))))),
% 0.46/0.69 inference(rewrite,[status(thm)],[])).
% 0.46/0.69 tff(1015,plain,
% 0.46/0.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z))))))),
% 0.46/0.69 inference(monotonicity,[status(thm)],[1014])).
% 0.46/0.69 tff(1016,plain,
% 0.46/0.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))))),
% 0.46/0.69 inference(transitivity,[status(thm)],[1015, 1013])).
% 0.46/0.69 tff(1017,plain,
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% 0.46/0.69 inference(quant_inst,[status(thm)],[])).
% 0.46/0.69 tff(1018,plain,
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% 0.46/0.69 inference(modus_ponens,[status(thm)],[1017, 1016])).
% 0.46/0.69 tff(1019,plain,
% 0.46/0.69 ($false),
% 0.46/0.69 inference(unit_resolution,[status(thm)],[1018, 188, 951, 96, 1012, 118])).
% 0.46/0.69 tff(1020,plain,((~r(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 0.46/0.69 tff(1021,plain,
% 0.46/0.69 (~r(s(z), s(s(s(s(s(s(z)))))))),
% 0.46/0.69 inference(unit_resolution,[status(thm)],[1020, 96, 89, 88])).
% 0.46/0.69 tff(1022,plain,
% 0.46/0.69 (b(s(z), s(s(s(s(s(s(z)))))))),
% 0.46/0.69 inference(unit_resolution,[status(thm)],[84, 1021])).
% 0.46/0.69 tff(1023,plain,
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% 0.46/0.69 inference(unit_resolution,[status(thm)],[346, 14, 88, 1, 25])).
% 0.46/0.69 tff(1024,plain,((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 0.46/0.69 tff(1025,plain,
% 0.46/0.69 (~r(s(s(z)), z)),
% 0.46/0.69 inference(unit_resolution,[status(thm)],[1024, 1, 88])).
% 0.46/0.69 tff(1026,plain,
% 0.46/0.69 (b(s(s(z)), z)),
% 0.46/0.69 inference(unit_resolution,[status(thm)],[792, 1025])).
% 0.46/0.69 tff(1027,plain,
% 0.46/0.69 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 0.46/0.69 inference(rewrite,[status(thm)],[])).
% 0.46/0.69 tff(1028,plain,
% 0.46/0.69 (((~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), z))) <=> ((~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 0.46/0.69 inference(rewrite,[status(thm)],[])).
% 0.46/0.69 tff(1029,plain,
% 0.46/0.69 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))))),
% 0.46/0.69 inference(monotonicity,[status(thm)],[1028])).
% 0.46/0.69 tff(1030,plain,
% 0.46/0.69 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 0.53/0.70 inference(transitivity,[status(thm)],[1029, 1027])).
% 0.53/0.70 tff(1031,plain,
% 0.53/0.70 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), z)))),
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% 0.53/0.70 inference(unit_resolution,[status(thm)],[117, 79, 114, 1084])).
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% 0.53/0.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 0.53/0.70 inference(rewrite,[status(thm)],[])).
% 0.53/0.70 tff(1087,plain,
% 0.53/0.70 (((~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 0.53/0.70 inference(rewrite,[status(thm)],[])).
% 0.53/0.70 tff(1088,plain,
% 0.53/0.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))))),
% 0.53/0.70 inference(monotonicity,[status(thm)],[1087])).
% 0.53/0.70 tff(1089,plain,
% 0.53/0.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))))),
% 0.53/0.70 inference(transitivity,[status(thm)],[1088, 1086])).
% 0.53/0.70 tff(1090,plain,
% 0.53/0.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))))),
% 0.53/0.70 inference(quant_inst,[status(thm)],[])).
% 0.53/0.70 tff(1091,plain,
% 0.53/0.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))),
% 0.53/0.70 inference(modus_ponens,[status(thm)],[1090, 1089])).
% 0.53/0.70 tff(1092,plain,
% 0.53/0.70 (~b(z, s(s(z)))),
% 0.53/0.70 inference(unit_resolution,[status(thm)],[1091, 188, 96, 258, 892])).
% 0.53/0.70 tff(1093,plain,
% 0.53/0.70 (r(z, s(s(z)))),
% 0.53/0.70 inference(unit_resolution,[status(thm)],[519, 79, 1092, 95])).
% 0.53/0.70 tff(1094,assumption,(r(s(z), s(s(z)))), introduced(assumption)).
% 0.53/0.70 tff(1095,plain,
% 0.53/0.70 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))))),
% 0.53/0.70 inference(rewrite,[status(thm)],[])).
% 0.53/0.70 tff(1096,plain,
% 0.53/0.70 (((~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))))),
% 0.53/0.70 inference(rewrite,[status(thm)],[])).
% 0.53/0.70 tff(1097,plain,
% 0.53/0.70 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z))))))),
% 0.53/0.70 inference(monotonicity,[status(thm)],[1096])).
% 0.53/0.70 tff(1098,plain,
% 0.53/0.70 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))))),
% 0.53/0.70 inference(transitivity,[status(thm)],[1097, 1095])).
% 0.53/0.70 tff(1099,plain,
% 0.53/0.70 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z))))),
% 0.53/0.70 inference(quant_inst,[status(thm)],[])).
% 0.53/0.70 tff(1100,plain,
% 0.53/0.70 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z))))),
% 0.53/0.70 inference(modus_ponens,[status(thm)],[1099, 1098])).
% 0.53/0.70 tff(1101,plain,
% 0.53/0.70 ($false),
% 0.53/0.70 inference(unit_resolution,[status(thm)],[1100, 14, 373, 1094, 1093])).
% 0.53/0.70 tff(1102,plain,((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.53/0.71 tff(1103,plain,
% 0.53/0.71 (~r(z, s(z))),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[1102, 1085, 96, 1083, 892])).
% 0.53/0.71 tff(1104,plain,
% 0.53/0.71 (b(z, s(z))),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[300, 1103])).
% 0.53/0.71 tff(1105,plain,
% 0.53/0.71 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 0.53/0.71 inference(rewrite,[status(thm)],[])).
% 0.53/0.71 tff(1106,plain,
% 0.53/0.71 (((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(z))))))))) <=> ((~r(z, s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 0.53/0.71 inference(rewrite,[status(thm)],[])).
% 0.53/0.71 tff(1107,plain,
% 0.53/0.71 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))))),
% 0.53/0.71 inference(monotonicity,[status(thm)],[1106])).
% 0.53/0.71 tff(1108,plain,
% 0.53/0.71 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 0.53/0.71 inference(transitivity,[status(thm)],[1107, 1105])).
% 0.53/0.71 tff(1109,plain,
% 0.53/0.71 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(z)))))))))),
% 0.53/0.71 inference(quant_inst,[status(thm)],[])).
% 0.53/0.71 tff(1110,plain,
% 0.53/0.71 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 0.53/0.71 inference(modus_ponens,[status(thm)],[1109, 1108])).
% 0.53/0.71 tff(1111,plain,
% 0.53/0.71 ($false),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[1110, 14, 1, 222, 284])).
% 0.53/0.71 tff(1112,plain,((~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.53/0.71 tff(1113,plain,
% 0.53/0.71 (~r(z, s(s(s(z))))),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[1112, 1, 222])).
% 0.53/0.71 tff(1114,plain,
% 0.53/0.71 (b(z, s(s(s(z))))),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[281, 1113])).
% 0.53/0.71 tff(1115,plain,
% 0.53/0.71 (~b(s(s(z)), s(s(s(z))))),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[1045, 1114, 427, 813])).
% 0.53/0.71 tff(1116,plain,
% 0.53/0.71 (r(s(s(z)), s(s(s(z))))),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[425, 1115])).
% 0.53/0.71 tff(1117,plain,
% 0.53/0.71 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))))),
% 0.53/0.71 inference(rewrite,[status(thm)],[])).
% 0.53/0.71 tff(1118,plain,
% 0.53/0.71 (((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))))),
% 0.53/0.71 inference(rewrite,[status(thm)],[])).
% 0.53/0.71 tff(1119,plain,
% 0.53/0.71 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z)))))),
% 0.53/0.71 inference(monotonicity,[status(thm)],[1118])).
% 0.53/0.71 tff(1120,plain,
% 0.53/0.71 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))))),
% 0.53/0.71 inference(transitivity,[status(thm)],[1119, 1117])).
% 0.53/0.71 tff(1121,plain,
% 0.53/0.71 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 0.53/0.71 inference(quant_inst,[status(thm)],[])).
% 0.53/0.71 tff(1122,plain,
% 0.53/0.71 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z)))),
% 0.53/0.71 inference(modus_ponens,[status(thm)],[1121, 1120])).
% 0.53/0.71 tff(1123,plain,
% 0.53/0.71 ($false),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[1122, 14, 140, 522, 119])).
% 0.53/0.71 tff(1124,plain,((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.53/0.71 tff(1125,plain,
% 0.53/0.71 (~r(s(s(z)), s(z))),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[1124, 1116, 140])).
% 0.53/0.71 tff(1126,plain,
% 0.53/0.71 (b(s(s(z)), s(z))),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[137, 1125])).
% 0.53/0.71 tff(1127,plain,
% 0.53/0.71 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(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(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 0.53/0.71 inference(rewrite,[status(thm)],[])).
% 0.53/0.71 tff(1128,plain,
% 0.53/0.71 (((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 0.53/0.71 inference(rewrite,[status(thm)],[])).
% 0.53/0.71 tff(1129,plain,
% 0.53/0.71 (((~![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(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))))),
% 0.53/0.71 inference(monotonicity,[status(thm)],[1128])).
% 0.53/0.71 tff(1130,plain,
% 0.53/0.71 (((~![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(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 0.53/0.71 inference(transitivity,[status(thm)],[1129, 1127])).
% 0.53/0.71 tff(1131,plain,
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% 0.53/0.71 inference(quant_inst,[status(thm)],[])).
% 0.53/0.71 tff(1132,plain,
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% 0.53/0.71 inference(modus_ponens,[status(thm)],[1131, 1130])).
% 0.53/0.71 tff(1133,plain,
% 0.53/0.71 (~r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[1132, 14, 222, 1116])).
% 0.53/0.71 tff(1134,plain,
% 0.53/0.71 (b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[453, 1133])).
% 0.53/0.71 tff(1135,plain,
% 0.53/0.71 ($false),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[659, 188, 406, 87, 86, 139])).
% 0.53/0.71 tff(1136,plain,((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.53/0.71 tff(1137,plain,
% 0.53/0.71 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[1136, 86, 406, 139])).
% 0.53/0.71 tff(1138,plain,
% 0.53/0.71 (r(s(s(s(s(s(s(z)))))), s(z))),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[627, 1137])).
% 0.53/0.71 tff(1139,plain,
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% 0.53/0.71 inference(rewrite,[status(thm)],[])).
% 0.53/0.71 tff(1140,plain,
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% 0.53/0.71 inference(rewrite,[status(thm)],[])).
% 0.53/0.71 tff(1141,plain,
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% 0.53/0.71 inference(monotonicity,[status(thm)],[1140])).
% 0.53/0.71 tff(1142,plain,
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% 0.53/0.71 inference(transitivity,[status(thm)],[1141, 1139])).
% 0.53/0.71 tff(1143,plain,
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% 0.53/0.71 inference(quant_inst,[status(thm)],[])).
% 0.53/0.71 tff(1144,plain,
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% 0.53/0.71 inference(modus_ponens,[status(thm)],[1143, 1142])).
% 0.53/0.71 tff(1145,plain,
% 0.53/0.71 ($false),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[1144, 14, 373, 1, 614])).
% 0.53/0.71 tff(1146,plain,((~r(z, s(z))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.53/0.71 tff(1147,plain,
% 0.53/0.71 (~r(z, s(z))),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[1146, 1138, 1])).
% 0.53/0.71 tff(1148,plain,
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% 0.53/0.71 inference(unit_resolution,[status(thm)],[300, 1147])).
% 0.53/0.71 tff(1149,plain,
% 0.53/0.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 0.53/0.71 inference(rewrite,[status(thm)],[])).
% 0.53/0.71 tff(1150,plain,
% 0.53/0.71 (((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 0.53/0.71 inference(rewrite,[status(thm)],[])).
% 0.53/0.71 tff(1151,plain,
% 0.53/0.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))))),
% 0.53/0.71 inference(monotonicity,[status(thm)],[1150])).
% 0.53/0.71 tff(1152,plain,
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% 0.53/0.71 inference(transitivity,[status(thm)],[1151, 1149])).
% 0.53/0.71 tff(1153,plain,
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% 0.53/0.71 inference(quant_inst,[status(thm)],[])).
% 0.53/0.71 tff(1154,plain,
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% 0.53/0.71 inference(modus_ponens,[status(thm)],[1153, 1152])).
% 0.53/0.71 tff(1155,plain,
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% 0.53/0.71 inference(unit_resolution,[status(thm)],[1154, 188, 1148, 406, 427, 86, 139])).
% 0.53/0.71 tff(1156,plain,((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~r(z, s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 0.53/0.71 tff(1157,plain,
% 0.53/0.71 (~b(s(z), s(s(s(s(s(s(z)))))))),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[1156, 1134, 427, 1126, 1])).
% 0.53/0.71 tff(1158,plain,
% 0.53/0.71 (r(s(z), s(s(s(s(s(s(z)))))))),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[84, 1157])).
% 0.53/0.71 tff(1159,plain,
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% 0.53/0.71 tff(1160,plain,((~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(z), z)) | (~b(s(s(z)), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.53/0.71 tff(1161,plain,
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% 0.53/0.71 inference(unit_resolution,[status(thm)],[1160, 222, 427, 3, 140])).
% 0.53/0.71 tff(1162,plain,
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% 0.53/0.71 tff(1163,plain,
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% 0.53/0.71 inference(unit_resolution,[status(thm)],[1081, 1162, 140, 813, 222])).
% 0.53/0.71 tff(1164,plain,
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% 0.53/0.71 inference(unit_resolution,[status(thm)],[281, 1163])).
% 0.53/0.71 tff(1165,plain,
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% 0.53/0.71 inference(unit_resolution,[status(thm)],[1045, 1164, 427, 813])).
% 0.53/0.71 tff(1166,plain,
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% 0.53/0.71 inference(unit_resolution,[status(thm)],[425, 1165])).
% 0.53/0.71 tff(1167,plain,
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% 0.53/0.71 inference(unit_resolution,[status(thm)],[1124, 1166, 140])).
% 0.53/0.71 tff(1168,plain,
% 0.53/0.71 (b(s(s(z)), s(z))),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[137, 1167])).
% 0.53/0.71 tff(1169,plain,
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% 0.53/0.71 inference(unit_resolution,[status(thm)],[1132, 14, 222, 1166])).
% 0.53/0.71 tff(1170,plain,
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% 0.53/0.71 inference(unit_resolution,[status(thm)],[453, 1169])).
% 0.53/0.71 tff(1171,plain,
% 0.53/0.71 (~b(s(s(s(s(s(s(z)))))), z)),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[435, 1170, 427, 1162])).
% 0.53/0.71 tff(1172,plain,
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% 0.53/0.71 inference(unit_resolution,[status(thm)],[492, 1171])).
% 0.53/0.71 tff(1173,plain,
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% 0.53/0.71 inference(unit_resolution,[status(thm)],[705, 1172, 3])).
% 0.53/0.71 tff(1174,plain,
% 0.53/0.71 (b(s(s(s(s(s(s(z)))))), s(z))),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[627, 1173])).
% 0.53/0.71 tff(1175,plain,
% 0.53/0.71 (~b(s(z), s(s(s(s(s(s(z)))))))),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[1136, 1174, 1170, 1168])).
% 0.53/0.71 tff(1176,plain,
% 0.53/0.71 (r(s(z), s(s(s(s(s(s(z)))))))),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[84, 1175])).
% 0.53/0.71 tff(1177,plain,
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% 0.53/0.71 tff(1178,plain,((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(z), z)) | (~b(s(s(z)), z)) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.53/0.71 tff(1179,plain,
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% 0.53/0.71 inference(unit_resolution,[status(thm)],[1178, 1064, 1054, 140])).
% 0.53/0.71 tff(1180,plain,
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% 0.53/0.71 inference(unit_resolution,[status(thm)],[792, 1179])).
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% 0.53/0.71 inference(rewrite,[status(thm)],[])).
% 0.53/0.71 tff(1182,plain,
% 0.53/0.71 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))),
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% 0.53/0.71 tff(1183,plain,
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% 0.53/0.71 inference(modus_ponens,[status(thm)],[1182, 1181])).
% 0.53/0.71 tff(1184,plain,
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% 0.53/0.71 inference(unit_resolution,[status(thm)],[1183, 14, 3, 25, 119])).
% 0.53/0.71 tff(1185,plain,((~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.53/0.71 tff(1186,plain,
% 0.53/0.71 (~r(s(s(z)), s(z))),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[1185, 1180, 1054])).
% 0.53/0.71 tff(1187,plain,
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% 0.53/0.71 inference(unit_resolution,[status(thm)],[137, 1186])).
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% 0.53/0.71 inference(rewrite,[status(thm)],[])).
% 0.53/0.71 tff(1189,plain,
% 0.53/0.71 (((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z))))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))))),
% 0.53/0.71 inference(rewrite,[status(thm)],[])).
% 0.53/0.71 tff(1190,plain,
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% 0.53/0.71 inference(monotonicity,[status(thm)],[1189])).
% 0.53/0.71 tff(1191,plain,
% 0.53/0.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))))),
% 0.53/0.71 inference(transitivity,[status(thm)],[1190, 1188])).
% 0.53/0.71 tff(1192,plain,
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% 0.53/0.71 inference(quant_inst,[status(thm)],[])).
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% 0.53/0.71 inference(modus_ponens,[status(thm)],[1192, 1191])).
% 0.53/0.71 tff(1194,plain,
% 0.53/0.71 ((~b(z, s(z))) | (~b(z, s(s(z))))),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[1193, 188, 27, 86, 1187])).
% 0.53/0.71 tff(1195,plain,
% 0.53/0.71 (~b(z, s(s(z)))),
% 0.53/0.71 inference(unit_resolution,[status(thm)],[1194, 1104])).
% 0.53/0.71 tff(1196,plain,
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% 0.53/0.71 inference(unit_resolution,[status(thm)],[519, 79, 1195, 95])).
% 0.53/0.71 tff(1197,plain,
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% 0.53/0.72 inference(rewrite,[status(thm)],[])).
% 0.53/0.72 tff(1198,plain,
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% 0.53/0.72 inference(rewrite,[status(thm)],[])).
% 0.53/0.72 tff(1199,plain,
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% 0.53/0.72 inference(monotonicity,[status(thm)],[1198])).
% 0.53/0.72 tff(1200,plain,
% 0.53/0.72 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))))),
% 0.53/0.72 inference(transitivity,[status(thm)],[1199, 1197])).
% 0.53/0.72 tff(1201,plain,
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% 0.53/0.72 inference(quant_inst,[status(thm)],[])).
% 0.53/0.72 tff(1202,plain,
% 0.53/0.72 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z))))),
% 0.53/0.72 inference(modus_ponens,[status(thm)],[1201, 1200])).
% 0.53/0.72 tff(1203,plain,
% 0.53/0.72 ($false),
% 0.53/0.72 inference(unit_resolution,[status(thm)],[1202, 14, 1054, 1085, 1196])).
% 0.53/0.72 tff(1204,plain,((~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.53/0.72 tff(1205,plain,
% 0.53/0.72 (~b(s(z), s(s(s(z))))),
% 0.53/0.72 inference(unit_resolution,[status(thm)],[1204, 140, 86, 96, 892, 27, 89, 628])).
% 0.53/0.72 tff(1206,plain,
% 0.53/0.72 (r(s(z), s(s(s(z))))),
% 0.53/0.72 inference(unit_resolution,[status(thm)],[177, 1205])).
% 0.53/0.72 tff(1207,plain,
% 0.53/0.72 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.53/0.72 inference(unit_resolution,[status(thm)],[1081, 284, 283, 27, 140])).
% 0.53/0.72 tff(1208,plain,
% 0.53/0.72 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.53/0.72 inference(unit_resolution,[status(thm)],[243, 1207])).
% 0.53/0.72 tff(1209,plain,
% 0.53/0.72 ((s(s(s(s(s(s(z)))))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(s(s(s(z)))))))),
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% 0.53/0.72 tff(1210,plain,
% 0.53/0.72 ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(z)))))) = s(s(s(s(z)))))),
% 0.53/0.72 inference(symmetry,[status(thm)],[1209])).
% 0.53/0.72 tff(1211,plain,
% 0.53/0.72 ((~(s(s(s(s(z)))) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(s(s(s(s(z)))))) = s(s(s(s(z))))))),
% 0.53/0.72 inference(monotonicity,[status(thm)],[1210])).
% 0.53/0.72 tff(1212,plain,
% 0.53/0.72 (~(s(s(s(s(s(s(z)))))) = s(s(s(s(z)))))),
% 0.53/0.72 inference(modus_ponens,[status(thm)],[924, 1211])).
% 0.53/0.72 tff(1213,plain,
% 0.53/0.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 0.53/0.72 inference(rewrite,[status(thm)],[])).
% 0.53/0.72 tff(1214,plain,
% 0.53/0.72 (((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 0.53/0.72 inference(rewrite,[status(thm)],[])).
% 0.53/0.72 tff(1215,plain,
% 0.53/0.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z))))),
% 0.53/0.72 inference(monotonicity,[status(thm)],[1214])).
% 0.53/0.72 tff(1216,plain,
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% 0.53/0.72 inference(transitivity,[status(thm)],[1215, 1213])).
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% 0.53/0.72 inference(quant_inst,[status(thm)],[])).
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% 0.53/0.72 inference(modus_ponens,[status(thm)],[1217, 1216])).
% 0.53/0.72 tff(1219,plain,
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% 0.53/0.72 tff(1220,plain,
% 0.53/0.72 (~b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.53/0.72 inference(unit_resolution,[status(thm)],[1219, 259])).
% 0.53/0.72 tff(1221,assumption,(~r(s(s(s(s(s(s(z)))))), s(s(z)))), introduced(assumption)).
% 0.53/0.72 tff(1222,assumption,(~b(s(s(s(s(s(s(z)))))), s(s(z)))), introduced(assumption)).
% 0.53/0.72 tff(1223,plain,
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% 0.53/0.72 inference(unit_resolution,[status(thm)],[500, 79, 1222, 1221, 395])).
% 0.53/0.72 tff(1224,plain,(b(s(s(s(s(s(s(z)))))), s(s(z))) | r(s(s(s(s(s(s(z)))))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.53/0.72 tff(1225,plain,
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% 0.53/0.72 inference(unit_resolution,[status(thm)],[1224, 1220])).
% 0.53/0.72 tff(1226,plain,
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% 0.53/0.72 inference(rewrite,[status(thm)],[])).
% 0.53/0.72 tff(1227,plain,
% 0.53/0.72 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 0.53/0.72 inference(quant_inst,[status(thm)],[])).
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% 0.53/0.72 inference(modus_ponens,[status(thm)],[1227, 1226])).
% 0.53/0.72 tff(1229,plain,
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% 0.53/0.72 tff(1230,plain,
% 0.53/0.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 0.53/0.72 inference(rewrite,[status(thm)],[])).
% 0.53/0.72 tff(1231,plain,
% 0.53/0.72 (((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 0.53/0.72 inference(rewrite,[status(thm)],[])).
% 0.53/0.72 tff(1232,plain,
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% 0.53/0.72 inference(monotonicity,[status(thm)],[1231])).
% 0.53/0.72 tff(1233,plain,
% 0.53/0.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 0.53/0.72 inference(transitivity,[status(thm)],[1232, 1230])).
% 0.53/0.72 tff(1234,plain,
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% 0.53/0.72 inference(quant_inst,[status(thm)],[])).
% 0.53/0.72 tff(1235,plain,
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% 0.53/0.72 inference(modus_ponens,[status(thm)],[1234, 1233])).
% 0.53/0.72 tff(1236,plain,
% 0.53/0.72 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 0.53/0.72 inference(unit_resolution,[status(thm)],[1235, 188, 283, 259, 89, 893])).
% 0.53/0.72 tff(1237,plain,
% 0.53/0.72 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 0.53/0.72 inference(rewrite,[status(thm)],[])).
% 0.53/0.72 tff(1238,plain,
% 0.53/0.72 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 0.53/0.72 inference(quant_inst,[status(thm)],[])).
% 0.53/0.72 tff(1239,plain,
% 0.53/0.72 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 0.53/0.72 inference(modus_ponens,[status(thm)],[1238, 1237])).
% 0.53/0.72 tff(1240,plain,
% 0.53/0.72 ((s(s(s(s(s(s(z)))))) = s(s(s(s(z))))) | r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 0.53/0.72 inference(unit_resolution,[status(thm)],[1239, 79, 1236])).
% 0.53/0.72 tff(1241,plain,
% 0.53/0.72 ($false),
% 0.53/0.72 inference(unit_resolution,[status(thm)],[1240, 1229, 1212])).
% 0.53/0.72 tff(1242,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z))), inference(lemma,lemma(discharge,[]))).
% 0.53/0.72 tff(1243,plain,
% 0.53/0.72 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 0.53/0.72 inference(unit_resolution,[status(thm)],[1242, 1208, 892, 283, 96, 89])).
% 0.53/0.72 tff(1244,plain,
% 0.53/0.72 (r(s(s(s(s(z)))), s(s(s(z))))),
% 0.53/0.72 inference(unit_resolution,[status(thm)],[890, 1243])).
% 0.53/0.72 tff(1245,plain,
% 0.53/0.72 (~r(s(s(s(s(z)))), s(z))),
% 0.53/0.72 inference(unit_resolution,[status(thm)],[870, 14, 26, 1244])).
% 0.53/0.72 tff(1246,plain,
% 0.53/0.72 ((s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z))),
% 0.53/0.72 inference(unit_resolution,[status(thm)],[874, 79, 1245])).
% 0.53/0.72 tff(1247,plain,
% 0.53/0.72 (b(s(s(s(s(z)))), s(z))),
% 0.53/0.72 inference(unit_resolution,[status(thm)],[1246, 844])).
% 0.53/0.72 tff(1248,plain,
% 0.53/0.72 (~r(s(s(s(s(z)))), z)),
% 0.53/0.72 inference(unit_resolution,[status(thm)],[851, 1244, 284])).
% 0.53/0.72 tff(1249,plain,
% 0.53/0.72 (b(s(s(s(s(z)))), z)),
% 0.53/0.72 inference(unit_resolution,[status(thm)],[859, 1248])).
% 0.53/0.72 tff(1250,plain,
% 0.53/0.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(z))))),
% 0.53/0.72 inference(rewrite,[status(thm)],[])).
% 0.53/0.72 tff(1251,plain,
% 0.53/0.72 (((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))) <=> ((~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(z))))),
% 0.53/0.72 inference(rewrite,[status(thm)],[])).
% 0.53/0.72 tff(1252,plain,
% 0.53/0.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 0.53/0.72 inference(monotonicity,[status(thm)],[1251])).
% 0.53/0.72 tff(1253,plain,
% 0.53/0.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(z))))),
% 0.53/0.72 inference(transitivity,[status(thm)],[1252, 1250])).
% 0.53/0.72 tff(1254,plain,
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% 0.53/0.72 inference(quant_inst,[status(thm)],[])).
% 0.53/0.72 tff(1255,plain,
% 0.53/0.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(z)))),
% 0.53/0.72 inference(modus_ponens,[status(thm)],[1254, 1253])).
% 0.53/0.72 tff(1256,plain,
% 0.53/0.72 (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.53/0.72 inference(unit_resolution,[status(thm)],[1255, 188, 1074, 89, 1249, 1247])).
% 0.53/0.72 tff(1257,plain,
% 0.53/0.72 (r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.53/0.72 inference(unit_resolution,[status(thm)],[927, 79, 924, 1256])).
% 0.53/0.72 tff(1258,plain,
% 0.53/0.72 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 0.53/0.73 inference(rewrite,[status(thm)],[])).
% 0.53/0.73 tff(1259,plain,
% 0.53/0.73 (((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 0.53/0.73 inference(rewrite,[status(thm)],[])).
% 0.53/0.73 tff(1260,plain,
% 0.53/0.73 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))))),
% 0.53/0.73 inference(monotonicity,[status(thm)],[1259])).
% 0.53/0.73 tff(1261,plain,
% 0.53/0.73 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 0.53/0.73 inference(transitivity,[status(thm)],[1260, 1258])).
% 0.53/0.73 tff(1262,plain,
% 0.53/0.73 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 0.53/0.73 inference(quant_inst,[status(thm)],[])).
% 0.53/0.73 tff(1263,plain,
% 0.53/0.73 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 0.53/0.73 inference(modus_ponens,[status(thm)],[1262, 1261])).
% 0.53/0.73 tff(1264,plain,
% 0.53/0.73 ($false),
% 0.53/0.73 inference(unit_resolution,[status(thm)],[1263, 14, 24, 1244, 1257])).
