%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUN066+2 : TPTP v9.0.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 : Sat Jun 21 05:22:36 AM UTC 2025
% Result : Theorem 0.19s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUN066+2 : TPTP v9.0.0. Released v7.3.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 02:10:25 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.38 % SZS status Theorem
% 0.19/0.38 % SZS output start Proof
% 0.19/0.38 tff(r2_type, type, (
% 0.19/0.38 r2: ( $i * $i ) > $o)).
% 0.19/0.38 tff(tptp_fun_Y21_1_type, type, (
% 0.19/0.38 tptp_fun_Y21_1: $i > $i)).
% 0.19/0.38 tff(tptp_fun_Y24_0_type, type, (
% 0.19/0.38 tptp_fun_Y24_0: $i)).
% 0.19/0.38 tff(tptp_fun_Y22_2_type, type, (
% 0.19/0.38 tptp_fun_Y22_2: ( $i * $i ) > $i)).
% 0.19/0.38 tff(tptp_fun_Y16_10_type, type, (
% 0.19/0.38 tptp_fun_Y16_10: $i > $i)).
% 0.19/0.38 tff(r3_type, type, (
% 0.19/0.38 r3: ( $i * $i * $i ) > $o)).
% 0.19/0.38 tff(r1_type, type, (
% 0.19/0.38 r1: $i > $o)).
% 0.19/0.38 tff(tptp_fun_Y3_14_type, type, (
% 0.19/0.38 tptp_fun_Y3_14: $i > $i)).
% 0.19/0.38 tff(tptp_fun_Y4_15_type, type, (
% 0.19/0.38 tptp_fun_Y4_15: $i > $i)).
% 0.19/0.38 tff(1,plain,
% 0.19/0.38 (^[X4: $i] : rewrite((r1(tptp_fun_Y16_10(X4)) & r3(X4, tptp_fun_Y16_10(X4), X4)) <=> (~((~r1(tptp_fun_Y16_10(X4))) | (~r3(X4, tptp_fun_Y16_10(X4), X4)))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(2,plain,
% 0.19/0.38 (![X4: $i] : (r1(tptp_fun_Y16_10(X4)) & r3(X4, tptp_fun_Y16_10(X4), X4)) <=> ![X4: $i] : (~((~r1(tptp_fun_Y16_10(X4))) | (~r3(X4, tptp_fun_Y16_10(X4), X4))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.38 tff(3,plain,
% 0.19/0.38 (![X4: $i] : ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4)) <=> ![X4: $i] : ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(4,plain,
% 0.19/0.38 (^[X4: $i] : trans(der(?[Y9: $i] : (?[Y16: $i] : (r1(Y16) & r3(X4, Y16, Y9)) & (Y9 = X4)) <=> ?[Y9: $i] : ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4))), elim_unused(?[Y9: $i] : ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4)) <=> ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4))), (?[Y9: $i] : (?[Y16: $i] : (r1(Y16) & r3(X4, Y16, Y9)) & (Y9 = X4)) <=> ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(5,plain,
% 0.19/0.38 (![X4: $i] : ?[Y9: $i] : (?[Y16: $i] : (r1(Y16) & r3(X4, Y16, Y9)) & (Y9 = X4)) <=> ![X4: $i] : ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[4])).
% 0.19/0.38 tff(6,axiom,(![X4: $i] : ?[Y9: $i] : (?[Y16: $i] : (r1(Y16) & r3(X4, Y16, Y9)) & (Y9 = X4))), file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax','axiom_4a')).
% 0.19/0.38 tff(7,plain,
% 0.19/0.38 (![X4: $i] : ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.19/0.38 tff(8,plain,
% 0.19/0.38 (![X4: $i] : ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.19/0.38 tff(9,plain,(
% 0.19/0.38 ![X4: $i] : (r1(tptp_fun_Y16_10(X4)) & r3(X4, tptp_fun_Y16_10(X4), X4))),
% 0.19/0.38 inference(skolemize,[status(sab)],[8])).
% 0.19/0.38 tff(10,plain,
% 0.19/0.38 (![X4: $i] : (~((~r1(tptp_fun_Y16_10(X4))) | (~r3(X4, tptp_fun_Y16_10(X4), X4))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.19/0.38 tff(11,plain,
% 0.19/0.38 ((~![X4: $i] : (~((~r1(tptp_fun_Y16_10(X4))) | (~r3(X4, tptp_fun_Y16_10(X4), X4))))) | (~((~r1(tptp_fun_Y16_10(Y24!0))) | (~r3(Y24!0, tptp_fun_Y16_10(Y24!0), Y24!0))))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(12,plain,
% 0.19/0.38 (~((~r1(tptp_fun_Y16_10(Y24!0))) | (~r3(Y24!0, tptp_fun_Y16_10(Y24!0), Y24!0)))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.19/0.38 tff(13,plain,
% 0.19/0.38 (((~r1(tptp_fun_Y16_10(Y24!0))) | (~r3(Y24!0, tptp_fun_Y16_10(Y24!0), Y24!0))) | r3(Y24!0, tptp_fun_Y16_10(Y24!0), Y24!0)),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(14,plain,
% 0.19/0.38 (r3(Y24!0, tptp_fun_Y16_10(Y24!0), Y24!0)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[13, 12])).
% 0.19/0.38 tff(15,plain,
% 0.19/0.38 ((r3(Y24!0, tptp_fun_Y16_10(Y24!0), Y24!0) | (Y24!0 = tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0))) | (~r3(Y24!0, tptp_fun_Y16_10(Y24!0), Y24!0))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(16,plain,
% 0.19/0.38 (r3(Y24!0, tptp_fun_Y16_10(Y24!0), Y24!0) | (Y24!0 = tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[15, 14])).
% 0.19/0.38 tff(17,plain,
% 0.19/0.38 (^[X13: $i, X14: $i, X15: $i] : refl(((~(r3(X13, X14, X15) | (X15 = tptp_fun_Y22_2(X14, X13)))) | (~((~r3(X13, X14, X15)) | (~(X15 = tptp_fun_Y22_2(X14, X13)))))) <=> ((~(r3(X13, X14, X15) | (X15 = tptp_fun_Y22_2(X14, X13)))) | (~((~r3(X13, X14, X15)) | (~(X15 = tptp_fun_Y22_2(X14, X13)))))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(18,plain,
% 0.19/0.38 (![X13: $i, X14: $i, X15: $i] : ((~(r3(X13, X14, X15) | (X15 = tptp_fun_Y22_2(X14, X13)))) | (~((~r3(X13, X14, X15)) | (~(X15 = tptp_fun_Y22_2(X14, X13)))))) <=> ![X13: $i, X14: $i, X15: $i] : ((~(r3(X13, X14, X15) | (X15 = tptp_fun_Y22_2(X14, X13)))) | (~((~r3(X13, X14, X15)) | (~(X15 = tptp_fun_Y22_2(X14, X13))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[17])).
% 0.19/0.39 tff(19,plain,
% 0.19/0.39 (^[X13: $i, X14: $i, X15: $i] : rewrite((((~r3(X13, X14, X15)) & (~(X15 = tptp_fun_Y22_2(X14, X13)))) | (r3(X13, X14, X15) & (X15 = tptp_fun_Y22_2(X14, X13)))) <=> ((~(r3(X13, X14, X15) | (X15 = tptp_fun_Y22_2(X14, X13)))) | (~((~r3(X13, X14, X15)) | (~(X15 = tptp_fun_Y22_2(X14, X13)))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(20,plain,
% 0.19/0.39 (![X13: $i, X14: $i, X15: $i] : (((~r3(X13, X14, X15)) & (~(X15 = tptp_fun_Y22_2(X14, X13)))) | (r3(X13, X14, X15) & (X15 = tptp_fun_Y22_2(X14, X13)))) <=> ![X13: $i, X14: $i, X15: $i] : ((~(r3(X13, X14, X15) | (X15 = tptp_fun_Y22_2(X14, X13)))) | (~((~r3(X13, X14, X15)) | (~(X15 = tptp_fun_Y22_2(X14, X13))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[19])).
% 0.19/0.39 tff(21,plain,
% 0.19/0.39 (![X13: $i, X14: $i] : ![X15: $i] : (((~r3(X13, X14, X15)) & (~(X15 = tptp_fun_Y22_2(X14, X13)))) | (r3(X13, X14, X15) & (X15 = tptp_fun_Y22_2(X14, X13)))) <=> ![X13: $i, X14: $i, X15: $i] : (((~r3(X13, X14, X15)) & (~(X15 = tptp_fun_Y22_2(X14, X13)))) | (r3(X13, X14, X15) & (X15 = tptp_fun_Y22_2(X14, X13))))),
% 0.19/0.39 inference(pull_quant,[status(thm)],[])).
