%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUN054+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 05:22:34 AM UTC 2025
% Result : Theorem 0.12s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUN054+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 02:09:56 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.39 % SZS status Theorem
% 0.12/0.39 % SZS output start Proof
% 0.12/0.39 tff(r1_type, type, (
% 0.12/0.39 r1: $i > $o)).
% 0.12/0.39 tff(tptp_fun_Y7_6_type, type, (
% 0.12/0.39 tptp_fun_Y7_6: ( $i * $i ) > $i)).
% 0.12/0.39 tff(tptp_fun_Y24_0_type, type, (
% 0.12/0.39 tptp_fun_Y24_0: $i)).
% 0.12/0.39 tff(tptp_fun_Y22_2_type, type, (
% 0.12/0.39 tptp_fun_Y22_2: ( $i * $i ) > $i)).
% 0.12/0.39 tff(tptp_fun_Y16_10_type, type, (
% 0.12/0.39 tptp_fun_Y16_10: $i > $i)).
% 0.12/0.39 tff(r3_type, type, (
% 0.12/0.39 r3: ( $i * $i * $i ) > $o)).
% 0.12/0.39 tff(r2_type, type, (
% 0.12/0.39 r2: ( $i * $i ) > $o)).
% 0.12/0.39 tff(tptp_fun_Y4_4_type, type, (
% 0.12/0.39 tptp_fun_Y4_4: ( $i * $i ) > $i)).
% 0.12/0.39 tff(tptp_fun_Y15_5_type, type, (
% 0.12/0.39 tptp_fun_Y15_5: ( $i * $i ) > $i)).
% 0.12/0.39 tff(1,plain,
% 0.12/0.39 (^[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)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(2,plain,
% 0.12/0.39 (![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))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.39 tff(3,plain,
% 0.12/0.39 (![X4: $i] : ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4)) <=> ![X4: $i] : ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(4,plain,
% 0.12/0.39 (^[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))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(5,plain,
% 0.12/0.39 (![X4: $i] : ?[Y9: $i] : (?[Y16: $i] : (r1(Y16) & r3(X4, Y16, Y9)) & (Y9 = X4)) <=> ![X4: $i] : ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[4])).
% 0.12/0.39 tff(6,axiom,(![X4: $i] : ?[Y9: $i] : (?[Y16: $i] : (r1(Y16) & r3(X4, Y16, Y9)) & (Y9 = X4))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax','axiom_4a')).
% 0.12/0.39 tff(7,plain,
% 0.12/0.39 (![X4: $i] : ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.12/0.39 tff(8,plain,
% 0.12/0.39 (![X4: $i] : ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.12/0.39 tff(9,plain,(
% 0.12/0.39 ![X4: $i] : (r1(tptp_fun_Y16_10(X4)) & r3(X4, tptp_fun_Y16_10(X4), X4))),
% 0.12/0.39 inference(skolemize,[status(sab)],[8])).
% 0.12/0.39 tff(10,plain,
% 0.12/0.39 (![X4: $i] : (~((~r1(tptp_fun_Y16_10(X4))) | (~r3(X4, tptp_fun_Y16_10(X4), X4))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.12/0.39 tff(11,plain,
% 0.12/0.39 ((~![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))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(12,plain,
% 0.12/0.39 (~((~r1(tptp_fun_Y16_10(Y24!0))) | (~r3(Y24!0, tptp_fun_Y16_10(Y24!0), Y24!0)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.12/0.39 tff(13,plain,
% 0.12/0.39 (((~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)),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(14,plain,
% 0.12/0.39 (r3(Y24!0, tptp_fun_Y16_10(Y24!0), Y24!0)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[13, 12])).
% 0.12/0.39 tff(15,plain,
% 0.12/0.39 ((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))) | (~r3(Y24!0, tptp_fun_Y16_10(Y24!0), Y24!0))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(16,plain,
% 0.12/0.39 (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))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[15, 14])).
% 0.12/0.39 tff(17,plain,
% 0.12/0.39 (^[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)))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(18,plain,
% 0.12/0.39 (![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))))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[17])).
% 0.12/0.39 tff(19,plain,
% 0.12/0.39 (^[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)))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(20,plain,
% 0.12/0.39 (![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))))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[19])).
% 0.12/0.39 tff(21,plain,
% 0.12/0.39 (![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))))),
% 0.12/0.39 inference(pull_quant,[status(thm)],[])).
% 0.12/0.39 tff(22,plain,
% 0.12/0.39 (![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)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 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/sandbox2/benchmark/Axioms/NUM008+0.ax','axiom_3')).
% 0.12/0.39 tff(24,plain,
% 0.12/0.39 (![X13: $i, X14: $i] : ?[Y22: $i] : ![X15: $i] : (((~r3(X13, X14, X15)) & (~(X15 = Y22))) | (r3(X13, X14, X15) & (X15 = Y22)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.12/0.39 tff(25,plain,(
% 0.12/0.39 ![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))))),
% 0.12/0.39 inference(skolemize,[status(sab)],[24])).
% 0.12/0.39 tff(26,plain,
% 0.12/0.39 (![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))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.12/0.39 tff(27,plain,
% 0.12/0.39 (![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))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[26, 20])).
% 0.12/0.39 tff(28,plain,
% 0.12/0.39 (![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))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[27, 18])).
% 0.12/0.39 tff(29,plain,
% 0.12/0.39 (((~![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))))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(30,plain,
% 0.12/0.39 ((~![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))))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(31,plain,
% 0.12/0.39 ((~![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)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.12/0.39 tff(32,plain,
% 0.12/0.39 (~((~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))))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[31, 28, 16])).
% 0.12/0.39 tff(33,plain,
% 0.12/0.39 (((~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))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(34,plain,
% 0.12/0.39 (Y24!0 = tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.12/0.39 tff(35,plain,
% 0.12/0.39 (tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0) = Y24!0),
% 0.12/0.39 inference(symmetry,[status(thm)],[34])).
% 0.12/0.39 tff(36,plain,
% 0.12/0.39 (((~r1(tptp_fun_Y16_10(Y24!0))) | (~r3(Y24!0, tptp_fun_Y16_10(Y24!0), Y24!0))) | r1(tptp_fun_Y16_10(Y24!0))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(37,plain,
% 0.12/0.39 (r1(tptp_fun_Y16_10(Y24!0))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[36, 12])).
% 0.12/0.39 tff(38,plain,
% 0.12/0.39 ((r1(tptp_fun_Y16_10(Y24!0)) | (tptp_fun_Y16_10(Y24!0) = Y24!0)) | (~r1(tptp_fun_Y16_10(Y24!0)))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(39,plain,
% 0.12/0.39 (r1(tptp_fun_Y16_10(Y24!0)) | (tptp_fun_Y16_10(Y24!0) = Y24!0)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.12/0.39 tff(40,plain,
% 0.12/0.39 (^[X19: $i] : refl(((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))) <=> ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(41,plain,
% 0.12/0.39 (![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))) <=> ![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[40])).