% 0.53/0.73 tff(1265,plain,((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~r(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.53/0.73 tff(1266,plain,
% 0.53/0.73 (~r(z, s(s(s(z))))),
% 0.53/0.73 inference(unit_resolution,[status(thm)],[1265, 1206, 89, 24, 892, 1056, 96, 27, 140])).
% 0.53/0.73 tff(1267,plain,
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% 0.53/0.73 inference(unit_resolution,[status(thm)],[281, 1266])).
% 0.53/0.73 tff(1268,plain,
% 0.53/0.73 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.53/0.73 inference(unit_resolution,[status(thm)],[547, 1267, 89, 1056])).
% 0.53/0.73 tff(1269,plain,
% 0.53/0.73 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.53/0.73 inference(unit_resolution,[status(thm)],[243, 1268])).
% 0.53/0.73 tff(1270,plain,
% 0.53/0.73 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 0.53/0.73 inference(rewrite,[status(thm)],[])).
% 0.53/0.73 tff(1271,plain,
% 0.53/0.73 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 0.53/0.73 inference(quant_inst,[status(thm)],[])).
% 0.53/0.73 tff(1272,plain,
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% 0.53/0.73 inference(modus_ponens,[status(thm)],[1271, 1270])).
% 0.53/0.73 tff(1273,plain,
% 0.53/0.73 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.53/0.73 inference(unit_resolution,[status(thm)],[1272, 14, 222, 845])).
% 0.53/0.73 tff(1274,plain,
% 0.53/0.73 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.53/0.73 inference(unit_resolution,[status(thm)],[927, 79, 924, 1273])).
% 0.53/0.73 tff(1275,plain,
% 0.53/0.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(z))))),
% 0.53/0.73 inference(rewrite,[status(thm)],[])).
% 0.53/0.73 tff(1276,plain,
% 0.53/0.73 (((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(z))))),
% 0.53/0.73 inference(rewrite,[status(thm)],[])).
% 0.53/0.73 tff(1277,plain,
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% 0.53/0.73 inference(monotonicity,[status(thm)],[1276])).
% 0.53/0.73 tff(1278,plain,
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% 0.53/0.73 inference(transitivity,[status(thm)],[1277, 1275])).
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% 0.53/0.73 inference(quant_inst,[status(thm)],[])).
% 0.53/0.73 tff(1280,plain,
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% 0.53/0.73 inference(modus_ponens,[status(thm)],[1279, 1278])).
% 0.53/0.73 tff(1281,plain,
% 0.53/0.73 (~b(s(s(s(s(z)))), s(z))),
% 0.53/0.73 inference(unit_resolution,[status(thm)],[1280, 188, 87, 86, 1274])).
% 0.53/0.73 tff(1282,plain,
% 0.53/0.73 ($false),
% 0.53/0.73 inference(unit_resolution,[status(thm)],[875, 1281, 844])).
% 0.53/0.73 tff(1283,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.53/0.73 tff(1284,plain,
% 0.53/0.73 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 0.53/0.73 inference(unit_resolution,[status(thm)],[1283, 628, 86, 1269, 1206])).
% 0.53/0.73 tff(1285,plain,
% 0.53/0.73 (b(s(s(s(s(z)))), s(s(s(z))))),
% 0.53/0.73 inference(unit_resolution,[status(thm)],[890, 1284])).
% 0.53/0.73 tff(1286,plain,
% 0.53/0.73 (~b(s(s(s(s(z)))), s(s(z)))),
% 0.53/0.73 inference(unit_resolution,[status(thm)],[899, 188, 96, 1285, 892])).
% 0.53/0.73 tff(1287,plain,
% 0.53/0.73 (r(s(s(s(s(z)))), s(s(z)))),
% 0.53/0.73 inference(unit_resolution,[status(thm)],[909, 79, 906, 1286])).
% 0.53/0.73 tff(1288,plain,
% 0.53/0.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 0.53/0.73 inference(rewrite,[status(thm)],[])).
% 0.53/0.73 tff(1289,plain,
% 0.53/0.73 (((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 0.53/0.73 inference(rewrite,[status(thm)],[])).
% 0.53/0.73 tff(1290,plain,
% 0.53/0.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 0.53/0.73 inference(monotonicity,[status(thm)],[1289])).
% 0.53/0.73 tff(1291,plain,
% 0.53/0.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 0.53/0.73 inference(transitivity,[status(thm)],[1290, 1288])).
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% 0.53/0.73 inference(modus_ponens,[status(thm)],[1292, 1291])).
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% 0.53/0.73 tff(1295,plain,
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% 0.53/0.73 inference(unit_resolution,[status(thm)],[1091, 188, 96, 1267, 892])).
% 0.53/0.73 tff(1297,plain,
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% 0.53/0.73 inference(unit_resolution,[status(thm)],[519, 79, 1296, 95])).
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% 0.53/0.73 inference(rewrite,[status(thm)],[])).
% 0.53/0.73 tff(1299,plain,
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% 0.53/0.73 inference(quant_inst,[status(thm)],[])).
% 0.53/0.73 tff(1300,plain,
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% 0.53/0.73 inference(modus_ponens,[status(thm)],[1299, 1298])).
% 0.53/0.73 tff(1301,plain,
% 0.53/0.73 ($false),
% 0.53/0.73 inference(unit_resolution,[status(thm)],[1300, 14, 1297, 1295, 1287])).
% 0.53/0.73 tff(1302,plain,((~r(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 0.53/0.73 tff(1303,plain,
% 0.53/0.73 (~r(s(s(s(z))), s(z))),
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% 0.53/0.73 tff(1304,plain,
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% 0.53/0.73 tff(1305,plain,
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% 0.53/0.73 inference(unit_resolution,[status(thm)],[333, 14, 1054, 2])).
% 0.53/0.73 tff(1306,plain,
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% 0.53/0.73 inference(unit_resolution,[status(thm)],[177, 1305])).
% 0.53/0.73 tff(1307,plain,
% 0.53/0.73 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))),
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% 0.53/0.73 inference(quant_inst,[status(thm)],[])).
% 0.53/0.73 tff(1309,plain,
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% 0.53/0.73 inference(modus_ponens,[status(thm)],[1308, 1307])).
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% 0.53/0.73 inference(rewrite,[status(thm)],[])).
% 0.53/0.73 tff(1312,plain,
% 0.53/0.73 (((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 0.53/0.73 inference(rewrite,[status(thm)],[])).
% 0.53/0.73 tff(1313,plain,
% 0.53/0.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 0.53/0.73 inference(monotonicity,[status(thm)],[1312])).
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% 0.53/0.73 inference(modus_ponens,[status(thm)],[1315, 1314])).
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% 0.53/0.75 tff(1423,plain,
% 0.53/0.75 (~r(s(z), s(s(z)))),
% 0.53/0.75 inference(unit_resolution,[status(thm)],[1102, 1422, 96, 1413, 892])).
% 0.53/0.75 tff(1424,assumption,(~b(s(z), s(s(z)))), introduced(assumption)).
% 0.53/0.75 tff(1425,assumption,(~r(s(z), s(s(z)))), introduced(assumption)).
% 0.53/0.75 tff(1426,plain,
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% 0.53/0.75 tff(1427,plain,(b(s(z), s(s(z))) | r(s(z), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.53/0.75 tff(1428,plain,
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% 0.53/0.75 inference(unit_resolution,[status(thm)],[1427, 1423])).
% 0.53/0.75 tff(1429,plain,
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% 0.53/0.75 inference(unit_resolution,[status(thm)],[1045, 1413, 96, 1395])).
% 0.53/0.75 tff(1430,plain,
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% 0.53/0.75 inference(unit_resolution,[status(thm)],[792, 1429])).
% 0.53/0.75 tff(1431,plain,
% 0.53/0.75 (~r(s(s(z)), s(z))),
% 0.53/0.75 inference(unit_resolution,[status(thm)],[1185, 1430, 1054])).
% 0.53/0.75 tff(1432,plain,
% 0.53/0.75 (b(s(s(z)), s(z))),
% 0.53/0.75 inference(unit_resolution,[status(thm)],[137, 1431])).
% 0.53/0.75 tff(1433,plain,
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% 0.53/0.75 tff(1434,plain,((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 0.53/0.75 tff(1435,plain,
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% 0.53/0.75 inference(unit_resolution,[status(thm)],[1434, 1050, 96, 1049, 1022, 89, 24])).
% 0.53/0.75 tff(1436,plain,
% 0.53/0.75 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.53/0.75 inference(unit_resolution,[status(thm)],[243, 1435])).
% 0.53/0.75 tff(1437,plain,
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% 0.53/0.75 inference(unit_resolution,[status(thm)],[1052, 1049, 89, 1022])).
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% 0.53/0.75 inference(unit_resolution,[status(thm)],[312, 1437])).
% 0.53/0.75 tff(1439,plain,
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% 0.53/0.75 inference(unit_resolution,[status(thm)],[547, 258, 89, 259])).
% 0.53/0.75 tff(1440,plain,
% 0.53/0.75 (r(s(s(s(z))), z)),
% 0.53/0.75 inference(unit_resolution,[status(thm)],[326, 1439])).
% 0.53/0.75 tff(1441,plain,
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% 0.53/0.75 inference(unit_resolution,[status(thm)],[1345, 1440, 3])).
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% 0.53/0.75 inference(unit_resolution,[status(thm)],[1381, 1440, 89, 24, 86, 96, 258])).
% 0.53/0.75 tff(1443,plain,
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% 0.53/0.75 inference(unit_resolution,[status(thm)],[792, 1442, 1441])).
% 0.53/0.75 tff(1444,plain,((~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(z))))) | (~r(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.53/0.75 tff(1445,plain,
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% 0.53/0.75 inference(unit_resolution,[status(thm)],[1444, 24, 89, 1022, 96, 1438, 1436])).
% 0.53/0.75 tff(1446,plain,
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% 0.53/0.75 inference(unit_resolution,[status(thm)],[281, 1445])).
% 0.53/0.75 tff(1447,plain,
% 0.53/0.75 (~r(s(s(s(z))), s(z))),
% 0.53/0.75 inference(unit_resolution,[status(thm)],[1302, 1050, 96, 1022, 89, 24, 1049])).
% 0.53/0.75 tff(1448,plain,
% 0.53/0.75 (b(s(s(s(z))), s(z))),
% 0.53/0.75 inference(unit_resolution,[status(thm)],[170, 1447])).
% 0.53/0.75 tff(1449,plain,
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% 0.53/0.75 inference(rewrite,[status(thm)],[])).
% 0.53/0.75 tff(1450,plain,
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% 0.53/0.75 tff(1451,plain,
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% 0.53/0.75 inference(transitivity,[status(thm)],[1451, 1449])).
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% 0.53/0.75 inference(quant_inst,[status(thm)],[])).
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% 0.53/0.75 inference(modus_ponens,[status(thm)],[1453, 1452])).
% 0.53/0.75 tff(1455,plain,
% 0.53/0.75 (~b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.53/0.75 inference(unit_resolution,[status(thm)],[1454, 188, 259, 96, 892])).
% 0.53/0.75 tff(1456,plain,
% 0.53/0.75 (r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.53/0.75 inference(unit_resolution,[status(thm)],[1224, 1455])).
% 0.53/0.75 tff(1457,plain,
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% 0.53/0.75 inference(unit_resolution,[status(thm)],[698, 188, 684, 246, 259, 87])).
% 0.53/0.75 tff(1458,plain,((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.53/0.75 tff(1459,plain,
% 0.53/0.75 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 0.53/0.75 inference(unit_resolution,[status(thm)],[1458, 684, 246, 259])).
% 0.53/0.75 tff(1460,plain,
% 0.53/0.75 (r(s(s(s(s(s(s(z)))))), s(z))),
% 0.53/0.75 inference(unit_resolution,[status(thm)],[627, 1459])).
% 0.53/0.75 tff(1461,assumption,(r(s(s(s(s(s(s(z)))))), s(s(z)))), introduced(assumption)).
% 0.53/0.75 tff(1462,plain,
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% 0.53/0.75 tff(1464,plain,
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% 0.53/0.75 inference(unit_resolution,[status(thm)],[1467, 14, 614, 1094, 1461])).
% 0.53/0.75 tff(1469,plain,((~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.53/0.75 tff(1470,plain,
% 0.53/0.75 (~r(s(z), s(s(z)))),
% 0.53/0.75 inference(unit_resolution,[status(thm)],[1469, 1460, 1456])).
% 0.53/0.75 tff(1471,plain,
% 0.53/0.75 (b(s(z), s(s(z)))),
% 0.53/0.75 inference(unit_resolution,[status(thm)],[1427, 1470])).
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% 0.53/0.75 inference(unit_resolution,[status(thm)],[1018, 188, 684, 96, 892, 1471])).
% 0.53/0.75 tff(1473,plain,((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.53/0.75 tff(1474,plain,
% 0.53/0.75 (~b(s(z), s(s(s(z))))),
% 0.53/0.75 inference(unit_resolution,[status(thm)],[1473, 1050, 96, 1448, 1436])).
% 0.53/0.75 tff(1475,plain,
% 0.53/0.75 (r(s(z), s(s(s(z))))),
% 0.53/0.75 inference(unit_resolution,[status(thm)],[177, 1474])).
% 0.53/0.75 tff(1476,plain,
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% 0.53/0.75 inference(unit_resolution,[status(thm)],[307, 14, 1438, 1475, 1446])).
% 0.53/0.75 tff(1477,plain,((~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 0.53/0.75 tff(1478,plain,
% 0.53/0.75 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 0.53/0.75 inference(unit_resolution,[status(thm)],[1477, 96, 89, 88])).
% 0.53/0.75 tff(1479,plain,
% 0.53/0.75 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 0.53/0.75 inference(unit_resolution,[status(thm)],[220, 1478])).
% 0.53/0.75 tff(1480,plain,
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% 0.53/0.75 inference(unit_resolution,[status(thm)],[1052, 360, 89, 1022])).
% 0.53/0.75 tff(1481,plain,
% 0.53/0.75 (r(z, s(s(s(s(s(s(z)))))))),
% 0.53/0.75 inference(unit_resolution,[status(thm)],[256, 1480])).
% 0.53/0.75 tff(1482,plain,
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% 0.53/0.75 inference(unit_resolution,[status(thm)],[1112, 1481, 222])).
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% 0.53/0.75 inference(unit_resolution,[status(thm)],[281, 1482])).
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% 0.53/0.75 inference(rewrite,[status(thm)],[])).
% 0.53/0.75 tff(1485,plain,
% 0.53/0.75 (((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(z, s(s(z))))) <=> ((~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 0.53/0.75 inference(rewrite,[status(thm)],[])).
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% 0.53/0.75 inference(monotonicity,[status(thm)],[1485])).
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% 0.53/0.75 inference(transitivity,[status(thm)],[1486, 1484])).
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% 0.53/0.75 inference(quant_inst,[status(thm)],[])).
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% 0.53/0.75 inference(unit_resolution,[status(thm)],[519, 79, 1490])).
% 0.53/0.75 tff(1492,plain,
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% 0.53/0.75 inference(unit_resolution,[status(thm)],[1491, 380])).
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% 0.53/0.75 inference(unit_resolution,[status(thm)],[974, 140, 2])).
% 0.53/0.75 tff(1494,plain,
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% 0.53/0.75 inference(unit_resolution,[status(thm)],[300, 1493])).
% 0.53/0.75 tff(1495,plain,
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% 0.53/0.76 tff(1501,plain,
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% 0.53/0.76 inference(quant_inst,[status(thm)],[])).
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% 0.53/0.76 inference(unit_resolution,[status(thm)],[1505, 14, 140, 1502])).
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% 0.53/0.76 inference(unit_resolution,[status(thm)],[1124, 1502, 140])).
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% 0.53/0.76 tff(1513,plain,
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% 0.53/0.76 inference(unit_resolution,[status(thm)],[82, 79, 69])).
% 0.53/0.76 tff(1516,plain,
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% 0.53/0.76 inference(unit_resolution,[status(thm)],[1515, 610])).
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% 0.53/0.76 tff(1525,plain,
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% 0.53/0.76 tff(1598,plain,
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% 0.53/0.76 inference(unit_resolution,[status(thm)],[1597, 140, 1005])).
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% 0.53/0.76 inference(unit_resolution,[status(thm)],[1024, 1595, 88])).
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% 0.53/0.77 tff(1603,plain,
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% 0.53/0.77 tff(1604,plain,
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% 0.53/0.77 inference(unit_resolution,[status(thm)],[811, 1603, 140])).
% 0.53/0.77 tff(1605,plain,
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% 0.53/0.77 inference(unit_resolution,[status(thm)],[326, 1604])).
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% 0.53/0.77 tff(1607,plain,
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% 0.53/0.77 tff(1608,plain,
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% 0.53/0.77 inference(monotonicity,[status(thm)],[1607])).
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% 0.53/0.77 inference(transitivity,[status(thm)],[1608, 1606])).
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% 0.53/0.77 inference(modus_ponens,[status(thm)],[1610, 1609])).
% 0.53/0.77 tff(1612,plain,
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% 0.53/0.77 inference(unit_resolution,[status(thm)],[1611, 188, 776, 1605, 96, 427, 139])).
% 0.53/0.77 tff(1613,plain,((~b(s(s(z)), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.53/0.77 tff(1614,plain,
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% 0.53/0.77 inference(unit_resolution,[status(thm)],[1613, 1601, 96, 1599, 140])).
% 0.53/0.77 tff(1615,plain,
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% 0.53/0.77 inference(unit_resolution,[status(thm)],[300, 1614])).
% 0.53/0.77 tff(1616,plain,
% 0.53/0.77 (~r(s(s(s(z))), s(z))),
% 0.53/0.77 inference(unit_resolution,[status(thm)],[974, 373, 2])).
% 0.53/0.77 tff(1617,plain,
% 0.53/0.77 (b(s(s(s(z))), s(z))),
% 0.53/0.77 inference(unit_resolution,[status(thm)],[170, 1616])).
% 0.53/0.77 tff(1618,plain,
% 0.53/0.77 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 0.53/0.77 inference(unit_resolution,[status(thm)],[1146, 373, 1])).
% 0.53/0.77 tff(1619,plain,
% 0.53/0.77 (b(s(s(s(s(s(s(z)))))), s(z))),
% 0.53/0.77 inference(unit_resolution,[status(thm)],[627, 1618])).
% 0.53/0.77 tff(1620,plain,
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% 0.53/0.77 inference(unit_resolution,[status(thm)],[1524, 1619, 1617, 245, 69])).
% 0.53/0.77 tff(1621,plain,((~r(z, s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | r(s(z), s(s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 0.53/0.77 tff(1622,plain,
% 0.53/0.77 (~r(s(s(s(z))), z)),
% 0.53/0.77 inference(unit_resolution,[status(thm)],[1621, 1615, 1595, 1021, 1479])).
% 0.53/0.77 tff(1623,plain,
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% 0.53/0.77 inference(unit_resolution,[status(thm)],[326, 1622])).
% 0.53/0.77 tff(1624,plain,
% 0.53/0.77 (~b(s(z), s(s(s(z))))),
% 0.53/0.77 inference(unit_resolution,[status(thm)],[1591, 259, 1022, 1479])).
% 0.53/0.77 tff(1625,plain,
% 0.53/0.77 (r(s(z), s(s(s(z))))),
% 0.53/0.77 inference(unit_resolution,[status(thm)],[177, 1624])).
% 0.53/0.77 tff(1626,plain,
% 0.53/0.77 (~r(z, s(s(s(z))))),
% 0.53/0.77 inference(unit_resolution,[status(thm)],[375, 1615, 1625])).
% 0.53/0.77 tff(1627,plain,
% 0.53/0.77 (b(z, s(s(s(z))))),
% 0.53/0.77 inference(unit_resolution,[status(thm)],[281, 1626])).
% 0.53/0.77 tff(1628,plain,
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% 0.53/0.77 inference(unit_resolution,[status(thm)],[547, 1627, 1623, 89, 259])).
% 0.53/0.77 tff(1629,plain,((~r(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.53/0.77 tff(1630,plain,
% 0.53/0.77 (~r(s(s(s(z))), s(z))),
% 0.53/0.77 inference(unit_resolution,[status(thm)],[1629, 259, 89, 96, 88, 1005])).
% 0.53/0.77 tff(1631,plain,
% 0.53/0.77 (b(s(s(s(z))), s(z))),
% 0.53/0.77 inference(unit_resolution,[status(thm)],[170, 1630])).
% 0.53/0.77 tff(1632,plain,
% 0.53/0.77 (~b(s(s(s(z))), z)),
% 0.53/0.77 inference(unit_resolution,[status(thm)],[1569, 1631, 89, 1022, 1479])).
% 0.53/0.77 tff(1633,plain,
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% 0.53/0.77 inference(unit_resolution,[status(thm)],[326, 1632])).
% 0.53/0.77 tff(1634,plain,
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% 0.53/0.77 inference(unit_resolution,[status(thm)],[1010, 1633, 1005])).
% 0.53/0.77 tff(1635,plain,
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% 0.53/0.77 tff(1636,plain,
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% 0.53/0.77 inference(monotonicity,[status(thm)],[1636])).
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% 0.53/0.77 inference(modus_ponens,[status(thm)],[1639, 1638])).
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% 0.53/0.77 tff(1642,plain,((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.53/0.77 tff(1643,plain,
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% 0.53/0.77 tff(1645,plain,
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% 0.53/0.77 tff(1646,plain,
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% 0.53/0.77 tff(1648,plain,
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% 0.53/0.77 inference(unit_resolution,[status(thm)],[256, 1647])).
% 0.53/0.77 tff(1649,plain,
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% 0.53/0.77 inference(unit_resolution,[status(thm)],[1024, 1648, 88])).
% 0.53/0.77 tff(1650,plain,
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% 0.53/0.77 inference(unit_resolution,[status(thm)],[792, 1649])).
% 0.53/0.77 tff(1651,assumption,(b(s(z), s(s(z)))), introduced(assumption)).
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% 0.53/0.77 inference(modus_ponens,[status(thm)],[1656, 1655])).
% 0.53/0.77 tff(1658,plain,
% 0.53/0.77 ($false),
% 0.53/0.77 inference(unit_resolution,[status(thm)],[1657, 188, 360, 427, 1508, 1651])).
% 0.53/0.77 tff(1659,plain,((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.53/0.77 tff(1660,plain,
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% 0.53/0.77 inference(unit_resolution,[status(thm)],[1659, 1650, 1646, 1644])).
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% 0.53/0.77 tff(1703,plain,
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% 0.53/0.77 tff(1715,plain,
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% 0.53/0.79 inference(unit_resolution,[status(thm)],[117, 79, 114, 1951])).
% 0.53/0.79 tff(1953,plain,
% 0.53/0.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(z)))))),
% 0.53/0.79 inference(rewrite,[status(thm)],[])).
% 0.53/0.79 tff(1954,plain,
% 0.53/0.79 (((~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(z)))))),
% 0.53/0.79 inference(rewrite,[status(thm)],[])).
% 0.53/0.79 tff(1955,plain,
% 0.53/0.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(z))))))),
% 0.53/0.79 inference(monotonicity,[status(thm)],[1954])).
% 0.53/0.79 tff(1956,plain,
% 0.53/0.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(z)))))),
% 0.53/0.79 inference(transitivity,[status(thm)],[1955, 1953])).
% 0.53/0.79 tff(1957,plain,
% 0.53/0.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))),
% 0.53/0.79 inference(quant_inst,[status(thm)],[])).
% 0.53/0.79 tff(1958,plain,
% 0.53/0.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(z))))),
% 0.53/0.79 inference(modus_ponens,[status(thm)],[1957, 1956])).
% 0.53/0.79 tff(1959,plain,
% 0.53/0.79 (~b(s(s(s(z))), s(s(z)))),
% 0.53/0.79 inference(unit_resolution,[status(thm)],[1958, 188, 1948, 1929, 1908, 1952])).
% 0.53/0.79 tff(1960,plain,
% 0.53/0.79 (r(s(s(s(z))), s(s(z)))),
% 0.53/0.79 inference(unit_resolution,[status(thm)],[475, 79, 472, 1959])).
% 0.53/0.79 tff(1961,plain,
% 0.53/0.79 (~r(z, s(s(z)))),
% 0.53/0.79 inference(unit_resolution,[status(thm)],[1010, 1960, 2])).
% 0.53/0.79 tff(1962,plain,
% 0.53/0.79 ((z = s(s(z))) | b(z, s(s(z)))),
% 0.53/0.79 inference(unit_resolution,[status(thm)],[519, 79, 1961])).
% 0.53/0.79 tff(1963,plain,
% 0.53/0.79 (b(z, s(s(z)))),
% 0.53/0.79 inference(unit_resolution,[status(thm)],[1962, 380])).
% 0.53/0.79 tff(1964,plain,
% 0.53/0.79 ($false),
% 0.53/0.79 inference(unit_resolution,[status(thm)],[1657, 188, 360, 1933, 1963, 1952])).
% 0.53/0.79 tff(1965,plain,((~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(z)))))), z))), inference(lemma,lemma(discharge,[]))).
% 0.53/0.79 tff(1966,plain,
% 0.53/0.79 (~b(z, s(s(s(z))))),
% 0.53/0.79 inference(unit_resolution,[status(thm)],[1965, 1906, 1904, 2])).
% 0.53/0.79 tff(1967,plain,
% 0.53/0.79 (r(z, s(s(s(z))))),
% 0.53/0.79 inference(unit_resolution,[status(thm)],[281, 1966])).
% 0.53/0.79 tff(1968,plain,
% 0.53/0.79 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.53/0.79 inference(unit_resolution,[status(thm)],[604, 1967, 1904])).
% 0.53/0.79 tff(1969,plain,
% 0.53/0.79 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.53/0.79 inference(unit_resolution,[status(thm)],[243, 1968])).
% 0.53/0.79 tff(1970,plain,
% 0.53/0.79 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 0.53/0.79 inference(unit_resolution,[status(thm)],[738, 1904, 88])).
% 0.53/0.79 tff(1971,plain,
% 0.53/0.79 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 0.53/0.79 inference(unit_resolution,[status(thm)],[220, 1970])).
% 0.53/0.79 tff(1972,plain,
% 0.53/0.79 ($false),
% 0.53/0.79 inference(unit_resolution,[status(thm)],[507, 14, 88, 554, 25])).
% 0.53/0.79 tff(1973,plain,((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 0.53/0.79 tff(1974,plain,
% 0.53/0.79 (~r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 0.53/0.79 inference(unit_resolution,[status(thm)],[1973, 25, 554])).
% 0.53/0.79 tff(1975,plain,
% 0.53/0.79 (b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 0.53/0.79 inference(unit_resolution,[status(thm)],[453, 1974])).
% 0.53/0.79 tff(1976,plain,
% 0.53/0.79 ($false),
% 0.53/0.79 inference(unit_resolution,[status(thm)],[496, 14, 554, 25, 1461])).
% 0.53/0.79 tff(1977,plain,((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.53/0.79 tff(1978,plain,
% 0.53/0.79 (~r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.53/0.79 inference(unit_resolution,[status(thm)],[1977, 25, 554])).
% 0.53/0.79 tff(1979,plain,
% 0.53/0.79 (b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.53/0.79 inference(unit_resolution,[status(thm)],[500, 79, 1978, 395])).
% 0.53/0.79 tff(1980,plain,
% 0.53/0.79 (~b(s(s(s(z))), s(s(z)))),
% 0.53/0.79 inference(unit_resolution,[status(thm)],[1855, 188, 1975, 245, 1979])).
% 0.53/0.79 tff(1981,plain,
% 0.53/0.79 (r(s(s(s(z))), s(s(z)))),
% 0.53/0.79 inference(unit_resolution,[status(thm)],[476, 1980])).
% 0.53/0.79 tff(1982,plain,
% 0.53/0.79 (~b(z, s(s(z)))),
% 0.53/0.79 inference(unit_resolution,[status(thm)],[515, 188, 1975, 27, 1979])).
% 0.53/0.79 tff(1983,plain,
% 0.53/0.79 (r(z, s(s(z)))),
% 0.53/0.79 inference(unit_resolution,[status(thm)],[519, 79, 1982, 95])).
% 0.53/0.79 tff(1984,plain,
% 0.53/0.79 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))))),
% 0.53/0.79 inference(rewrite,[status(thm)],[])).
% 0.53/0.79 tff(1985,plain,
% 0.53/0.79 (((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z)))))) <=> ((~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))))),
% 0.53/0.79 inference(rewrite,[status(thm)],[])).
% 0.53/0.79 tff(1986,plain,
% 0.53/0.79 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z)))))))),
% 0.53/0.79 inference(monotonicity,[status(thm)],[1985])).
% 0.53/0.79 tff(1987,plain,
% 0.53/0.79 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))))),
% 0.53/0.79 inference(transitivity,[status(thm)],[1986, 1984])).
% 0.53/0.79 tff(1988,plain,
% 0.53/0.79 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z))))))),
% 0.53/0.79 inference(quant_inst,[status(thm)],[])).
% 0.53/0.79 tff(1989,plain,
% 0.53/0.79 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z)))))),
% 0.53/0.79 inference(modus_ponens,[status(thm)],[1988, 1987])).