% 0.19/0.39 tff(22,plain,
% 0.19/0.39 (![X13: $i, X14: $i] : ?[Y22: $i] : ![X15: $i] : (((~r3(X13, X14, X15)) & (~(X15 = Y22))) | (r3(X13, X14, X15) & (X15 = Y22))) <=> ![X13: $i, X14: $i] : ?[Y22: $i] : ![X15: $i] : (((~r3(X13, X14, X15)) & (~(X15 = Y22))) | (r3(X13, X14, X15) & (X15 = Y22)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(23,axiom,(![X13: $i, X14: $i] : ?[Y22: $i] : ![X15: $i] : (((~r3(X13, X14, X15)) & (~(X15 = Y22))) | (r3(X13, X14, X15) & (X15 = Y22)))), file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax','axiom_3')).
% 0.19/0.39 tff(24,plain,
% 0.19/0.39 (![X13: $i, X14: $i] : ?[Y22: $i] : ![X15: $i] : (((~r3(X13, X14, X15)) & (~(X15 = Y22))) | (r3(X13, X14, X15) & (X15 = Y22)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.19/0.39 tff(25,plain,(
% 0.19/0.39 ![X13: $i, X14: $i] : ![X15: $i] : (((~r3(X13, X14, X15)) & (~(X15 = tptp_fun_Y22_2(X14, X13)))) | (r3(X13, X14, X15) & (X15 = tptp_fun_Y22_2(X14, X13))))),
% 0.19/0.39 inference(skolemize,[status(sab)],[24])).
% 0.19/0.39 tff(26,plain,
% 0.19/0.39 (![X13: $i, X14: $i, X15: $i] : (((~r3(X13, X14, X15)) & (~(X15 = tptp_fun_Y22_2(X14, X13)))) | (r3(X13, X14, X15) & (X15 = tptp_fun_Y22_2(X14, X13))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.19/0.39 tff(27,plain,
% 0.19/0.39 (![X13: $i, X14: $i, X15: $i] : ((~(r3(X13, X14, X15) | (X15 = tptp_fun_Y22_2(X14, X13)))) | (~((~r3(X13, X14, X15)) | (~(X15 = tptp_fun_Y22_2(X14, X13))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[26, 20])).
% 0.19/0.39 tff(28,plain,
% 0.19/0.39 (![X13: $i, X14: $i, X15: $i] : ((~(r3(X13, X14, X15) | (X15 = tptp_fun_Y22_2(X14, X13)))) | (~((~r3(X13, X14, X15)) | (~(X15 = tptp_fun_Y22_2(X14, X13))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[27, 18])).
% 0.19/0.39 tff(29,plain,
% 0.19/0.39 (((~![X13: $i, X14: $i, X15: $i] : ((~(r3(X13, X14, X15) | (X15 = tptp_fun_Y22_2(X14, X13)))) | (~((~r3(X13, X14, X15)) | (~(X15 = tptp_fun_Y22_2(X14, X13))))))) | ((~(r3(Y24!0, tptp_fun_Y16_10(Y24!0), Y24!0) | (Y24!0 = tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))) | (~((~r3(Y24!0, tptp_fun_Y16_10(Y24!0), Y24!0)) | (~(Y24!0 = tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0))))))) <=> ((~![X13: $i, X14: $i, X15: $i] : ((~(r3(X13, X14, X15) | (X15 = tptp_fun_Y22_2(X14, X13)))) | (~((~r3(X13, X14, X15)) | (~(X15 = tptp_fun_Y22_2(X14, X13))))))) | (~(r3(Y24!0, tptp_fun_Y16_10(Y24!0), Y24!0) | (Y24!0 = tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))) | (~((~r3(Y24!0, tptp_fun_Y16_10(Y24!0), Y24!0)) | (~(Y24!0 = tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0))))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(30,plain,
% 0.19/0.39 ((~![X13: $i, X14: $i, X15: $i] : ((~(r3(X13, X14, X15) | (X15 = tptp_fun_Y22_2(X14, X13)))) | (~((~r3(X13, X14, X15)) | (~(X15 = tptp_fun_Y22_2(X14, X13))))))) | ((~(r3(Y24!0, tptp_fun_Y16_10(Y24!0), Y24!0) | (Y24!0 = tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))) | (~((~r3(Y24!0, tptp_fun_Y16_10(Y24!0), Y24!0)) | (~(Y24!0 = tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0))))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(31,plain,
% 0.19/0.39 ((~![X13: $i, X14: $i, X15: $i] : ((~(r3(X13, X14, X15) | (X15 = tptp_fun_Y22_2(X14, X13)))) | (~((~r3(X13, X14, X15)) | (~(X15 = tptp_fun_Y22_2(X14, X13))))))) | (~(r3(Y24!0, tptp_fun_Y16_10(Y24!0), Y24!0) | (Y24!0 = tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))) | (~((~r3(Y24!0, tptp_fun_Y16_10(Y24!0), Y24!0)) | (~(Y24!0 = tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.19/0.39 tff(32,plain,
% 0.19/0.39 (~((~r3(Y24!0, tptp_fun_Y16_10(Y24!0), Y24!0)) | (~(Y24!0 = tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[31, 28, 16])).
% 0.19/0.39 tff(33,plain,
% 0.19/0.39 (((~r3(Y24!0, tptp_fun_Y16_10(Y24!0), Y24!0)) | (~(Y24!0 = tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))) | (Y24!0 = tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(34,plain,
% 0.19/0.39 (Y24!0 = tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.19/0.39 tff(35,plain,
% 0.19/0.39 (tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0) = Y24!0),
% 0.19/0.39 inference(symmetry,[status(thm)],[34])).
% 0.19/0.39 tff(36,plain,
% 0.19/0.39 (r2(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) <=> r2(Y24!0, tptp_fun_Y21_1(Y24!0))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[35])).
% 0.19/0.39 tff(37,plain,
% 0.19/0.39 (r2(Y24!0, tptp_fun_Y21_1(Y24!0)) <=> r2(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))),
% 0.19/0.39 inference(symmetry,[status(thm)],[36])).
% 0.19/0.39 tff(38,plain,
% 0.19/0.39 (^[X11: $i, X12: $i] : refl(((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11)))))) <=> ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11)))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(39,plain,
% 0.19/0.39 (![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11)))))) <=> ![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[38])).
% 0.19/0.39 tff(40,plain,
% 0.19/0.39 (^[X11: $i, X12: $i] : rewrite((((~r2(X11, X12)) & (~(X12 = tptp_fun_Y21_1(X11)))) | (r2(X11, X12) & (X12 = tptp_fun_Y21_1(X11)))) <=> ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11)))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(41,plain,
% 0.19/0.39 (![X11: $i, X12: $i] : (((~r2(X11, X12)) & (~(X12 = tptp_fun_Y21_1(X11)))) | (r2(X11, X12) & (X12 = tptp_fun_Y21_1(X11)))) <=> ![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[40])).
% 0.19/0.39 tff(42,plain,
% 0.19/0.39 (![X11: $i] : ![X12: $i] : (((~r2(X11, X12)) & (~(X12 = tptp_fun_Y21_1(X11)))) | (r2(X11, X12) & (X12 = tptp_fun_Y21_1(X11)))) <=> ![X11: $i, X12: $i] : (((~r2(X11, X12)) & (~(X12 = tptp_fun_Y21_1(X11)))) | (r2(X11, X12) & (X12 = tptp_fun_Y21_1(X11))))),
% 0.19/0.39 inference(pull_quant,[status(thm)],[])).
% 0.19/0.39 tff(43,plain,
% 0.19/0.39 (![X11: $i] : ?[Y21: $i] : ![X12: $i] : (((~r2(X11, X12)) & (~(X12 = Y21))) | (r2(X11, X12) & (X12 = Y21))) <=> ![X11: $i] : ?[Y21: $i] : ![X12: $i] : (((~r2(X11, X12)) & (~(X12 = Y21))) | (r2(X11, X12) & (X12 = Y21)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(44,axiom,(![X11: $i] : ?[Y21: $i] : ![X12: $i] : (((~r2(X11, X12)) & (~(X12 = Y21))) | (r2(X11, X12) & (X12 = Y21)))), file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax','axiom_2')).