% 0.12/0.39 tff(42,plain,
% 0.12/0.39 (^[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))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(43,plain,
% 0.12/0.39 (![X19: $i] : ((r1(X19) & (X19 = Y24!0)) | ((~r1(X19)) & (~(X19 = Y24!0)))) <=> ![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[42])).
% 0.12/0.39 tff(44,plain,
% 0.12/0.39 (?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24)))) <=> ?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(45,plain,
% 0.12/0.39 (^[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))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(46,plain,
% 0.12/0.39 (?[Y24: $i] : ![X19: $i] : (((~r1(X19)) & (~(X19 = Y24))) | (r1(X19) & (X19 = Y24))) <=> ?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[45])).
% 0.12/0.39 tff(47,axiom,(?[Y24: $i] : ![X19: $i] : (((~r1(X19)) & (~(X19 = Y24))) | (r1(X19) & (X19 = Y24)))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax','axiom_1')).
% 0.12/0.39 tff(48,plain,
% 0.12/0.39 (?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.12/0.39 tff(49,plain,
% 0.12/0.39 (?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.12/0.39 tff(50,plain,(
% 0.12/0.39 $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)))))),
% 0.12/0.39 inference(transitivity,[status(sab)],[49])).
% 0.12/0.39 tff(51,plain,
% 0.12/0.39 (![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[50, 43])).
% 0.12/0.39 tff(52,plain,
% 0.12/0.39 (![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[51, 41])).
% 0.12/0.39 tff(53,plain,
% 0.12/0.39 (((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(tptp_fun_Y16_10(Y24!0))) | (~(tptp_fun_Y16_10(Y24!0) = Y24!0)))) | (~(r1(tptp_fun_Y16_10(Y24!0)) | (tptp_fun_Y16_10(Y24!0) = Y24!0))))) <=> ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~((~r1(tptp_fun_Y16_10(Y24!0))) | (~(tptp_fun_Y16_10(Y24!0) = Y24!0)))) | (~(r1(tptp_fun_Y16_10(Y24!0)) | (tptp_fun_Y16_10(Y24!0) = Y24!0))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(54,plain,
% 0.12/0.39 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(tptp_fun_Y16_10(Y24!0))) | (~(tptp_fun_Y16_10(Y24!0) = Y24!0)))) | (~(r1(tptp_fun_Y16_10(Y24!0)) | (tptp_fun_Y16_10(Y24!0) = Y24!0))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(55,plain,
% 0.12/0.39 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~((~r1(tptp_fun_Y16_10(Y24!0))) | (~(tptp_fun_Y16_10(Y24!0) = Y24!0)))) | (~(r1(tptp_fun_Y16_10(Y24!0)) | (tptp_fun_Y16_10(Y24!0) = Y24!0)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.12/0.39 tff(56,plain,
% 0.12/0.39 (~((~r1(tptp_fun_Y16_10(Y24!0))) | (~(tptp_fun_Y16_10(Y24!0) = Y24!0)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[55, 52, 39])).
% 0.12/0.39 tff(57,plain,
% 0.12/0.39 (((~r1(tptp_fun_Y16_10(Y24!0))) | (~(tptp_fun_Y16_10(Y24!0) = Y24!0))) | (tptp_fun_Y16_10(Y24!0) = Y24!0)),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(58,plain,
% 0.12/0.39 (tptp_fun_Y16_10(Y24!0) = Y24!0),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.12/0.39 tff(59,plain,
% 0.12/0.39 (Y24!0 = tptp_fun_Y16_10(Y24!0)),
% 0.12/0.39 inference(symmetry,[status(thm)],[58])).
% 0.12/0.39 tff(60,plain,
% 0.12/0.39 (tptp_fun_Y22_2(Y24!0, Y24!0) = tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)),
% 0.12/0.39 inference(monotonicity,[status(thm)],[59])).
% 0.12/0.39 tff(61,plain,
% 0.12/0.39 (^[X1: $i, X8: $i] : rewrite((r2(X8, tptp_fun_Y15_5(X8, X1)) & r3(X1, tptp_fun_Y15_5(X8, X1), tptp_fun_Y4_4(X8, X1)) & r2(tptp_fun_Y7_6(X8, X1), tptp_fun_Y4_4(X8, X1)) & r3(X1, X8, tptp_fun_Y7_6(X8, X1))) <=> (~((~r2(X8, tptp_fun_Y15_5(X8, X1))) | (~r3(X1, tptp_fun_Y15_5(X8, X1), tptp_fun_Y4_4(X8, X1))) | (~r2(tptp_fun_Y7_6(X8, X1), tptp_fun_Y4_4(X8, X1))) | (~r3(X1, X8, tptp_fun_Y7_6(X8, X1))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(62,plain,
% 0.12/0.39 (![X1: $i, X8: $i] : (r2(X8, tptp_fun_Y15_5(X8, X1)) & r3(X1, tptp_fun_Y15_5(X8, X1), tptp_fun_Y4_4(X8, X1)) & r2(tptp_fun_Y7_6(X8, X1), tptp_fun_Y4_4(X8, X1)) & r3(X1, X8, tptp_fun_Y7_6(X8, X1))) <=> ![X1: $i, X8: $i] : (~((~r2(X8, tptp_fun_Y15_5(X8, X1))) | (~r3(X1, tptp_fun_Y15_5(X8, X1), tptp_fun_Y4_4(X8, X1))) | (~r2(tptp_fun_Y7_6(X8, X1), tptp_fun_Y4_4(X8, X1))) | (~r3(X1, X8, tptp_fun_Y7_6(X8, X1)))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[61])).
% 0.12/0.39 tff(63,plain,
% 0.12/0.39 (^[X1: $i, X8: $i] : rewrite(((r2(X8, tptp_fun_Y15_5(X8, X1)) & r3(X1, tptp_fun_Y15_5(X8, X1), tptp_fun_Y4_4(X8, X1))) & (r2(tptp_fun_Y7_6(X8, X1), tptp_fun_Y4_4(X8, X1)) & r3(X1, X8, tptp_fun_Y7_6(X8, X1)))) <=> (r2(X8, tptp_fun_Y15_5(X8, X1)) & r3(X1, tptp_fun_Y15_5(X8, X1), tptp_fun_Y4_4(X8, X1)) & r2(tptp_fun_Y7_6(X8, X1), tptp_fun_Y4_4(X8, X1)) & r3(X1, X8, tptp_fun_Y7_6(X8, X1))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(64,plain,
% 0.12/0.39 (![X1: $i, X8: $i] : ((r2(X8, tptp_fun_Y15_5(X8, X1)) & r3(X1, tptp_fun_Y15_5(X8, X1), tptp_fun_Y4_4(X8, X1))) & (r2(tptp_fun_Y7_6(X8, X1), tptp_fun_Y4_4(X8, X1)) & r3(X1, X8, tptp_fun_Y7_6(X8, X1)))) <=> ![X1: $i, X8: $i] : (r2(X8, tptp_fun_Y15_5(X8, X1)) & r3(X1, tptp_fun_Y15_5(X8, X1), tptp_fun_Y4_4(X8, X1)) & r2(tptp_fun_Y7_6(X8, X1), tptp_fun_Y4_4(X8, X1)) & r3(X1, X8, tptp_fun_Y7_6(X8, X1)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[63])).