% 0.53/0.79 tff(1990,plain,
% 0.53/0.79 (~r(z, s(s(s(z))))),
% 0.53/0.79 inference(unit_resolution,[status(thm)],[1989, 14, 1983, 1981])).
% 0.53/0.79 tff(1991,plain,
% 0.53/0.79 (b(z, s(s(s(z))))),
% 0.53/0.79 inference(unit_resolution,[status(thm)],[281, 1990])).
% 0.53/0.79 tff(1992,plain,
% 0.53/0.79 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.53/0.79 inference(unit_resolution,[status(thm)],[267, 1991, 245, 27])).
% 0.53/0.79 tff(1993,plain,
% 0.53/0.79 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.53/0.79 inference(unit_resolution,[status(thm)],[243, 1992])).
% 0.53/0.79 tff(1994,plain,
% 0.53/0.79 (((~![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(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)))))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 0.53/0.79 inference(rewrite,[status(thm)],[])).
% 0.53/0.79 tff(1995,plain,
% 0.53/0.79 (((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(z)))) <=> ((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 0.53/0.79 inference(rewrite,[status(thm)],[])).
% 0.53/0.79 tff(1996,plain,
% 0.53/0.79 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))))),
% 0.53/0.79 inference(monotonicity,[status(thm)],[1995])).
% 0.53/0.79 tff(1997,plain,
% 0.53/0.79 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 0.53/0.79 inference(transitivity,[status(thm)],[1996, 1994])).
% 0.53/0.79 tff(1998,plain,
% 0.53/0.79 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(z))))),
% 0.53/0.79 inference(quant_inst,[status(thm)],[])).
% 0.53/0.79 tff(1999,plain,
% 0.53/0.79 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 0.53/0.79 inference(modus_ponens,[status(thm)],[1998, 1997])).
% 0.53/0.79 tff(2000,plain,
% 0.53/0.79 ($false),
% 0.53/0.79 inference(unit_resolution,[status(thm)],[1999, 14, 26, 222, 614])).
% 0.53/0.79 tff(2001,plain,((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.53/0.79 tff(2002,plain,
% 0.53/0.79 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 0.53/0.79 inference(unit_resolution,[status(thm)],[2001, 26, 222])).
% 0.53/0.79 tff(2003,plain,
% 0.53/0.79 (b(s(s(s(s(s(s(z)))))), s(z))),
% 0.53/0.79 inference(unit_resolution,[status(thm)],[627, 2002])).
% 0.53/0.79 tff(2004,plain,
% 0.53/0.79 (~r(s(z), s(s(s(s(s(s(z)))))))),
% 0.53/0.79 inference(unit_resolution,[status(thm)],[228, 14, 26, 222])).
% 0.53/0.79 tff(2005,plain,
% 0.53/0.79 (b(s(z), s(s(s(s(s(s(z)))))))),
% 0.53/0.79 inference(unit_resolution,[status(thm)],[84, 2004])).
% 0.53/0.79 tff(2006,plain,
% 0.53/0.79 (~b(s(s(z)), s(z))),
% 0.53/0.79 inference(unit_resolution,[status(thm)],[1136, 2005, 2003, 406])).
% 0.53/0.79 tff(2007,plain,
% 0.53/0.79 (r(s(s(z)), s(z))),
% 0.53/0.79 inference(unit_resolution,[status(thm)],[137, 2006])).
% 0.53/0.79 tff(2008,plain,
% 0.53/0.79 (~b(s(s(s(z))), s(z))),
% 0.53/0.79 inference(unit_resolution,[status(thm)],[1524, 2004, 2003, 245])).
% 0.53/0.79 tff(2009,plain,
% 0.53/0.79 (r(s(s(s(z))), s(z))),
% 0.53/0.79 inference(unit_resolution,[status(thm)],[170, 2008])).
% 0.53/0.79 tff(2010,plain,
% 0.53/0.79 ($false),
% 0.53/0.79 inference(unit_resolution,[status(thm)],[1505, 14, 2009, 2007, 1005])).
% 0.53/0.79 tff(2011,plain,((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.53/0.79 tff(2012,plain,
% 0.53/0.79 (~r(s(z), s(s(s(z))))),
% 0.53/0.79 inference(unit_resolution,[status(thm)],[2011, 1981, 1975, 245, 1993])).
% 0.53/0.79 tff(2013,plain,
% 0.53/0.79 (b(s(z), s(s(s(z))))),
% 0.53/0.79 inference(unit_resolution,[status(thm)],[177, 2012])).
% 0.53/0.79 tff(2014,plain,
% 0.53/0.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))),
% 0.53/0.79 inference(rewrite,[status(thm)],[])).
% 0.53/0.79 tff(2015,plain,
% 0.53/0.79 (((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))),
% 0.53/0.79 inference(rewrite,[status(thm)],[])).
% 0.53/0.79 tff(2016,plain,
% 0.53/0.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z)))))))),
% 0.53/0.79 inference(monotonicity,[status(thm)],[2015])).
% 0.53/0.79 tff(2017,plain,
% 0.53/0.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))),
% 0.53/0.79 inference(transitivity,[status(thm)],[2016, 2014])).
% 0.53/0.79 tff(2018,plain,
% 0.53/0.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))),
% 0.53/0.79 inference(quant_inst,[status(thm)],[])).
% 0.53/0.79 tff(2019,plain,
% 0.53/0.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z)))))),
% 0.53/0.79 inference(modus_ponens,[status(thm)],[2018, 2017])).
% 0.53/0.79 tff(2020,plain,
% 0.53/0.79 (~b(s(z), z)),
% 0.53/0.79 inference(unit_resolution,[status(thm)],[2019, 188, 2013, 283, 1991])).
% 0.53/0.79 tff(2021,plain,
% 0.53/0.79 (r(s(z), z)),
% 0.53/0.79 inference(unit_resolution,[status(thm)],[312, 2020])).
% 0.53/0.79 tff(2022,plain,
% 0.53/0.79 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 0.53/0.79 inference(unit_resolution,[status(thm)],[705, 2021, 554])).
% 0.53/0.79 tff(2023,plain,
% 0.53/0.79 (b(s(s(s(s(s(s(z)))))), s(z))),
% 0.53/0.79 inference(unit_resolution,[status(thm)],[627, 2022])).
% 0.53/0.79 tff(2024,plain,
% 0.53/0.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 0.53/0.79 inference(rewrite,[status(thm)],[])).
% 0.53/0.79 tff(2025,plain,
% 0.53/0.79 (((~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 0.53/0.79 inference(rewrite,[status(thm)],[])).
% 0.53/0.79 tff(2026,plain,
% 0.53/0.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(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(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[2025])).
% 0.63/0.80 tff(2027,plain,
% 0.63/0.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(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(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 0.63/0.80 inference(transitivity,[status(thm)],[2026, 2024])).
% 0.63/0.80 tff(2028,plain,
% 0.63/0.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))))),
% 0.63/0.80 inference(quant_inst,[status(thm)],[])).
% 0.63/0.80 tff(2029,plain,
% 0.63/0.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[2028, 2027])).
% 0.63/0.80 tff(2030,plain,
% 0.63/0.80 (~b(z, s(z))),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[2029, 188, 2013, 27, 245, 1991])).
% 0.63/0.80 tff(2031,plain,
% 0.63/0.80 (r(z, s(z))),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[300, 2030])).
% 0.63/0.80 tff(2032,plain,
% 0.63/0.80 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(z))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(z))) | (~r(s(s(z)), s(z))))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(2033,plain,
% 0.63/0.80 (((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z))) <=> ((~r(s(s(z)), z)) | (~r(z, s(z))) | (~r(s(s(z)), s(z))))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(2034,plain,
% 0.63/0.80 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(z))) | (~r(s(s(z)), s(z)))))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[2033])).
% 0.63/0.80 tff(2035,plain,
% 0.63/0.80 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(z))) | (~r(s(s(z)), s(z))))),
% 0.63/0.80 inference(transitivity,[status(thm)],[2034, 2032])).
% 0.63/0.80 tff(2036,plain,
% 0.63/0.80 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))),
% 0.63/0.80 inference(quant_inst,[status(thm)],[])).
% 0.63/0.80 tff(2037,plain,
% 0.63/0.80 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(z))) | (~r(s(s(z)), s(z)))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[2036, 2035])).
% 0.63/0.80 tff(2038,plain,
% 0.63/0.80 ($false),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[2037, 14, 373, 25, 119])).
% 0.63/0.80 tff(2039,plain,((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.80 tff(2040,plain,
% 0.63/0.80 (~r(s(s(z)), s(z))),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[2039, 2031, 25])).
% 0.63/0.80 tff(2041,plain,
% 0.63/0.80 (b(s(s(z)), s(z))),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[137, 2040])).
% 0.63/0.80 tff(2042,plain,
% 0.63/0.80 (~r(s(z), s(s(s(s(s(s(z)))))))),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[802, 2021, 554])).
% 0.63/0.80 tff(2043,plain,
% 0.63/0.80 (b(s(z), s(s(s(s(s(s(z)))))))),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[84, 2042])).
% 0.63/0.80 tff(2044,plain,
% 0.63/0.80 ($false),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[1136, 2043, 2041, 2023, 1975])).
% 0.63/0.80 tff(2045,plain,((~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.80 tff(2046,plain,
% 0.63/0.80 (~r(s(s(z)), z)),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[2045, 283, 554, 27, 245])).
% 0.63/0.80 tff(2047,plain,
% 0.63/0.80 (b(s(s(z)), z)),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[792, 2046])).
% 0.63/0.80 tff(2048,plain,
% 0.63/0.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), z)))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(2049,plain,
% 0.63/0.80 (((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), z)))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(2050,plain,
% 0.63/0.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), z))))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[2049])).
% 0.63/0.80 tff(2051,plain,
% 0.63/0.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), z)))),
% 0.63/0.80 inference(transitivity,[status(thm)],[2050, 2048])).
% 0.63/0.80 tff(2052,plain,
% 0.63/0.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 0.63/0.80 inference(quant_inst,[status(thm)],[])).
% 0.63/0.80 tff(2053,plain,
% 0.63/0.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), z))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[2052, 2051])).
% 0.63/0.80 tff(2054,plain,
% 0.63/0.80 (~b(s(s(s(z))), s(s(z)))),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[2053, 188, 27, 283, 245, 2047])).
% 0.63/0.80 tff(2055,plain,
% 0.63/0.80 (r(s(s(s(z))), s(s(z)))),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[476, 2054])).
% 0.63/0.80 tff(2056,plain,
% 0.63/0.80 (~r(s(z), z)),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[802, 4, 554])).
% 0.63/0.80 tff(2057,plain,
% 0.63/0.80 (b(s(z), z)),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[312, 2056])).
% 0.63/0.80 tff(2058,plain,
% 0.63/0.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(2059,plain,
% 0.63/0.80 (((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(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(z), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(2060,plain,
% 0.63/0.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(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(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[2059])).
% 0.63/0.80 tff(2061,plain,
% 0.63/0.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(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(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 0.63/0.80 inference(transitivity,[status(thm)],[2060, 2058])).
% 0.63/0.80 tff(2062,plain,
% 0.63/0.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 0.63/0.80 inference(quant_inst,[status(thm)],[])).
% 0.63/0.80 tff(2063,plain,
% 0.63/0.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[2062, 2061])).
% 0.63/0.80 tff(2064,plain,
% 0.63/0.80 (~b(s(s(s(z))), s(z))),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[2063, 188, 2057, 27, 283, 245])).
% 0.63/0.80 tff(2065,plain,
% 0.63/0.80 (r(s(s(s(z))), s(z))),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[170, 2064])).
% 0.63/0.80 tff(2066,plain,
% 0.63/0.80 (~b(s(s(z)), z)),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[366, 188, 360, 776, 340])).
% 0.63/0.80 tff(2067,plain,
% 0.63/0.80 (r(s(s(z)), z)),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[350, 79, 93, 2066])).
% 0.63/0.80 tff(2068,plain,
% 0.63/0.80 ($false),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[507, 14, 88, 554, 2067])).
% 0.63/0.80 tff(2069,plain,((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~r(s(z), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.80 tff(2070,plain,
% 0.63/0.80 (~b(z, s(z))),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[2069, 88, 554, 4, 2057])).
% 0.63/0.80 tff(2071,plain,
% 0.63/0.80 (r(z, s(z))),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[300, 2070])).
% 0.63/0.80 tff(2072,plain,
% 0.63/0.80 (~r(z, s(s(s(z))))),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[644, 2071, 2065])).
% 0.63/0.80 tff(2073,plain,
% 0.63/0.80 (b(z, s(s(s(z))))),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[281, 2072])).
% 0.63/0.80 tff(2074,plain,
% 0.63/0.80 (~b(s(s(z)), s(s(s(z))))),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[1045, 2073, 283, 2047])).
% 0.63/0.80 tff(2075,plain,
% 0.63/0.80 (r(s(s(z)), s(s(s(z))))),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[425, 2074])).
% 0.63/0.80 tff(2076,plain,
% 0.63/0.80 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[267, 2073, 245, 27])).
% 0.63/0.80 tff(2077,plain,
% 0.63/0.80 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[243, 2076])).
% 0.63/0.80 tff(2078,plain,
% 0.63/0.80 ($false),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[1132, 14, 88, 2077, 2075])).
% 0.63/0.80 tff(2079,plain,((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(z), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.80 tff(2080,plain,
% 0.63/0.80 (~r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[2079, 4, 245, 27, 554, 283])).
% 0.63/0.80 tff(2081,plain,
% 0.63/0.80 (b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[453, 2080])).
% 0.63/0.80 tff(2082,plain,
% 0.63/0.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(2083,plain,
% 0.63/0.80 (((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))) <=> ((~b(s(z), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(2084,plain,
% 0.63/0.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[2083])).
% 0.63/0.80 tff(2085,plain,
% 0.63/0.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 0.63/0.80 inference(transitivity,[status(thm)],[2084, 2082])).
% 0.63/0.80 tff(2086,plain,
% 0.63/0.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 0.63/0.80 inference(quant_inst,[status(thm)],[])).
% 0.63/0.80 tff(2087,plain,
% 0.63/0.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[2086, 2085])).
% 0.63/0.80 tff(2088,plain,
% 0.63/0.80 (~b(s(s(z)), s(z))),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[2087, 188, 2057, 2081, 27, 2047])).
% 0.63/0.80 tff(2089,plain,
% 0.63/0.80 (r(s(s(z)), s(z))),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[137, 2088])).
% 0.63/0.80 tff(2090,plain,
% 0.63/0.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), z)))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(2091,plain,
% 0.63/0.80 (((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), z)))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(2092,plain,
% 0.63/0.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), z))))),
% 0.63/0.80 inference(monotonicity,[status(thm)],[2091])).
% 0.63/0.80 tff(2093,plain,
% 0.63/0.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), z)))),
% 0.63/0.80 inference(transitivity,[status(thm)],[2092, 2090])).
% 0.63/0.80 tff(2094,plain,
% 0.63/0.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 0.63/0.80 inference(quant_inst,[status(thm)],[])).
% 0.63/0.80 tff(2095,plain,
% 0.63/0.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), z))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[2094, 2093])).
% 0.63/0.80 tff(2096,plain,
% 0.63/0.80 (~b(s(s(z)), s(s(s(z))))),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[2095, 188, 2081, 27, 283, 2047])).
% 0.63/0.80 tff(2097,plain,
% 0.63/0.80 (r(s(s(z)), s(s(s(z))))),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[425, 2096])).
% 0.63/0.80 tff(2098,plain,
% 0.63/0.80 ($false),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[1124, 2097, 2089, 2065])).
% 0.63/0.80 tff(2099,plain,((~r(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), z))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.80 tff(2100,plain,
% 0.63/0.80 (~r(s(z), s(s(s(s(s(s(z)))))))),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[2099, 283, 27, 245, 554])).
% 0.63/0.80 tff(2101,plain,
% 0.63/0.80 (b(s(z), s(s(s(s(s(s(z)))))))),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[84, 2100])).
% 0.63/0.80 tff(2102,plain,
% 0.63/0.80 (~b(s(s(z)), s(s(s(z))))),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[2095, 188, 406, 27, 283, 2047])).
% 0.63/0.80 tff(2103,plain,
% 0.63/0.80 (r(s(s(z)), s(s(s(z))))),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[425, 2102])).
% 0.63/0.80 tff(2104,plain,
% 0.63/0.80 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[604, 284, 554])).
% 0.63/0.80 tff(2105,plain,
% 0.63/0.80 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[243, 2104])).
% 0.63/0.80 tff(2106,plain,
% 0.63/0.80 (~b(s(z), s(s(s(z))))),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[1591, 2105, 245, 86])).
% 0.63/0.80 tff(2107,plain,
% 0.63/0.80 (r(s(z), s(s(s(z))))),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[177, 2106])).
% 0.63/0.80 tff(2108,plain,
% 0.63/0.80 (~r(s(s(z)), s(z))),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[1746, 2107, 522])).
% 0.63/0.80 tff(2109,plain,
% 0.63/0.80 (b(s(s(z)), s(z))),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[137, 2108])).
% 0.63/0.80 tff(2110,plain,
% 0.63/0.80 (~r(s(s(s(z))), s(z))),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[644, 373, 284])).
% 0.63/0.80 tff(2111,plain,
% 0.63/0.80 (b(s(s(s(z))), s(z))),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[170, 2110])).
% 0.63/0.80 tff(2112,plain,
% 0.63/0.80 (~r(s(z), s(s(s(z))))),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[375, 373, 284])).
% 0.63/0.80 tff(2113,plain,
% 0.63/0.80 (b(s(z), s(s(s(z))))),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[177, 2112])).
% 0.63/0.80 tff(2114,plain,
% 0.63/0.80 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 0.63/0.80 inference(unit_resolution,[status(thm)],[1458, 2113, 259, 2111])).
% 0.63/0.80 tff(2115,plain,
% 0.63/0.80 (r(s(s(s(s(s(s(z)))))), s(z))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[627, 2114])).
% 0.63/0.81 tff(2116,plain,
% 0.63/0.81 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), z)))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(2117,plain,
% 0.63/0.81 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), z)))),
% 0.63/0.81 inference(quant_inst,[status(thm)],[])).
% 0.63/0.81 tff(2118,plain,
% 0.63/0.81 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), z))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[2117, 2116])).
% 0.63/0.81 tff(2119,plain,
% 0.63/0.81 ($false),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[2118, 14, 373, 554, 2115])).
% 0.63/0.81 tff(2120,plain,((~r(z, s(z))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.81 tff(2121,plain,
% 0.63/0.81 (~r(z, s(z))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[2120, 2105, 554, 284])).
% 0.63/0.81 tff(2122,plain,
% 0.63/0.81 (b(z, s(z))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[300, 2121])).
% 0.63/0.81 tff(2123,plain,
% 0.63/0.81 (~r(s(s(z)), s(z))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[1744, 14, 26, 522])).
% 0.63/0.81 tff(2124,plain,
% 0.63/0.81 ((s(s(z)) = s(z)) | b(s(s(z)), s(z))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[135, 79, 2123])).
% 0.63/0.81 tff(2125,plain,
% 0.63/0.81 (b(s(s(z)), s(z))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[2124, 132])).
% 0.63/0.81 tff(2126,plain,
% 0.63/0.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(2127,plain,
% 0.63/0.81 (((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), z))) <=> ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(2128,plain,
% 0.63/0.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))))),
% 0.63/0.81 inference(monotonicity,[status(thm)],[2127])).
% 0.63/0.81 tff(2129,plain,
% 0.63/0.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 0.63/0.81 inference(transitivity,[status(thm)],[2128, 2126])).
% 0.63/0.81 tff(2130,plain,
% 0.63/0.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), z)))),
% 0.63/0.81 inference(quant_inst,[status(thm)],[])).
% 0.63/0.81 tff(2131,plain,
% 0.63/0.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[2130, 2129])).
% 0.63/0.81 tff(2132,plain,
% 0.63/0.81 (~b(s(s(z)), z)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[2131, 188, 406, 27, 87, 2125])).
% 0.63/0.81 tff(2133,plain,
% 0.63/0.81 (r(s(s(z)), z)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[350, 79, 93, 2132])).
% 0.63/0.81 tff(2134,plain,
% 0.63/0.81 (~r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[496, 14, 554, 2133])).
% 0.63/0.81 tff(2135,plain,
% 0.63/0.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), s(z))))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(2136,plain,
% 0.63/0.81 (((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z)))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), s(z))))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(2137,plain,
% 0.63/0.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), s(z)))))),
% 0.63/0.81 inference(monotonicity,[status(thm)],[2136])).
% 0.63/0.81 tff(2138,plain,
% 0.63/0.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), s(z))))),
% 0.63/0.81 inference(transitivity,[status(thm)],[2137, 2135])).
% 0.63/0.81 tff(2139,plain,
% 0.63/0.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 0.63/0.81 inference(quant_inst,[status(thm)],[])).
% 0.63/0.81 tff(2140,plain,
% 0.63/0.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), s(z)))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[2139, 2138])).
% 0.63/0.81 tff(2141,plain,
% 0.63/0.81 (~b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[2140, 188, 87, 527, 2125])).
% 0.63/0.81 tff(2142,plain,
% 0.63/0.81 ((s(s(s(s(s(s(z)))))) = s(s(z))) | r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[500, 79, 2141])).
% 0.63/0.81 tff(2143,plain,
% 0.63/0.81 ($false),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[2142, 2134, 1828])).
% 0.63/0.81 tff(2144,plain,((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.81 tff(2145,plain,
% 0.63/0.81 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[2144, 2107, 27, 406, 522, 554])).
% 0.63/0.81 tff(2146,plain,
% 0.63/0.81 (r(s(s(s(s(s(s(z)))))), s(z))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[627, 2145])).
% 0.63/0.81 tff(2147,plain,
% 0.63/0.81 (~r(s(z), z)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[705, 2146, 554])).
% 0.63/0.81 tff(2148,plain,
% 0.63/0.81 (b(s(z), z)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[312, 2147])).
% 0.63/0.81 tff(2149,plain,
% 0.63/0.81 ($false),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[1499, 188, 2148, 2122, 427, 2109])).
% 0.63/0.81 tff(2150,plain,((~r(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.81 tff(2151,plain,
% 0.63/0.81 (~r(z, s(s(s(z))))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[2150, 406, 554, 27, 2047, 2103, 245, 2101])).
% 0.63/0.81 tff(2152,plain,
% 0.63/0.81 (b(z, s(s(s(z))))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[281, 2151])).
% 0.63/0.81 tff(2153,plain,
% 0.63/0.81 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[267, 2152, 245, 27])).
% 0.63/0.81 tff(2154,plain,
% 0.63/0.81 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[243, 2153])).
% 0.63/0.81 tff(2155,plain,
% 0.63/0.81 (~r(s(z), s(s(s(z))))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[2011, 2154, 2055, 245, 406])).
% 0.63/0.81 tff(2156,plain,
% 0.63/0.81 (b(s(z), s(s(s(z))))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[177, 2155])).
% 0.63/0.81 tff(2157,plain,
% 0.63/0.81 (~b(s(z), z)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[2019, 188, 2156, 283, 2152])).
% 0.63/0.81 tff(2158,plain,
% 0.63/0.81 (r(s(z), z)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[312, 2157])).
% 0.63/0.81 tff(2159,plain,
% 0.63/0.81 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[705, 2158, 554])).
% 0.63/0.81 tff(2160,plain,
% 0.63/0.81 (b(s(s(s(s(s(s(z)))))), s(z))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[627, 2159])).
% 0.63/0.81 tff(2161,plain,
% 0.63/0.81 (~r(s(s(s(z))), s(z))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[1178, 2158, 2047, 2154])).
% 0.63/0.81 tff(2162,plain,
% 0.63/0.81 (b(s(s(s(z))), s(z))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[170, 2161])).
% 0.63/0.81 tff(2163,plain,
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% 0.63/0.81 tff(2165,plain,
% 0.63/0.81 (~b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[2164, 283, 554, 245, 27])).
% 0.63/0.81 tff(2166,plain,
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% 0.63/0.81 inference(unit_resolution,[status(thm)],[453, 2165])).
% 0.63/0.81 tff(2167,plain,
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% 0.63/0.81 inference(unit_resolution,[status(thm)],[425, 2167])).
% 0.63/0.81 tff(2169,plain,
% 0.63/0.81 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[267, 258, 245, 27])).
% 0.63/0.81 tff(2170,plain,
% 0.63/0.81 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[243, 2169])).
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% 0.63/0.81 tff(2172,plain,((~b(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.81 tff(2173,plain,
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% 0.63/0.81 inference(unit_resolution,[status(thm)],[2172, 2166, 283, 2047, 245, 27])).
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% 0.63/0.81 inference(unit_resolution,[status(thm)],[604, 2174, 554])).
% 0.63/0.81 tff(2176,plain,
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% 0.63/0.81 inference(unit_resolution,[status(thm)],[243, 2175])).
% 0.63/0.81 tff(2177,plain,
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% 0.63/0.81 tff(2178,plain,
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% 0.63/0.81 inference(unit_resolution,[status(thm)],[300, 2177])).
% 0.63/0.81 tff(2179,plain,
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% 0.63/0.81 inference(unit_resolution,[status(thm)],[1591, 2176, 245, 2101])).
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% 0.63/0.81 inference(unit_resolution,[status(thm)],[177, 2179])).
% 0.63/0.81 tff(2181,plain,
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% 0.63/0.81 inference(unit_resolution,[status(thm)],[321, 2180, 283, 2174])).
% 0.63/0.81 tff(2182,plain,
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% 0.63/0.81 inference(unit_resolution,[status(thm)],[170, 2181])).
% 0.63/0.81 tff(2183,plain,
% 0.63/0.81 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[679, 27, 140, 259, 554])).
% 0.63/0.81 tff(2184,plain,
% 0.63/0.81 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[220, 2183])).
% 0.63/0.81 tff(2185,plain,
% 0.63/0.81 (~b(z, s(s(s(z))))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[267, 2184, 259, 27])).
% 0.63/0.81 tff(2186,plain,
% 0.63/0.81 (r(z, s(s(s(z))))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[281, 2185])).
% 0.63/0.81 tff(2187,plain,
% 0.63/0.81 (~b(s(z), s(s(s(z))))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[1591, 2184, 259, 86])).
% 0.63/0.81 tff(2188,plain,
% 0.63/0.81 (r(s(z), s(s(s(z))))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[177, 2187])).
% 0.63/0.81 tff(2189,plain,
% 0.63/0.81 (~r(z, s(z))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[375, 2188, 2186])).
% 0.63/0.81 tff(2190,plain,
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% 0.63/0.81 inference(unit_resolution,[status(thm)],[300, 2189])).
% 0.63/0.81 tff(2191,plain,
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% 0.63/0.81 inference(unit_resolution,[status(thm)],[634, 188, 2190, 27, 87, 86])).
% 0.63/0.81 tff(2192,plain,((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), z))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.81 tff(2193,plain,
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% 0.63/0.81 inference(unit_resolution,[status(thm)],[2192, 2182, 2101, 27, 2176, 554])).
% 0.63/0.81 tff(2194,plain,
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% 0.63/0.81 inference(unit_resolution,[status(thm)],[627, 2193])).
% 0.63/0.81 tff(2195,plain,
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% 0.63/0.81 tff(2197,plain,
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% 0.63/0.81 inference(unit_resolution,[status(thm)],[1499, 188, 2196, 2178, 2047])).
% 0.63/0.81 tff(2198,plain,
% 0.63/0.81 (r(s(s(z)), s(z))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[137, 2197])).
% 0.63/0.81 tff(2199,plain,
% 0.63/0.81 ($false),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[1505, 14, 2182, 2198, 2055])).
% 0.63/0.81 tff(2200,plain,((~b(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.81 tff(2201,plain,
% 0.63/0.81 (~b(s(s(s(z))), z)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[2200, 27, 554, 245])).
% 0.63/0.81 tff(2202,plain,
% 0.63/0.81 (r(s(s(s(z))), z)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[326, 2201])).
% 0.63/0.81 tff(2203,plain,
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% 0.63/0.81 inference(unit_resolution,[status(thm)],[1822, 2202, 554])).
% 0.63/0.81 tff(2204,plain,
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% 0.63/0.81 inference(unit_resolution,[status(thm)],[1965, 2204, 554, 2202])).
% 0.63/0.81 tff(2206,plain,
% 0.63/0.81 (r(z, s(s(s(z))))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[281, 2205])).
% 0.63/0.81 tff(2207,plain,
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% 0.63/0.81 inference(unit_resolution,[status(thm)],[604, 2206, 554])).
% 0.63/0.81 tff(2208,plain,
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% 0.63/0.81 inference(unit_resolution,[status(thm)],[243, 2207])).
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% 0.63/0.81 tff(2210,plain,
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% 0.63/0.81 inference(unit_resolution,[status(thm)],[425, 2211])).
% 0.63/0.81 tff(2213,plain,
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% 0.63/0.81 inference(unit_resolution,[status(thm)],[1822, 2, 554])).
% 0.63/0.81 tff(2214,plain,
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% 0.63/0.81 inference(unit_resolution,[status(thm)],[1965, 2214, 554, 2])).