% 0.19/0.39 tff(45,plain,
% 0.19/0.39 (![X11: $i] : ?[Y21: $i] : ![X12: $i] : (((~r2(X11, X12)) & (~(X12 = Y21))) | (r2(X11, X12) & (X12 = Y21)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.19/0.39 tff(46,plain,(
% 0.19/0.39 ![X11: $i] : ![X12: $i] : (((~r2(X11, X12)) & (~(X12 = tptp_fun_Y21_1(X11)))) | (r2(X11, X12) & (X12 = tptp_fun_Y21_1(X11))))),
% 0.19/0.39 inference(skolemize,[status(sab)],[45])).
% 0.19/0.39 tff(47,plain,
% 0.19/0.39 (![X11: $i, X12: $i] : (((~r2(X11, X12)) & (~(X12 = tptp_fun_Y21_1(X11)))) | (r2(X11, X12) & (X12 = tptp_fun_Y21_1(X11))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.19/0.39 tff(48,plain,
% 0.19/0.39 (![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[47, 41])).
% 0.19/0.39 tff(49,plain,
% 0.19/0.39 (![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[48, 39])).
% 0.19/0.39 tff(50,plain,
% 0.19/0.39 (((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | r2(Y24!0, tptp_fun_Y21_1(Y24!0))) <=> ((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | r2(Y24!0, tptp_fun_Y21_1(Y24!0)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(51,plain,
% 0.19/0.39 (($false | r2(Y24!0, tptp_fun_Y21_1(Y24!0))) <=> r2(Y24!0, tptp_fun_Y21_1(Y24!0))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(52,plain,
% 0.19/0.39 ((~(~r2(Y24!0, tptp_fun_Y21_1(Y24!0)))) <=> r2(Y24!0, tptp_fun_Y21_1(Y24!0))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(53,plain,
% 0.19/0.39 (((~r2(Y24!0, tptp_fun_Y21_1(Y24!0))) | $false) <=> (~r2(Y24!0, tptp_fun_Y21_1(Y24!0)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(54,plain,
% 0.19/0.39 ((~$true) <=> $false),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(55,plain,
% 0.19/0.39 ((tptp_fun_Y21_1(Y24!0) = tptp_fun_Y21_1(Y24!0)) <=> $true),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(56,plain,
% 0.19/0.39 ((~(tptp_fun_Y21_1(Y24!0) = tptp_fun_Y21_1(Y24!0))) <=> (~$true)),
% 0.19/0.39 inference(monotonicity,[status(thm)],[55])).
% 0.19/0.39 tff(57,plain,
% 0.19/0.39 ((~(tptp_fun_Y21_1(Y24!0) = tptp_fun_Y21_1(Y24!0))) <=> $false),
% 0.19/0.39 inference(transitivity,[status(thm)],[56, 54])).
% 0.19/0.39 tff(58,plain,
% 0.19/0.39 (((~r2(Y24!0, tptp_fun_Y21_1(Y24!0))) | (~(tptp_fun_Y21_1(Y24!0) = tptp_fun_Y21_1(Y24!0)))) <=> ((~r2(Y24!0, tptp_fun_Y21_1(Y24!0))) | $false)),
% 0.19/0.39 inference(monotonicity,[status(thm)],[57])).
% 0.19/0.39 tff(59,plain,
% 0.19/0.39 (((~r2(Y24!0, tptp_fun_Y21_1(Y24!0))) | (~(tptp_fun_Y21_1(Y24!0) = tptp_fun_Y21_1(Y24!0)))) <=> (~r2(Y24!0, tptp_fun_Y21_1(Y24!0)))),
% 0.19/0.39 inference(transitivity,[status(thm)],[58, 53])).
% 0.19/0.39 tff(60,plain,
% 0.19/0.39 ((~((~r2(Y24!0, tptp_fun_Y21_1(Y24!0))) | (~(tptp_fun_Y21_1(Y24!0) = tptp_fun_Y21_1(Y24!0))))) <=> (~(~r2(Y24!0, tptp_fun_Y21_1(Y24!0))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[59])).
% 0.19/0.39 tff(61,plain,
% 0.19/0.39 ((~((~r2(Y24!0, tptp_fun_Y21_1(Y24!0))) | (~(tptp_fun_Y21_1(Y24!0) = tptp_fun_Y21_1(Y24!0))))) <=> r2(Y24!0, tptp_fun_Y21_1(Y24!0))),
% 0.19/0.39 inference(transitivity,[status(thm)],[60, 52])).
% 0.19/0.39 tff(62,plain,
% 0.19/0.39 ((r2(Y24!0, tptp_fun_Y21_1(Y24!0)) | $true) <=> $true),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(63,plain,
% 0.19/0.39 ((r2(Y24!0, tptp_fun_Y21_1(Y24!0)) | (tptp_fun_Y21_1(Y24!0) = tptp_fun_Y21_1(Y24!0))) <=> (r2(Y24!0, tptp_fun_Y21_1(Y24!0)) | $true)),
% 0.19/0.39 inference(monotonicity,[status(thm)],[55])).
% 0.19/0.39 tff(64,plain,
% 0.19/0.39 ((r2(Y24!0, tptp_fun_Y21_1(Y24!0)) | (tptp_fun_Y21_1(Y24!0) = tptp_fun_Y21_1(Y24!0))) <=> $true),
% 0.19/0.39 inference(transitivity,[status(thm)],[63, 62])).
% 0.19/0.39 tff(65,plain,
% 0.19/0.39 ((~(r2(Y24!0, tptp_fun_Y21_1(Y24!0)) | (tptp_fun_Y21_1(Y24!0) = tptp_fun_Y21_1(Y24!0)))) <=> (~$true)),
% 0.19/0.39 inference(monotonicity,[status(thm)],[64])).
% 0.19/0.39 tff(66,plain,
% 0.19/0.39 ((~(r2(Y24!0, tptp_fun_Y21_1(Y24!0)) | (tptp_fun_Y21_1(Y24!0) = tptp_fun_Y21_1(Y24!0)))) <=> $false),
% 0.19/0.39 inference(transitivity,[status(thm)],[65, 54])).
% 0.19/0.39 tff(67,plain,
% 0.19/0.39 (((~(r2(Y24!0, tptp_fun_Y21_1(Y24!0)) | (tptp_fun_Y21_1(Y24!0) = tptp_fun_Y21_1(Y24!0)))) | (~((~r2(Y24!0, tptp_fun_Y21_1(Y24!0))) | (~(tptp_fun_Y21_1(Y24!0) = tptp_fun_Y21_1(Y24!0)))))) <=> ($false | r2(Y24!0, tptp_fun_Y21_1(Y24!0)))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[66, 61])).
% 0.19/0.39 tff(68,plain,
% 0.19/0.39 (((~(r2(Y24!0, tptp_fun_Y21_1(Y24!0)) | (tptp_fun_Y21_1(Y24!0) = tptp_fun_Y21_1(Y24!0)))) | (~((~r2(Y24!0, tptp_fun_Y21_1(Y24!0))) | (~(tptp_fun_Y21_1(Y24!0) = tptp_fun_Y21_1(Y24!0)))))) <=> r2(Y24!0, tptp_fun_Y21_1(Y24!0))),
% 0.19/0.39 inference(transitivity,[status(thm)],[67, 51])).
% 0.19/0.39 tff(69,plain,
% 0.19/0.39 (((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | ((~(r2(Y24!0, tptp_fun_Y21_1(Y24!0)) | (tptp_fun_Y21_1(Y24!0) = tptp_fun_Y21_1(Y24!0)))) | (~((~r2(Y24!0, tptp_fun_Y21_1(Y24!0))) | (~(tptp_fun_Y21_1(Y24!0) = tptp_fun_Y21_1(Y24!0))))))) <=> ((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | r2(Y24!0, tptp_fun_Y21_1(Y24!0)))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[68])).
% 0.19/0.39 tff(70,plain,
% 0.19/0.39 (((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | ((~(r2(Y24!0, tptp_fun_Y21_1(Y24!0)) | (tptp_fun_Y21_1(Y24!0) = tptp_fun_Y21_1(Y24!0)))) | (~((~r2(Y24!0, tptp_fun_Y21_1(Y24!0))) | (~(tptp_fun_Y21_1(Y24!0) = tptp_fun_Y21_1(Y24!0))))))) <=> ((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | r2(Y24!0, tptp_fun_Y21_1(Y24!0)))),
% 0.19/0.39 inference(transitivity,[status(thm)],[69, 50])).