% 0.12/0.39 tff(65,plain,
% 0.12/0.39 (![X1: $i, X8: $i] : ?[Y4: $i] : (?[Y15: $i] : (r2(X8, Y15) & r3(X1, Y15, Y4)) & ?[Y7: $i] : (r2(Y7, Y4) & r3(X1, X8, Y7))) <=> ![X1: $i, X8: $i] : ?[Y4: $i] : (?[Y15: $i] : (r2(X8, Y15) & r3(X1, Y15, Y4)) & ?[Y7: $i] : (r2(Y7, Y4) & r3(X1, X8, Y7)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(66,plain,
% 0.12/0.39 (^[X1: $i, X8: $i] : quant_intro(proof_bind(^[Y4: $i] : rewrite((?[Y5: $i] : (?[Y15: $i] : (r2(X8, Y15) & r3(X1, Y15, Y5)) & (Y5 = Y4)) & ?[Y7: $i] : (r2(Y7, Y4) & r3(X1, X8, Y7))) <=> (?[Y15: $i] : (r2(X8, Y15) & r3(X1, Y15, Y4)) & ?[Y7: $i] : (r2(Y7, Y4) & r3(X1, X8, Y7))))), (?[Y4: $i] : (?[Y5: $i] : (?[Y15: $i] : (r2(X8, Y15) & r3(X1, Y15, Y5)) & (Y5 = Y4)) & ?[Y7: $i] : (r2(Y7, Y4) & r3(X1, X8, Y7))) <=> ?[Y4: $i] : (?[Y15: $i] : (r2(X8, Y15) & r3(X1, Y15, Y4)) & ?[Y7: $i] : (r2(Y7, Y4) & r3(X1, X8, Y7)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(67,plain,
% 0.12/0.39 (![X1: $i, X8: $i] : ?[Y4: $i] : (?[Y5: $i] : (?[Y15: $i] : (r2(X8, Y15) & r3(X1, Y15, Y5)) & (Y5 = Y4)) & ?[Y7: $i] : (r2(Y7, Y4) & r3(X1, X8, Y7))) <=> ![X1: $i, X8: $i] : ?[Y4: $i] : (?[Y15: $i] : (r2(X8, Y15) & r3(X1, Y15, Y4)) & ?[Y7: $i] : (r2(Y7, Y4) & r3(X1, X8, Y7)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[66])).
% 0.12/0.39 tff(68,axiom,(![X1: $i, X8: $i] : ?[Y4: $i] : (?[Y5: $i] : (?[Y15: $i] : (r2(X8, Y15) & r3(X1, Y15, Y5)) & (Y5 = Y4)) & ?[Y7: $i] : (r2(Y7, Y4) & r3(X1, X8, Y7)))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax','axiom_1a')).
% 0.12/0.39 tff(69,plain,
% 0.12/0.39 (![X1: $i, X8: $i] : ?[Y4: $i] : (?[Y15: $i] : (r2(X8, Y15) & r3(X1, Y15, Y4)) & ?[Y7: $i] : (r2(Y7, Y4) & r3(X1, X8, Y7)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.12/0.39 tff(70,plain,
% 0.12/0.39 (![X1: $i, X8: $i] : ?[Y4: $i] : (?[Y15: $i] : (r2(X8, Y15) & r3(X1, Y15, Y4)) & ?[Y7: $i] : (r2(Y7, Y4) & r3(X1, X8, Y7)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.12/0.39 tff(71,plain,(
% 0.12/0.39 ![X1: $i, X8: $i] : ((r2(X8, tptp_fun_Y15_5(X8, X1)) & r3(X1, tptp_fun_Y15_5(X8, X1), tptp_fun_Y4_4(X8, X1))) & (r2(tptp_fun_Y7_6(X8, X1), tptp_fun_Y4_4(X8, X1)) & r3(X1, X8, tptp_fun_Y7_6(X8, X1))))),
% 0.12/0.39 inference(skolemize,[status(sab)],[70])).
% 0.12/0.39 tff(72,plain,
% 0.12/0.39 (![X1: $i, X8: $i] : (r2(X8, tptp_fun_Y15_5(X8, X1)) & r3(X1, tptp_fun_Y15_5(X8, X1), tptp_fun_Y4_4(X8, X1)) & r2(tptp_fun_Y7_6(X8, X1), tptp_fun_Y4_4(X8, X1)) & r3(X1, X8, tptp_fun_Y7_6(X8, X1)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[71, 64])).
% 0.12/0.39 tff(73,plain,
% 0.12/0.39 (![X1: $i, X8: $i] : (~((~r2(X8, tptp_fun_Y15_5(X8, X1))) | (~r3(X1, tptp_fun_Y15_5(X8, X1), tptp_fun_Y4_4(X8, X1))) | (~r2(tptp_fun_Y7_6(X8, X1), tptp_fun_Y4_4(X8, X1))) | (~r3(X1, X8, tptp_fun_Y7_6(X8, X1)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[72, 62])).
% 0.12/0.39 tff(74,plain,
% 0.12/0.39 ((~![X1: $i, X8: $i] : (~((~r2(X8, tptp_fun_Y15_5(X8, X1))) | (~r3(X1, tptp_fun_Y15_5(X8, X1), tptp_fun_Y4_4(X8, X1))) | (~r2(tptp_fun_Y7_6(X8, X1), tptp_fun_Y4_4(X8, X1))) | (~r3(X1, X8, tptp_fun_Y7_6(X8, X1)))))) | (~((~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))) | (~r3(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r2(tptp_fun_Y7_6(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r3(Y24!0, Y24!0, tptp_fun_Y7_6(Y24!0, Y24!0)))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(75,plain,
% 0.12/0.39 (~((~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))) | (~r3(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r2(tptp_fun_Y7_6(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r3(Y24!0, Y24!0, tptp_fun_Y7_6(Y24!0, Y24!0))))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.12/0.40 tff(76,plain,
% 0.12/0.40 (((~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))) | (~r3(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r2(tptp_fun_Y7_6(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r3(Y24!0, Y24!0, tptp_fun_Y7_6(Y24!0, Y24!0)))) | r3(Y24!0, Y24!0, tptp_fun_Y7_6(Y24!0, Y24!0))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(77,plain,
% 0.12/0.40 (r3(Y24!0, Y24!0, tptp_fun_Y7_6(Y24!0, Y24!0))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[76, 75])).