% 0.63/0.81 tff(2216,plain,
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% 0.63/0.81 inference(unit_resolution,[status(thm)],[281, 2215])).
% 0.63/0.81 tff(2217,plain,
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% 0.63/0.81 inference(unit_resolution,[status(thm)],[1758, 14, 2216, 2212])).
% 0.63/0.81 tff(2218,plain,
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% 0.63/0.81 inference(unit_resolution,[status(thm)],[519, 79, 2217, 95])).
% 0.63/0.81 tff(2219,plain,
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% 0.63/0.81 inference(unit_resolution,[status(thm)],[1694, 25, 2216])).
% 0.63/0.81 tff(2220,plain,
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% 0.63/0.81 inference(unit_resolution,[status(thm)],[425, 2219])).
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% 0.63/0.81 tff(2222,plain,((~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.81 tff(2223,plain,
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% 0.63/0.81 inference(unit_resolution,[status(thm)],[792, 2223])).
% 0.63/0.81 tff(2225,plain,
% 0.63/0.81 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[604, 2216, 554])).
% 0.63/0.81 tff(2226,plain,
% 0.63/0.81 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[243, 2225])).
% 0.63/0.81 tff(2227,plain,
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% 0.63/0.81 tff(2228,plain,
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% 0.63/0.81 tff(2229,plain,
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% 0.63/0.81 inference(unit_resolution,[status(thm)],[795, 2214, 2228, 2224])).
% 0.63/0.81 tff(2230,plain,
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% 0.63/0.81 inference(unit_resolution,[status(thm)],[137, 2229])).
% 0.63/0.81 tff(2231,plain,
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% 0.63/0.81 inference(unit_resolution,[status(thm)],[1746, 2212, 2230])).
% 0.63/0.81 tff(2232,plain,
% 0.63/0.81 (b(s(z), s(s(s(z))))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[177, 2231])).
% 0.63/0.81 tff(2233,plain,
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% 0.63/0.81 inference(unit_resolution,[status(thm)],[1124, 2212, 2230])).
% 0.63/0.81 tff(2234,plain,
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% 0.63/0.81 inference(unit_resolution,[status(thm)],[170, 2233])).
% 0.63/0.81 tff(2235,plain,
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% 0.63/0.81 inference(unit_resolution,[status(thm)],[1458, 2234, 2226, 2232])).
% 0.63/0.81 tff(2236,plain,
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% 0.63/0.81 inference(unit_resolution,[status(thm)],[627, 2235])).
% 0.63/0.81 tff(2237,plain,
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% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(2238,plain,
% 0.63/0.81 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 0.63/0.81 inference(quant_inst,[status(thm)],[])).
% 0.63/0.81 tff(2239,plain,
% 0.63/0.81 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(z))))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[2238, 2237])).
% 0.63/0.81 tff(2240,plain,
% 0.63/0.81 (~r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[2239, 14, 2236, 2230])).
% 0.63/0.81 tff(2241,plain,
% 0.63/0.81 (b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[500, 79, 2240, 395])).
% 0.63/0.81 tff(2242,plain,
% 0.63/0.81 ($false),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[515, 188, 406, 27, 2241, 2218])).
% 0.63/0.81 tff(2243,plain,((~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.81 tff(2244,plain,
% 0.63/0.81 (~b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[2243, 27, 554, 2202])).
% 0.63/0.81 tff(2245,plain,
% 0.63/0.81 (r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[453, 2244])).
% 0.63/0.81 tff(2246,plain,
% 0.63/0.81 (~r(s(z), s(s(s(s(s(s(z)))))))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[2069, 2245, 554, 2210, 2204])).
% 0.63/0.81 tff(2247,plain,
% 0.63/0.81 (b(s(z), s(s(s(s(s(s(z)))))))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[84, 2246])).
% 0.63/0.81 tff(2248,plain,
% 0.63/0.81 (~b(s(z), s(s(s(z))))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[1591, 2247, 245, 2208])).
% 0.63/0.81 tff(2249,plain,
% 0.63/0.81 (r(s(z), s(s(s(z))))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[177, 2248])).
% 0.63/0.81 tff(2250,plain,
% 0.63/0.81 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[877, 2249, 2210, 2204, 2206])).
% 0.63/0.81 tff(2251,plain,
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% 0.63/0.81 inference(unit_resolution,[status(thm)],[890, 2250])).
% 0.63/0.81 tff(2252,plain,
% 0.63/0.81 (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[916, 188, 245, 2208, 2251])).
% 0.63/0.81 tff(2253,plain,
% 0.63/0.81 (r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[927, 79, 924, 2252])).
% 0.63/0.81 tff(2254,plain,
% 0.63/0.81 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(2255,plain,
% 0.63/0.81 (((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(2256,plain,
% 0.63/0.81 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 0.63/0.81 inference(monotonicity,[status(thm)],[2255])).
% 0.63/0.81 tff(2257,plain,
% 0.63/0.81 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 0.63/0.81 inference(transitivity,[status(thm)],[2256, 2254])).
% 0.63/0.81 tff(2258,plain,
% 0.63/0.81 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 0.63/0.81 inference(quant_inst,[status(thm)],[])).
% 0.63/0.81 tff(2259,plain,
% 0.63/0.81 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[2258, 2257])).
% 0.63/0.81 tff(2260,plain,
% 0.63/0.81 (~r(s(s(z)), s(s(s(s(z)))))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[2259, 14, 2245, 2253])).
% 0.63/0.81 tff(2261,plain,
% 0.63/0.81 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(z)))),
% 0.63/0.81 inference(commutativity,[status(thm)],[])).
% 0.63/0.81 tff(2262,plain,
% 0.63/0.81 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(z)) = s(s(s(s(z)))))),
% 0.63/0.81 inference(symmetry,[status(thm)],[2261])).
% 0.63/0.81 tff(2263,plain,
% 0.63/0.81 ((~(s(s(s(s(z)))) = s(s(z)))) <=> (~(s(s(z)) = s(s(s(s(z))))))),
% 0.63/0.81 inference(monotonicity,[status(thm)],[2262])).
% 0.63/0.81 tff(2264,plain,
% 0.63/0.81 (~(s(s(z)) = s(s(s(s(z)))))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[906, 2263])).
% 0.63/0.81 tff(2265,plain,
% 0.63/0.81 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z))))))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(2266,plain,
% 0.63/0.81 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z))))))),
% 0.63/0.81 inference(quant_inst,[status(thm)],[])).
% 0.63/0.81 tff(2267,plain,
% 0.63/0.81 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z)))))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[2266, 2265])).
% 0.63/0.81 tff(2268,plain,
% 0.63/0.81 ((s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z)))))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[2267, 79])).
% 0.63/0.81 tff(2269,plain,
% 0.63/0.81 (b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z)))))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[2268, 2264])).
% 0.63/0.81 tff(2270,plain,
% 0.63/0.81 (b(s(s(z)), s(s(s(s(z)))))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[2269, 2260])).
% 0.63/0.81 tff(2271,plain,
% 0.63/0.81 (~r(s(s(s(s(z)))), s(s(z)))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[934, 14, 2245, 2253])).
% 0.63/0.81 tff(2272,plain,
% 0.63/0.81 (b(s(s(s(s(z)))), s(s(z)))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[909, 79, 906, 2271])).
% 0.63/0.81 tff(2273,plain,
% 0.63/0.81 (~r(s(s(z)), z)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[2222, 2202, 554])).
% 0.63/0.81 tff(2274,plain,
% 0.63/0.81 (b(s(s(z)), z)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[792, 2273])).
% 0.63/0.81 tff(2275,plain,
% 0.63/0.81 (~b(s(s(z)), s(z))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[795, 2204, 2210, 2274])).
% 0.63/0.81 tff(2276,plain,
% 0.63/0.81 (r(s(s(z)), s(z))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[137, 2275])).
% 0.63/0.81 tff(2277,plain,
% 0.63/0.81 (~r(s(s(z)), s(s(s(z))))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[1746, 2249, 2276])).
% 0.63/0.81 tff(2278,plain,
% 0.63/0.81 (b(s(s(z)), s(s(s(z))))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[425, 2277])).
% 0.63/0.81 tff(2279,plain,
% 0.63/0.81 (~b(s(s(s(z))), s(s(z)))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[936, 2278, 2251, 2245, 245, 2208])).
% 0.63/0.81 tff(2280,plain,
% 0.63/0.81 (r(s(s(s(z))), s(s(z)))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[476, 2279])).
% 0.63/0.81 tff(2281,plain,
% 0.63/0.81 (~r(s(z), s(s(z)))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[1642, 2249, 2280])).
% 0.63/0.81 tff(2282,plain,
% 0.63/0.81 (b(s(z), s(s(z)))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[117, 79, 114, 2281])).
% 0.63/0.81 tff(2283,plain,
% 0.63/0.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(2284,plain,
% 0.63/0.81 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(2285,plain,
% 0.63/0.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 0.63/0.81 inference(monotonicity,[status(thm)],[2284])).
% 0.63/0.81 tff(2286,plain,
% 0.63/0.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 0.63/0.81 inference(transitivity,[status(thm)],[2285, 2283])).
% 0.63/0.82 tff(2287,plain,
% 0.63/0.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))),
% 0.63/0.82 inference(quant_inst,[status(thm)],[])).
% 0.63/0.82 tff(2288,plain,
% 0.63/0.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[2287, 2286])).
% 0.63/0.82 tff(2289,plain,
% 0.63/0.82 (~b(s(z), s(s(s(s(z)))))),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[2288, 188, 2270, 2282, 2272])).
% 0.63/0.82 tff(2290,plain,
% 0.63/0.82 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z))))))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(2291,plain,
% 0.63/0.82 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z))))))),
% 0.63/0.82 inference(quant_inst,[status(thm)],[])).
% 0.63/0.82 tff(2292,plain,
% 0.63/0.82 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z)))))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[2291, 2290])).
% 0.63/0.82 tff(2293,plain,
% 0.63/0.82 ((s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z)))))),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[2292, 79])).
% 0.63/0.82 tff(2294,plain,
% 0.63/0.82 (b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z)))))),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[2293, 843])).
% 0.63/0.82 tff(2295,plain,
% 0.63/0.82 (r(s(z), s(s(s(s(z)))))),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[2294, 2289])).
% 0.63/0.82 tff(2296,assumption,(r(s(z), s(s(s(s(z)))))), introduced(assumption)).
% 0.63/0.82 tff(2297,assumption,(r(s(s(s(z))), s(s(s(s(z)))))), introduced(assumption)).
% 0.63/0.82 tff(2298,plain,
% 0.63/0.82 (((~![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(z)))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(2299,plain,
% 0.63/0.82 (((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(2300,plain,
% 0.63/0.82 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))))),
% 0.63/0.82 inference(monotonicity,[status(thm)],[2299])).
% 0.63/0.82 tff(2301,plain,
% 0.63/0.82 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 0.63/0.82 inference(transitivity,[status(thm)],[2300, 2298])).
% 0.63/0.82 tff(2302,plain,
% 0.63/0.82 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))))),
% 0.63/0.82 inference(quant_inst,[status(thm)],[])).
% 0.63/0.82 tff(2303,plain,
% 0.63/0.82 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[2302, 2301])).
% 0.63/0.82 tff(2304,plain,
% 0.63/0.82 ($false),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[2303, 14, 26, 2297, 2296])).
% 0.63/0.82 tff(2305,plain,((~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.82 tff(2306,plain,
% 0.63/0.82 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[2305, 2295, 2249])).
% 0.63/0.82 tff(2307,plain,
% 0.63/0.82 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(s(z)))))),
% 0.63/0.82 inference(commutativity,[status(thm)],[])).
% 0.63/0.82 tff(2308,plain,
% 0.63/0.82 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(s(s(z))))))),
% 0.63/0.82 inference(monotonicity,[status(thm)],[2307])).
% 0.63/0.82 tff(2309,plain,
% 0.63/0.82 (~(s(s(s(z))) = s(s(s(s(z)))))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[885, 2308])).
% 0.63/0.82 tff(2310,plain,
% 0.63/0.82 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z))))))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(2311,plain,
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% 0.63/0.82 inference(quant_inst,[status(thm)],[])).
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% 0.63/0.82 inference(modus_ponens,[status(thm)],[2311, 2310])).
% 0.63/0.82 tff(2313,plain,
% 0.63/0.82 ((s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z)))))),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[2312, 79])).
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% 0.63/0.82 (b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z)))))),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[2313, 2309])).
% 0.63/0.82 tff(2315,plain,
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% 0.63/0.82 inference(unit_resolution,[status(thm)],[2314, 2306])).
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% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(2317,plain,
% 0.63/0.82 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(2318,plain,
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% 0.63/0.82 inference(monotonicity,[status(thm)],[2317])).
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% 0.63/0.82 inference(transitivity,[status(thm)],[2318, 2316])).
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% 0.63/0.82 inference(quant_inst,[status(thm)],[])).
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% 0.63/0.82 inference(modus_ponens,[status(thm)],[2320, 2319])).
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% 0.63/0.82 inference(unit_resolution,[status(thm)],[2321, 188, 2278, 2315, 2270, 2251])).
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% 0.63/0.82 tff(2324,plain,
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% 0.63/0.82 inference(unit_resolution,[status(thm)],[2323, 1971, 1904])).
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% 0.63/0.82 inference(unit_resolution,[status(thm)],[256, 2324])).
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% 0.63/0.82 inference(unit_resolution,[status(thm)],[368, 1906, 88, 2325])).
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% 0.63/0.82 (b(s(z), s(s(s(s(s(s(z)))))))),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[84, 2328])).
% 0.63/0.82 tff(2330,plain,
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% 0.63/0.82 inference(unit_resolution,[status(thm)],[1591, 1969, 2329, 1971])).
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% 0.63/0.82 inference(unit_resolution,[status(thm)],[177, 2330])).
% 0.63/0.82 tff(2332,plain,
% 0.63/0.82 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[1672, 2331, 1967])).
% 0.63/0.82 tff(2333,plain,
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% 0.63/0.82 inference(unit_resolution,[status(thm)],[890, 2332])).
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% 0.63/0.82 inference(unit_resolution,[status(thm)],[792, 2334])).
% 0.63/0.82 tff(2336,plain,
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% 0.63/0.82 tff(2339,plain,
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% 0.63/0.82 inference(unit_resolution,[status(thm)],[1427, 2338])).
% 0.63/0.82 tff(2340,plain,
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% 0.63/0.82 inference(unit_resolution,[status(thm)],[1642, 2331, 2339])).
% 0.63/0.82 tff(2341,plain,
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% 0.63/0.82 inference(unit_resolution,[status(thm)],[476, 2340])).
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% 0.63/0.82 tff(2343,plain,((~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.82 tff(2344,plain,
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% 0.63/0.82 inference(unit_resolution,[status(thm)],[2343, 88])).
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% 0.63/0.82 inference(unit_resolution,[status(thm)],[326, 2344])).
% 0.63/0.82 tff(2346,plain,
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% 0.63/0.82 inference(unit_resolution,[status(thm)],[1112, 222, 2325])).
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% 0.63/0.82 inference(unit_resolution,[status(thm)],[281, 2346])).
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% 0.63/0.82 inference(unit_resolution,[status(thm)],[1686, 222, 88])).
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% 0.63/0.82 tff(2351,plain,((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.82 tff(2352,plain,
% 0.63/0.82 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[2351, 88])).
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% 0.63/0.82 inference(unit_resolution,[status(thm)],[243, 2352])).
% 0.63/0.82 tff(2354,plain,
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% 0.63/0.82 inference(unit_resolution,[status(thm)],[1045, 258, 2335, 2345])).
% 0.63/0.82 tff(2355,plain,
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% 0.63/0.82 inference(unit_resolution,[status(thm)],[425, 2354])).
% 0.63/0.82 tff(2356,plain,
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% 0.63/0.82 inference(unit_resolution,[status(thm)],[2323, 554, 245])).
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% 0.63/0.82 inference(unit_resolution,[status(thm)],[256, 2356])).
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% 0.63/0.82 inference(unit_resolution,[status(thm)],[792, 2358])).
% 0.63/0.82 tff(2360,plain,
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% 0.63/0.82 inference(unit_resolution,[status(thm)],[802, 3, 554])).
% 0.63/0.82 tff(2361,plain,
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% 0.63/0.82 inference(unit_resolution,[status(thm)],[84, 2360])).
% 0.63/0.82 tff(2362,plain,
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% 0.63/0.82 inference(unit_resolution,[status(thm)],[1591, 2361, 245, 684])).
% 0.63/0.82 tff(2363,plain,
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% 0.63/0.82 tff(2364,plain,
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% 0.63/0.82 inference(unit_resolution,[status(thm)],[705, 3, 554])).
% 0.63/0.82 tff(2365,plain,
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% 0.63/0.82 inference(unit_resolution,[status(thm)],[627, 2364])).
% 0.63/0.82 tff(2366,plain,
% 0.63/0.82 (~b(s(s(s(z))), s(z))),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[1524, 2365, 2360, 245])).
% 0.63/0.82 tff(2367,plain,
% 0.63/0.82 (r(s(s(s(z))), s(z))),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[170, 2366])).
% 0.63/0.82 tff(2368,plain,
% 0.63/0.82 ($false),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[1160, 2367, 2363, 2357, 427, 3])).
% 0.63/0.82 tff(2369,plain,((~r(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), z))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.82 tff(2370,plain,
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% 0.63/0.82 inference(unit_resolution,[status(thm)],[368, 2371, 2357, 88])).
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% 0.63/0.82 inference(unit_resolution,[status(thm)],[84, 2372])).
% 0.63/0.82 tff(2374,plain,
% 0.63/0.82 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[1591, 2373, 245, 684])).
% 0.63/0.82 tff(2375,plain,
% 0.63/0.82 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[243, 2374])).
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% 0.63/0.82 tff(2377,plain,((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), z))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.82 tff(2378,plain,
% 0.63/0.82 (~b(s(z), s(s(s(z))))),
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% 0.63/0.82 tff(2379,plain,
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% 0.63/0.82 tff(2380,plain,
% 0.63/0.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(2381,plain,
% 0.63/0.82 (((~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z))) <=> ((~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(2382,plain,
% 0.63/0.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z))))),
% 0.63/0.82 inference(monotonicity,[status(thm)],[2381])).
% 0.63/0.82 tff(2383,plain,
% 0.63/0.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)))),
% 0.63/0.82 inference(transitivity,[status(thm)],[2382, 2380])).
% 0.63/0.82 tff(2384,plain,
% 0.63/0.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))),
% 0.63/0.82 inference(quant_inst,[status(thm)],[])).
% 0.63/0.82 tff(2385,plain,
% 0.63/0.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[2384, 2383])).
% 0.63/0.82 tff(2386,plain,
% 0.63/0.82 (~b(s(s(s(z))), s(s(z)))),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[2385, 188, 2345, 2335, 2337])).
% 0.63/0.82 tff(2387,plain,
% 0.63/0.82 (r(s(s(s(z))), s(s(z)))),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[476, 2386])).
% 0.63/0.82 tff(2388,plain,
% 0.63/0.82 (~r(s(z), s(s(z)))),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[1642, 2379, 2387])).
% 0.63/0.82 tff(2389,plain,
% 0.63/0.82 (b(s(z), s(s(z)))),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[1427, 2388])).
% 0.63/0.82 tff(2390,plain,
% 0.63/0.82 (~r(s(s(s(s(z)))), s(s(z)))),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[1884, 14, 522, 845])).
% 0.63/0.82 tff(2391,plain,
% 0.63/0.82 (b(s(s(s(s(z)))), s(s(z)))),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[909, 79, 906, 2390])).
% 0.63/0.82 tff(2392,plain,
% 0.63/0.82 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(2393,plain,
% 0.63/0.82 (((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(2394,plain,
% 0.63/0.82 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 0.63/0.82 inference(monotonicity,[status(thm)],[2393])).
% 0.63/0.82 tff(2395,plain,
% 0.63/0.82 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 0.63/0.82 inference(transitivity,[status(thm)],[2394, 2392])).
% 0.63/0.82 tff(2396,plain,
% 0.63/0.82 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 0.63/0.82 inference(quant_inst,[status(thm)],[])).
% 0.63/0.82 tff(2397,plain,
% 0.63/0.82 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[2396, 2395])).
% 0.63/0.82 tff(2398,plain,
% 0.63/0.82 (~r(s(s(z)), s(s(s(s(z)))))),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[2397, 14, 522, 845])).
% 0.63/0.82 tff(2399,plain,
% 0.63/0.82 (b(s(s(z)), s(s(s(s(z)))))),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[2269, 2398])).
% 0.63/0.82 tff(2400,plain,
% 0.63/0.82 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(2401,plain,
% 0.63/0.82 (((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(2402,plain,
% 0.63/0.82 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z))))))))),
% 0.63/0.82 inference(monotonicity,[status(thm)],[2401])).
% 0.63/0.82 tff(2403,plain,
% 0.63/0.82 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 0.63/0.82 inference(transitivity,[status(thm)],[2402, 2400])).
% 0.63/0.82 tff(2404,plain,
% 0.63/0.82 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 0.63/0.82 inference(quant_inst,[status(thm)],[])).
% 0.63/0.82 tff(2405,plain,
% 0.63/0.82 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z))))))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[2404, 2403])).
% 0.63/0.82 tff(2406,plain,
% 0.63/0.82 (~r(s(z), s(s(s(s(z)))))),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[2405, 14, 26, 845])).
% 0.63/0.82 tff(2407,plain,
% 0.63/0.82 (b(s(z), s(s(s(s(z)))))),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[2294, 2406])).
% 0.63/0.82 tff(2408,plain,
% 0.63/0.82 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(2409,plain,
% 0.63/0.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 0.63/0.82 inference(monotonicity,[status(thm)],[2408])).
% 0.63/0.82 tff(2410,plain,
% 0.63/0.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 0.63/0.82 inference(transitivity,[status(thm)],[2409, 2283])).
% 0.63/0.82 tff(2411,plain,
% 0.63/0.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 0.63/0.82 inference(quant_inst,[status(thm)],[])).
% 0.63/0.82 tff(2412,plain,
% 0.63/0.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[2411, 2410])).
% 0.63/0.82 tff(2413,plain,
% 0.63/0.82 ($false),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[2412, 188, 2407, 2399, 1651, 2391])).
% 0.63/0.82 tff(2414,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.82 tff(2415,plain,
% 0.63/0.82 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[2414, 2389, 2355, 2379])).
% 0.63/0.82 tff(2416,plain,
% 0.63/0.82 (b(s(s(s(s(z)))), s(s(s(z))))),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[890, 2415])).
% 0.63/0.82 tff(2417,plain,
% 0.63/0.82 (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.63/0.82 inference(unit_resolution,[status(thm)],[916, 188, 1971, 2353, 2416])).
% 0.63/0.82 tff(2418,plain,
% 0.63/0.82 (r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[927, 79, 924, 2417])).
% 0.63/0.83 tff(2419,plain,
% 0.63/0.83 (~b(s(s(s(s(z)))), z)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[1293, 188, 2345, 258, 2416])).
% 0.63/0.83 tff(2420,plain,
% 0.63/0.83 (r(s(s(s(s(z)))), z)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[859, 2419])).
% 0.63/0.83 tff(2421,plain,
% 0.63/0.83 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), z)))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(2422,plain,
% 0.63/0.83 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), z)))),
% 0.63/0.83 inference(quant_inst,[status(thm)],[])).
% 0.63/0.83 tff(2423,plain,
% 0.63/0.83 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), z))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[2422, 2421])).
% 0.63/0.83 tff(2424,plain,
% 0.63/0.83 ($false),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[2423, 14, 2325, 2420, 2418])).
% 0.63/0.83 tff(2425,plain,((~b(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.83 tff(2426,plain,
% 0.63/0.83 (~b(z, s(s(s(z))))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[2425, 88])).
% 0.63/0.83 tff(2427,plain,
% 0.63/0.83 (r(z, s(s(s(z))))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[281, 2426])).
% 0.63/0.83 tff(2428,plain,
% 0.63/0.83 (~r(z, s(z))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[2120, 2427, 1904, 2353])).
% 0.63/0.83 tff(2429,plain,
% 0.63/0.83 (b(z, s(z))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[300, 2428])).
% 0.63/0.83 tff(2430,plain,
% 0.63/0.83 (~b(s(z), s(s(s(z))))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[2377, 522, 88, 1904, 1971])).
% 0.63/0.83 tff(2431,plain,
% 0.63/0.83 (r(s(z), s(s(s(z))))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[177, 2430])).
% 0.63/0.83 tff(2432,plain,
% 0.63/0.83 (~r(s(s(z)), s(z))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[1746, 2431, 522])).
% 0.63/0.83 tff(2433,plain,
% 0.63/0.83 (b(s(s(z)), s(z))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[137, 2432])).
% 0.63/0.83 tff(2434,plain,
% 0.63/0.83 (~b(s(z), z)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[795, 2433, 2429, 2335])).
% 0.63/0.83 tff(2435,plain,
% 0.63/0.83 (r(s(z), z)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[312, 2434])).
% 0.63/0.83 tff(2436,plain,
% 0.63/0.83 ($false),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[307, 14, 2435, 2431, 2427])).
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% 0.63/0.83 inference(unit_resolution,[status(thm)],[2437, 88])).
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% 0.63/0.83 inference(unit_resolution,[status(thm)],[425, 2438])).
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% 0.63/0.83 inference(unit_resolution,[status(thm)],[2445, 88])).
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% 0.63/0.83 inference(unit_resolution,[status(thm)],[453, 2453])).
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% 0.63/0.83 inference(unit_resolution,[status(thm)],[1136, 2454])).
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% 0.63/0.83 inference(unit_resolution,[status(thm)],[137, 2456])).
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% 0.63/0.83 inference(unit_resolution,[status(thm)],[2039, 2457, 25])).
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% 0.63/0.83 tff(2462,plain,
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% 0.63/0.83 inference(unit_resolution,[status(thm)],[2461, 85, 27, 25])).
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% 0.63/0.83 inference(unit_resolution,[status(thm)],[1345, 3, 25])).
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% 0.63/0.83 inference(unit_resolution,[status(thm)],[326, 2466])).
% 0.63/0.83 tff(2468,plain,
% 0.63/0.83 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[2001, 614, 26])).
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% 0.63/0.83 inference(unit_resolution,[status(thm)],[243, 2468])).
% 0.63/0.83 tff(2470,plain,
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% 0.63/0.83 inference(unit_resolution,[status(thm)],[547, 2465, 2469, 2467])).
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% 0.63/0.83 (r(z, s(s(s(z))))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[281, 2470])).
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% 0.63/0.83 inference(unit_resolution,[status(thm)],[321, 2471, 26, 2467])).
% 0.63/0.83 tff(2473,plain,
% 0.63/0.83 (r(s(s(s(z))), s(z))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[170, 2472])).
% 0.63/0.83 tff(2474,plain,
% 0.63/0.83 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[619, 2473, 614])).
% 0.63/0.83 tff(2475,plain,
% 0.63/0.83 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[220, 2474])).
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% 0.63/0.83 tff(2478,plain,
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% 0.63/0.83 inference(unit_resolution,[status(thm)],[2477, 2463, 25, 27, 26])).
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% 0.63/0.83 inference(unit_resolution,[status(thm)],[619, 2463, 24])).
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% 0.63/0.83 inference(unit_resolution,[status(thm)],[170, 2480])).
% 0.63/0.83 tff(2482,plain,
% 0.63/0.83 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[2001, 2463, 26])).
% 0.63/0.83 tff(2483,plain,
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% 0.63/0.83 inference(unit_resolution,[status(thm)],[243, 2482])).
% 0.63/0.83 tff(2484,plain,
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% 0.63/0.83 inference(unit_resolution,[status(thm)],[787, 2483, 2481, 25, 27, 26, 2479])).
% 0.63/0.83 tff(2485,plain,((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.83 tff(2486,plain,
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% 0.63/0.83 inference(unit_resolution,[status(thm)],[2485, 27, 25, 24])).
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% 0.63/0.83 inference(unit_resolution,[status(thm)],[177, 2486])).
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% 0.63/0.83 inference(unit_resolution,[status(thm)],[148, 4, 24])).
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% 0.63/0.83 inference(unit_resolution,[status(thm)],[170, 2488])).
% 0.63/0.83 tff(2490,plain,
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% 0.63/0.83 inference(unit_resolution,[status(thm)],[1427, 1333])).
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% 0.63/0.83 inference(unit_resolution,[status(thm)],[1185, 3, 25])).
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% 0.63/0.83 inference(unit_resolution,[status(thm)],[137, 2491])).
% 0.63/0.83 tff(2493,plain,
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% 0.63/0.83 inference(unit_resolution,[status(thm)],[196, 4, 2492, 24])).
% 0.63/0.83 tff(2494,plain,
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% 0.63/0.83 inference(unit_resolution,[status(thm)],[425, 2493])).
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% 0.63/0.83 inference(unit_resolution,[status(thm)],[1832, 14, 222, 2494])).
% 0.63/0.83 tff(2496,plain,
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% 0.63/0.83 inference(unit_resolution,[status(thm)],[1224, 2495])).