% 0.19/0.39 tff(71,plain,
% 0.19/0.39 ((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | ((~(r2(Y24!0, tptp_fun_Y21_1(Y24!0)) | (tptp_fun_Y21_1(Y24!0) = tptp_fun_Y21_1(Y24!0)))) | (~((~r2(Y24!0, tptp_fun_Y21_1(Y24!0))) | (~(tptp_fun_Y21_1(Y24!0) = tptp_fun_Y21_1(Y24!0))))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(72,plain,
% 0.19/0.39 ((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | r2(Y24!0, tptp_fun_Y21_1(Y24!0))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.19/0.39 tff(73,plain,
% 0.19/0.39 (r2(Y24!0, tptp_fun_Y21_1(Y24!0))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[72, 49])).
% 0.19/0.39 tff(74,plain,
% 0.19/0.39 (r2(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[73, 37])).
% 0.19/0.39 tff(75,plain,
% 0.19/0.39 (^[X7: $i, Y10: $i] : refl(((~r1(Y10)) | (~r2(X7, Y10))) <=> ((~r1(Y10)) | (~r2(X7, Y10))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(76,plain,
% 0.19/0.39 (![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10))) <=> ![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[75])).
% 0.19/0.39 tff(77,plain,
% 0.19/0.39 (![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10))) <=> ![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(78,plain,
% 0.19/0.39 (^[X7: $i, Y10: $i] : rewrite((![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))) | (~r2(X7, Y10))) <=> ((~r1(Y10)) | (~r2(X7, Y10))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(79,plain,
% 0.19/0.39 (![X7: $i, Y10: $i] : (![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))) | (~r2(X7, Y10))) <=> ![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[78])).
% 0.19/0.39 tff(80,axiom,(![X7: $i, Y10: $i] : (![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))) | (~r2(X7, Y10)))), file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax','axiom_7a')).
% 0.19/0.39 tff(81,plain,
% 0.19/0.39 (![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.19/0.39 tff(82,plain,
% 0.19/0.39 (![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[81, 77])).
% 0.19/0.39 tff(83,plain,(
% 0.19/0.39 ![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))),
% 0.19/0.39 inference(skolemize,[status(sab)],[82])).
% 0.19/0.39 tff(84,plain,
% 0.19/0.39 (![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[83, 76])).
% 0.19/0.39 tff(85,plain,
% 0.19/0.39 (((~![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))) | ((~r1(tptp_fun_Y21_1(Y24!0))) | (~r2(Y24!0, tptp_fun_Y21_1(Y24!0))))) <=> ((~![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))) | (~r1(tptp_fun_Y21_1(Y24!0))) | (~r2(Y24!0, tptp_fun_Y21_1(Y24!0))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(86,plain,
% 0.19/0.39 ((~![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))) | ((~r1(tptp_fun_Y21_1(Y24!0))) | (~r2(Y24!0, tptp_fun_Y21_1(Y24!0))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(87,plain,
% 0.19/0.40 ((~![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))) | (~r1(tptp_fun_Y21_1(Y24!0))) | (~r2(Y24!0, tptp_fun_Y21_1(Y24!0)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.19/0.40 tff(88,plain,
% 0.19/0.40 (~r1(tptp_fun_Y21_1(Y24!0))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[87, 84, 73])).
% 0.19/0.40 tff(89,plain,
% 0.19/0.40 (^[Y1: $i] : refl((r1(Y1) | (~((~r2(tptp_fun_Y3_14(Y1), Y1)) | (~r1(tptp_fun_Y4_15(Y1))) | (~r2(tptp_fun_Y4_15(Y1), tptp_fun_Y3_14(Y1)))))) <=> (r1(Y1) | (~((~r2(tptp_fun_Y3_14(Y1), Y1)) | (~r1(tptp_fun_Y4_15(Y1))) | (~r2(tptp_fun_Y4_15(Y1), tptp_fun_Y3_14(Y1)))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(90,plain,
% 0.19/0.40 (![Y1: $i] : (r1(Y1) | (~((~r2(tptp_fun_Y3_14(Y1), Y1)) | (~r1(tptp_fun_Y4_15(Y1))) | (~r2(tptp_fun_Y4_15(Y1), tptp_fun_Y3_14(Y1)))))) <=> ![Y1: $i] : (r1(Y1) | (~((~r2(tptp_fun_Y3_14(Y1), Y1)) | (~r1(tptp_fun_Y4_15(Y1))) | (~r2(tptp_fun_Y4_15(Y1), tptp_fun_Y3_14(Y1))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[89])).
% 0.19/0.40 tff(91,plain,
% 0.19/0.40 (^[Y1: $i] : rewrite((r1(Y1) | (r2(tptp_fun_Y3_14(Y1), Y1) & (~((~r1(tptp_fun_Y4_15(Y1))) | (~r2(tptp_fun_Y4_15(Y1), tptp_fun_Y3_14(Y1))))))) <=> (r1(Y1) | (~((~r2(tptp_fun_Y3_14(Y1), Y1)) | (~r1(tptp_fun_Y4_15(Y1))) | (~r2(tptp_fun_Y4_15(Y1), tptp_fun_Y3_14(Y1)))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(92,plain,
% 0.19/0.40 (![Y1: $i] : (r1(Y1) | (r2(tptp_fun_Y3_14(Y1), Y1) & (~((~r1(tptp_fun_Y4_15(Y1))) | (~r2(tptp_fun_Y4_15(Y1), tptp_fun_Y3_14(Y1))))))) <=> ![Y1: $i] : (r1(Y1) | (~((~r2(tptp_fun_Y3_14(Y1), Y1)) | (~r1(tptp_fun_Y4_15(Y1))) | (~r2(tptp_fun_Y4_15(Y1), tptp_fun_Y3_14(Y1))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[91])).
% 0.19/0.40 tff(93,plain,
% 0.19/0.40 (^[Y1: $i] : rewrite(((r2(tptp_fun_Y3_14(Y1), Y1) & (~((~r1(tptp_fun_Y4_15(Y1))) | (~r2(tptp_fun_Y4_15(Y1), tptp_fun_Y3_14(Y1)))))) | r1(Y1)) <=> (r1(Y1) | (r2(tptp_fun_Y3_14(Y1), Y1) & (~((~r1(tptp_fun_Y4_15(Y1))) | (~r2(tptp_fun_Y4_15(Y1), tptp_fun_Y3_14(Y1))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(94,plain,
% 0.19/0.40 (![Y1: $i] : ((r2(tptp_fun_Y3_14(Y1), Y1) & (~((~r1(tptp_fun_Y4_15(Y1))) | (~r2(tptp_fun_Y4_15(Y1), tptp_fun_Y3_14(Y1)))))) | r1(Y1)) <=> ![Y1: $i] : (r1(Y1) | (r2(tptp_fun_Y3_14(Y1), Y1) & (~((~r1(tptp_fun_Y4_15(Y1))) | (~r2(tptp_fun_Y4_15(Y1), tptp_fun_Y3_14(Y1)))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[93])).
% 0.19/0.40 tff(95,plain,
% 0.19/0.40 ((~?[Y1: $i] : (![Y3: $i] : ((~r2(Y3, Y1)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y3)))) & (~r1(Y1)))) <=> (~?[Y1: $i] : (![Y3: $i] : ((~r2(Y3, Y1)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y3)))) & (~r1(Y1))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(96,plain,
% 0.19/0.40 ((~?[Y1: $i] : (![Y2: $i] : (![Y3: $i] : (![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y3))) | (~r2(Y3, Y2))) | (~(Y1 = Y2))) & ![Y5: $i] : ((~r1(Y5)) | (~(Y1 = Y5))))) <=> (~?[Y1: $i] : (![Y3: $i] : ((~r2(Y3, Y1)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y3)))) & (~r1(Y1))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(97,axiom,(~?[Y1: $i] : (![Y2: $i] : (![Y3: $i] : (![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y3))) | (~r2(Y3, Y2))) | (~(Y1 = Y2))) & ![Y5: $i] : ((~r1(Y5)) | (~(Y1 = Y5))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','nonzerononetwoexist')).
% 0.19/0.40 tff(98,plain,
% 0.19/0.40 (~?[Y1: $i] : (![Y3: $i] : ((~r2(Y3, Y1)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y3)))) & (~r1(Y1)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.19/0.40 tff(99,plain,
% 0.19/0.40 (~?[Y1: $i] : (![Y3: $i] : ((~r2(Y3, Y1)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y3)))) & (~r1(Y1)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[98, 95])).
% 0.19/0.40 tff(100,plain,
% 0.19/0.40 (~?[Y1: $i] : (![Y3: $i] : ((~r2(Y3, Y1)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y3)))) & (~r1(Y1)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[99, 95])).