% 0.12/0.40 tff(78,plain,
% 0.12/0.40 ((r3(Y24!0, Y24!0, tptp_fun_Y7_6(Y24!0, Y24!0)) | (tptp_fun_Y7_6(Y24!0, Y24!0) = tptp_fun_Y22_2(Y24!0, Y24!0))) | (~r3(Y24!0, Y24!0, tptp_fun_Y7_6(Y24!0, Y24!0)))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(79,plain,
% 0.12/0.40 (r3(Y24!0, Y24!0, tptp_fun_Y7_6(Y24!0, Y24!0)) | (tptp_fun_Y7_6(Y24!0, Y24!0) = tptp_fun_Y22_2(Y24!0, Y24!0))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.12/0.40 tff(80,plain,
% 0.12/0.40 (((~![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, Y24!0, tptp_fun_Y7_6(Y24!0, Y24!0)) | (tptp_fun_Y7_6(Y24!0, Y24!0) = tptp_fun_Y22_2(Y24!0, Y24!0)))) | (~((~r3(Y24!0, Y24!0, tptp_fun_Y7_6(Y24!0, Y24!0))) | (~(tptp_fun_Y7_6(Y24!0, Y24!0) = tptp_fun_Y22_2(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, Y24!0, tptp_fun_Y7_6(Y24!0, Y24!0)) | (tptp_fun_Y7_6(Y24!0, Y24!0) = tptp_fun_Y22_2(Y24!0, Y24!0)))) | (~((~r3(Y24!0, Y24!0, tptp_fun_Y7_6(Y24!0, Y24!0))) | (~(tptp_fun_Y7_6(Y24!0, Y24!0) = tptp_fun_Y22_2(Y24!0, Y24!0))))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(81,plain,
% 0.12/0.40 ((~![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, Y24!0, tptp_fun_Y7_6(Y24!0, Y24!0)) | (tptp_fun_Y7_6(Y24!0, Y24!0) = tptp_fun_Y22_2(Y24!0, Y24!0)))) | (~((~r3(Y24!0, Y24!0, tptp_fun_Y7_6(Y24!0, Y24!0))) | (~(tptp_fun_Y7_6(Y24!0, Y24!0) = tptp_fun_Y22_2(Y24!0, Y24!0))))))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(82,plain,
% 0.12/0.40 ((~![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, Y24!0, tptp_fun_Y7_6(Y24!0, Y24!0)) | (tptp_fun_Y7_6(Y24!0, Y24!0) = tptp_fun_Y22_2(Y24!0, Y24!0)))) | (~((~r3(Y24!0, Y24!0, tptp_fun_Y7_6(Y24!0, Y24!0))) | (~(tptp_fun_Y7_6(Y24!0, Y24!0) = tptp_fun_Y22_2(Y24!0, Y24!0)))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.12/0.40 tff(83,plain,
% 0.12/0.40 (~((~r3(Y24!0, Y24!0, tptp_fun_Y7_6(Y24!0, Y24!0))) | (~(tptp_fun_Y7_6(Y24!0, Y24!0) = tptp_fun_Y22_2(Y24!0, Y24!0))))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[82, 28, 79])).
% 0.12/0.40 tff(84,plain,
% 0.12/0.40 (((~r3(Y24!0, Y24!0, tptp_fun_Y7_6(Y24!0, Y24!0))) | (~(tptp_fun_Y7_6(Y24!0, Y24!0) = tptp_fun_Y22_2(Y24!0, Y24!0)))) | (tptp_fun_Y7_6(Y24!0, Y24!0) = tptp_fun_Y22_2(Y24!0, Y24!0))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(85,plain,
% 0.12/0.40 (tptp_fun_Y7_6(Y24!0, Y24!0) = tptp_fun_Y22_2(Y24!0, Y24!0)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[84, 83])).
% 0.12/0.40 tff(86,plain,
% 0.12/0.40 (tptp_fun_Y7_6(Y24!0, Y24!0) = Y24!0),
% 0.12/0.40 inference(transitivity,[status(thm)],[85, 60, 35])).
% 0.12/0.40 tff(87,plain,
% 0.12/0.40 (r1(tptp_fun_Y7_6(Y24!0, Y24!0)) <=> r1(Y24!0)),
% 0.12/0.40 inference(monotonicity,[status(thm)],[86])).
% 0.12/0.40 tff(88,plain,
% 0.12/0.40 (r1(Y24!0) <=> r1(tptp_fun_Y7_6(Y24!0, Y24!0))),
% 0.12/0.40 inference(symmetry,[status(thm)],[87])).
% 0.12/0.40 tff(89,plain,
% 0.12/0.40 (((~![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))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(90,plain,
% 0.12/0.40 ((r1(Y24!0) | $false) <=> r1(Y24!0)),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(91,plain,
% 0.12/0.40 ((~$true) <=> $false),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(92,plain,
% 0.12/0.40 ((r1(Y24!0) | $true) <=> $true),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(93,plain,
% 0.12/0.40 ((Y24!0 = Y24!0) <=> $true),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(94,plain,
% 0.12/0.40 ((r1(Y24!0) | (Y24!0 = Y24!0)) <=> (r1(Y24!0) | $true)),
% 0.12/0.40 inference(monotonicity,[status(thm)],[93])).
% 0.12/0.40 tff(95,plain,
% 0.12/0.40 ((r1(Y24!0) | (Y24!0 = Y24!0)) <=> $true),
% 0.12/0.40 inference(transitivity,[status(thm)],[94, 92])).
% 0.12/0.40 tff(96,plain,
% 0.12/0.40 ((~(r1(Y24!0) | (Y24!0 = Y24!0))) <=> (~$true)),
% 0.12/0.40 inference(monotonicity,[status(thm)],[95])).
% 0.12/0.40 tff(97,plain,
% 0.12/0.40 ((~(r1(Y24!0) | (Y24!0 = Y24!0))) <=> $false),
% 0.12/0.40 inference(transitivity,[status(thm)],[96, 91])).
% 0.12/0.40 tff(98,plain,
% 0.12/0.40 ((~(~r1(Y24!0))) <=> r1(Y24!0)),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(99,plain,
% 0.12/0.40 (((~r1(Y24!0)) | $false) <=> (~r1(Y24!0))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(100,plain,
% 0.12/0.40 ((~(Y24!0 = Y24!0)) <=> (~$true)),
% 0.12/0.40 inference(monotonicity,[status(thm)],[93])).