% 0.63/0.83 tff(2497,plain,
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% 0.63/0.83 inference(rewrite,[status(thm)],[])).
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% 0.63/0.83 inference(rewrite,[status(thm)],[])).
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% 0.63/0.83 inference(monotonicity,[status(thm)],[2498])).
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% 0.63/0.83 inference(transitivity,[status(thm)],[2499, 2497])).
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% 0.63/0.83 inference(quant_inst,[status(thm)],[])).
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% 0.63/0.83 inference(modus_ponens,[status(thm)],[2501, 2500])).
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% 0.63/0.83 inference(unit_resolution,[status(thm)],[2502, 188, 406, 1836, 2391, 1274])).
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% 0.63/0.83 tff(2505,plain,
% 0.63/0.83 ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[2504, 2454])).
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% 0.63/0.83 inference(unit_resolution,[status(thm)],[1316, 188, 684, 2509, 2507])).
% 0.63/0.83 tff(2511,plain,
% 0.63/0.83 ((s(s(s(s(z)))) = s(z)) | r(s(s(s(s(z)))), s(z))),
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% 0.63/0.83 tff(2512,plain,
% 0.63/0.83 (r(s(s(s(s(z)))), s(z))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[2511, 844])).
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% 0.63/0.83 (~r(z, s(s(s(z))))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[1694, 2494, 25])).
% 0.63/0.83 tff(2514,plain,
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% 0.63/0.83 tff(2515,plain,
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% 0.63/0.83 tff(2516,plain,
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% 0.63/0.83 inference(unit_resolution,[status(thm)],[300, 2515])).
% 0.63/0.83 tff(2517,plain,
% 0.63/0.83 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(2518,plain,
% 0.63/0.83 (((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(2519,plain,
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% 0.63/0.83 inference(monotonicity,[status(thm)],[2518])).
% 0.63/0.83 tff(2520,plain,
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% 0.63/0.83 inference(transitivity,[status(thm)],[2519, 2517])).
% 0.63/0.83 tff(2521,plain,
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% 0.63/0.83 inference(quant_inst,[status(thm)],[])).
% 0.63/0.83 tff(2522,plain,
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% 0.63/0.83 inference(modus_ponens,[status(thm)],[2521, 2520])).
% 0.63/0.83 tff(2523,plain,
% 0.63/0.83 (~r(s(s(s(s(z)))), z)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[2522, 14, 2516, 2512])).
% 0.63/0.83 tff(2524,plain,
% 0.63/0.83 (b(s(s(s(s(z)))), z)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[859, 2523])).
% 0.63/0.83 tff(2525,plain,
% 0.63/0.83 (((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(2526,plain,
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% 0.63/0.83 inference(monotonicity,[status(thm)],[2525])).
% 0.63/0.83 tff(2527,plain,
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% 0.63/0.83 inference(transitivity,[status(thm)],[2526, 1288])).
% 0.63/0.83 tff(2528,plain,
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% 0.63/0.83 inference(quant_inst,[status(thm)],[])).
% 0.63/0.83 tff(2529,plain,
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% 0.63/0.83 inference(modus_ponens,[status(thm)],[2528, 2527])).
% 0.63/0.83 tff(2530,plain,
% 0.63/0.83 ($false),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[2529, 188, 2467, 2514, 2524, 2507])).
% 0.63/0.83 tff(2531,plain,((~r(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.83 tff(2532,plain,
% 0.63/0.83 (~r(s(z), s(s(s(s(s(s(z)))))))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[2531, 3, 222, 25, 24, 2487])).
% 0.63/0.83 tff(2533,plain,
% 0.63/0.83 (b(s(z), s(s(s(s(s(s(z)))))))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[84, 2532])).
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% 0.63/0.83 ($false),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[746, 188, 406, 1836, 86, 1651])).
% 0.63/0.83 tff(2535,plain,((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.83 tff(2536,plain,
% 0.63/0.83 ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(z))))))))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[2535, 2454])).
% 0.63/0.83 tff(2537,plain,
% 0.63/0.83 (~b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[2536, 2533, 2490])).
% 0.63/0.83 tff(2538,plain,
% 0.63/0.83 (r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[1224, 2537])).
% 0.63/0.83 tff(2539,plain,
% 0.63/0.83 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[2461, 2533, 27, 25])).
% 0.63/0.83 tff(2540,plain,
% 0.63/0.83 (r(s(s(s(s(s(s(z)))))), s(z))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[627, 2539])).
% 0.63/0.83 tff(2541,plain,
% 0.63/0.83 (~r(s(s(s(z))), s(z))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[619, 2540, 24])).
% 0.63/0.83 tff(2542,plain,
% 0.63/0.83 (b(s(s(s(z))), s(z))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[170, 2541])).
% 0.63/0.83 tff(2543,plain,
% 0.63/0.83 (~b(s(s(z)), s(s(s(z))))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[958, 2542, 2492, 2487])).
% 0.63/0.83 tff(2544,plain,
% 0.63/0.83 (r(s(s(z)), s(s(s(z))))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[425, 2543])).
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% 0.63/0.83 ($false),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[1832, 14, 222, 2544, 2538])).
% 0.63/0.83 tff(2546,plain,((~r(s(z), z)) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.83 tff(2547,plain,
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% 0.63/0.83 inference(unit_resolution,[status(thm)],[2546, 222, 24, 27, 25])).
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% 0.63/0.83 inference(unit_resolution,[status(thm)],[312, 2547])).
% 0.63/0.83 tff(2549,plain,
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% 0.63/0.83 inference(unit_resolution,[status(thm)],[196, 4, 96, 24])).
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% 0.63/0.83 inference(unit_resolution,[status(thm)],[137, 2549])).
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% 0.63/0.83 inference(unit_resolution,[status(thm)],[2039, 2550, 25])).
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% 0.63/0.83 inference(unit_resolution,[status(thm)],[300, 2551])).
% 0.63/0.83 tff(2553,plain,
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% 0.63/0.83 inference(unit_resolution,[status(thm)],[783, 2552, 2548, 2489])).
% 0.63/0.83 tff(2554,plain,
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% 0.63/0.83 inference(unit_resolution,[status(thm)],[326, 2553])).
% 0.63/0.83 tff(2555,plain,
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% 0.63/0.83 inference(unit_resolution,[status(thm)],[463, 14, 2554, 25])).
% 0.63/0.83 tff(2556,plain,
% 0.63/0.83 (b(s(s(s(z))), s(s(z)))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[476, 2555])).
% 0.63/0.83 tff(2557,plain,
% 0.63/0.83 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[1320, 2556, 2487, 96, 2489])).
% 0.63/0.83 tff(2558,plain,
% 0.63/0.83 (r(s(s(s(s(z)))), s(s(s(z))))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[890, 2557])).
% 0.63/0.83 tff(2559,plain,
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% 0.63/0.83 inference(unit_resolution,[status(thm)],[1272, 14, 222, 2558])).
% 0.63/0.83 tff(2560,plain,
% 0.63/0.83 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[927, 79, 924, 2559])).
% 0.63/0.83 tff(2561,plain,
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% 0.63/0.83 inference(unit_resolution,[status(thm)],[1369, 2552, 2489, 2487])).
% 0.63/0.83 tff(2562,plain,
% 0.63/0.83 (r(z, s(s(s(z))))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[281, 2561])).
% 0.63/0.83 tff(2563,plain,
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% 0.63/0.83 inference(unit_resolution,[status(thm)],[851, 846, 284])).
% 0.63/0.83 tff(2564,plain,
% 0.63/0.83 (b(s(s(s(s(z)))), s(s(s(z))))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[890, 2563])).
% 0.63/0.83 tff(2565,plain,
% 0.63/0.83 (~b(s(s(s(s(z)))), s(s(z)))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[899, 188, 96, 2564, 892])).
% 0.63/0.83 tff(2566,plain,
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% 0.63/0.83 inference(unit_resolution,[status(thm)],[909, 79, 906, 2565])).
% 0.63/0.83 tff(2567,plain,
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% 0.63/0.83 inference(rewrite,[status(thm)],[])).
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% 0.63/0.83 inference(quant_inst,[status(thm)],[])).
% 0.63/0.83 tff(2569,plain,
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% 0.63/0.83 inference(modus_ponens,[status(thm)],[2568, 2567])).
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% 0.63/0.83 ($false),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[2569, 14, 25, 846, 2566])).
% 0.63/0.83 tff(2571,plain,((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.83 tff(2572,plain,
% 0.63/0.83 (~r(s(s(s(s(z)))), z)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[2571, 2556, 25, 96, 2562])).
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% 0.63/0.83 inference(unit_resolution,[status(thm)],[859, 2572])).
% 0.63/0.83 tff(2574,plain,
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% 0.63/0.83 inference(unit_resolution,[status(thm)],[2222, 2554, 25])).
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% 0.63/0.83 tff(2577,plain,((~r(s(z), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.83 tff(2578,plain,
% 0.63/0.83 (~r(s(z), s(s(s(s(s(s(z)))))))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[2577, 96, 222, 25, 27, 24])).
% 0.63/0.83 tff(2579,plain,
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% 0.63/0.83 inference(unit_resolution,[status(thm)],[84, 2578])).
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% 0.63/0.83 inference(unit_resolution,[status(thm)],[2461, 2579, 27, 25])).
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% 0.63/0.83 inference(unit_resolution,[status(thm)],[619, 2581, 24])).
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% 0.63/0.83 inference(unit_resolution,[status(thm)],[958, 2583, 96, 2487])).
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% 0.63/0.83 inference(unit_resolution,[status(thm)],[137, 2584])).
% 0.63/0.83 tff(2586,plain,
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% 0.63/0.83 inference(unit_resolution,[status(thm)],[1052, 2579, 2548, 27])).
% 0.63/0.83 tff(2587,plain,
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% 0.63/0.83 ((~r(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[773, 2454])).
% 0.63/0.83 tff(2589,plain,
% 0.63/0.83 (~r(s(s(s(z))), z)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[2588, 2587, 96])).
% 0.63/0.83 tff(2590,plain,
% 0.63/0.83 (b(s(s(s(z))), z)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[326, 2589])).
% 0.63/0.83 tff(2591,plain,
% 0.63/0.83 (~b(z, s(z))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[783, 2590, 2548, 2583])).
% 0.63/0.83 tff(2592,plain,
% 0.63/0.83 (r(z, s(z))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[300, 2591])).
% 0.63/0.83 tff(2593,plain,
% 0.63/0.83 ($false),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[2039, 2592, 2585, 25])).
% 0.63/0.83 tff(2594,plain,((~b(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.83 tff(2595,plain,
% 0.63/0.83 (~b(s(s(z)), s(s(s(z))))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[2594, 222, 24, 27, 25])).
% 0.63/0.83 tff(2596,plain,
% 0.63/0.83 (r(s(s(z)), s(s(s(z))))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[425, 2595])).
% 0.63/0.83 tff(2597,plain,
% 0.63/0.83 (~r(z, s(s(s(z))))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[1694, 2596, 25])).
% 0.63/0.83 tff(2598,plain,
% 0.63/0.83 (b(z, s(s(s(z))))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[281, 2597])).
% 0.63/0.83 tff(2599,plain,
% 0.63/0.83 (~r(s(s(s(z))), z)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[535, 2596, 25])).
% 0.63/0.83 tff(2600,plain,
% 0.63/0.83 (b(s(s(s(z))), z)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[326, 2599])).
% 0.63/0.83 tff(2601,plain,
% 0.63/0.83 (((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(2602,plain,
% 0.63/0.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z)))))))),
% 0.63/0.83 inference(monotonicity,[status(thm)],[2601])).
% 0.63/0.83 tff(2603,plain,
% 0.63/0.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))),
% 0.63/0.83 inference(transitivity,[status(thm)],[2602, 2014])).
% 0.63/0.83 tff(2604,plain,
% 0.63/0.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)))),
% 0.63/0.83 inference(quant_inst,[status(thm)],[])).
% 0.63/0.83 tff(2605,plain,
% 0.63/0.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z)))))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[2604, 2603])).
% 0.63/0.83 tff(2606,plain,
% 0.63/0.83 ($false),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[2605, 188, 2548, 2487, 2600, 2598])).
% 0.63/0.83 tff(2607,plain,((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.83 tff(2608,plain,
% 0.63/0.83 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[2607, 27, 24, 25])).
% 0.63/0.83 tff(2609,plain,
% 0.63/0.83 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[243, 2608])).
% 0.63/0.83 tff(2610,plain,
% 0.63/0.83 (~r(z, s(s(s(z))))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[1694, 522, 25])).
% 0.63/0.83 tff(2611,plain,
% 0.63/0.83 (b(z, s(s(s(z))))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[281, 2610])).
% 0.63/0.83 tff(2612,plain,
% 0.63/0.83 (~b(s(s(s(s(s(s(z)))))), z)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[547, 537, 2609, 2611])).
% 0.63/0.83 tff(2613,plain,
% 0.63/0.83 (r(s(s(s(s(s(s(z)))))), z)),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[492, 2612])).
% 0.63/0.83 tff(2614,plain,
% 0.63/0.83 (~r(s(s(s(z))), s(z))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[679, 2613, 24, 27, 2609])).
% 0.63/0.83 tff(2615,plain,
% 0.63/0.83 (b(s(s(s(z))), s(z))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[170, 2614])).
% 0.63/0.83 tff(2616,plain,
% 0.63/0.83 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[1458, 2615, 2487, 2609])).
% 0.63/0.83 tff(2617,plain,
% 0.63/0.83 (r(s(s(s(s(s(s(z)))))), s(z))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[627, 2616])).
% 0.63/0.83 tff(2618,plain,
% 0.63/0.83 (~b(z, s(z))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[1369, 2615, 2611, 2487])).
% 0.63/0.83 tff(2619,plain,
% 0.63/0.83 (r(z, s(z))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[300, 2618])).
% 0.63/0.83 tff(2620,plain,
% 0.63/0.83 ($false),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[2118, 14, 2619, 2613, 2617])).
% 0.63/0.83 tff(2621,plain,((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.84 tff(2622,plain,
% 0.63/0.84 (~r(s(s(z)), s(s(s(z))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[2621, 27, 24, 25])).
% 0.63/0.84 tff(2623,plain,
% 0.63/0.84 (b(s(s(z)), s(s(s(z))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[425, 2622])).
% 0.63/0.84 tff(2624,plain,
% 0.63/0.84 (~r(s(z), z)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1345, 2, 25])).
% 0.63/0.84 tff(2625,plain,
% 0.63/0.84 (b(s(z), z)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[312, 2624])).
% 0.63/0.84 tff(2626,plain,
% 0.63/0.84 (~r(s(s(s(s(s(s(z)))))), z)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[2222, 2, 25])).
% 0.63/0.84 tff(2627,plain,
% 0.63/0.84 (b(s(s(s(s(s(s(z)))))), z)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[492, 2626])).
% 0.63/0.84 tff(2628,plain,
% 0.63/0.84 (~b(s(z), s(s(s(s(s(s(z)))))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1052, 2627, 2625, 27])).
% 0.63/0.84 tff(2629,plain,
% 0.63/0.84 (r(s(z), s(s(s(s(s(s(z)))))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[84, 2628])).
% 0.63/0.84 tff(2630,plain,
% 0.63/0.84 (~r(s(s(s(z))), s(z))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[148, 2629, 24])).
% 0.63/0.84 tff(2631,plain,
% 0.63/0.84 (b(s(s(s(z))), s(z))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[170, 2630])).
% 0.63/0.84 tff(2632,plain,
% 0.63/0.84 (~b(s(s(s(z))), s(s(z)))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1473, 2631, 2487, 2609, 2623])).
% 0.63/0.84 tff(2633,plain,
% 0.63/0.84 (r(s(s(s(z))), s(s(z)))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[476, 2632])).
% 0.63/0.84 tff(2634,plain,
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% 0.63/0.84 inference(unit_resolution,[status(thm)],[463, 14, 2, 25, 2633])).
% 0.63/0.84 tff(2635,plain,((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.84 tff(2636,plain,
% 0.63/0.84 (~r(s(s(s(z))), z)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[2635, 27, 24, 25])).
% 0.63/0.84 tff(2637,plain,
% 0.63/0.84 (b(s(s(s(z))), z)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[326, 2636])).
% 0.63/0.84 tff(2638,plain,
% 0.63/0.84 (~b(s(s(z)), s(z))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[958, 246, 96, 684])).
% 0.63/0.84 tff(2639,plain,
% 0.63/0.84 (r(s(s(z)), s(z))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[137, 2638])).
% 0.63/0.84 tff(2640,plain,
% 0.63/0.84 (~r(s(z), z)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1185, 2639, 25])).
% 0.63/0.84 tff(2641,plain,
% 0.63/0.84 (b(s(z), z)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[312, 2640])).
% 0.63/0.84 tff(2642,plain,
% 0.63/0.84 (~r(z, s(z))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[2039, 2639, 25])).
% 0.63/0.84 tff(2643,plain,
% 0.63/0.84 (b(z, s(z))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[300, 2642])).
% 0.63/0.84 tff(2644,plain,
% 0.63/0.84 ($false),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[783, 2643, 2641, 283, 246])).
% 0.63/0.84 tff(2645,plain,((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.84 tff(2646,plain,
% 0.63/0.84 (~b(s(s(s(z))), s(z))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[2645, 2637, 25, 2623, 2487])).
% 0.63/0.84 tff(2647,plain,
% 0.63/0.84 (r(s(s(s(z))), s(z))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[170, 2646])).
% 0.63/0.84 tff(2648,plain,
% 0.63/0.84 (~r(s(z), s(s(s(s(s(s(z)))))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[148, 2647, 24])).
% 0.63/0.84 tff(2649,plain,
% 0.63/0.84 (b(s(z), s(s(s(s(s(s(z)))))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[84, 2648])).
% 0.63/0.84 tff(2650,plain,
% 0.63/0.84 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[619, 2647, 24])).
% 0.63/0.84 tff(2651,plain,
% 0.63/0.84 (b(s(s(s(s(s(s(z)))))), s(z))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[627, 2650])).
% 0.63/0.84 tff(2652,plain,
% 0.63/0.84 ($false),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[2461, 2651, 2649, 27, 25])).
% 0.63/0.84 tff(2653,plain,((~b(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.84 tff(2654,plain,
% 0.63/0.84 (~b(z, s(s(s(s(s(s(z)))))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[2653, 25, 24])).
% 0.63/0.84 tff(2655,plain,
% 0.63/0.84 (r(z, s(s(s(s(s(s(z)))))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[256, 2654])).
% 0.63/0.84 tff(2656,plain,
% 0.63/0.84 (~r(s(s(s(z))), z)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1034, 2655, 24])).
% 0.63/0.84 tff(2657,plain,
% 0.63/0.84 (b(s(s(s(z))), z)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[326, 2656])).
% 0.63/0.84 tff(2658,plain,
% 0.63/0.84 (~r(z, s(s(s(z))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[594, 2655, 24])).
% 0.63/0.84 tff(2659,plain,
% 0.63/0.84 (b(z, s(s(s(z))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[281, 2658])).
% 0.63/0.84 tff(2660,plain,
% 0.63/0.84 (~b(s(s(s(s(s(s(z)))))), z)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[547, 2469, 2659, 2657])).
% 0.63/0.84 tff(2661,plain,
% 0.63/0.84 (r(s(s(s(s(s(s(z)))))), z)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[492, 2660])).
% 0.63/0.84 tff(2662,plain,
% 0.63/0.84 (~r(s(s(s(z))), s(z))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[619, 614, 24])).
% 0.63/0.84 tff(2663,plain,
% 0.63/0.84 (b(s(s(s(z))), s(z))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[170, 2662])).
% 0.63/0.84 tff(2664,plain,
% 0.63/0.84 (~r(z, s(z))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1146, 614, 2655])).
% 0.63/0.84 tff(2665,plain,
% 0.63/0.84 (b(z, s(z))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[300, 2664])).
% 0.63/0.84 tff(2666,plain,
% 0.63/0.84 (~b(s(z), z)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[783, 2665, 2657, 2663])).
% 0.63/0.84 tff(2667,plain,
% 0.63/0.84 (r(s(z), z)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[312, 2666])).
% 0.63/0.84 tff(2668,plain,
% 0.63/0.84 ($false),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1136, 2365, 2361, 406, 2492])).
% 0.63/0.84 tff(2669,plain,((~r(s(z), z)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(z)))))), z))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.84 tff(2670,plain,
% 0.63/0.84 ((~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(z)))))), z))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[2669, 2454])).
% 0.63/0.84 tff(2671,plain,
% 0.63/0.84 ($false),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[2670, 2667, 2661, 25])).
% 0.63/0.84 tff(2672,plain,((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.84 tff(2673,plain,
% 0.63/0.84 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[2672, 26, 25, 24])).
% 0.63/0.84 tff(2674,plain,
% 0.63/0.84 (b(s(s(s(s(s(s(z)))))), s(z))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[627, 2673])).
% 0.63/0.84 tff(2675,plain,
% 0.63/0.84 (~b(s(s(z)), s(z))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[2455, 2674, 85])).
% 0.63/0.84 tff(2676,plain,
% 0.63/0.84 (r(s(s(z)), s(z))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[137, 2675])).
% 0.63/0.84 tff(2677,plain,
% 0.63/0.84 (~r(s(z), z)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1185, 2676, 25])).
% 0.63/0.84 tff(2678,plain,
% 0.63/0.84 (b(s(z), z)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[312, 2677])).
% 0.63/0.84 tff(2679,plain,
% 0.63/0.84 (~r(z, s(z))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[2039, 2676, 25])).
% 0.63/0.84 tff(2680,plain,
% 0.63/0.84 (b(z, s(z))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[300, 2679])).
% 0.63/0.84 tff(2681,plain,
% 0.63/0.84 (~b(s(s(s(z))), s(z))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[783, 2680, 2657, 2678])).
% 0.63/0.84 tff(2682,plain,
% 0.63/0.84 (r(s(s(s(z))), s(z))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[170, 2681])).
% 0.63/0.84 tff(2683,plain,
% 0.63/0.84 (~r(s(s(s(z))), s(s(z)))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1597, 2682, 2676])).
% 0.63/0.84 tff(2684,plain,
% 0.63/0.84 (b(s(s(s(z))), s(s(z)))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[476, 2683])).
% 0.63/0.84 tff(2685,plain,
% 0.63/0.84 (~r(s(s(z)), s(s(s(z))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1746, 2676, 26])).
% 0.63/0.84 tff(2686,plain,
% 0.63/0.84 (b(s(s(z)), s(s(s(z))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[425, 2685])).
% 0.63/0.84 tff(2687,plain,
% 0.63/0.84 (~b(s(s(s(s(s(s(z)))))), z)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[547, 259, 258, 283])).
% 0.63/0.84 tff(2688,plain,
% 0.63/0.84 (r(s(s(s(s(s(s(z)))))), z)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[492, 2687])).
% 0.63/0.84 tff(2689,plain,
% 0.63/0.84 (~r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1977, 2688, 25])).
% 0.63/0.84 tff(2690,plain,
% 0.63/0.84 (b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1224, 2689])).
% 0.63/0.84 tff(2691,plain,
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% 0.63/0.84 inference(unit_resolution,[status(thm)],[1454, 188, 259, 96, 2690, 892])).
% 0.63/0.84 tff(2692,plain,((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.84 tff(2693,plain,
% 0.63/0.84 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[2692, 2686, 2684, 25, 2659, 2657])).
% 0.63/0.84 tff(2694,plain,
% 0.63/0.84 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[243, 2693])).
% 0.63/0.84 tff(2695,plain,
% 0.63/0.84 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1283, 2694, 85, 2674, 26])).
% 0.63/0.84 tff(2696,plain,
% 0.63/0.84 (b(s(s(s(s(z)))), s(s(s(z))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[890, 2695])).
% 0.63/0.84 tff(2697,plain,
% 0.63/0.84 (~b(s(s(s(s(z)))), z)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1293, 188, 2657, 2659, 2696])).
% 0.63/0.84 tff(2698,plain,
% 0.63/0.84 (r(s(s(s(s(z)))), z)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[859, 2697])).
% 0.63/0.84 tff(2699,plain,
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% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(2700,plain,
% 0.63/0.84 (((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), z)))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(2701,plain,
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% 0.63/0.84 inference(monotonicity,[status(thm)],[2700])).
% 0.63/0.84 tff(2702,plain,
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% 0.63/0.84 inference(transitivity,[status(thm)],[2701, 2699])).
% 0.63/0.84 tff(2703,plain,
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% 0.63/0.84 inference(quant_inst,[status(thm)],[])).
% 0.63/0.84 tff(2704,plain,
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% 0.63/0.84 inference(modus_ponens,[status(thm)],[2703, 2702])).
% 0.63/0.84 tff(2705,plain,
% 0.63/0.84 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[2704, 14, 554, 846])).
% 0.63/0.84 tff(2706,plain,
% 0.63/0.84 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[927, 79, 924, 2705])).
% 0.63/0.84 tff(2707,plain,
% 0.63/0.84 (~r(s(s(s(s(z)))), s(s(z)))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[2569, 14, 25, 846])).
% 0.63/0.84 tff(2708,plain,
% 0.63/0.84 (b(s(s(s(s(z)))), s(s(z)))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[909, 79, 906, 2707])).
% 0.63/0.84 tff(2709,plain,
% 0.63/0.84 (b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1224, 1978])).
% 0.63/0.84 tff(2710,plain,
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% 0.63/0.84 inference(unit_resolution,[status(thm)],[2502, 188, 406, 2709, 2708, 2706])).
% 0.63/0.84 tff(2711,plain,((~r(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(z)))))), z))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.84 tff(2712,plain,
% 0.63/0.84 ((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(z)))))), z))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[2711, 2454])).
% 0.63/0.84 tff(2713,plain,
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% 0.63/0.84 inference(unit_resolution,[status(thm)],[2712, 2698, 25])).
% 0.63/0.84 tff(2714,plain,
% 0.63/0.84 (b(s(s(s(s(s(s(z)))))), z)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[492, 2713])).
% 0.63/0.84 tff(2715,plain,
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% 0.63/0.84 inference(unit_resolution,[status(thm)],[982, 188, 2678, 2680, 2714, 2674])).
% 0.63/0.84 tff(2716,plain,((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.84 tff(2717,plain,
% 0.63/0.84 (~r(s(z), s(s(s(z))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[2716, 25, 24])).
% 0.63/0.84 tff(2718,plain,
% 0.63/0.84 (b(s(z), s(s(s(z))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[177, 2717])).
% 0.63/0.84 tff(2719,plain,
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% 0.63/0.84 inference(unit_resolution,[status(thm)],[2019, 188, 2718, 2657, 2659])).
% 0.63/0.84 tff(2720,plain,
% 0.63/0.84 (r(s(z), z)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[312, 2719])).
% 0.63/0.84 tff(2721,plain,
% 0.63/0.84 (~r(s(z), s(s(s(s(s(s(z)))))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[22, 2720, 2655])).
% 0.63/0.84 tff(2722,plain,
% 0.63/0.84 (b(s(z), s(s(s(s(s(s(z)))))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[84, 2721])).
% 0.63/0.84 tff(2723,plain,
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% 0.63/0.84 inference(unit_resolution,[status(thm)],[1185, 2720, 25])).
% 0.63/0.84 tff(2724,plain,
% 0.63/0.84 (b(s(s(z)), s(z))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[137, 2723])).
% 0.63/0.84 tff(2725,plain,
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% 0.63/0.84 inference(unit_resolution,[status(thm)],[2455, 2724, 2722])).
% 0.63/0.84 tff(2726,plain,
% 0.63/0.84 (r(s(s(s(s(s(s(z)))))), s(z))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[627, 2725])).
% 0.63/0.84 tff(2727,plain,
% 0.63/0.84 (~r(s(s(s(z))), s(z))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[619, 2726, 24])).
% 0.63/0.84 tff(2728,plain,
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% 0.63/0.84 inference(unit_resolution,[status(thm)],[170, 2727])).
% 0.63/0.84 tff(2729,plain,
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% 0.63/0.84 inference(unit_resolution,[status(thm)],[1146, 2726, 2655])).
% 0.63/0.84 tff(2730,plain,
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% 0.63/0.84 inference(unit_resolution,[status(thm)],[300, 2729])).
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% 0.63/0.84 tff(2732,plain,((~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.84 tff(2733,plain,
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% 0.63/0.84 inference(unit_resolution,[status(thm)],[792, 2733])).
% 0.63/0.84 tff(2735,plain,
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% 0.63/0.84 inference(unit_resolution,[status(thm)],[1034, 2, 24])).
% 0.63/0.84 tff(2736,plain,
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% 0.63/0.84 inference(unit_resolution,[status(thm)],[256, 2735])).
% 0.63/0.84 tff(2737,plain,
% 0.63/0.84 (~r(s(s(s(s(s(s(z)))))), z)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[562, 2, 24])).
% 0.63/0.84 tff(2738,plain,
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% 0.63/0.84 inference(unit_resolution,[status(thm)],[492, 2737])).