% 0.19/0.40 tff(101,plain,
% 0.19/0.40 (~?[Y1: $i] : (![Y3: $i] : ((~r2(Y3, Y1)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y3)))) & (~r1(Y1)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[100, 95])).
% 0.19/0.40 tff(102,plain,
% 0.19/0.40 (^[Y1: $i] : nnf_neg(trans(sk($oeq((~![Y3: $i] : ((~r2(Y3, Y1)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y3))))), (~((~r2(tptp_fun_Y3_14(Y1), Y1)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, tptp_fun_Y3_14(Y1)))))))), nnf_neg(refl($oeq(r2(tptp_fun_Y3_14(Y1), Y1), r2(tptp_fun_Y3_14(Y1), Y1))), sk($oeq((~![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, tptp_fun_Y3_14(Y1))))), (~((~r1(tptp_fun_Y4_15(Y1))) | (~r2(tptp_fun_Y4_15(Y1), tptp_fun_Y3_14(Y1))))))), $oeq((~((~r2(tptp_fun_Y3_14(Y1), Y1)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, tptp_fun_Y3_14(Y1)))))), (r2(tptp_fun_Y3_14(Y1), Y1) & (~((~r1(tptp_fun_Y4_15(Y1))) | (~r2(tptp_fun_Y4_15(Y1), tptp_fun_Y3_14(Y1)))))))), $oeq((~![Y3: $i] : ((~r2(Y3, Y1)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y3))))), (r2(tptp_fun_Y3_14(Y1), Y1) & (~((~r1(tptp_fun_Y4_15(Y1))) | (~r2(tptp_fun_Y4_15(Y1), tptp_fun_Y3_14(Y1)))))))), refl($oeq(r1(Y1), r1(Y1))), $oeq((~(![Y3: $i] : ((~r2(Y3, Y1)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y3)))) & (~r1(Y1)))), ((r2(tptp_fun_Y3_14(Y1), Y1) & (~((~r1(tptp_fun_Y4_15(Y1))) | (~r2(tptp_fun_Y4_15(Y1), tptp_fun_Y3_14(Y1)))))) | r1(Y1))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(103,plain,(
% 0.19/0.40 ![Y1: $i] : ((r2(tptp_fun_Y3_14(Y1), Y1) & (~((~r1(tptp_fun_Y4_15(Y1))) | (~r2(tptp_fun_Y4_15(Y1), tptp_fun_Y3_14(Y1)))))) | r1(Y1))),
% 0.19/0.40 inference(nnf-neg,[status(sab)],[101, 102])).
% 0.19/0.40 tff(104,plain,
% 0.19/0.40 (![Y1: $i] : (r1(Y1) | (r2(tptp_fun_Y3_14(Y1), Y1) & (~((~r1(tptp_fun_Y4_15(Y1))) | (~r2(tptp_fun_Y4_15(Y1), tptp_fun_Y3_14(Y1)))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[103, 94])).
% 0.19/0.40 tff(105,plain,
% 0.19/0.40 (![Y1: $i] : (r1(Y1) | (~((~r2(tptp_fun_Y3_14(Y1), Y1)) | (~r1(tptp_fun_Y4_15(Y1))) | (~r2(tptp_fun_Y4_15(Y1), tptp_fun_Y3_14(Y1))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[104, 92])).
% 0.19/0.40 tff(106,plain,
% 0.19/0.40 (![Y1: $i] : (r1(Y1) | (~((~r2(tptp_fun_Y3_14(Y1), Y1)) | (~r1(tptp_fun_Y4_15(Y1))) | (~r2(tptp_fun_Y4_15(Y1), tptp_fun_Y3_14(Y1))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[105, 90])).
% 0.19/0.40 tff(107,plain,
% 0.19/0.40 (((~![Y1: $i] : (r1(Y1) | (~((~r2(tptp_fun_Y3_14(Y1), Y1)) | (~r1(tptp_fun_Y4_15(Y1))) | (~r2(tptp_fun_Y4_15(Y1), tptp_fun_Y3_14(Y1))))))) | (r1(tptp_fun_Y21_1(Y24!0)) | (~((~r2(tptp_fun_Y3_14(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))) | (~r1(tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0)))) | (~r2(tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y3_14(tptp_fun_Y21_1(Y24!0)))))))) <=> ((~![Y1: $i] : (r1(Y1) | (~((~r2(tptp_fun_Y3_14(Y1), Y1)) | (~r1(tptp_fun_Y4_15(Y1))) | (~r2(tptp_fun_Y4_15(Y1), tptp_fun_Y3_14(Y1))))))) | r1(tptp_fun_Y21_1(Y24!0)) | (~((~r2(tptp_fun_Y3_14(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))) | (~r1(tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0)))) | (~r2(tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y3_14(tptp_fun_Y21_1(Y24!0)))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(108,plain,
% 0.19/0.40 ((~![Y1: $i] : (r1(Y1) | (~((~r2(tptp_fun_Y3_14(Y1), Y1)) | (~r1(tptp_fun_Y4_15(Y1))) | (~r2(tptp_fun_Y4_15(Y1), tptp_fun_Y3_14(Y1))))))) | (r1(tptp_fun_Y21_1(Y24!0)) | (~((~r2(tptp_fun_Y3_14(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))) | (~r1(tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0)))) | (~r2(tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y3_14(tptp_fun_Y21_1(Y24!0)))))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(109,plain,
% 0.19/0.40 ((~![Y1: $i] : (r1(Y1) | (~((~r2(tptp_fun_Y3_14(Y1), Y1)) | (~r1(tptp_fun_Y4_15(Y1))) | (~r2(tptp_fun_Y4_15(Y1), tptp_fun_Y3_14(Y1))))))) | r1(tptp_fun_Y21_1(Y24!0)) | (~((~r2(tptp_fun_Y3_14(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))) | (~r1(tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0)))) | (~r2(tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y3_14(tptp_fun_Y21_1(Y24!0))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.19/0.40 tff(110,plain,
% 0.19/0.40 (~((~r2(tptp_fun_Y3_14(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))) | (~r1(tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0)))) | (~r2(tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y3_14(tptp_fun_Y21_1(Y24!0)))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[109, 106, 88])).
% 0.19/0.40 tff(111,plain,
% 0.19/0.40 (((~r2(tptp_fun_Y3_14(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))) | (~r1(tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0)))) | (~r2(tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y3_14(tptp_fun_Y21_1(Y24!0))))) | r2(tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y3_14(tptp_fun_Y21_1(Y24!0)))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(112,plain,
% 0.19/0.40 (r2(tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y3_14(tptp_fun_Y21_1(Y24!0)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[111, 110])).
% 0.19/0.40 tff(113,plain,
% 0.19/0.40 ((r2(tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y3_14(tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y3_14(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0))))) | (~r2(tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y3_14(tptp_fun_Y21_1(Y24!0))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(114,plain,
% 0.19/0.40 (r2(tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y3_14(tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y3_14(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[113, 112])).
% 0.19/0.40 tff(115,plain,
% 0.19/0.40 (((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | ((~(r2(tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y3_14(tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y3_14(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0)))))) | (~((~r2(tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y3_14(tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y3_14(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0))))))))) <=> ((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | (~(r2(tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y3_14(tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y3_14(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0)))))) | (~((~r2(tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y3_14(tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y3_14(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0))))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(116,plain,
% 0.19/0.40 ((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | ((~(r2(tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y3_14(tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y3_14(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0)))))) | (~((~r2(tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y3_14(tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y3_14(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0))))))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(117,plain,
% 0.19/0.40 ((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | (~(r2(tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y3_14(tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y3_14(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0)))))) | (~((~r2(tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y3_14(tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y3_14(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0)))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.19/0.40 tff(118,plain,
% 0.19/0.40 (~((~r2(tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y3_14(tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y3_14(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0))))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[117, 49, 114])).
% 0.19/0.40 tff(119,plain,
% 0.19/0.40 (((~r2(tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y3_14(tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y3_14(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0)))))) | (tptp_fun_Y3_14(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(120,plain,
% 0.19/0.40 (tptp_fun_Y3_14(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[119, 118])).
% 0.19/0.40 tff(121,plain,
% 0.19/0.40 (tptp_fun_Y21_1(tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0))) = tptp_fun_Y3_14(tptp_fun_Y21_1(Y24!0))),
% 0.19/0.40 inference(symmetry,[status(thm)],[120])).
% 0.19/0.40 tff(122,plain,
% 0.19/0.40 (((~r2(tptp_fun_Y3_14(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))) | (~r1(tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0)))) | (~r2(tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y3_14(tptp_fun_Y21_1(Y24!0))))) | r1(tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0)))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(123,plain,
% 0.19/0.40 (r1(tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[122, 110])).