% 0.12/0.40 tff(101,plain,
% 0.12/0.40 ((~(Y24!0 = Y24!0)) <=> $false),
% 0.12/0.40 inference(transitivity,[status(thm)],[100, 91])).
% 0.12/0.40 tff(102,plain,
% 0.12/0.40 (((~r1(Y24!0)) | (~(Y24!0 = Y24!0))) <=> ((~r1(Y24!0)) | $false)),
% 0.12/0.40 inference(monotonicity,[status(thm)],[101])).
% 0.12/0.40 tff(103,plain,
% 0.12/0.40 (((~r1(Y24!0)) | (~(Y24!0 = Y24!0))) <=> (~r1(Y24!0))),
% 0.12/0.40 inference(transitivity,[status(thm)],[102, 99])).
% 0.12/0.40 tff(104,plain,
% 0.12/0.40 ((~((~r1(Y24!0)) | (~(Y24!0 = Y24!0)))) <=> (~(~r1(Y24!0)))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[103])).
% 0.12/0.40 tff(105,plain,
% 0.12/0.40 ((~((~r1(Y24!0)) | (~(Y24!0 = Y24!0)))) <=> r1(Y24!0)),
% 0.12/0.40 inference(transitivity,[status(thm)],[104, 98])).
% 0.12/0.40 tff(106,plain,
% 0.12/0.40 (((~((~r1(Y24!0)) | (~(Y24!0 = Y24!0)))) | (~(r1(Y24!0) | (Y24!0 = Y24!0)))) <=> (r1(Y24!0) | $false)),
% 0.12/0.40 inference(monotonicity,[status(thm)],[105, 97])).
% 0.12/0.40 tff(107,plain,
% 0.12/0.40 (((~((~r1(Y24!0)) | (~(Y24!0 = Y24!0)))) | (~(r1(Y24!0) | (Y24!0 = Y24!0)))) <=> r1(Y24!0)),
% 0.12/0.40 inference(transitivity,[status(thm)],[106, 90])).
% 0.12/0.40 tff(108,plain,
% 0.12/0.40 (((~![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))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[107])).
% 0.12/0.40 tff(109,plain,
% 0.12/0.40 (((~![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))),
% 0.12/0.40 inference(transitivity,[status(thm)],[108, 89])).
% 0.12/0.40 tff(110,plain,
% 0.12/0.40 ((~![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))))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(111,plain,
% 0.12/0.40 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | r1(Y24!0)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.12/0.40 tff(112,plain,
% 0.12/0.40 (r1(Y24!0)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[111, 52])).
% 0.12/0.40 tff(113,plain,
% 0.12/0.40 (r1(tptp_fun_Y7_6(Y24!0, Y24!0))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[112, 88])).
% 0.12/0.40 tff(114,plain,
% 0.12/0.40 (((~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))) | (~r3(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r2(tptp_fun_Y7_6(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r3(Y24!0, Y24!0, tptp_fun_Y7_6(Y24!0, Y24!0)))) | r2(tptp_fun_Y7_6(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(115,plain,
% 0.12/0.40 (r2(tptp_fun_Y7_6(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[114, 75])).
% 0.12/0.40 tff(116,plain,
% 0.12/0.40 (((~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))) | (~r3(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r2(tptp_fun_Y7_6(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r3(Y24!0, Y24!0, tptp_fun_Y7_6(Y24!0, Y24!0)))) | r3(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(117,plain,
% 0.12/0.40 (r3(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[116, 75])).
% 0.12/0.40 tff(118,plain,
% 0.12/0.40 (((~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))) | (~r3(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r2(tptp_fun_Y7_6(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r3(Y24!0, Y24!0, tptp_fun_Y7_6(Y24!0, Y24!0)))) | r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(119,plain,
% 0.12/0.40 (r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[118, 75])).
% 0.12/0.40 tff(120,plain,
% 0.12/0.40 (^[Y1: $i, Y6: $i, Y2: $i, Y5: $i, Y4: $i] : trans(monotonicity(rewrite((((~r1(Y4)) | (~r3(Y4, Y2, Y1))) | ((~r1(Y5)) | (~r2(Y5, Y2)))) <=> ((~r1(Y4)) | (~r3(Y4, Y2, Y1)) | (~r1(Y5)) | (~r2(Y5, Y2)))), (((((~r1(Y4)) | (~r3(Y4, Y2, Y1))) | ((~r1(Y5)) | (~r2(Y5, Y2)))) | ((~r1(Y6)) | (~r2(Y6, Y1)))) <=> (((~r1(Y4)) | (~r3(Y4, Y2, Y1)) | (~r1(Y5)) | (~r2(Y5, Y2))) | ((~r1(Y6)) | (~r2(Y6, Y1)))))), rewrite((((~r1(Y4)) | (~r3(Y4, Y2, Y1)) | (~r1(Y5)) | (~r2(Y5, Y2))) | ((~r1(Y6)) | (~r2(Y6, Y1)))) <=> ((~r1(Y4)) | (~r3(Y4, Y2, Y1)) | (~r1(Y6)) | (~r1(Y5)) | (~r2(Y5, Y2)) | (~r2(Y6, Y1)))), (((((~r1(Y4)) | (~r3(Y4, Y2, Y1))) | ((~r1(Y5)) | (~r2(Y5, Y2)))) | ((~r1(Y6)) | (~r2(Y6, Y1)))) <=> ((~r1(Y4)) | (~r3(Y4, Y2, Y1)) | (~r1(Y6)) | (~r1(Y5)) | (~r2(Y5, Y2)) | (~r2(Y6, Y1)))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(121,plain,
% 0.12/0.40 (![Y1: $i, Y6: $i, Y2: $i, Y5: $i, Y4: $i] : ((((~r1(Y4)) | (~r3(Y4, Y2, Y1))) | ((~r1(Y5)) | (~r2(Y5, Y2)))) | ((~r1(Y6)) | (~r2(Y6, Y1)))) <=> ![Y1: $i, Y6: $i, Y2: $i, Y5: $i, Y4: $i] : ((~r1(Y4)) | (~r3(Y4, Y2, Y1)) | (~r1(Y6)) | (~r1(Y5)) | (~r2(Y5, Y2)) | (~r2(Y6, Y1)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[120])).