% 0.63/0.84 tff(2739,plain,
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% 0.63/0.84 inference(unit_resolution,[status(thm)],[435, 2454])).
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% 0.63/0.84 tff(2741,plain,((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.84 tff(2742,plain,
% 0.63/0.84 (~r(s(s(s(z))), z)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[2741, 24])).
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% 0.63/0.84 inference(unit_resolution,[status(thm)],[326, 2742])).
% 0.63/0.84 tff(2744,plain,
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% 0.63/0.84 inference(unit_resolution,[status(thm)],[1746, 26, 522])).
% 0.63/0.84 tff(2745,plain,
% 0.63/0.84 (b(s(s(z)), s(z))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[137, 2744])).
% 0.63/0.84 tff(2746,plain,
% 0.63/0.84 ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~r(z, s(s(s(s(s(s(z))))))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1156, 2454])).
% 0.63/0.84 tff(2747,plain,
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% 0.63/0.84 inference(unit_resolution,[status(thm)],[2746, 2745, 85, 2734, 1])).
% 0.63/0.84 tff(2748,plain,((~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.84 tff(2749,plain,
% 0.63/0.84 (~r(s(z), s(s(s(z))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[2748, 1, 522, 24])).
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% 0.63/0.84 (b(s(z), s(s(s(z))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[177, 2749])).
% 0.63/0.84 tff(2751,plain,
% 0.63/0.84 (b(s(z), s(s(s(s(s(s(z)))))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[84, 611])).
% 0.63/0.84 tff(2752,plain,
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% 0.63/0.84 inference(unit_resolution,[status(thm)],[2455, 628, 2751])).
% 0.63/0.84 tff(2753,plain,
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% 0.63/0.84 inference(unit_resolution,[status(thm)],[137, 2752])).
% 0.63/0.84 tff(2754,plain,
% 0.63/0.84 (~r(s(s(z)), s(s(s(z))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1124, 2753, 140])).
% 0.63/0.84 tff(2755,plain,
% 0.63/0.84 (b(s(s(z)), s(s(s(z))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[425, 2754])).
% 0.63/0.84 tff(2756,plain,
% 0.63/0.84 (~b(z, s(s(s(z))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1045, 2755, 2734, 2743])).
% 0.63/0.84 tff(2757,plain,
% 0.63/0.84 (r(z, s(s(s(z))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[281, 2756])).
% 0.63/0.84 tff(2758,plain,
% 0.63/0.84 (~r(z, s(s(s(s(s(s(z)))))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[594, 2757, 24])).
% 0.63/0.84 tff(2759,plain,
% 0.63/0.84 (b(z, s(s(s(s(s(s(z)))))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[256, 2758])).
% 0.63/0.84 tff(2760,plain,
% 0.63/0.84 (~b(s(s(s(s(s(s(z)))))), z)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[2739, 2759, 2734])).
% 0.63/0.84 tff(2761,plain,
% 0.63/0.84 (r(s(s(s(s(s(s(z)))))), z)),
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% 0.63/0.84 tff(2762,plain,
% 0.63/0.84 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1081, 2759, 2757, 140, 2743])).
% 0.63/0.84 tff(2763,plain,
% 0.63/0.84 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[243, 2762])).
% 0.63/0.84 tff(2764,plain,
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% 0.63/0.84 tff(2765,plain,((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.84 tff(2766,plain,
% 0.63/0.84 (~r(s(s(s(z))), s(z))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[2765, 24])).
% 0.63/0.84 tff(2767,plain,
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% 0.63/0.84 inference(unit_resolution,[status(thm)],[170, 2766])).
% 0.63/0.84 tff(2768,plain,
% 0.63/0.84 (~b(z, s(z))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1369, 2750, 2767, 1038])).
% 0.63/0.84 tff(2769,plain,
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% 0.63/0.84 inference(unit_resolution,[status(thm)],[300, 2768])).
% 0.63/0.84 tff(2770,plain,
% 0.63/0.84 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1146, 2769, 1])).
% 0.63/0.84 tff(2771,plain,
% 0.63/0.84 (b(s(s(s(s(s(s(z)))))), s(z))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[627, 2770])).
% 0.63/0.84 tff(2772,plain,
% 0.63/0.84 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1458, 2771, 2767, 2750])).
% 0.63/0.84 tff(2773,plain,
% 0.63/0.84 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[243, 2772])).
% 0.63/0.84 tff(2774,plain,
% 0.63/0.84 (~r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1832, 14, 2773, 522])).
% 0.63/0.84 tff(2775,plain,
% 0.63/0.84 (b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1224, 2774])).
% 0.63/0.84 tff(2776,plain,
% 0.63/0.84 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[2505, 2775, 2773, 522])).
% 0.63/0.84 tff(2777,plain,
% 0.63/0.84 (b(s(s(s(s(z)))), s(s(s(z))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[890, 2776])).
% 0.63/0.84 tff(2778,plain,
% 0.63/0.84 (~b(s(s(s(s(z)))), z)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1293, 188, 2743, 1038, 2777])).
% 0.63/0.84 tff(2779,plain,
% 0.63/0.84 (r(s(s(s(s(z)))), z)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[859, 2778])).
% 0.63/0.84 tff(2780,plain,
% 0.63/0.84 (~b(s(z), z)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[2019, 188, 2750, 2743, 1038])).
% 0.63/0.84 tff(2781,plain,
% 0.63/0.84 (r(s(z), z)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[312, 2780])).
% 0.63/0.84 tff(2782,plain,
% 0.63/0.84 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(2783,plain,
% 0.63/0.84 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 0.63/0.84 inference(quant_inst,[status(thm)],[])).
% 0.63/0.84 tff(2784,plain,
% 0.63/0.84 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z)))),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[2783, 2782])).
% 0.63/0.84 tff(2785,plain,
% 0.63/0.84 (~r(s(s(s(s(z)))), s(z))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[2784, 14, 2781, 2779])).
% 0.63/0.84 tff(2786,plain,
% 0.63/0.84 (~b(s(s(s(s(z)))), s(z))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1316, 188, 2750, 2767, 2777])).
% 0.63/0.84 tff(2787,plain,
% 0.63/0.84 ((s(s(s(s(z)))) = s(z)) | r(s(s(s(s(z)))), s(z))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[874, 79, 2786])).
% 0.63/0.84 tff(2788,plain,
% 0.63/0.84 ($false),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[2787, 2785, 844])).
% 0.63/0.84 tff(2789,plain,((~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.84 tff(2790,plain,
% 0.63/0.84 (~r(z, s(s(s(s(s(s(z)))))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[2789, 522, 24])).
% 0.63/0.84 tff(2791,plain,
% 0.63/0.84 (b(z, s(s(s(s(s(s(z)))))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[256, 2790])).
% 0.63/0.84 tff(2792,plain,
% 0.63/0.84 (~b(s(s(s(s(s(s(z)))))), z)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[2739, 2791, 2734])).
% 0.63/0.84 tff(2793,plain,
% 0.63/0.84 (r(s(s(s(s(s(s(z)))))), z)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[492, 2792])).
% 0.63/0.84 tff(2794,plain,
% 0.63/0.84 (~b(s(s(s(s(s(s(z)))))), z)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[2739, 27, 427])).
% 0.63/0.84 tff(2795,plain,
% 0.63/0.84 (r(s(s(s(s(s(s(z)))))), z)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[492, 2794])).
% 0.63/0.84 tff(2796,plain,
% 0.63/0.84 ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(z)))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[2144, 2454])).
% 0.63/0.84 tff(2797,plain,
% 0.63/0.84 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[2796, 26, 27, 522, 2795])).
% 0.63/0.84 tff(2798,plain,
% 0.63/0.84 (r(s(s(s(s(s(s(z)))))), s(z))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[627, 2797])).
% 0.63/0.84 tff(2799,plain,
% 0.63/0.84 (~r(s(z), z)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[705, 2798, 2795])).
% 0.63/0.84 tff(2800,plain,
% 0.63/0.84 (b(s(z), z)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[312, 2799])).
% 0.63/0.84 tff(2801,plain,
% 0.63/0.84 ($false),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[2087, 188, 2800, 2454, 27, 427, 2745])).
% 0.63/0.84 tff(2802,plain,((~r(s(z), s(s(s(z))))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.84 tff(2803,plain,
% 0.63/0.84 (~r(s(z), s(s(s(z))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[2802, 2791, 2734, 522])).
% 0.63/0.84 tff(2804,plain,
% 0.63/0.84 (b(s(z), s(s(s(z))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[177, 2803])).
% 0.63/0.84 tff(2805,plain,
% 0.63/0.84 (~b(s(s(z)), s(z))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[2455, 2365, 2361])).
% 0.63/0.84 tff(2806,plain,
% 0.63/0.84 (r(s(s(z)), s(z))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[137, 2805])).
% 0.63/0.84 tff(2807,plain,
% 0.63/0.84 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1458, 2365, 246, 684])).
% 0.63/0.84 tff(2808,plain,
% 0.63/0.84 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[243, 2807])).
% 0.63/0.84 tff(2809,plain,
% 0.63/0.84 (~r(z, s(s(s(z))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[604, 2808, 554])).
% 0.63/0.84 tff(2810,plain,
% 0.63/0.84 (b(z, s(s(s(z))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[281, 2809])).
% 0.63/0.84 tff(2811,plain,
% 0.63/0.84 (~b(z, s(z))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1369, 2810, 246, 684])).
% 0.63/0.84 tff(2812,plain,
% 0.63/0.84 (r(z, s(z))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[300, 2811])).
% 0.63/0.84 tff(2813,plain,
% 0.63/0.84 (~r(z, s(s(z)))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[677, 14, 2812, 2806])).
% 0.63/0.84 tff(2814,plain,
% 0.63/0.84 (b(z, s(s(z)))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[519, 79, 2813, 95])).
% 0.63/0.84 tff(2815,plain,
% 0.63/0.84 (~r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1832, 14, 2808, 522])).
% 0.63/0.84 tff(2816,plain,
% 0.63/0.84 (b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1224, 2815])).
% 0.63/0.84 tff(2817,plain,
% 0.63/0.84 ($false),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[515, 188, 2454, 27, 2816, 2814])).
% 0.63/0.84 tff(2818,plain,((~r(s(z), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), z))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.84 tff(2819,plain,
% 0.63/0.84 (~r(s(z), z)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[2818, 2791, 522, 2767, 2804, 2793])).
% 0.63/0.84 tff(2820,plain,
% 0.63/0.84 (b(s(z), z)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[312, 2819])).
% 0.63/0.84 tff(2821,plain,
% 0.63/0.84 (~b(s(s(z)), s(z))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[2087, 188, 2820, 2454, 2791, 2734])).
% 0.63/0.84 tff(2822,plain,
% 0.63/0.84 (r(s(s(z)), s(z))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[137, 2821])).
% 0.63/0.84 tff(2823,plain,
% 0.63/0.84 (~b(z, s(z))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[783, 2820, 2743, 2767])).
% 0.63/0.84 tff(2824,plain,
% 0.63/0.84 (r(z, s(z))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[300, 2823])).
% 0.63/0.84 tff(2825,plain,
% 0.63/0.84 (~r(z, s(s(z)))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[677, 14, 2824, 2822])).
% 0.63/0.84 tff(2826,plain,
% 0.63/0.84 (b(z, s(s(z)))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[519, 79, 2825, 95])).
% 0.63/0.84 tff(2827,plain,
% 0.63/0.84 ($false),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[515, 188, 2454, 27, 1836, 1508])).
% 0.63/0.84 tff(2828,plain,((~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.84 tff(2829,plain,
% 0.63/0.84 (~b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[2828, 2791, 2826])).
% 0.63/0.84 tff(2830,plain,
% 0.63/0.84 (r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1224, 2829])).
% 0.63/0.84 tff(2831,plain,
% 0.63/0.84 (~b(s(z), s(s(z)))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1659, 2826, 2820, 2734])).
% 0.63/0.84 tff(2832,plain,
% 0.63/0.84 (r(s(z), s(s(z)))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1427, 2831])).
% 0.63/0.84 tff(2833,plain,
% 0.63/0.84 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(2834,plain,
% 0.63/0.84 (((~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(z))))))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(2835,plain,
% 0.63/0.84 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z))))))),
% 0.63/0.84 inference(monotonicity,[status(thm)],[2834])).
% 0.63/0.84 tff(2836,plain,
% 0.63/0.84 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 0.63/0.84 inference(transitivity,[status(thm)],[2835, 2833])).
% 0.63/0.84 tff(2837,plain,
% 0.63/0.84 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(z)))))))))),
% 0.63/0.84 inference(quant_inst,[status(thm)],[])).
% 0.63/0.84 tff(2838,plain,
% 0.63/0.84 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z))))),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[2837, 2836])).
% 0.63/0.84 tff(2839,plain,
% 0.63/0.84 ($false),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[2838, 14, 4, 1461, 1094])).
% 0.63/0.84 tff(2840,plain,((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.84 tff(2841,plain,
% 0.63/0.84 (~r(s(z), s(s(s(s(s(s(z)))))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[2840, 2830, 2832])).
% 0.63/0.84 tff(2842,plain,
% 0.63/0.84 (b(s(z), s(s(s(s(s(s(z)))))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[84, 2841])).
% 0.63/0.84 tff(2843,plain,
% 0.63/0.84 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[707, 2842, 2791, 2793, 2804, 2767])).
% 0.63/0.84 tff(2844,plain,
% 0.63/0.84 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[243, 2843])).
% 0.63/0.84 tff(2845,plain,
% 0.63/0.84 ($false),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1832, 14, 2844, 522, 2830])).
% 0.63/0.84 tff(2846,plain,((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.84 tff(2847,plain,
% 0.63/0.84 (~r(s(s(z)), s(s(s(z))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[2846, 24])).
% 0.63/0.84 tff(2848,plain,
% 0.63/0.84 (b(s(s(z)), s(s(s(z))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[425, 2847])).
% 0.63/0.84 tff(2849,plain,
% 0.63/0.84 (~b(z, s(s(s(z))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1045, 2848, 2734, 2743])).
% 0.63/0.84 tff(2850,plain,
% 0.63/0.84 (r(z, s(s(s(z))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[281, 2849])).
% 0.63/0.84 tff(2851,plain,
% 0.63/0.84 (~r(z, s(s(s(s(s(s(z)))))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[594, 2850, 24])).
% 0.63/0.84 tff(2852,plain,
% 0.63/0.84 (b(z, s(s(s(s(s(s(z)))))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[256, 2851])).
% 0.63/0.84 tff(2853,plain,
% 0.63/0.84 (~b(s(s(s(s(s(s(z)))))), z)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[2739, 2852, 2734])).
% 0.63/0.84 tff(2854,plain,
% 0.63/0.84 (r(s(s(s(s(s(s(z)))))), z)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[492, 2853])).
% 0.63/0.84 tff(2855,plain,
% 0.63/0.84 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[2120, 284, 554, 373])).
% 0.63/0.84 tff(2856,plain,
% 0.63/0.84 ($false),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[243, 2104, 2855])).
% 0.63/0.84 tff(2857,plain,((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.84 tff(2858,plain,
% 0.63/0.84 (~r(z, s(z))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[2857, 2854, 2850])).
% 0.63/0.84 tff(2859,plain,
% 0.63/0.84 (b(z, s(z))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[300, 2858])).
% 0.63/0.84 tff(2860,plain,
% 0.63/0.84 (~b(s(z), z)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[783, 2859, 2743, 2767])).
% 0.63/0.84 tff(2861,plain,
% 0.63/0.84 (r(s(z), z)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[312, 2860])).
% 0.63/0.84 tff(2862,plain,
% 0.63/0.84 (~r(s(z), s(s(s(z))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[321, 2850, 2743, 2767])).
% 0.63/0.84 tff(2863,plain,
% 0.63/0.84 (b(s(z), s(s(s(z))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[177, 2862])).
% 0.63/0.84 tff(2864,plain,
% 0.63/0.84 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[604, 2854, 2850])).
% 0.63/0.84 tff(2865,plain,
% 0.63/0.84 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[243, 2864])).
% 0.63/0.84 tff(2866,plain,
% 0.63/0.84 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1458, 2865, 2767, 2863])).
% 0.63/0.84 tff(2867,plain,
% 0.63/0.84 (r(s(s(s(s(s(s(z)))))), s(z))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[627, 2866])).
% 0.63/0.84 tff(2868,plain,
% 0.63/0.84 ($false),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[705, 2867, 2861, 2854])).
% 0.63/0.84 tff(2869,plain,(~r(s(s(s(z))), s(s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.84 tff(2870,plain,
% 0.63/0.84 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[220, 2869])).
% 0.63/0.84 tff(2871,plain,
% 0.63/0.84 (~r(s(s(s(s(s(s(z)))))), z)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[2588, 96, 2])).
% 0.63/0.84 tff(2872,plain,
% 0.63/0.84 (b(s(s(s(s(s(s(z)))))), z)),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[492, 2871])).
% 0.63/0.84 tff(2873,plain,
% 0.63/0.84 ($false),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[412, 188, 2454, 2870, 259, 96])).
% 0.63/0.84 tff(2874,plain,((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.84 tff(2875,plain,
% 0.63/0.84 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[2874, 96])).
% 0.63/0.84 tff(2876,plain,
% 0.63/0.84 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[243, 2875])).
% 0.63/0.84 tff(2877,plain,
% 0.63/0.84 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[982, 188, 360, 1494, 89])).
% 0.63/0.84 tff(2878,plain,
% 0.63/0.84 (r(s(s(s(s(s(s(z)))))), s(z))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[627, 2877])).
% 0.63/0.84 tff(2879,plain,
% 0.63/0.84 ($false),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[987, 14, 140, 222, 2878])).
% 0.63/0.84 tff(2880,plain,((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.84 tff(2881,plain,
% 0.63/0.84 (~r(s(s(s(z))), s(z))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[2880, 222, 360, 89, 2])).
% 0.63/0.84 tff(2882,plain,
% 0.63/0.84 (b(s(s(s(z))), s(z))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[170, 2881])).
% 0.63/0.84 tff(2883,plain,
% 0.63/0.84 (~r(s(z), s(s(s(s(s(s(z)))))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[230, 26, 222])).
% 0.63/0.84 tff(2884,plain,
% 0.63/0.84 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[1524, 2883, 2870, 246])).
% 0.63/0.84 tff(2885,plain,
% 0.63/0.84 ($false),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[627, 2884, 2002])).
% 0.63/0.84 tff(2886,plain,((~r(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.84 tff(2887,plain,
% 0.63/0.84 (~r(s(z), s(s(s(z))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[2886, 2882, 222])).
% 0.63/0.84 tff(2888,plain,
% 0.63/0.84 (b(s(z), s(s(s(z))))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[177, 2887])).
% 0.63/0.84 tff(2889,plain,
% 0.63/0.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 0.63/0.85 inference(rewrite,[status(thm)],[])).
% 0.63/0.85 tff(2890,plain,
% 0.63/0.85 (((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 0.63/0.85 inference(rewrite,[status(thm)],[])).
% 0.63/0.85 tff(2891,plain,
% 0.63/0.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z))))),
% 0.63/0.85 inference(monotonicity,[status(thm)],[2890])).
% 0.63/0.85 tff(2892,plain,
% 0.63/0.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 0.63/0.85 inference(transitivity,[status(thm)],[2891, 2889])).
% 0.63/0.85 tff(2893,plain,
% 0.63/0.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(z))))))),
% 0.63/0.85 inference(quant_inst,[status(thm)],[])).
% 0.63/0.85 tff(2894,plain,
% 0.63/0.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z))),
% 0.63/0.85 inference(modus_ponens,[status(thm)],[2893, 2892])).
% 0.63/0.85 tff(2895,plain,
% 0.63/0.85 ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(z)))))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[2894, 188, 360, 2870, 89])).
% 0.63/0.85 tff(2896,plain,
% 0.63/0.85 (~b(s(z), s(s(s(s(s(s(z)))))))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[2895, 2888])).
% 0.63/0.85 tff(2897,plain,
% 0.63/0.85 (r(s(z), s(s(s(s(s(s(z)))))))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[84, 2896])).
% 0.63/0.85 tff(2898,plain,
% 0.63/0.85 (~r(z, s(s(s(z))))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[1112, 222, 1])).
% 0.63/0.85 tff(2899,plain,
% 0.63/0.85 (b(z, s(s(s(z))))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[281, 2898])).
% 0.63/0.85 tff(2900,plain,
% 0.63/0.85 (~b(z, s(z))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[1369, 2888, 2899, 2882])).
% 0.63/0.85 tff(2901,plain,
% 0.63/0.85 (r(z, s(z))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[300, 2900])).
% 0.63/0.85 tff(2902,plain,
% 0.63/0.85 ($false),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[357, 14, 2901, 1, 2897])).
% 0.63/0.85 tff(2903,plain,((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.85 tff(2904,plain,
% 0.63/0.85 (~b(s(z), z)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[2903, 2876, 1, 2872, 2])).
% 0.63/0.85 tff(2905,plain,
% 0.63/0.85 (r(s(z), z)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[312, 2904])).
% 0.63/0.85 tff(2906,plain,
% 0.63/0.85 (~r(s(z), s(s(s(s(s(s(z)))))))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[22, 2905, 1])).
% 0.63/0.85 tff(2907,plain,
% 0.63/0.85 (~r(z, s(z))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[1621, 2906, 1, 2, 2870])).
% 0.63/0.85 tff(2908,plain,
% 0.63/0.85 (~r(s(s(s(z))), s(z))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[811, 2905, 2])).
% 0.63/0.85 tff(2909,plain,
% 0.63/0.85 (b(s(s(s(z))), s(z))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[170, 2908])).
% 0.63/0.85 tff(2910,plain,
% 0.63/0.85 (~r(z, s(s(s(z))))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[1112, 2876, 1])).
% 0.63/0.85 tff(2911,plain,
% 0.63/0.85 (b(z, s(s(s(z))))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[281, 2910])).
% 0.63/0.85 tff(2912,plain,
% 0.63/0.85 (~r(s(z), s(s(s(z))))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[1551, 2905, 2])).
% 0.63/0.85 tff(2913,plain,
% 0.63/0.85 (b(s(z), s(s(s(z))))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[177, 2912])).
% 0.63/0.85 tff(2914,plain,
% 0.63/0.85 (~b(z, s(z))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[1369, 2913, 2911, 2909])).
% 0.63/0.85 tff(2915,plain,
% 0.63/0.85 ($false),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[300, 2914, 2907])).
% 0.63/0.85 tff(2916,plain,((~b(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.85 tff(2917,plain,
% 0.63/0.85 (~b(s(s(z)), s(s(s(z))))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[2916, 2, 1])).
% 0.63/0.85 tff(2918,plain,
% 0.63/0.85 (r(s(s(z)), s(s(s(z))))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[425, 2917])).
% 0.63/0.85 tff(2919,plain,
% 0.63/0.85 (~r(s(s(z)), z)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[535, 2918, 2])).
% 0.63/0.85 tff(2920,plain,
% 0.63/0.85 (b(s(s(z)), z)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[792, 2919])).
% 0.63/0.85 tff(2921,plain,
% 0.63/0.85 (~b(s(z), s(s(s(s(s(s(z)))))))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[1871, 3, 2, 2917, 2920])).
% 0.63/0.85 tff(2922,plain,
% 0.63/0.85 ($false),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[84, 2921, 23])).
% 0.63/0.85 tff(2923,plain,((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.85 tff(2924,plain,
% 0.63/0.85 (~r(s(z), z)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[2923, 2, 1])).
% 0.63/0.85 tff(2925,plain,
% 0.63/0.85 (b(s(z), z)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[312, 2924])).
% 0.63/0.85 tff(2926,plain,
% 0.63/0.85 (~r(s(s(z)), z)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[535, 522, 2])).
% 0.63/0.85 tff(2927,plain,
% 0.63/0.85 (b(s(s(z)), z)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[792, 2926])).
% 0.63/0.85 tff(2928,plain,
% 0.63/0.85 (~r(s(z), z)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[811, 140, 2])).
% 0.63/0.85 tff(2929,plain,
% 0.63/0.85 (b(s(z), z)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[312, 2928])).
% 0.63/0.85 tff(2930,plain,
% 0.63/0.85 ($false),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[795, 1698, 2929, 2927, 1494])).
% 0.63/0.85 tff(2931,plain,((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.85 tff(2932,plain,
% 0.63/0.85 (~r(s(s(s(z))), s(z))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[2931, 2918, 2])).
% 0.63/0.85 tff(2933,plain,
% 0.63/0.85 (b(s(s(s(z))), s(z))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[170, 2932])).
% 0.63/0.85 tff(2934,plain,
% 0.63/0.85 (~b(s(s(z)), s(z))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[795, 776, 427, 360])).
% 0.63/0.85 tff(2935,plain,
% 0.63/0.85 (r(s(s(z)), s(z))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[137, 2934])).
% 0.63/0.85 tff(2936,plain,
% 0.63/0.85 (~r(s(z), s(s(s(z))))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[1746, 2935, 522])).
% 0.63/0.85 tff(2937,plain,
% 0.63/0.85 (b(s(z), s(s(s(z))))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[177, 2936])).
% 0.63/0.85 tff(2938,plain,
% 0.63/0.85 (~b(s(z), s(s(s(s(s(s(z)))))))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[1591, 2937, 2870, 259])).
% 0.63/0.85 tff(2939,plain,
% 0.63/0.85 (r(s(z), s(s(s(s(s(s(z)))))))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[84, 2938])).
% 0.63/0.85 tff(2940,plain,
% 0.63/0.85 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[1879, 2939, 2870, 259, 2937, 246])).
% 0.63/0.85 tff(2941,plain,
% 0.63/0.85 (r(s(s(s(s(z)))), s(s(s(z))))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[890, 2940])).
% 0.63/0.85 tff(2942,plain,
% 0.63/0.85 (~r(s(s(s(s(z)))), s(s(z)))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[1884, 14, 522, 2941])).
% 0.63/0.85 tff(2943,plain,
% 0.63/0.85 (b(s(s(s(s(z)))), s(s(z)))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[909, 79, 906, 2942])).
% 0.63/0.85 tff(2944,plain,
% 0.63/0.85 (~b(z, s(s(s(z))))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[1942, 776, 522, 427, 360])).
% 0.63/0.85 tff(2945,plain,
% 0.63/0.85 (r(z, s(s(s(z))))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[281, 2944])).
% 0.63/0.85 tff(2946,plain,
% 0.63/0.85 (~r(s(s(s(s(z)))), z)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[851, 2941, 2945])).
% 0.63/0.85 tff(2947,plain,
% 0.63/0.85 (b(s(s(s(s(z)))), z)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[859, 2946])).
% 0.63/0.85 tff(2948,plain,
% 0.63/0.85 (~r(z, s(s(z)))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[1758, 14, 2945, 522])).
% 0.63/0.85 tff(2949,plain,
% 0.63/0.85 (b(z, s(s(z)))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[519, 79, 2948, 95])).
% 0.63/0.85 tff(2950,plain,
% 0.63/0.85 ($false),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[1900, 188, 427, 2949, 2947, 2943])).
% 0.63/0.85 tff(2951,plain,((~b(z, s(z))) | (~b(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.85 tff(2952,plain,
% 0.63/0.85 (~b(z, s(z))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[2951, 259, 2918, 2920, 2933, 2925])).
% 0.63/0.85 tff(2953,plain,
% 0.63/0.85 (r(z, s(z))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[300, 2952])).
% 0.63/0.85 tff(2954,plain,
% 0.63/0.85 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[1146, 2953, 1])).
% 0.63/0.85 tff(2955,plain,
% 0.63/0.85 (b(s(s(s(s(s(s(z)))))), s(z))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[627, 2954])).
% 0.63/0.85 tff(2956,plain,
% 0.63/0.85 (~b(s(z), s(s(s(z))))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[1458, 2955, 2933, 259])).
% 0.63/0.85 tff(2957,plain,
% 0.63/0.85 (r(s(z), s(s(s(z))))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[177, 2956])).
% 0.63/0.85 tff(2958,plain,
% 0.63/0.85 (~r(z, s(s(s(z))))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[375, 2957, 2953])).
% 0.63/0.85 tff(2959,plain,
% 0.63/0.85 (b(z, s(s(s(z))))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[281, 2958])).
% 0.63/0.85 tff(2960,plain,
% 0.63/0.85 (~r(s(s(s(s(s(s(z)))))), z)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[1965, 2959, 2, 2925])).
% 0.63/0.85 tff(2961,plain,
% 0.63/0.85 (b(s(s(s(s(s(s(z)))))), z)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[492, 2960])).
% 0.63/0.85 tff(2962,plain,
% 0.63/0.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 0.63/0.85 inference(rewrite,[status(thm)],[])).
% 0.63/0.85 tff(2963,plain,
% 0.63/0.85 (((~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))) <=> ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 0.63/0.85 inference(rewrite,[status(thm)],[])).
% 0.63/0.85 tff(2964,plain,
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% 0.63/0.85 inference(monotonicity,[status(thm)],[2963])).
% 0.63/0.85 tff(2965,plain,
% 0.63/0.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 0.63/0.85 inference(transitivity,[status(thm)],[2964, 2962])).