% 0.19/0.40 tff(124,plain,
% 0.19/0.40 ((r1(tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0)) = Y24!0)) | (~r1(tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(125,plain,
% 0.19/0.40 (r1(tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0)) = Y24!0)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[124, 123])).
% 0.19/0.40 tff(126,plain,
% 0.19/0.40 (^[X19: $i] : refl(((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))) <=> ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(127,plain,
% 0.19/0.40 (![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))) <=> ![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[126])).
% 0.19/0.40 tff(128,plain,
% 0.19/0.40 (^[X19: $i] : trans(monotonicity(rewrite((r1(X19) & (X19 = Y24!0)) <=> (~((~r1(X19)) | (~(X19 = Y24!0))))), rewrite(((~r1(X19)) & (~(X19 = Y24!0))) <=> (~(r1(X19) | (X19 = Y24!0)))), (((r1(X19) & (X19 = Y24!0)) | ((~r1(X19)) & (~(X19 = Y24!0)))) <=> ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))))), rewrite(((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))) <=> ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))), (((r1(X19) & (X19 = Y24!0)) | ((~r1(X19)) & (~(X19 = Y24!0)))) <=> ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(129,plain,
% 0.19/0.40 (![X19: $i] : ((r1(X19) & (X19 = Y24!0)) | ((~r1(X19)) & (~(X19 = Y24!0)))) <=> ![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[128])).
% 0.19/0.40 tff(130,plain,
% 0.19/0.40 (?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24)))) <=> ?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(131,plain,
% 0.19/0.40 (^[Y24: $i] : quant_intro(proof_bind(^[X19: $i] : rewrite((((~r1(X19)) & (~(X19 = Y24))) | (r1(X19) & (X19 = Y24))) <=> ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24)))))), (![X19: $i] : (((~r1(X19)) & (~(X19 = Y24))) | (r1(X19) & (X19 = Y24))) <=> ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(132,plain,
% 0.19/0.40 (?[Y24: $i] : ![X19: $i] : (((~r1(X19)) & (~(X19 = Y24))) | (r1(X19) & (X19 = Y24))) <=> ?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[131])).
% 0.19/0.40 tff(133,axiom,(?[Y24: $i] : ![X19: $i] : (((~r1(X19)) & (~(X19 = Y24))) | (r1(X19) & (X19 = Y24)))), file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax','axiom_1')).
% 0.19/0.40 tff(134,plain,
% 0.19/0.40 (?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.19/0.40 tff(135,plain,
% 0.19/0.40 (?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[134, 130])).
% 0.19/0.40 tff(136,plain,(
% 0.19/0.40 $oeq(![X19: $i] : ((r1(X19) & (X19 = Y24!0)) | ((~r1(X19)) & (~(X19 = Y24!0)))), ![X19: $i] : ((r1(X19) & (X19 = Y24!0)) | ((~r1(X19)) & (~(X19 = Y24!0)))))),
% 0.19/0.40 inference(transitivity,[status(sab)],[135])).
% 0.19/0.40 tff(137,plain,
% 0.19/0.40 (![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[136, 129])).
% 0.19/0.40 tff(138,plain,
% 0.19/0.40 (![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[137, 127])).
% 0.19/0.40 tff(139,plain,
% 0.19/0.40 (((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0)) = Y24!0)))) | (~(r1(tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0)) = Y24!0))))) <=> ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~((~r1(tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0)) = Y24!0)))) | (~(r1(tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0)) = Y24!0))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(140,plain,
% 0.19/0.40 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0)) = Y24!0)))) | (~(r1(tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0)) = Y24!0))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(141,plain,
% 0.19/0.40 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~((~r1(tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0)) = Y24!0)))) | (~(r1(tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0)) = Y24!0)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.19/0.40 tff(142,plain,
% 0.19/0.40 (~((~r1(tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0)) = Y24!0)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[141, 138, 125])).
% 0.19/0.40 tff(143,plain,
% 0.19/0.40 (((~r1(tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0)) = Y24!0))) | (tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0)) = Y24!0)),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(144,plain,
% 0.19/0.40 (tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0)) = Y24!0),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[143, 142])).
% 0.19/0.40 tff(145,plain,
% 0.19/0.40 (tptp_fun_Y21_1(tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0))) = tptp_fun_Y21_1(Y24!0)),
% 0.19/0.40 inference(monotonicity,[status(thm)],[144])).
% 0.19/0.40 tff(146,plain,
% 0.19/0.40 (tptp_fun_Y21_1(Y24!0) = tptp_fun_Y21_1(tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0)))),
% 0.19/0.40 inference(symmetry,[status(thm)],[145])).
% 0.19/0.40 tff(147,plain,
% 0.19/0.40 (tptp_fun_Y21_1(Y24!0) = tptp_fun_Y3_14(tptp_fun_Y21_1(Y24!0))),
% 0.19/0.40 inference(transitivity,[status(thm)],[146, 121])).
% 0.19/0.40 tff(148,plain,
% 0.19/0.40 ((Y24!0 = tptp_fun_Y21_1(Y24!0)) <=> (tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0) = tptp_fun_Y3_14(tptp_fun_Y21_1(Y24!0)))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[34, 147])).
% 0.19/0.40 tff(149,plain,
% 0.19/0.40 ((~(Y24!0 = tptp_fun_Y21_1(Y24!0))) <=> (~(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0) = tptp_fun_Y3_14(tptp_fun_Y21_1(Y24!0))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[148])).
% 0.19/0.40 tff(150,assumption,(~r1(Y24!0)), introduced(assumption)).
% 0.19/0.40 tff(151,plain,
% 0.19/0.40 (((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | r1(Y24!0)) <=> ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | r1(Y24!0))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(152,plain,
% 0.19/0.40 ((r1(Y24!0) | $false) <=> r1(Y24!0)),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(153,plain,
% 0.19/0.40 ((r1(Y24!0) | $true) <=> $true),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(154,plain,
% 0.19/0.40 ((Y24!0 = Y24!0) <=> $true),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(155,plain,
% 0.19/0.40 ((r1(Y24!0) | (Y24!0 = Y24!0)) <=> (r1(Y24!0) | $true)),
% 0.19/0.40 inference(monotonicity,[status(thm)],[154])).
% 0.19/0.40 tff(156,plain,
% 0.19/0.40 ((r1(Y24!0) | (Y24!0 = Y24!0)) <=> $true),
% 0.19/0.40 inference(transitivity,[status(thm)],[155, 153])).
% 0.19/0.40 tff(157,plain,
% 0.19/0.40 ((~(r1(Y24!0) | (Y24!0 = Y24!0))) <=> (~$true)),
% 0.19/0.40 inference(monotonicity,[status(thm)],[156])).
% 0.19/0.40 tff(158,plain,
% 0.19/0.40 ((~(r1(Y24!0) | (Y24!0 = Y24!0))) <=> $false),
% 0.19/0.40 inference(transitivity,[status(thm)],[157, 54])).
% 0.19/0.40 tff(159,plain,
% 0.19/0.40 ((~(~r1(Y24!0))) <=> r1(Y24!0)),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(160,plain,
% 0.19/0.40 (((~r1(Y24!0)) | $false) <=> (~r1(Y24!0))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(161,plain,
% 0.19/0.40 ((~(Y24!0 = Y24!0)) <=> (~$true)),
% 0.19/0.40 inference(monotonicity,[status(thm)],[154])).
% 0.19/0.40 tff(162,plain,
% 0.19/0.40 ((~(Y24!0 = Y24!0)) <=> $false),
% 0.19/0.40 inference(transitivity,[status(thm)],[161, 54])).
% 0.19/0.40 tff(163,plain,
% 0.19/0.41 (((~r1(Y24!0)) | (~(Y24!0 = Y24!0))) <=> ((~r1(Y24!0)) | $false)),
% 0.19/0.41 inference(monotonicity,[status(thm)],[162])).
% 0.19/0.41 tff(164,plain,
% 0.19/0.41 (((~r1(Y24!0)) | (~(Y24!0 = Y24!0))) <=> (~r1(Y24!0))),
% 0.19/0.41 inference(transitivity,[status(thm)],[163, 160])).
% 0.19/0.41 tff(165,plain,
% 0.19/0.41 ((~((~r1(Y24!0)) | (~(Y24!0 = Y24!0)))) <=> (~(~r1(Y24!0)))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[164])).