% 0.12/0.40 tff(122,plain,
% 0.12/0.40 (^[Y1: $i, Y6: $i, Y2: $i, Y5: $i, Y4: $i] : refl(((((~r1(Y4)) | (~r3(Y4, Y2, Y1))) | ((~r1(Y5)) | (~r2(Y5, Y2)))) | ((~r1(Y6)) | (~r2(Y6, Y1)))) <=> ((((~r1(Y4)) | (~r3(Y4, Y2, Y1))) | ((~r1(Y5)) | (~r2(Y5, Y2)))) | ((~r1(Y6)) | (~r2(Y6, Y1)))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(123,plain,
% 0.12/0.40 (![Y1: $i, Y6: $i, Y2: $i, Y5: $i, Y4: $i] : ((((~r1(Y4)) | (~r3(Y4, Y2, Y1))) | ((~r1(Y5)) | (~r2(Y5, Y2)))) | ((~r1(Y6)) | (~r2(Y6, Y1)))) <=> ![Y1: $i, Y6: $i, Y2: $i, Y5: $i, Y4: $i] : ((((~r1(Y4)) | (~r3(Y4, Y2, Y1))) | ((~r1(Y5)) | (~r2(Y5, Y2)))) | ((~r1(Y6)) | (~r2(Y6, Y1))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[122])).
% 0.12/0.40 tff(124,plain,
% 0.12/0.40 (![Y1: $i] : ![Y6: $i, Y2: $i, Y5: $i, Y4: $i] : ((((~r1(Y4)) | (~r3(Y4, Y2, Y1))) | ((~r1(Y5)) | (~r2(Y5, Y2)))) | ((~r1(Y6)) | (~r2(Y6, Y1)))) <=> ![Y1: $i, Y6: $i, Y2: $i, Y5: $i, Y4: $i] : ((((~r1(Y4)) | (~r3(Y4, Y2, Y1))) | ((~r1(Y5)) | (~r2(Y5, Y2)))) | ((~r1(Y6)) | (~r2(Y6, Y1))))),
% 0.12/0.40 inference(pull_quant,[status(thm)],[])).
% 0.12/0.40 tff(125,plain,
% 0.12/0.40 (^[Y1: $i] : pull_quant((![Y2: $i, Y5: $i, Y4: $i] : (((~r1(Y4)) | (~r3(Y4, Y2, Y1))) | ((~r1(Y5)) | (~r2(Y5, Y2)))) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y1)))) <=> ![Y6: $i, Y2: $i, Y5: $i, Y4: $i] : ((((~r1(Y4)) | (~r3(Y4, Y2, Y1))) | ((~r1(Y5)) | (~r2(Y5, Y2)))) | ((~r1(Y6)) | (~r2(Y6, Y1)))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(126,plain,
% 0.12/0.40 (![Y1: $i] : (![Y2: $i, Y5: $i, Y4: $i] : (((~r1(Y4)) | (~r3(Y4, Y2, Y1))) | ((~r1(Y5)) | (~r2(Y5, Y2)))) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y1)))) <=> ![Y1: $i] : ![Y6: $i, Y2: $i, Y5: $i, Y4: $i] : ((((~r1(Y4)) | (~r3(Y4, Y2, Y1))) | ((~r1(Y5)) | (~r2(Y5, Y2)))) | ((~r1(Y6)) | (~r2(Y6, Y1))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[125])).
% 0.12/0.40 tff(127,plain,
% 0.12/0.40 (![Y1: $i] : (![Y2: $i, Y5: $i, Y4: $i] : (((~r1(Y4)) | (~r3(Y4, Y2, Y1))) | ((~r1(Y5)) | (~r2(Y5, Y2)))) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y1)))) <=> ![Y1: $i, Y6: $i, Y2: $i, Y5: $i, Y4: $i] : ((((~r1(Y4)) | (~r3(Y4, Y2, Y1))) | ((~r1(Y5)) | (~r2(Y5, Y2)))) | ((~r1(Y6)) | (~r2(Y6, Y1))))),
% 0.12/0.40 inference(transitivity,[status(thm)],[126, 124])).
% 0.12/0.40 tff(128,plain,
% 0.12/0.40 (![Y1: $i] : (![Y2: $i, Y5: $i, Y4: $i] : (((~r1(Y4)) | (~r3(Y4, Y2, Y1))) | ((~r1(Y5)) | (~r2(Y5, Y2)))) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y1)))) <=> ![Y1: $i, Y6: $i, Y2: $i, Y5: $i, Y4: $i] : ((((~r1(Y4)) | (~r3(Y4, Y2, Y1))) | ((~r1(Y5)) | (~r2(Y5, Y2)))) | ((~r1(Y6)) | (~r2(Y6, Y1))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[127, 123])).
% 0.20/0.41 tff(129,plain,
% 0.20/0.41 (^[Y1: $i] : rewrite((![Y2: $i] : (![Y4: $i] : ((~r1(Y4)) | (~r3(Y4, Y2, Y1))) | ![Y5: $i] : ((~r1(Y5)) | (~r2(Y5, Y2)))) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y1)))) <=> (![Y2: $i, Y5: $i, Y4: $i] : (((~r1(Y4)) | (~r3(Y4, Y2, Y1))) | ((~r1(Y5)) | (~r2(Y5, Y2)))) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y1)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(130,plain,
% 0.20/0.41 (![Y1: $i] : (![Y2: $i] : (![Y4: $i] : ((~r1(Y4)) | (~r3(Y4, Y2, Y1))) | ![Y5: $i] : ((~r1(Y5)) | (~r2(Y5, Y2)))) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y1)))) <=> ![Y1: $i] : (![Y2: $i, Y5: $i, Y4: $i] : (((~r1(Y4)) | (~r3(Y4, Y2, Y1))) | ((~r1(Y5)) | (~r2(Y5, Y2)))) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y1))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[129])).
% 0.20/0.41 tff(131,plain,
% 0.20/0.41 (![Y1: $i] : (![Y2: $i] : (![Y4: $i] : ((~r1(Y4)) | (~r3(Y4, Y2, Y1))) | ![Y5: $i] : ((~r1(Y5)) | (~r2(Y5, Y2)))) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y1)))) <=> ![Y1: $i, Y6: $i, Y2: $i, Y5: $i, Y4: $i] : ((((~r1(Y4)) | (~r3(Y4, Y2, Y1))) | ((~r1(Y5)) | (~r2(Y5, Y2)))) | ((~r1(Y6)) | (~r2(Y6, Y1))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[130, 128])).
% 0.20/0.41 tff(132,plain,
% 0.20/0.41 (^[Y1: $i] : rewrite((![Y2: $i] : (![Y4: $i] : (~(r1(Y4) & r3(Y4, Y2, Y1))) | ![Y5: $i] : (~(r1(Y5) & r2(Y5, Y2)))) | ![Y6: $i] : (~(r1(Y6) & r2(Y6, Y1)))) <=> (![Y2: $i] : (![Y4: $i] : ((~r1(Y4)) | (~r3(Y4, Y2, Y1))) | ![Y5: $i] : ((~r1(Y5)) | (~r2(Y5, Y2)))) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y1)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(133,plain,
% 0.20/0.41 (![Y1: $i] : (![Y2: $i] : (![Y4: $i] : (~(r1(Y4) & r3(Y4, Y2, Y1))) | ![Y5: $i] : (~(r1(Y5) & r2(Y5, Y2)))) | ![Y6: $i] : (~(r1(Y6) & r2(Y6, Y1)))) <=> ![Y1: $i] : (![Y2: $i] : (![Y4: $i] : ((~r1(Y4)) | (~r3(Y4, Y2, Y1))) | ![Y5: $i] : ((~r1(Y5)) | (~r2(Y5, Y2)))) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y1))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[132])).