% 0.63/0.85 tff(2966,plain,
% 0.63/0.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 0.63/0.85 inference(quant_inst,[status(thm)],[])).
% 0.63/0.85 tff(2967,plain,
% 0.63/0.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z))),
% 0.63/0.85 inference(modus_ponens,[status(thm)],[2966, 2965])).
% 0.63/0.85 tff(2968,plain,
% 0.63/0.85 ($false),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[2967, 188, 2925, 2933, 259, 2961, 2955])).
% 0.63/0.85 tff(2969,plain,((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.85 tff(2970,plain,
% 0.63/0.85 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[2969, 2, 1])).
% 0.63/0.85 tff(2971,plain,
% 0.63/0.85 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[243, 2970])).
% 0.63/0.85 tff(2972,plain,
% 0.63/0.85 (~r(z, s(s(s(z))))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[1112, 2971, 1])).
% 0.63/0.85 tff(2973,plain,
% 0.63/0.85 (b(z, s(s(s(z))))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[281, 2972])).
% 0.63/0.85 tff(2974,plain,
% 0.63/0.85 (~b(s(s(s(s(s(s(z)))))), z)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[1865, 2971, 2, 2917, 2920])).
% 0.63/0.85 tff(2975,plain,
% 0.63/0.85 (r(s(s(s(s(s(s(z)))))), z)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[492, 2974])).
% 0.63/0.85 tff(2976,plain,
% 0.63/0.85 ($false),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[1965, 2975, 2973, 2, 2925])).
% 0.63/0.85 tff(2977,plain,((~r(s(s(s(z))), z)) | (~r(z, s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.85 tff(2978,plain,
% 0.63/0.85 (~r(s(s(s(z))), z)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[2977, 1])).
% 0.63/0.85 tff(2979,plain,
% 0.63/0.85 (b(s(s(s(z))), z)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[326, 2978])).
% 0.63/0.85 tff(2980,plain,
% 0.63/0.85 (~r(s(s(z)), z)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[445, 14, 284, 426])).
% 0.63/0.85 tff(2981,plain,
% 0.63/0.85 (b(s(s(z)), z)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[350, 79, 93, 2980])).
% 0.63/0.85 tff(2982,plain,
% 0.63/0.85 (~r(z, s(s(z)))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[1758, 14, 284, 426])).
% 0.63/0.85 tff(2983,plain,
% 0.63/0.85 ((z = s(s(z))) | b(z, s(s(z)))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[519, 79, 2982])).
% 0.63/0.85 tff(2984,plain,
% 0.63/0.85 (b(z, s(s(z)))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[2983, 380])).
% 0.63/0.85 tff(2985,plain,
% 0.63/0.85 (~b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[1844, 2984, 2981, 89])).
% 0.63/0.85 tff(2986,plain,
% 0.63/0.85 ((s(s(s(s(s(s(z)))))) = s(s(z))) | r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[500, 79, 2985])).
% 0.63/0.85 tff(2987,plain,
% 0.63/0.85 (r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[2986, 1828])).
% 0.63/0.85 tff(2988,plain,
% 0.63/0.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 0.63/0.85 inference(rewrite,[status(thm)],[])).
% 0.63/0.85 tff(2989,plain,
% 0.63/0.85 (((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 0.63/0.85 inference(rewrite,[status(thm)],[])).
% 0.63/0.85 tff(2990,plain,
% 0.63/0.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z))))),
% 0.63/0.85 inference(monotonicity,[status(thm)],[2989])).
% 0.63/0.85 tff(2991,plain,
% 0.63/0.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 0.63/0.85 inference(transitivity,[status(thm)],[2990, 2988])).
% 0.63/0.85 tff(2992,plain,
% 0.63/0.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(z)))))),
% 0.63/0.85 inference(quant_inst,[status(thm)],[])).
% 0.63/0.85 tff(2993,plain,
% 0.63/0.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), z))),
% 0.63/0.85 inference(modus_ponens,[status(thm)],[2992, 2991])).
% 0.63/0.85 tff(2994,plain,
% 0.63/0.85 ($false),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[2993, 188, 313, 406, 89, 86, 527])).
% 0.63/0.85 tff(2995,plain,((~r(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.85 tff(2996,plain,
% 0.63/0.85 (~r(s(z), s(s(s(z))))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[2995, 86, 89, 406, 426, 284])).
% 0.63/0.85 tff(2997,plain,
% 0.63/0.85 (b(s(z), s(s(s(z))))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[177, 2996])).
% 0.63/0.85 tff(2998,plain,
% 0.63/0.85 ($false),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[1589, 188, 2997, 245, 259, 86])).
% 0.63/0.85 tff(2999,plain,((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.85 tff(3000,plain,
% 0.63/0.85 (~b(s(z), s(s(s(s(s(s(z)))))))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[2999, 284, 259, 89, 406, 245])).
% 0.63/0.85 tff(3001,plain,
% 0.63/0.85 (r(s(z), s(s(s(s(s(s(z)))))))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[84, 3000])).
% 0.63/0.85 tff(3002,plain,
% 0.63/0.85 (~r(s(z), s(s(z)))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[2840, 3001, 2987])).
% 0.63/0.85 tff(3003,plain,
% 0.63/0.85 (b(s(z), s(s(z)))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[117, 79, 114, 3002])).
% 0.63/0.85 tff(3004,plain,
% 0.63/0.85 (~b(z, s(s(s(s(s(s(z)))))))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[447, 89, 259, 245, 406])).
% 0.63/0.85 tff(3005,plain,
% 0.63/0.85 (r(z, s(s(s(s(s(s(z)))))))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[256, 3004])).
% 0.63/0.85 tff(3006,plain,
% 0.63/0.85 (~r(s(z), z)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[20, 14, 3005, 3001])).
% 0.63/0.85 tff(3007,plain,
% 0.63/0.85 (b(s(z), z)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[312, 3006])).
% 0.63/0.85 tff(3008,plain,
% 0.63/0.85 (((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))),
% 0.63/0.85 inference(rewrite,[status(thm)],[])).
% 0.63/0.85 tff(3009,plain,
% 0.63/0.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z))))),
% 0.63/0.85 inference(monotonicity,[status(thm)],[3008])).
% 0.63/0.85 tff(3010,plain,
% 0.63/0.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))),
% 0.63/0.85 inference(transitivity,[status(thm)],[3009, 1652])).
% 0.63/0.85 tff(3011,plain,
% 0.63/0.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))),
% 0.63/0.85 inference(quant_inst,[status(thm)],[])).
% 0.63/0.85 tff(3012,plain,
% 0.63/0.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z))),
% 0.63/0.85 inference(modus_ponens,[status(thm)],[3011, 3010])).
% 0.63/0.85 tff(3013,plain,
% 0.63/0.85 ($false),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[3012, 188, 3007, 2981, 2984, 3003])).
% 0.63/0.85 tff(3014,plain,((~r(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.85 tff(3015,plain,
% 0.63/0.85 (~r(z, s(s(s(z))))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[3014, 89, 259, 406, 245])).
% 0.63/0.85 tff(3016,plain,
% 0.63/0.85 (~b(z, s(s(s(z))))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[547, 89, 259, 283])).
% 0.63/0.85 tff(3017,plain,
% 0.63/0.85 ($false),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[281, 3016, 3015])).
% 0.63/0.85 tff(3018,plain,((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.85 tff(3019,plain,
% 0.63/0.85 ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[3018, 2454])).
% 0.63/0.85 tff(3020,plain,
% 0.63/0.85 (~b(s(s(s(s(s(s(z)))))), z)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[3019, 259, 2870, 2979])).
% 0.63/0.85 tff(3021,plain,
% 0.63/0.85 (r(s(s(s(s(s(s(z)))))), z)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[492, 3020])).
% 0.63/0.85 tff(3022,plain,
% 0.63/0.85 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[2455, 139, 1915])).
% 0.63/0.85 tff(3023,plain,
% 0.63/0.85 (r(s(s(s(s(s(s(z)))))), s(z))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[627, 3022])).
% 0.63/0.85 tff(3024,plain,
% 0.63/0.85 (~r(s(z), s(s(s(z))))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[2001, 3023, 222])).
% 0.63/0.85 tff(3025,plain,
% 0.63/0.85 (b(s(z), s(s(s(z))))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[177, 3024])).
% 0.63/0.85 tff(3026,plain,
% 0.63/0.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(z))))),
% 0.63/0.85 inference(rewrite,[status(thm)],[])).
% 0.63/0.85 tff(3027,plain,
% 0.63/0.85 (((~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z)))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(z))))),
% 0.63/0.85 inference(rewrite,[status(thm)],[])).
% 0.63/0.85 tff(3028,plain,
% 0.63/0.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(z)))))),
% 0.63/0.86 inference(monotonicity,[status(thm)],[3027])).
% 0.63/0.86 tff(3029,plain,
% 0.63/0.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(z))))),
% 0.63/0.86 inference(transitivity,[status(thm)],[3028, 3026])).
% 0.63/0.86 tff(3030,plain,
% 0.63/0.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 0.63/0.86 inference(quant_inst,[status(thm)],[])).
% 0.63/0.86 tff(3031,plain,
% 0.63/0.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(z)))),
% 0.63/0.86 inference(modus_ponens,[status(thm)],[3030, 3029])).
% 0.63/0.86 tff(3032,plain,
% 0.63/0.86 (~b(s(s(z)), s(s(s(z))))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[3031, 188, 3025, 2454, 2870, 139])).
% 0.63/0.86 tff(3033,plain,
% 0.63/0.86 (r(s(s(z)), s(s(s(z))))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[425, 3032])).
% 0.63/0.86 tff(3034,plain,
% 0.63/0.86 (~b(s(s(s(z))), s(s(z)))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[1855, 188, 406, 245, 1836])).
% 0.63/0.86 tff(3035,plain,
% 0.63/0.86 (r(s(s(s(z))), s(s(z)))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[476, 3034])).
% 0.63/0.86 tff(3036,plain,
% 0.63/0.86 (~b(s(z), s(s(z)))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[2535, 1915, 1836, 406])).
% 0.63/0.86 tff(3037,plain,
% 0.63/0.86 (r(s(z), s(s(z)))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[117, 79, 114, 3036])).
% 0.63/0.86 tff(3038,plain,
% 0.63/0.86 (~b(s(s(s(z))), s(z))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[1524, 87, 69, 245])).
% 0.63/0.86 tff(3039,plain,
% 0.63/0.86 (r(s(s(s(z))), s(z))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[170, 3038])).
% 0.63/0.86 tff(3040,plain,
% 0.63/0.86 (~b(s(s(z)), s(z))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[1136, 87, 406, 1915])).
% 0.63/0.86 tff(3041,plain,
% 0.63/0.86 (r(s(s(z)), s(z))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[137, 3040])).
% 0.63/0.86 tff(3042,plain,
% 0.63/0.86 ($false),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[1124, 3041, 3039, 522])).
% 0.63/0.86 tff(3043,plain,((~b(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | r(s(z), s(s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.86 tff(3044,plain,
% 0.63/0.86 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[3043, 69, 406, 522, 245])).
% 0.63/0.86 tff(3045,plain,
% 0.63/0.86 (r(s(s(s(s(s(s(z)))))), s(z))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[627, 3044])).
% 0.63/0.86 tff(3046,plain,
% 0.63/0.86 (~r(z, s(z))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[1146, 3045, 1])).
% 0.63/0.86 tff(3047,plain,
% 0.63/0.86 (b(z, s(z))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[300, 3046])).
% 0.63/0.86 tff(3048,plain,
% 0.63/0.86 (~b(s(s(s(z))), s(z))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[1369, 3047, 258, 684])).
% 0.63/0.86 tff(3049,plain,
% 0.63/0.86 (r(s(s(s(z))), s(z))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[170, 3048])).
% 0.63/0.86 tff(3050,plain,
% 0.63/0.86 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(z)))))),
% 0.63/0.86 inference(rewrite,[status(thm)],[])).
% 0.63/0.86 tff(3051,plain,
% 0.63/0.86 (((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(z)))))),
% 0.63/0.86 inference(rewrite,[status(thm)],[])).
% 0.63/0.86 tff(3052,plain,
% 0.63/0.86 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(z))))))),
% 0.63/0.86 inference(monotonicity,[status(thm)],[3051])).
% 0.63/0.86 tff(3053,plain,
% 0.63/0.86 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(z)))))),
% 0.63/0.86 inference(transitivity,[status(thm)],[3052, 3050])).
% 0.63/0.86 tff(3054,plain,
% 0.63/0.86 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z))))),
% 0.63/0.86 inference(quant_inst,[status(thm)],[])).
% 0.63/0.86 tff(3055,plain,
% 0.63/0.86 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(z))))),
% 0.63/0.86 inference(modus_ponens,[status(thm)],[3054, 3053])).
% 0.63/0.86 tff(3056,plain,
% 0.63/0.86 ($false),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[3055, 14, 3049, 3037, 3035])).
% 0.63/0.86 tff(3057,plain,(r(s(z), s(s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.86 tff(3058,plain,
% 0.63/0.86 (r(s(z), s(s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[3057, 2454])).
% 0.63/0.86 tff(3059,plain,
% 0.63/0.86 (~b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[3058, 3033, 2870, 1, 69, 2899, 3025])).
% 0.63/0.86 tff(3060,plain,
% 0.63/0.86 (r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[1224, 3059])).
% 0.63/0.86 tff(3061,plain,
% 0.63/0.86 ($false),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[1832, 14, 222, 3033, 3060])).
% 0.63/0.86 tff(3062,plain,((~b(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(z)))))))) | r(s(z), s(s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.86 tff(3063,plain,
% 0.63/0.86 (~b(s(s(z)), s(z))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[3062, 69, 1, 2876])).
% 0.63/0.86 tff(3064,plain,
% 0.63/0.86 (r(s(s(z)), s(z))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[137, 3063])).
% 0.63/0.86 tff(3065,plain,
% 0.63/0.86 (~b(s(s(z)), s(z))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[3062, 222, 1, 23])).
% 0.63/0.86 tff(3066,plain,
% 0.63/0.86 (r(s(s(z)), s(z))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[137, 3065])).
% 0.63/0.86 tff(3067,plain,
% 0.63/0.86 (~r(s(s(z)), z)),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[1185, 3066, 3])).
% 0.63/0.86 tff(3068,plain,
% 0.63/0.86 (b(s(s(z)), z)),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[792, 3067])).
% 0.63/0.86 tff(3069,plain,
% 0.63/0.86 (~b(s(s(z)), s(s(s(z))))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[1045, 3068, 2979, 2899])).
% 0.63/0.86 tff(3070,plain,
% 0.63/0.86 (r(s(s(z)), s(s(s(z))))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[425, 3069])).
% 0.63/0.86 tff(3071,plain,
% 0.63/0.86 ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | r(s(z), s(s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[3043, 2454])).
% 0.63/0.86 tff(3072,plain,
% 0.63/0.86 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[3071, 3070, 2870, 23])).
% 0.63/0.86 tff(3073,plain,
% 0.63/0.86 (r(s(s(s(s(s(s(z)))))), s(z))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[627, 3072])).
% 0.63/0.86 tff(3074,plain,
% 0.63/0.86 (b(s(z), s(s(s(s(s(s(z)))))))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[84, 23])).
% 0.63/0.86 tff(3075,plain,
% 0.63/0.86 (~r(s(s(s(z))), s(z))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[1160, 3068, 222, 1, 3])).
% 0.63/0.86 tff(3076,plain,
% 0.63/0.86 (b(s(s(s(z))), s(z))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[170, 3075])).
% 0.63/0.86 tff(3077,plain,
% 0.63/0.86 (~b(s(s(s(s(s(s(z)))))), z)),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[1569, 3076, 2870, 2979, 3074])).
% 0.63/0.86 tff(3078,plain,
% 0.63/0.86 (r(s(s(s(s(s(s(z)))))), z)),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[492, 3077])).
% 0.63/0.86 tff(3079,plain,
% 0.63/0.86 ($false),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[705, 3078, 3073, 3])).
% 0.63/0.86 tff(3080,plain,((~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.86 tff(3081,plain,
% 0.63/0.86 (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[3080, 3, 1])).
% 0.63/0.86 tff(3082,plain,
% 0.63/0.86 (b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[243, 3081])).
% 0.63/0.86 tff(3083,plain,
% 0.63/0.86 (~b(s(s(s(s(s(s(z)))))), z)),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[3019, 3082, 2870, 2979])).
% 0.63/0.86 tff(3084,plain,
% 0.63/0.86 (r(s(s(s(s(s(s(z)))))), z)),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[492, 3083])).
% 0.63/0.86 tff(3085,plain,
% 0.63/0.86 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[705, 3084, 3])).
% 0.63/0.86 tff(3086,plain,
% 0.63/0.86 (~b(s(s(z)), s(s(s(z))))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[2874, 3082])).
% 0.63/0.86 tff(3087,plain,
% 0.63/0.86 (r(s(s(z)), s(s(s(z))))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[425, 3086])).
% 0.63/0.86 tff(3088,plain,
% 0.63/0.86 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[3071, 3087, 2870, 23])).
% 0.63/0.86 tff(3089,plain,
% 0.63/0.86 ($false),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[627, 3088, 3085])).
% 0.63/0.86 tff(3090,plain,((~r(s(z), z)) | (~r(z, s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.86 tff(3091,plain,
% 0.63/0.86 (~r(s(z), z)),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[3090, 1])).
% 0.63/0.86 tff(3092,plain,
% 0.63/0.86 (b(s(z), z)),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[312, 3091])).
% 0.63/0.86 tff(3093,plain,
% 0.63/0.86 (~b(s(s(z)), z)),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[1045, 2911, 2979, 96])).
% 0.63/0.86 tff(3094,plain,
% 0.63/0.86 (r(s(s(z)), z)),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[792, 3093])).
% 0.63/0.86 tff(3095,plain,
% 0.63/0.86 (~r(z, s(z))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[2039, 3064, 3094])).
% 0.63/0.86 tff(3096,plain,
% 0.63/0.86 (b(z, s(z))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[300, 3095])).
% 0.63/0.86 tff(3097,plain,
% 0.63/0.86 (~b(s(s(s(z))), s(z))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[783, 3096, 2979, 3092])).
% 0.63/0.86 tff(3098,plain,
% 0.63/0.86 (r(s(s(s(z))), s(z))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[170, 3097])).
% 0.63/0.86 tff(3099,plain,
% 0.63/0.86 (~r(s(s(s(z))), s(s(z)))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[1597, 3098, 3064])).
% 0.63/0.86 tff(3100,plain,
% 0.63/0.86 (b(s(s(s(z))), s(s(z)))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[476, 3099])).
% 0.63/0.86 tff(3101,plain,
% 0.63/0.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 0.63/0.86 inference(rewrite,[status(thm)],[])).
% 0.63/0.86 tff(3102,plain,
% 0.63/0.86 (((~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 0.63/0.86 inference(rewrite,[status(thm)],[])).
% 0.63/0.86 tff(3103,plain,
% 0.63/0.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 0.63/0.86 inference(monotonicity,[status(thm)],[3102])).
% 0.63/0.86 tff(3104,plain,
% 0.63/0.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 0.63/0.86 inference(transitivity,[status(thm)],[3103, 3101])).
% 0.63/0.86 tff(3105,plain,
% 0.63/0.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 0.63/0.86 inference(quant_inst,[status(thm)],[])).
% 0.63/0.86 tff(3106,plain,
% 0.63/0.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 0.63/0.86 inference(modus_ponens,[status(thm)],[3105, 3104])).
% 0.63/0.86 tff(3107,plain,
% 0.63/0.86 (~b(s(s(z)), s(s(s(s(z)))))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[3106, 188, 2454, 2870, 96, 893])).
% 0.63/0.86 tff(3108,plain,
% 0.63/0.86 (r(s(s(z)), s(s(s(s(z)))))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[2269, 3107])).
% 0.63/0.86 tff(3109,assumption,(b(s(z), s(s(s(s(z)))))), introduced(assumption)).
% 0.63/0.86 tff(3110,plain,
% 0.63/0.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 0.63/0.86 inference(rewrite,[status(thm)],[])).
% 0.63/0.86 tff(3111,plain,
% 0.63/0.86 (((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 0.63/0.86 inference(rewrite,[status(thm)],[])).
% 0.63/0.86 tff(3112,plain,
% 0.63/0.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))))),
% 0.63/0.86 inference(monotonicity,[status(thm)],[3111])).
% 0.63/0.86 tff(3113,plain,
% 0.63/0.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 0.63/0.86 inference(transitivity,[status(thm)],[3112, 3110])).
% 0.63/0.86 tff(3114,plain,
% 0.63/0.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 0.63/0.86 inference(quant_inst,[status(thm)],[])).
% 0.63/0.86 tff(3115,plain,
% 0.63/0.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))),
% 0.63/0.86 inference(modus_ponens,[status(thm)],[3114, 3113])).
% 0.63/0.86 tff(3116,plain,
% 0.63/0.86 ($false),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[3115, 188, 360, 684, 283, 3109, 893])).
% 0.63/0.86 tff(3117,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.86 tff(3118,plain,
% 0.63/0.86 (~b(s(z), s(s(s(s(z)))))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[3117, 893, 684, 360, 283])).
% 0.63/0.86 tff(3119,plain,
% 0.63/0.86 (r(s(z), s(s(s(s(z)))))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[2294, 3118])).
% 0.63/0.86 tff(3120,plain,
% 0.63/0.86 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 0.63/0.86 inference(rewrite,[status(thm)],[])).
% 0.63/0.86 tff(3121,plain,
% 0.63/0.86 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z)))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 0.63/0.86 inference(rewrite,[status(thm)],[])).
% 0.63/0.86 tff(3122,plain,
% 0.63/0.86 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))))),
% 0.63/0.86 inference(monotonicity,[status(thm)],[3121])).
% 0.63/0.86 tff(3123,plain,
% 0.63/0.86 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 0.63/0.86 inference(transitivity,[status(thm)],[3122, 3120])).
% 0.63/0.86 tff(3124,plain,
% 0.63/0.86 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))))),
% 0.63/0.86 inference(quant_inst,[status(thm)],[])).
% 0.63/0.86 tff(3125,plain,
% 0.63/0.86 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))),
% 0.63/0.86 inference(modus_ponens,[status(thm)],[3124, 3123])).
% 0.63/0.86 tff(3126,plain,
% 0.63/0.86 ($false),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[3125, 14, 119, 3119, 3108])).
% 0.63/0.86 tff(3127,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.86 tff(3128,plain,
% 0.63/0.86 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[3127, 684, 96, 119, 360, 283])).
% 0.63/0.86 tff(3129,plain,
% 0.63/0.86 (r(s(s(s(s(z)))), s(s(s(z))))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[890, 3128])).
% 0.63/0.86 tff(3130,plain,
% 0.63/0.86 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 0.63/0.86 inference(rewrite,[status(thm)],[])).
% 0.63/0.86 tff(3131,plain,
% 0.63/0.86 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 0.63/0.86 inference(quant_inst,[status(thm)],[])).
% 0.63/0.86 tff(3132,plain,
% 0.63/0.86 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 0.63/0.86 inference(modus_ponens,[status(thm)],[3131, 3130])).
% 0.63/0.86 tff(3133,plain,
% 0.63/0.86 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[3132, 14, 2876, 3129])).
% 0.63/0.86 tff(3134,plain,
% 0.63/0.86 ((s(s(s(s(s(s(z)))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[1239, 79, 3133])).
% 0.63/0.86 tff(3135,plain,
% 0.63/0.86 (b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[3134, 1212])).
% 0.63/0.86 tff(3136,plain,
% 0.63/0.86 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[1272, 14, 2876, 3129])).
% 0.63/0.86 tff(3137,plain,
% 0.63/0.86 (b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[927, 79, 924, 3136])).
% 0.63/0.86 tff(3138,plain,
% 0.63/0.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 0.63/0.86 inference(rewrite,[status(thm)],[])).
% 0.63/0.86 tff(3139,plain,
% 0.63/0.86 (((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 0.63/0.86 inference(rewrite,[status(thm)],[])).
% 0.63/0.86 tff(3140,plain,
% 0.63/0.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 0.63/0.86 inference(monotonicity,[status(thm)],[3139])).
% 0.63/0.86 tff(3141,plain,
% 0.63/0.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 0.63/0.86 inference(transitivity,[status(thm)],[3140, 3138])).
% 0.63/0.86 tff(3142,plain,
% 0.63/0.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))))),
% 0.63/0.86 inference(quant_inst,[status(thm)],[])).
% 0.63/0.86 tff(3143,plain,
% 0.63/0.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 0.63/0.87 inference(modus_ponens,[status(thm)],[3142, 3141])).
% 0.63/0.87 tff(3144,plain,
% 0.63/0.87 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 0.63/0.87 inference(unit_resolution,[status(thm)],[3143, 188, 2870, 3137, 3135])).
% 0.63/0.87 tff(3145,plain,
% 0.63/0.87 (r(s(s(s(z))), s(s(s(s(z)))))),
% 0.63/0.87 inference(unit_resolution,[status(thm)],[2314, 3144])).
% 0.63/0.87 tff(3146,plain,
% 0.63/0.87 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 0.63/0.87 inference(rewrite,[status(thm)],[])).
% 0.63/0.87 tff(3147,plain,
% 0.63/0.87 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 0.63/0.87 inference(rewrite,[status(thm)],[])).
% 0.63/0.87 tff(3148,plain,
% 0.63/0.87 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))))),
% 0.63/0.87 inference(monotonicity,[status(thm)],[3147])).
% 0.63/0.87 tff(3149,plain,
% 0.63/0.87 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 0.63/0.87 inference(transitivity,[status(thm)],[3148, 3146])).
% 0.63/0.87 tff(3150,plain,
% 0.63/0.87 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))),
% 0.63/0.87 inference(quant_inst,[status(thm)],[])).
% 0.63/0.87 tff(3151,plain,
% 0.63/0.87 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))),
% 0.63/0.87 inference(modus_ponens,[status(thm)],[3150, 3149])).
% 0.63/0.87 tff(3152,plain,
% 0.63/0.87 ($false),
% 0.63/0.87 inference(unit_resolution,[status(thm)],[3151, 14, 140, 2297, 2296])).
% 0.63/0.87 tff(3153,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.87 tff(3154,plain,
% 0.63/0.87 (~r(s(z), s(s(s(s(z)))))),
% 0.63/0.87 inference(unit_resolution,[status(thm)],[3153, 3145, 140])).
% 0.63/0.87 tff(3155,plain,
% 0.63/0.87 (b(s(z), s(s(s(s(z)))))),
% 0.63/0.87 inference(unit_resolution,[status(thm)],[2294, 3154])).
% 0.63/0.87 tff(3156,plain,
% 0.63/0.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 0.63/0.87 inference(rewrite,[status(thm)],[])).
% 0.63/0.87 tff(3157,plain,
% 0.63/0.87 (((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 0.63/0.87 inference(rewrite,[status(thm)],[])).
% 0.63/0.87 tff(3158,plain,
% 0.63/0.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))))),
% 0.63/0.87 inference(monotonicity,[status(thm)],[3157])).
% 0.63/0.87 tff(3159,plain,
% 0.63/0.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 0.63/0.87 inference(transitivity,[status(thm)],[3158, 3156])).
% 0.63/0.87 tff(3160,plain,
% 0.63/0.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(z))))))),
% 0.63/0.87 inference(quant_inst,[status(thm)],[])).
% 0.63/0.87 tff(3161,plain,
% 0.63/0.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))),
% 0.63/0.87 inference(modus_ponens,[status(thm)],[3160, 3159])).
% 0.63/0.87 tff(3162,plain,
% 0.63/0.87 ($false),
% 0.63/0.87 inference(unit_resolution,[status(thm)],[3161, 188, 684, 2870, 86, 3155, 3135])).
% 0.63/0.87 tff(3163,plain,((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.87 tff(3164,plain,
% 0.63/0.87 (~b(s(z), s(s(s(z))))),
% 0.63/0.87 inference(unit_resolution,[status(thm)],[3163, 1915, 3098, 96, 3064, 3092, 2979])).
% 0.63/0.87 tff(3165,plain,
% 0.63/0.87 (r(s(z), s(s(s(z))))),
% 0.63/0.87 inference(unit_resolution,[status(thm)],[177, 3164])).
% 0.63/0.87 tff(3166,plain,
% 0.63/0.87 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 0.63/0.87 inference(unit_resolution,[status(thm)],[2001, 3165, 2876])).
% 0.63/0.87 tff(3167,plain,
% 0.63/0.87 (b(s(s(s(s(s(s(z)))))), s(z))),
% 0.63/0.87 inference(unit_resolution,[status(thm)],[627, 3166])).
% 0.63/0.87 tff(3168,plain,
% 0.63/0.87 (((~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(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)))),
% 0.63/0.87 inference(rewrite,[status(thm)],[])).
% 0.63/0.87 tff(3169,plain,
% 0.63/0.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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))))),
% 0.63/0.87 inference(monotonicity,[status(thm)],[3168])).
% 0.63/0.87 tff(3170,plain,
% 0.63/0.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, 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)))),
% 0.63/0.87 inference(transitivity,[status(thm)],[3169, 977])).