% 0.19/0.41 tff(166,plain,
% 0.19/0.41 ((~((~r1(Y24!0)) | (~(Y24!0 = Y24!0)))) <=> r1(Y24!0)),
% 0.19/0.41 inference(transitivity,[status(thm)],[165, 159])).
% 0.19/0.41 tff(167,plain,
% 0.19/0.41 (((~((~r1(Y24!0)) | (~(Y24!0 = Y24!0)))) | (~(r1(Y24!0) | (Y24!0 = Y24!0)))) <=> (r1(Y24!0) | $false)),
% 0.19/0.41 inference(monotonicity,[status(thm)],[166, 158])).
% 0.19/0.41 tff(168,plain,
% 0.19/0.41 (((~((~r1(Y24!0)) | (~(Y24!0 = Y24!0)))) | (~(r1(Y24!0) | (Y24!0 = Y24!0)))) <=> r1(Y24!0)),
% 0.19/0.41 inference(transitivity,[status(thm)],[167, 152])).
% 0.19/0.41 tff(169,plain,
% 0.19/0.41 (((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(Y24!0)) | (~(Y24!0 = Y24!0)))) | (~(r1(Y24!0) | (Y24!0 = Y24!0))))) <=> ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | r1(Y24!0))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[168])).
% 0.19/0.41 tff(170,plain,
% 0.19/0.41 (((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(Y24!0)) | (~(Y24!0 = Y24!0)))) | (~(r1(Y24!0) | (Y24!0 = Y24!0))))) <=> ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | r1(Y24!0))),
% 0.19/0.41 inference(transitivity,[status(thm)],[169, 151])).
% 0.19/0.41 tff(171,plain,
% 0.19/0.41 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(Y24!0)) | (~(Y24!0 = Y24!0)))) | (~(r1(Y24!0) | (Y24!0 = Y24!0))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(172,plain,
% 0.19/0.41 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | r1(Y24!0)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.19/0.41 tff(173,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[172, 138, 150])).
% 0.19/0.41 tff(174,plain,(r1(Y24!0)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(175,plain,
% 0.19/0.41 (((~![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))) | ((~r1(Y24!0)) | (~r2(Y24!0, Y24!0)))) <=> ((~![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))) | (~r1(Y24!0)) | (~r2(Y24!0, Y24!0)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(176,plain,
% 0.19/0.41 ((~![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))) | ((~r1(Y24!0)) | (~r2(Y24!0, Y24!0)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(177,plain,
% 0.19/0.41 ((~![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))) | (~r1(Y24!0)) | (~r2(Y24!0, Y24!0))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.19/0.41 tff(178,plain,
% 0.19/0.41 ((~r1(Y24!0)) | (~r2(Y24!0, Y24!0))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[177, 84])).
% 0.19/0.41 tff(179,plain,
% 0.19/0.41 (~r2(Y24!0, Y24!0)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[178, 174])).
% 0.19/0.41 tff(180,plain,
% 0.19/0.41 (((~r2(Y24!0, Y24!0)) | (~(Y24!0 = tptp_fun_Y21_1(Y24!0)))) | r2(Y24!0, Y24!0)),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(181,plain,
% 0.19/0.41 ((~r2(Y24!0, Y24!0)) | (~(Y24!0 = tptp_fun_Y21_1(Y24!0)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[180, 179])).
% 0.19/0.41 tff(182,plain,
% 0.19/0.41 (((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | ((~(r2(Y24!0, Y24!0) | (Y24!0 = tptp_fun_Y21_1(Y24!0)))) | (~((~r2(Y24!0, Y24!0)) | (~(Y24!0 = tptp_fun_Y21_1(Y24!0))))))) <=> ((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | (~(r2(Y24!0, Y24!0) | (Y24!0 = tptp_fun_Y21_1(Y24!0)))) | (~((~r2(Y24!0, Y24!0)) | (~(Y24!0 = tptp_fun_Y21_1(Y24!0))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(183,plain,
% 0.19/0.41 ((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | ((~(r2(Y24!0, Y24!0) | (Y24!0 = tptp_fun_Y21_1(Y24!0)))) | (~((~r2(Y24!0, Y24!0)) | (~(Y24!0 = tptp_fun_Y21_1(Y24!0))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(184,plain,
% 0.19/0.41 ((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | (~(r2(Y24!0, Y24!0) | (Y24!0 = tptp_fun_Y21_1(Y24!0)))) | (~((~r2(Y24!0, Y24!0)) | (~(Y24!0 = tptp_fun_Y21_1(Y24!0)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[183, 182])).
% 0.19/0.41 tff(185,plain,
% 0.19/0.41 (~(r2(Y24!0, Y24!0) | (Y24!0 = tptp_fun_Y21_1(Y24!0)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[184, 49, 181])).
% 0.19/0.41 tff(186,plain,
% 0.19/0.41 ((r2(Y24!0, Y24!0) | (Y24!0 = tptp_fun_Y21_1(Y24!0))) | (~(Y24!0 = tptp_fun_Y21_1(Y24!0)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(187,plain,
% 0.19/0.41 (~(Y24!0 = tptp_fun_Y21_1(Y24!0))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[186, 185])).
% 0.19/0.41 tff(188,plain,
% 0.19/0.41 (~(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0) = tptp_fun_Y3_14(tptp_fun_Y21_1(Y24!0)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[187, 149])).
% 0.19/0.41 tff(189,plain,
% 0.19/0.41 (((~r2(tptp_fun_Y3_14(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))) | (~r1(tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0)))) | (~r2(tptp_fun_Y4_15(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y3_14(tptp_fun_Y21_1(Y24!0))))) | r2(tptp_fun_Y3_14(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(190,plain,
% 0.19/0.41 (r2(tptp_fun_Y3_14(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[189, 110])).
% 0.19/0.41 tff(191,plain,
% 0.19/0.41 (^[X3: $i, X10: $i, Y12: $i] : trans(monotonicity(rewrite(((~r2(X3, Y12)) | (~r2(X10, Y12))) <=> ((~r2(X3, Y12)) | (~r2(X10, Y12)))), (((X3 = X10) | ((~r2(X3, Y12)) | (~r2(X10, Y12)))) <=> ((X3 = X10) | ((~r2(X3, Y12)) | (~r2(X10, Y12)))))), rewrite(((X3 = X10) | ((~r2(X3, Y12)) | (~r2(X10, Y12)))) <=> ((~r2(X3, Y12)) | (~r2(X10, Y12)) | (X3 = X10))), (((X3 = X10) | ((~r2(X3, Y12)) | (~r2(X10, Y12)))) <=> ((~r2(X3, Y12)) | (~r2(X10, Y12)) | (X3 = X10))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(192,plain,
% 0.19/0.41 (![X3: $i, X10: $i, Y12: $i] : ((X3 = X10) | ((~r2(X3, Y12)) | (~r2(X10, Y12)))) <=> ![X3: $i, X10: $i, Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12)) | (X3 = X10))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[191])).
% 0.19/0.41 tff(193,plain,
% 0.19/0.41 (^[X3: $i, X10: $i, Y12: $i] : refl(((X3 = X10) | ((~r2(X3, Y12)) | (~r2(X10, Y12)))) <=> ((X3 = X10) | ((~r2(X3, Y12)) | (~r2(X10, Y12)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(194,plain,
% 0.19/0.41 (![X3: $i, X10: $i, Y12: $i] : ((X3 = X10) | ((~r2(X3, Y12)) | (~r2(X10, Y12)))) <=> ![X3: $i, X10: $i, Y12: $i] : ((X3 = X10) | ((~r2(X3, Y12)) | (~r2(X10, Y12))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[193])).
% 0.19/0.41 tff(195,plain,
% 0.19/0.41 (![X3: $i, X10: $i] : ![Y12: $i] : ((X3 = X10) | ((~r2(X3, Y12)) | (~r2(X10, Y12)))) <=> ![X3: $i, X10: $i, Y12: $i] : ((X3 = X10) | ((~r2(X3, Y12)) | (~r2(X10, Y12))))),
% 0.19/0.41 inference(pull_quant,[status(thm)],[])).
% 0.19/0.41 tff(196,plain,
% 0.19/0.41 (^[X3: $i, X10: $i] : pull_quant(((X3 = X10) | ![Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12)))) <=> ![Y12: $i] : ((X3 = X10) | ((~r2(X3, Y12)) | (~r2(X10, Y12)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(197,plain,
% 0.19/0.41 (![X3: $i, X10: $i] : ((X3 = X10) | ![Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12)))) <=> ![X3: $i, X10: $i] : ![Y12: $i] : ((X3 = X10) | ((~r2(X3, Y12)) | (~r2(X10, Y12))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[196])).