% 0.20/0.41 tff(134,plain,
% 0.20/0.41 ((~?[Y1: $i] : (?[Y2: $i] : (?[Y4: $i] : (r1(Y4) & r3(Y4, Y2, Y1)) & ?[Y5: $i] : (r1(Y5) & r2(Y5, Y2))) & ?[Y6: $i] : (r1(Y6) & r2(Y6, Y1)))) <=> (~?[Y1: $i] : (?[Y2: $i] : (?[Y4: $i] : (r1(Y4) & r3(Y4, Y2, Y1)) & ?[Y5: $i] : (r1(Y5) & r2(Y5, Y2))) & ?[Y6: $i] : (r1(Y6) & r2(Y6, Y1))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(135,plain,
% 0.20/0.41 ((~?[Y1: $i] : (?[Y2: $i] : (?[Y4: $i] : (r1(Y4) & r3(Y4, Y2, Y1)) & ?[Y5: $i] : (r1(Y5) & r2(Y5, Y2))) & ?[Y3: $i] : ((Y1 = Y3) & ?[Y6: $i] : (r1(Y6) & r2(Y6, Y3))))) <=> (~?[Y1: $i] : (?[Y2: $i] : (?[Y4: $i] : (r1(Y4) & r3(Y4, Y2, Y1)) & ?[Y5: $i] : (r1(Y5) & r2(Y5, Y2))) & ?[Y6: $i] : (r1(Y6) & r2(Y6, Y1))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(136,axiom,(~?[Y1: $i] : (?[Y2: $i] : (?[Y4: $i] : (r1(Y4) & r3(Y4, Y2, Y1)) & ?[Y5: $i] : (r1(Y5) & r2(Y5, Y2))) & ?[Y3: $i] : ((Y1 = Y3) & ?[Y6: $i] : (r1(Y6) & r2(Y6, Y3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','zeroplusoneeqone')).
% 0.20/0.41 tff(137,plain,
% 0.20/0.41 (~?[Y1: $i] : (?[Y2: $i] : (?[Y4: $i] : (r1(Y4) & r3(Y4, Y2, Y1)) & ?[Y5: $i] : (r1(Y5) & r2(Y5, Y2))) & ?[Y6: $i] : (r1(Y6) & r2(Y6, Y1)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.20/0.41 tff(138,plain,
% 0.20/0.41 (~?[Y1: $i] : (?[Y2: $i] : (?[Y4: $i] : (r1(Y4) & r3(Y4, Y2, Y1)) & ?[Y5: $i] : (r1(Y5) & r2(Y5, Y2))) & ?[Y6: $i] : (r1(Y6) & r2(Y6, Y1)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[137, 134])).
% 0.20/0.41 tff(139,plain,
% 0.20/0.41 (~?[Y1: $i] : (?[Y2: $i] : (?[Y4: $i] : (r1(Y4) & r3(Y4, Y2, Y1)) & ?[Y5: $i] : (r1(Y5) & r2(Y5, Y2))) & ?[Y6: $i] : (r1(Y6) & r2(Y6, Y1)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[138, 134])).
% 0.20/0.41 tff(140,plain,
% 0.20/0.41 (~?[Y1: $i] : (?[Y2: $i] : (?[Y4: $i] : (r1(Y4) & r3(Y4, Y2, Y1)) & ?[Y5: $i] : (r1(Y5) & r2(Y5, Y2))) & ?[Y6: $i] : (r1(Y6) & r2(Y6, Y1)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[139, 134])).
% 0.20/0.41 tff(141,plain,
% 0.20/0.41 (^[Y1: $i] : nnf_neg(nnf_neg(proof_bind(^[Y2: $i] : nnf_neg(nnf_neg(proof_bind(^[Y4: $i] : refl($oeq((~(r1(Y4) & r3(Y4, Y2, Y1))), (~(r1(Y4) & r3(Y4, Y2, Y1)))))), $oeq((~?[Y4: $i] : (r1(Y4) & r3(Y4, Y2, Y1))), ![Y4: $i] : (~(r1(Y4) & r3(Y4, Y2, Y1))))), nnf_neg(proof_bind(^[Y5: $i] : refl($oeq((~(r1(Y5) & r2(Y5, Y2))), (~(r1(Y5) & r2(Y5, Y2)))))), $oeq((~?[Y5: $i] : (r1(Y5) & r2(Y5, Y2))), ![Y5: $i] : (~(r1(Y5) & r2(Y5, Y2))))), $oeq((~(?[Y4: $i] : (r1(Y4) & r3(Y4, Y2, Y1)) & ?[Y5: $i] : (r1(Y5) & r2(Y5, Y2)))), (![Y4: $i] : (~(r1(Y4) & r3(Y4, Y2, Y1))) | ![Y5: $i] : (~(r1(Y5) & r2(Y5, Y2))))))), $oeq((~?[Y2: $i] : (?[Y4: $i] : (r1(Y4) & r3(Y4, Y2, Y1)) & ?[Y5: $i] : (r1(Y5) & r2(Y5, Y2)))), ![Y2: $i] : (![Y4: $i] : (~(r1(Y4) & r3(Y4, Y2, Y1))) | ![Y5: $i] : (~(r1(Y5) & r2(Y5, Y2)))))), nnf_neg(proof_bind(^[Y6: $i] : refl($oeq((~(r1(Y6) & r2(Y6, Y1))), (~(r1(Y6) & r2(Y6, Y1)))))), $oeq((~?[Y6: $i] : (r1(Y6) & r2(Y6, Y1))), ![Y6: $i] : (~(r1(Y6) & r2(Y6, Y1))))), $oeq((~(?[Y2: $i] : (?[Y4: $i] : (r1(Y4) & r3(Y4, Y2, Y1)) & ?[Y5: $i] : (r1(Y5) & r2(Y5, Y2))) & ?[Y6: $i] : (r1(Y6) & r2(Y6, Y1)))), (![Y2: $i] : (![Y4: $i] : (~(r1(Y4) & r3(Y4, Y2, Y1))) | ![Y5: $i] : (~(r1(Y5) & r2(Y5, Y2)))) | ![Y6: $i] : (~(r1(Y6) & r2(Y6, Y1))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(142,plain,(
% 0.20/0.41 ![Y1: $i] : (![Y2: $i] : (![Y4: $i] : (~(r1(Y4) & r3(Y4, Y2, Y1))) | ![Y5: $i] : (~(r1(Y5) & r2(Y5, Y2)))) | ![Y6: $i] : (~(r1(Y6) & r2(Y6, Y1))))),
% 0.20/0.41 inference(nnf-neg,[status(sab)],[140, 141])).