% 0.63/0.87 tff(3171,plain,
% 0.63/0.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 0.63/0.87 inference(quant_inst,[status(thm)],[])).
% 0.63/0.87 tff(3172,plain,
% 0.63/0.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), z))),
% 0.63/0.87 inference(modus_ponens,[status(thm)],[3171, 3170])).
% 0.63/0.87 tff(3173,plain,
% 0.63/0.87 (~b(s(s(s(s(s(s(z)))))), z)),
% 0.63/0.87 inference(unit_resolution,[status(thm)],[3172, 188, 3092, 3096, 3167])).
% 0.63/0.87 tff(3174,plain,
% 0.63/0.87 (r(s(s(s(s(s(s(z)))))), z)),
% 0.63/0.87 inference(unit_resolution,[status(thm)],[492, 3173])).
% 0.63/0.87 tff(3175,plain,
% 0.63/0.87 (~r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.63/0.87 inference(unit_resolution,[status(thm)],[1977, 3174, 3094])).
% 0.63/0.87 tff(3176,plain,
% 0.63/0.87 (b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.63/0.87 inference(unit_resolution,[status(thm)],[1224, 3175])).
% 0.63/0.87 tff(3177,plain,
% 0.63/0.87 ($false),
% 0.63/0.87 inference(unit_resolution,[status(thm)],[1855, 188, 2454, 2870, 3176, 3100])).
% 0.63/0.87 tff(3178,plain,(r(s(z), s(s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.87 tff(3179,plain,
% 0.63/0.87 (r(s(z), s(s(s(s(s(s(z)))))))),
% 0.63/0.87 inference(unit_resolution,[status(thm)],[3178, 96, 1])).
% 0.63/0.87 tff(3180,plain,
% 0.63/0.87 (~r(s(z), s(s(s(z))))),
% 0.63/0.87 inference(unit_resolution,[status(thm)],[230, 3179, 2876])).
% 0.63/0.87 tff(3181,plain,
% 0.63/0.87 (b(s(z), s(s(s(z))))),
% 0.63/0.87 inference(unit_resolution,[status(thm)],[177, 3180])).
% 0.63/0.87 tff(3182,plain,
% 0.63/0.87 ($false),
% 0.63/0.87 inference(unit_resolution,[status(thm)],[2605, 188, 3092, 3181, 2979, 2911])).
% 0.63/0.87 tff(3183,plain,((~b(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.87 tff(3184,plain,
% 0.63/0.87 (~b(s(s(z)), s(s(s(z))))),
% 0.63/0.87 inference(unit_resolution,[status(thm)],[3183, 1])).
% 0.63/0.87 tff(3185,plain,
% 0.63/0.87 (r(s(s(z)), s(s(s(z))))),
% 0.63/0.87 inference(unit_resolution,[status(thm)],[425, 3184])).
% 0.63/0.87 tff(3186,plain,
% 0.63/0.87 ((z = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = z)),
% 0.63/0.87 inference(commutativity,[status(thm)],[])).
% 0.63/0.87 tff(3187,plain,
% 0.63/0.87 ((s(s(s(s(z)))) = z) <=> (z = s(s(s(s(z)))))),
% 0.63/0.87 inference(symmetry,[status(thm)],[3186])).
% 0.63/0.87 tff(3188,plain,
% 0.63/0.87 ((~(s(s(s(s(z)))) = z)) <=> (~(z = s(s(s(s(z))))))),
% 0.63/0.87 inference(monotonicity,[status(thm)],[3187])).
% 0.63/0.87 tff(3189,plain,
% 0.63/0.87 (~(z = s(s(s(s(z)))))),
% 0.63/0.87 inference(modus_ponens,[status(thm)],[391, 3188])).
% 0.63/0.87 tff(3190,plain,
% 0.63/0.87 (~r(s(z), s(s(z)))),
% 0.63/0.87 inference(unit_resolution,[status(thm)],[525, 14, 26, 3185])).
% 0.63/0.87 tff(3191,plain,
% 0.63/0.87 (b(s(z), s(s(z)))),
% 0.63/0.87 inference(unit_resolution,[status(thm)],[1427, 3190])).
% 0.63/0.87 tff(3192,plain,
% 0.63/0.87 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 0.63/0.87 inference(unit_resolution,[status(thm)],[2414, 3191, 26, 3185])).
% 0.63/0.87 tff(3193,plain,
% 0.63/0.87 (b(s(s(s(s(z)))), s(s(s(z))))),
% 0.63/0.87 inference(unit_resolution,[status(thm)],[890, 3192])).
% 0.63/0.87 tff(3194,plain,
% 0.63/0.87 (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.63/0.87 inference(unit_resolution,[status(thm)],[916, 188, 2870, 259, 3193])).
% 0.63/0.87 tff(3195,plain,
% 0.63/0.87 (r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.63/0.87 inference(unit_resolution,[status(thm)],[927, 79, 924, 3194])).
% 0.63/0.87 tff(3196,plain,
% 0.63/0.87 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 0.63/0.87 inference(rewrite,[status(thm)],[])).
% 0.63/0.87 tff(3197,plain,
% 0.63/0.87 (((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(z, s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 0.63/0.87 inference(rewrite,[status(thm)],[])).
% 0.63/0.87 tff(3198,plain,
% 0.63/0.87 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))))),
% 0.63/0.87 inference(monotonicity,[status(thm)],[3197])).
% 0.63/0.87 tff(3199,plain,
% 0.63/0.87 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 0.63/0.87 inference(transitivity,[status(thm)],[3198, 3196])).
% 0.63/0.87 tff(3200,plain,
% 0.63/0.87 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(z)))))))),
% 0.63/0.87 inference(quant_inst,[status(thm)],[])).
% 0.63/0.87 tff(3201,plain,
% 0.63/0.87 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 0.63/0.87 inference(modus_ponens,[status(thm)],[3200, 3199])).
% 0.63/0.87 tff(3202,plain,
% 0.63/0.87 (~r(z, s(s(s(s(z)))))),
% 0.63/0.87 inference(unit_resolution,[status(thm)],[3201, 14, 1, 3195])).
% 0.63/0.87 tff(3203,plain,
% 0.63/0.87 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(z))))) | b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(z))))) | b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z))))))),
% 0.63/0.87 inference(rewrite,[status(thm)],[])).
% 0.63/0.87 tff(3204,plain,
% 0.63/0.87 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(z))))) | b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z))))))),
% 0.63/0.87 inference(quant_inst,[status(thm)],[])).
% 0.63/0.87 tff(3205,plain,
% 0.63/0.87 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(z))))) | b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z)))))),
% 0.63/0.87 inference(modus_ponens,[status(thm)],[3204, 3203])).
% 0.63/0.87 tff(3206,plain,
% 0.63/0.87 ((z = s(s(s(s(z))))) | b(z, s(s(s(s(z)))))),
% 0.63/0.87 inference(unit_resolution,[status(thm)],[3205, 79, 3202])).
% 0.63/0.87 tff(3207,plain,
% 0.63/0.87 (b(z, s(s(s(s(z)))))),
% 0.63/0.87 inference(unit_resolution,[status(thm)],[3206, 3189])).
% 0.63/0.87 tff(3208,plain,
% 0.63/0.87 (~r(s(s(s(s(z)))), z)),
% 0.63/0.87 inference(unit_resolution,[status(thm)],[2423, 14, 1, 3195])).
% 0.63/0.87 tff(3209,plain,
% 0.63/0.87 (b(s(s(s(s(z)))), z)),
% 0.63/0.87 inference(unit_resolution,[status(thm)],[859, 3208])).
% 0.63/0.87 tff(3210,plain,
% 0.63/0.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 0.63/0.87 inference(rewrite,[status(thm)],[])).
% 0.63/0.87 tff(3211,plain,
% 0.63/0.87 (((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 0.63/0.87 inference(rewrite,[status(thm)],[])).
% 0.63/0.87 tff(3212,plain,
% 0.63/0.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z))))))))),
% 0.63/0.87 inference(monotonicity,[status(thm)],[3211])).
% 0.63/0.87 tff(3213,plain,
% 0.63/0.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 0.63/0.87 inference(transitivity,[status(thm)],[3212, 3210])).
% 0.63/0.87 tff(3214,plain,
% 0.63/0.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))),
% 0.63/0.87 inference(quant_inst,[status(thm)],[])).
% 0.63/0.87 tff(3215,plain,
% 0.63/0.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z))))))),
% 0.63/0.87 inference(modus_ponens,[status(thm)],[3214, 3213])).
% 0.63/0.87 tff(3216,plain,
% 0.63/0.87 (~b(s(z), s(s(s(s(z)))))),
% 0.63/0.87 inference(unit_resolution,[status(thm)],[3215, 188, 3092, 3209, 3207])).
% 0.63/0.87 tff(3217,plain,
% 0.63/0.87 (r(s(z), s(s(s(s(z)))))),
% 0.63/0.87 inference(unit_resolution,[status(thm)],[2294, 3216])).
% 0.63/0.87 tff(3218,plain,
% 0.63/0.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 0.63/0.87 inference(rewrite,[status(thm)],[])).
% 0.63/0.87 tff(3219,plain,
% 0.63/0.87 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 0.63/0.87 inference(rewrite,[status(thm)],[])).
% 0.63/0.87 tff(3220,plain,
% 0.63/0.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 0.63/0.87 inference(monotonicity,[status(thm)],[3219])).
% 0.63/0.87 tff(3221,plain,
% 0.63/0.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 0.63/0.87 inference(transitivity,[status(thm)],[3220, 3218])).
% 0.63/0.87 tff(3222,plain,
% 0.63/0.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))),
% 0.63/0.87 inference(quant_inst,[status(thm)],[])).
% 0.63/0.87 tff(3223,plain,
% 0.63/0.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 0.63/0.87 inference(modus_ponens,[status(thm)],[3222, 3221])).
% 0.63/0.87 tff(3224,plain,
% 0.63/0.87 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 0.63/0.87 inference(unit_resolution,[status(thm)],[3223, 188, 2979, 3209, 3207])).
% 0.63/0.87 tff(3225,plain,
% 0.63/0.87 (r(s(s(s(z))), s(s(s(s(z)))))),
% 0.63/0.87 inference(unit_resolution,[status(thm)],[2314, 3224])).
% 0.63/0.87 tff(3226,plain,
% 0.63/0.87 ($false),
% 0.63/0.87 inference(unit_resolution,[status(thm)],[2305, 3225, 3217, 26])).
% 0.63/0.87 tff(3227,plain,((~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.87 tff(3228,plain,
% 0.63/0.87 (~r(s(z), s(s(s(z))))),
% 0.63/0.87 inference(unit_resolution,[status(thm)],[3227, 259, 1])).
% 0.63/0.87 tff(3229,plain,
% 0.63/0.87 (b(s(z), s(s(s(z))))),
% 0.63/0.87 inference(unit_resolution,[status(thm)],[177, 3228])).
% 0.63/0.87 tff(3230,plain,
% 0.63/0.87 (~b(s(z), s(s(s(s(s(s(z)))))))),
% 0.63/0.87 inference(unit_resolution,[status(thm)],[1591, 3229, 2870, 259])).
% 0.63/0.87 tff(3231,plain,
% 0.63/0.87 (r(s(z), s(s(s(s(s(s(z)))))))),
% 0.63/0.87 inference(unit_resolution,[status(thm)],[84, 3230])).
% 0.63/0.87 tff(3232,plain,
% 0.63/0.87 (~r(z, s(z))),
% 0.63/0.87 inference(unit_resolution,[status(thm)],[357, 14, 1, 3231])).
% 0.63/0.87 tff(3233,plain,
% 0.63/0.87 (b(z, s(z))),
% 0.63/0.87 inference(unit_resolution,[status(thm)],[300, 3232])).
% 0.63/0.87 tff(3234,plain,
% 0.63/0.87 (~b(s(s(s(z))), s(z))),
% 0.63/0.87 inference(unit_resolution,[status(thm)],[783, 3233, 2979, 3092])).
% 0.63/0.87 tff(3235,plain,
% 0.63/0.87 (r(s(s(s(z))), s(z))),
% 0.63/0.87 inference(unit_resolution,[status(thm)],[170, 3234])).
% 0.63/0.87 tff(3236,plain,
% 0.63/0.87 (~r(z, s(s(s(z))))),
% 0.63/0.87 inference(unit_resolution,[status(thm)],[1702, 3235, 3185, 3092])).
% 0.63/0.87 tff(3237,plain,
% 0.63/0.87 (b(z, s(s(s(z))))),
% 0.63/0.87 inference(unit_resolution,[status(thm)],[281, 3236])).
% 0.63/0.87 tff(3238,plain,
% 0.63/0.87 (~b(s(s(z)), z)),
% 0.63/0.87 inference(unit_resolution,[status(thm)],[1942, 3237, 3092, 3233, 3185])).
% 0.63/0.87 tff(3239,plain,
% 0.63/0.87 (r(s(s(z)), z)),
% 0.63/0.87 inference(unit_resolution,[status(thm)],[792, 3238])).
% 0.63/0.87 tff(3240,plain,
% 0.63/0.87 (~r(s(s(s(s(z)))), z)),
% 0.63/0.87 inference(unit_resolution,[status(thm)],[2712, 3239, 3021])).
% 0.63/0.87 tff(3241,plain,
% 0.63/0.87 (b(s(s(s(s(z)))), z)),
% 0.63/0.87 inference(unit_resolution,[status(thm)],[859, 3240])).
% 0.63/0.87 tff(3242,assumption,(b(s(s(s(s(z)))), z)), introduced(assumption)).
% 0.63/0.87 tff(3243,plain,
% 0.63/0.87 (~b(s(s(s(s(z)))), s(z))),
% 0.63/0.87 inference(unit_resolution,[status(thm)],[866, 188, 360, 776, 3242])).
% 0.63/0.87 tff(3244,assumption,(~r(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 0.63/0.87 tff(3245,plain,
% 0.63/0.87 ((s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z))),
% 0.63/0.87 inference(unit_resolution,[status(thm)],[874, 79, 3244])).
% 0.63/0.87 tff(3246,plain,
% 0.63/0.87 ($false),
% 0.63/0.87 inference(unit_resolution,[status(thm)],[3245, 3243, 844])).
% 0.63/0.87 tff(3247,plain,(r(s(s(s(s(z)))), s(z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.87 tff(3248,plain,
% 0.63/0.87 (r(s(s(s(s(z)))), s(z))),
% 0.63/0.87 inference(unit_resolution,[status(thm)],[3247, 3233, 3092, 3241])).
% 0.63/0.87 tff(3249,plain,
% 0.63/0.87 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 0.63/0.87 inference(rewrite,[status(thm)],[])).
% 0.63/0.87 tff(3250,plain,
% 0.63/0.87 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 0.63/0.87 inference(quant_inst,[status(thm)],[])).
% 0.63/0.87 tff(3251,plain,
% 0.63/0.87 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 0.63/0.87 inference(modus_ponens,[status(thm)],[3250, 3249])).
% 0.63/0.87 tff(3252,plain,
% 0.63/0.87 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 0.63/0.87 inference(unit_resolution,[status(thm)],[3251, 14, 3235, 3248])).
% 0.63/0.87 tff(3253,plain,
% 0.63/0.87 (b(s(s(s(s(z)))), s(s(s(z))))),
% 0.63/0.87 inference(unit_resolution,[status(thm)],[890, 3252])).
% 0.63/0.87 tff(3254,plain,
% 0.63/0.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 0.63/0.87 inference(rewrite,[status(thm)],[])).
% 0.63/0.87 tff(3255,plain,
% 0.63/0.87 (((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 0.63/0.88 inference(rewrite,[status(thm)],[])).
% 0.63/0.88 tff(3256,plain,
% 0.63/0.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 0.63/0.88 inference(monotonicity,[status(thm)],[3255])).
% 0.63/0.88 tff(3257,plain,
% 0.63/0.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 0.63/0.88 inference(transitivity,[status(thm)],[3256, 3254])).
% 0.63/0.88 tff(3258,plain,
% 0.63/0.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 0.63/0.88 inference(quant_inst,[status(thm)],[])).
% 0.63/0.88 tff(3259,plain,
% 0.63/0.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 0.63/0.88 inference(modus_ponens,[status(thm)],[3258, 3257])).
% 0.63/0.88 tff(3260,plain,
% 0.63/0.88 ((~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 0.63/0.88 inference(unit_resolution,[status(thm)],[3259, 188, 2979, 259, 3241])).
% 0.63/0.88 tff(3261,plain,
% 0.63/0.88 (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.63/0.88 inference(unit_resolution,[status(thm)],[3260, 3253])).
% 0.63/0.88 tff(3262,plain,
% 0.63/0.88 (~r(s(s(z)), s(z))),
% 0.63/0.88 inference(unit_resolution,[status(thm)],[1124, 3235, 3185])).
% 0.63/0.88 tff(3263,plain,
% 0.63/0.88 (b(s(s(z)), s(z))),
% 0.63/0.88 inference(unit_resolution,[status(thm)],[137, 3262])).
% 0.63/0.88 tff(3264,plain,
% 0.63/0.88 (~r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.63/0.88 inference(unit_resolution,[status(thm)],[1977, 3239, 3021])).
% 0.63/0.88 tff(3265,plain,
% 0.63/0.88 (b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.63/0.88 inference(unit_resolution,[status(thm)],[1224, 3264])).
% 0.63/0.88 tff(3266,plain,
% 0.63/0.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), s(z))))),
% 0.63/0.88 inference(rewrite,[status(thm)],[])).
% 0.63/0.88 tff(3267,plain,
% 0.63/0.88 (((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), s(z))))),
% 0.63/0.88 inference(rewrite,[status(thm)],[])).
% 0.63/0.88 tff(3268,plain,
% 0.63/0.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), s(z)))))),
% 0.63/0.88 inference(monotonicity,[status(thm)],[3267])).
% 0.63/0.88 tff(3269,plain,
% 0.63/0.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), s(z))))),
% 0.63/0.88 inference(transitivity,[status(thm)],[3268, 3266])).
% 0.63/0.88 tff(3270,plain,
% 0.63/0.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 0.63/0.88 inference(quant_inst,[status(thm)],[])).
% 0.63/0.88 tff(3271,plain,
% 0.63/0.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X2, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), s(z)))),
% 0.63/0.88 inference(modus_ponens,[status(thm)],[3270, 3269])).
% 0.63/0.88 tff(3272,plain,
% 0.63/0.88 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 0.63/0.88 inference(unit_resolution,[status(thm)],[3271, 188, 3229, 259, 3265, 3263])).
% 0.63/0.88 tff(3273,plain,
% 0.63/0.88 (r(s(s(s(s(s(s(z)))))), s(z))),
% 0.63/0.88 inference(unit_resolution,[status(thm)],[627, 3272])).
% 0.63/0.88 tff(3274,plain,
% 0.63/0.88 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(z))))),
% 0.63/0.88 inference(rewrite,[status(thm)],[])).
% 0.63/0.88 tff(3275,plain,
% 0.63/0.88 (((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(z))))),
% 0.63/0.88 inference(rewrite,[status(thm)],[])).
% 0.63/0.88 tff(3276,plain,
% 0.63/0.88 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(z)))))),
% 0.63/0.88 inference(monotonicity,[status(thm)],[3275])).
% 0.63/0.88 tff(3277,plain,
% 0.63/0.88 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(z))))),
% 0.63/0.88 inference(transitivity,[status(thm)],[3276, 3274])).
% 0.63/0.88 tff(3278,plain,
% 0.63/0.88 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 0.63/0.88 inference(quant_inst,[status(thm)],[])).
% 0.63/0.88 tff(3279,plain,
% 0.63/0.88 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(z)))), s(z)))),
% 0.63/0.88 inference(modus_ponens,[status(thm)],[3278, 3277])).
% 0.63/0.88 tff(3280,plain,
% 0.63/0.88 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.63/0.88 inference(unit_resolution,[status(thm)],[3279, 14, 3273, 3248])).
% 0.63/0.88 tff(3281,plain,
% 0.63/0.88 ($false),
% 0.63/0.88 inference(unit_resolution,[status(thm)],[927, 79, 924, 3280, 3261])).
% 0.63/0.88 tff(3282,plain,((~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.88 tff(3283,plain,
% 0.63/0.88 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.63/0.88 inference(unit_resolution,[status(thm)],[3282, 1])).
% 0.63/0.88 tff(3284,plain,
% 0.63/0.88 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.63/0.88 inference(unit_resolution,[status(thm)],[243, 3283])).
% 0.63/0.88 tff(3285,plain,
% 0.63/0.88 (~r(z, s(s(s(z))))),
% 0.63/0.88 inference(unit_resolution,[status(thm)],[1112, 3284, 1])).
% 0.63/0.88 tff(3286,plain,
% 0.63/0.88 (b(z, s(s(s(z))))),
% 0.63/0.88 inference(unit_resolution,[status(thm)],[281, 3285])).
% 0.63/0.88 tff(3287,plain,
% 0.63/0.88 (~r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.63/0.88 inference(unit_resolution,[status(thm)],[1832, 14, 3284, 3185])).
% 0.63/0.88 tff(3288,plain,
% 0.63/0.88 (b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.63/0.88 inference(unit_resolution,[status(thm)],[1224, 3287])).
% 0.63/0.88 tff(3289,plain,
% 0.63/0.88 (~b(s(s(s(z))), s(s(z)))),
% 0.63/0.88 inference(unit_resolution,[status(thm)],[1855, 188, 2454, 2870, 3288])).
% 0.63/0.88 tff(3290,plain,
% 0.63/0.88 (r(s(s(s(z))), s(s(z)))),
% 0.63/0.88 inference(unit_resolution,[status(thm)],[476, 3289])).
% 0.63/0.88 tff(3291,plain,
% 0.63/0.88 ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 0.63/0.88 inference(unit_resolution,[status(thm)],[2011, 2454])).
% 0.63/0.88 tff(3292,plain,
% 0.63/0.88 (~r(s(z), s(s(s(z))))),
% 0.63/0.88 inference(unit_resolution,[status(thm)],[3291, 3290, 2870, 3284])).
% 0.63/0.88 tff(3293,plain,
% 0.63/0.88 (b(s(z), s(s(s(z))))),
% 0.63/0.88 inference(unit_resolution,[status(thm)],[177, 3292])).
% 0.63/0.88 tff(3294,plain,
% 0.63/0.88 ($false),
% 0.63/0.88 inference(unit_resolution,[status(thm)],[2605, 188, 3092, 3293, 2979, 3286])).
% 0.63/0.88 tff(3295,plain,(~r(z, s(s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.88 tff(3296,plain,
% 0.63/0.88 (b(z, s(s(s(s(s(s(z)))))))),
% 0.63/0.88 inference(unit_resolution,[status(thm)],[256, 3295])).
% 0.63/0.88 tff(3297,plain,
% 0.63/0.88 (~r(s(s(s(s(s(s(z)))))), z)),
% 0.63/0.88 inference(unit_resolution,[status(thm)],[2323, 3296, 2870])).
% 0.63/0.88 tff(3298,plain,
% 0.63/0.88 (b(s(s(s(s(s(s(z)))))), z)),
% 0.63/0.88 inference(unit_resolution,[status(thm)],[492, 3297])).
% 0.63/0.88 tff(3299,plain,
% 0.63/0.88 (~b(s(s(z)), z)),
% 0.63/0.88 inference(unit_resolution,[status(thm)],[2739, 3298, 3296])).
% 0.63/0.88 tff(3300,plain,
% 0.63/0.88 (r(s(s(z)), z)),
% 0.63/0.88 inference(unit_resolution,[status(thm)],[792, 3299])).
% 0.63/0.88 tff(3301,plain,
% 0.63/0.88 (~b(s(s(s(z))), z)),
% 0.63/0.88 inference(unit_resolution,[status(thm)],[945, 188, 3296, 2870, 3298])).
% 0.63/0.88 tff(3302,plain,
% 0.63/0.88 (r(s(s(s(z))), z)),
% 0.63/0.88 inference(unit_resolution,[status(thm)],[326, 3301])).
% 0.63/0.88 tff(3303,plain,
% 0.63/0.88 (~r(s(s(s(z))), s(s(z)))),
% 0.63/0.88 inference(unit_resolution,[status(thm)],[463, 14, 3302, 3300])).
% 0.63/0.88 tff(3304,plain,
% 0.63/0.88 (b(s(s(s(z))), s(s(z)))),
% 0.63/0.88 inference(unit_resolution,[status(thm)],[476, 3303])).
% 0.63/0.88 tff(3305,plain,
% 0.63/0.88 (~r(s(s(z)), s(s(s(z))))),
% 0.63/0.88 inference(unit_resolution,[status(thm)],[535, 3302, 3300])).
% 0.63/0.88 tff(3306,plain,
% 0.63/0.88 (b(s(s(z)), s(s(s(z))))),
% 0.63/0.88 inference(unit_resolution,[status(thm)],[425, 3305])).
% 0.63/0.88 tff(3307,plain,
% 0.63/0.88 ((~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))) | (~b(s(s(s(s(s(s(z)))))), z))),
% 0.63/0.88 inference(unit_resolution,[status(thm)],[447, 2454])).
% 0.63/0.88 tff(3308,plain,
% 0.63/0.88 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.63/0.88 inference(unit_resolution,[status(thm)],[3307, 3298, 2870, 3296])).
% 0.63/0.88 tff(3309,plain,
% 0.63/0.88 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.63/0.88 inference(unit_resolution,[status(thm)],[243, 3308])).
% 0.63/0.88 tff(3310,plain,
% 0.63/0.88 (~r(s(z), z)),
% 0.63/0.88 inference(unit_resolution,[status(thm)],[1345, 3302, 3300])).
% 0.63/0.88 tff(3311,plain,
% 0.63/0.88 (b(s(z), z)),
% 0.63/0.88 inference(unit_resolution,[status(thm)],[312, 3310])).
% 0.63/0.88 tff(3312,plain,
% 0.63/0.88 (~r(s(s(s(z))), s(z))),
% 0.63/0.88 inference(unit_resolution,[status(thm)],[2880, 3311, 3298, 3309, 3302])).
% 0.63/0.88 tff(3313,plain,
% 0.63/0.88 (b(s(s(s(z))), s(z))),
% 0.63/0.88 inference(unit_resolution,[status(thm)],[170, 3312])).
% 0.63/0.88 tff(3314,plain,
% 0.63/0.88 (~b(s(z), s(s(s(s(s(s(z)))))))),
% 0.63/0.88 inference(unit_resolution,[status(thm)],[1052, 3311, 3296, 3298])).
% 0.63/0.88 tff(3315,plain,
% 0.63/0.88 (r(s(z), s(s(s(s(s(s(z)))))))),
% 0.63/0.88 inference(unit_resolution,[status(thm)],[84, 3314])).
% 0.63/0.88 tff(3316,plain,
% 0.63/0.88 (~r(s(z), s(s(s(z))))),
% 0.63/0.88 inference(unit_resolution,[status(thm)],[230, 3315, 3309])).
% 0.63/0.88 tff(3317,plain,
% 0.63/0.88 (b(s(z), s(s(s(z))))),
% 0.63/0.88 inference(unit_resolution,[status(thm)],[177, 3316])).
% 0.63/0.88 tff(3318,plain,
% 0.63/0.88 (~b(s(s(z)), s(z))),
% 0.63/0.88 inference(unit_resolution,[status(thm)],[958, 3317, 3313, 3306])).
% 0.63/0.88 tff(3319,plain,
% 0.63/0.88 (r(s(s(z)), s(z))),
% 0.63/0.88 inference(unit_resolution,[status(thm)],[137, 3318])).
% 0.63/0.88 tff(3320,plain,
% 0.63/0.88 (~r(z, s(z))),
% 0.63/0.88 inference(unit_resolution,[status(thm)],[2039, 3319, 3300])).
% 0.63/0.88 tff(3321,plain,
% 0.63/0.88 (b(z, s(z))),
% 0.63/0.88 inference(unit_resolution,[status(thm)],[300, 3320])).
% 0.63/0.88 tff(3322,plain,
% 0.63/0.88 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 0.63/0.88 inference(unit_resolution,[status(thm)],[982, 188, 3311, 3321, 3298])).
% 0.63/0.88 tff(3323,plain,
% 0.63/0.88 (r(s(s(s(s(s(s(z)))))), s(z))),
% 0.63/0.88 inference(unit_resolution,[status(thm)],[627, 3322])).
% 0.63/0.88 tff(3324,plain,
% 0.63/0.88 (~r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.63/0.88 inference(unit_resolution,[status(thm)],[2239, 14, 3323, 3319])).
% 0.63/0.88 tff(3325,plain,
% 0.63/0.88 (b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.63/0.88 inference(unit_resolution,[status(thm)],[1224, 3324])).
% 0.63/0.88 tff(3326,plain,
% 0.63/0.88 ($false),
% 0.63/0.88 inference(unit_resolution,[status(thm)],[1855, 188, 2454, 2870, 3325, 3304])).
% 0.63/0.88 % SZS output end Proof
% 0.63/0.88 % E exiting
%------------------------------------------------------------------------------