% 0.19/0.41 tff(198,plain,
% 0.19/0.41 (![X3: $i, X10: $i] : ((X3 = X10) | ![Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12)))) <=> ![X3: $i, X10: $i, Y12: $i] : ((X3 = X10) | ((~r2(X3, Y12)) | (~r2(X10, Y12))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[197, 195])).
% 0.19/0.41 tff(199,plain,
% 0.19/0.41 (![X3: $i, X10: $i] : ((X3 = X10) | ![Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12)))) <=> ![X3: $i, X10: $i, Y12: $i] : ((X3 = X10) | ((~r2(X3, Y12)) | (~r2(X10, Y12))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[198, 194])).
% 0.19/0.41 tff(200,plain,
% 0.19/0.41 (^[X3: $i, X10: $i] : rewrite(((X3 = X10) | ![Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12)))) <=> ((X3 = X10) | ![Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(201,plain,
% 0.19/0.41 (![X3: $i, X10: $i] : ((X3 = X10) | ![Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12)))) <=> ![X3: $i, X10: $i] : ((X3 = X10) | ![Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[200])).
% 0.19/0.41 tff(202,plain,
% 0.19/0.41 (![X3: $i, X10: $i] : ((X3 = X10) | ![Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12)))) <=> ![X3: $i, X10: $i, Y12: $i] : ((X3 = X10) | ((~r2(X3, Y12)) | (~r2(X10, Y12))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[201, 199])).
% 0.19/0.41 tff(203,plain,
% 0.19/0.41 (![X3: $i, X10: $i] : ((X3 = X10) | ![Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12)))) <=> ![X3: $i, X10: $i] : ((X3 = X10) | ![Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(204,plain,
% 0.19/0.41 (^[X3: $i, X10: $i] : trans(monotonicity(quant_intro(proof_bind(^[Y12: $i] : trans(monotonicity(trans(quant_intro(proof_bind(^[Y13: $i] : rewrite(((~r2(X3, Y13)) | (~(Y13 = Y12))) <=> ((~(Y13 = Y12)) | (~r2(X3, Y13))))), (![Y13: $i] : ((~r2(X3, Y13)) | (~(Y13 = Y12))) <=> ![Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13))))), trans(der(![Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13))) <=> ![Y13: $i] : (~r2(X3, Y12))), elim_unused(![Y13: $i] : (~r2(X3, Y12)) <=> (~r2(X3, Y12))), (![Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13))) <=> (~r2(X3, Y12)))), (![Y13: $i] : ((~r2(X3, Y13)) | (~(Y13 = Y12))) <=> (~r2(X3, Y12)))), ((![Y13: $i] : ((~r2(X3, Y13)) | (~(Y13 = Y12))) | (~r2(X10, Y12))) <=> ((~r2(X3, Y12)) | (~r2(X10, Y12))))), rewrite(((~r2(X3, Y12)) | (~r2(X10, Y12))) <=> ((~r2(X3, Y12)) | (~r2(X10, Y12)))), ((![Y13: $i] : ((~r2(X3, Y13)) | (~(Y13 = Y12))) | (~r2(X10, Y12))) <=> ((~r2(X3, Y12)) | (~r2(X10, Y12)))))), (![Y12: $i] : (![Y13: $i] : ((~r2(X3, Y13)) | (~(Y13 = Y12))) | (~r2(X10, Y12))) <=> ![Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12))))), ((![Y12: $i] : (![Y13: $i] : ((~r2(X3, Y13)) | (~(Y13 = Y12))) | (~r2(X10, Y12))) | (X3 = X10)) <=> (![Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12))) | (X3 = X10)))), rewrite((![Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12))) | (X3 = X10)) <=> ((X3 = X10) | ![Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12))))), ((![Y12: $i] : (![Y13: $i] : ((~r2(X3, Y13)) | (~(Y13 = Y12))) | (~r2(X10, Y12))) | (X3 = X10)) <=> ((X3 = X10) | ![Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(205,plain,
% 0.19/0.41 (![X3: $i, X10: $i] : (![Y12: $i] : (![Y13: $i] : ((~r2(X3, Y13)) | (~(Y13 = Y12))) | (~r2(X10, Y12))) | (X3 = X10)) <=> ![X3: $i, X10: $i] : ((X3 = X10) | ![Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[204])).
% 0.19/0.41 tff(206,axiom,(![X3: $i, X10: $i] : (![Y12: $i] : (![Y13: $i] : ((~r2(X3, Y13)) | (~(Y13 = Y12))) | (~r2(X10, Y12))) | (X3 = X10))), file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax','axiom_3a')).
% 0.19/0.41 tff(207,plain,
% 0.19/0.41 (![X3: $i, X10: $i] : ((X3 = X10) | ![Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[206, 205])).
% 0.19/0.41 tff(208,plain,
% 0.19/0.41 (![X3: $i, X10: $i] : ((X3 = X10) | ![Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[207, 203])).
% 0.19/0.41 tff(209,plain,(
% 0.19/0.41 ![X3: $i, X10: $i] : ((X3 = X10) | ![Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[208])).
% 0.19/0.41 tff(210,plain,
% 0.19/0.41 (![X3: $i, X10: $i, Y12: $i] : ((X3 = X10) | ((~r2(X3, Y12)) | (~r2(X10, Y12))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[209, 202])).
% 0.19/0.41 tff(211,plain,
% 0.19/0.41 (![X3: $i, X10: $i, Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12)) | (X3 = X10))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[210, 192])).
% 0.19/0.41 tff(212,plain,
% 0.19/0.41 (((~![X3: $i, X10: $i, Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12)) | (X3 = X10))) | ((~r2(tptp_fun_Y3_14(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))) | (~r2(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0) = tptp_fun_Y3_14(tptp_fun_Y21_1(Y24!0))))) <=> ((~![X3: $i, X10: $i, Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12)) | (X3 = X10))) | (~r2(tptp_fun_Y3_14(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))) | (~r2(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0) = tptp_fun_Y3_14(tptp_fun_Y21_1(Y24!0))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(213,plain,
% 0.19/0.41 (((~r2(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))) | (~r2(tptp_fun_Y3_14(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0) = tptp_fun_Y3_14(tptp_fun_Y21_1(Y24!0)))) <=> ((~r2(tptp_fun_Y3_14(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))) | (~r2(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0) = tptp_fun_Y3_14(tptp_fun_Y21_1(Y24!0))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(214,plain,
% 0.19/0.41 (((~![X3: $i, X10: $i, Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12)) | (X3 = X10))) | ((~r2(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))) | (~r2(tptp_fun_Y3_14(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0) = tptp_fun_Y3_14(tptp_fun_Y21_1(Y24!0))))) <=> ((~![X3: $i, X10: $i, Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12)) | (X3 = X10))) | ((~r2(tptp_fun_Y3_14(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))) | (~r2(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0) = tptp_fun_Y3_14(tptp_fun_Y21_1(Y24!0)))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[213])).
% 0.19/0.41 tff(215,plain,
% 0.19/0.41 (((~![X3: $i, X10: $i, Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12)) | (X3 = X10))) | ((~r2(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))) | (~r2(tptp_fun_Y3_14(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0) = tptp_fun_Y3_14(tptp_fun_Y21_1(Y24!0))))) <=> ((~![X3: $i, X10: $i, Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12)) | (X3 = X10))) | (~r2(tptp_fun_Y3_14(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))) | (~r2(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0) = tptp_fun_Y3_14(tptp_fun_Y21_1(Y24!0))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[214, 212])).
% 0.19/0.41 tff(216,plain,
% 0.19/0.41 ((~![X3: $i, X10: $i, Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12)) | (X3 = X10))) | ((~r2(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))) | (~r2(tptp_fun_Y3_14(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0) = tptp_fun_Y3_14(tptp_fun_Y21_1(Y24!0))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(217,plain,
% 0.19/0.41 ((~![X3: $i, X10: $i, Y12: $i] : ((~r2(X3, Y12)) | (~r2(X10, Y12)) | (X3 = X10))) | (~r2(tptp_fun_Y3_14(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))) | (~r2(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0) = tptp_fun_Y3_14(tptp_fun_Y21_1(Y24!0)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[216, 215])).
% 0.19/0.41 tff(218,plain,
% 0.19/0.41 ((~r2(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0) = tptp_fun_Y3_14(tptp_fun_Y21_1(Y24!0)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[217, 211, 190])).
% 0.19/0.41 tff(219,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[218, 188, 74])).
% 0.19/0.41 % SZS output end Proof
% 0.19/0.42 % E exiting
%------------------------------------------------------------------------------