% 0.20/0.41 tff(143,plain,
% 0.20/0.41 (![Y1: $i] : (![Y2: $i] : (![Y4: $i] : ((~r1(Y4)) | (~r3(Y4, Y2, Y1))) | ![Y5: $i] : ((~r1(Y5)) | (~r2(Y5, Y2)))) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y1))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[142, 133])).
% 0.20/0.41 tff(144,plain,
% 0.20/0.41 (![Y1: $i, Y6: $i, Y2: $i, Y5: $i, Y4: $i] : ((((~r1(Y4)) | (~r3(Y4, Y2, Y1))) | ((~r1(Y5)) | (~r2(Y5, Y2)))) | ((~r1(Y6)) | (~r2(Y6, Y1))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[143, 131])).
% 0.20/0.41 tff(145,plain,
% 0.20/0.41 (![Y1: $i, Y6: $i, Y2: $i, Y5: $i, Y4: $i] : ((~r1(Y4)) | (~r3(Y4, Y2, Y1)) | (~r1(Y6)) | (~r1(Y5)) | (~r2(Y5, Y2)) | (~r2(Y6, Y1)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[144, 121])).
% 0.20/0.41 tff(146,plain,
% 0.20/0.41 (((~![Y1: $i, Y6: $i, Y2: $i, Y5: $i, Y4: $i] : ((~r1(Y4)) | (~r3(Y4, Y2, Y1)) | (~r1(Y6)) | (~r1(Y5)) | (~r2(Y5, Y2)) | (~r2(Y6, Y1)))) | ((~r1(Y24!0)) | (~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))) | (~r3(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r2(tptp_fun_Y7_6(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r1(tptp_fun_Y7_6(Y24!0, Y24!0))))) <=> ((~![Y1: $i, Y6: $i, Y2: $i, Y5: $i, Y4: $i] : ((~r1(Y4)) | (~r3(Y4, Y2, Y1)) | (~r1(Y6)) | (~r1(Y5)) | (~r2(Y5, Y2)) | (~r2(Y6, Y1)))) | (~r1(Y24!0)) | (~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))) | (~r3(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r2(tptp_fun_Y7_6(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r1(tptp_fun_Y7_6(Y24!0, Y24!0))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(147,plain,
% 0.20/0.41 (((~r1(Y24!0)) | (~r3(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r1(tptp_fun_Y7_6(Y24!0, Y24!0))) | (~r1(Y24!0)) | (~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))) | (~r2(tptp_fun_Y7_6(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)))) <=> ((~r1(Y24!0)) | (~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))) | (~r3(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r2(tptp_fun_Y7_6(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r1(tptp_fun_Y7_6(Y24!0, Y24!0))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(148,plain,
% 0.20/0.41 (((~![Y1: $i, Y6: $i, Y2: $i, Y5: $i, Y4: $i] : ((~r1(Y4)) | (~r3(Y4, Y2, Y1)) | (~r1(Y6)) | (~r1(Y5)) | (~r2(Y5, Y2)) | (~r2(Y6, Y1)))) | ((~r1(Y24!0)) | (~r3(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r1(tptp_fun_Y7_6(Y24!0, Y24!0))) | (~r1(Y24!0)) | (~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))) | (~r2(tptp_fun_Y7_6(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))))) <=> ((~![Y1: $i, Y6: $i, Y2: $i, Y5: $i, Y4: $i] : ((~r1(Y4)) | (~r3(Y4, Y2, Y1)) | (~r1(Y6)) | (~r1(Y5)) | (~r2(Y5, Y2)) | (~r2(Y6, Y1)))) | ((~r1(Y24!0)) | (~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))) | (~r3(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r2(tptp_fun_Y7_6(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r1(tptp_fun_Y7_6(Y24!0, Y24!0)))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[147])).
% 0.20/0.41 tff(149,plain,
% 0.20/0.41 (((~![Y1: $i, Y6: $i, Y2: $i, Y5: $i, Y4: $i] : ((~r1(Y4)) | (~r3(Y4, Y2, Y1)) | (~r1(Y6)) | (~r1(Y5)) | (~r2(Y5, Y2)) | (~r2(Y6, Y1)))) | ((~r1(Y24!0)) | (~r3(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r1(tptp_fun_Y7_6(Y24!0, Y24!0))) | (~r1(Y24!0)) | (~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))) | (~r2(tptp_fun_Y7_6(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))))) <=> ((~![Y1: $i, Y6: $i, Y2: $i, Y5: $i, Y4: $i] : ((~r1(Y4)) | (~r3(Y4, Y2, Y1)) | (~r1(Y6)) | (~r1(Y5)) | (~r2(Y5, Y2)) | (~r2(Y6, Y1)))) | (~r1(Y24!0)) | (~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))) | (~r3(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r2(tptp_fun_Y7_6(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r1(tptp_fun_Y7_6(Y24!0, Y24!0))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[148, 146])).
% 0.20/0.41 tff(150,plain,
% 0.20/0.41 ((~![Y1: $i, Y6: $i, Y2: $i, Y5: $i, Y4: $i] : ((~r1(Y4)) | (~r3(Y4, Y2, Y1)) | (~r1(Y6)) | (~r1(Y5)) | (~r2(Y5, Y2)) | (~r2(Y6, Y1)))) | ((~r1(Y24!0)) | (~r3(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r1(tptp_fun_Y7_6(Y24!0, Y24!0))) | (~r1(Y24!0)) | (~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))) | (~r2(tptp_fun_Y7_6(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(151,plain,
% 0.20/0.41 ((~![Y1: $i, Y6: $i, Y2: $i, Y5: $i, Y4: $i] : ((~r1(Y4)) | (~r3(Y4, Y2, Y1)) | (~r1(Y6)) | (~r1(Y5)) | (~r2(Y5, Y2)) | (~r2(Y6, Y1)))) | (~r1(Y24!0)) | (~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))) | (~r3(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r2(tptp_fun_Y7_6(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r1(tptp_fun_Y7_6(Y24!0, Y24!0)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.20/0.41 tff(152,plain,
% 0.20/0.41 (~r1(tptp_fun_Y7_6(Y24!0, Y24!0))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[151, 145, 112, 119, 117, 115])).
% 0.20/0.41 tff(153,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[152, 113])).
% 0.20/0.41 % SZS output end Proof
% 0.20/0.41 % E exiting
%------------------------------------------------------------------------------