%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUN069+2 : TPTP v9.0.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 0.12s 0.37s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUN069+2 : TPTP v9.0.0. Released v7.3.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n007.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 02:12:50 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.37 % SZS status Theorem
% 0.12/0.37 % SZS output start Proof
% 0.12/0.37 tff(r1_type, type, (
% 0.12/0.37 r1: $i > $o)).
% 0.12/0.37 tff(tptp_fun_Y16_10_type, type, (
% 0.12/0.37 tptp_fun_Y16_10: $i > $i)).
% 0.12/0.37 tff(tptp_fun_Y24_0_type, type, (
% 0.12/0.37 tptp_fun_Y24_0: $i)).
% 0.12/0.37 tff(r3_type, type, (
% 0.12/0.37 r3: ( $i * $i * $i ) > $o)).
% 0.12/0.37 tff(r2_type, type, (
% 0.12/0.37 r2: ( $i * $i ) > $o)).
% 0.12/0.37 tff(tptp_fun_Y15_5_type, type, (
% 0.12/0.37 tptp_fun_Y15_5: ( $i * $i ) > $i)).
% 0.12/0.37 tff(tptp_fun_Y7_6_type, type, (
% 0.12/0.37 tptp_fun_Y7_6: ( $i * $i ) > $i)).
% 0.12/0.37 tff(tptp_fun_Y4_4_type, type, (
% 0.12/0.37 tptp_fun_Y4_4: ( $i * $i ) > $i)).
% 0.12/0.37 tff(1,plain,
% 0.12/0.37 (^[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)))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(2,plain,
% 0.12/0.37 (![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))))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.37 tff(3,plain,
% 0.12/0.37 (![X4: $i] : ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4)) <=> ![X4: $i] : ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(4,plain,
% 0.12/0.38 (^[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))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(5,plain,
% 0.12/0.38 (![X4: $i] : ?[Y9: $i] : (?[Y16: $i] : (r1(Y16) & r3(X4, Y16, Y9)) & (Y9 = X4)) <=> ![X4: $i] : ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[4])).
% 0.12/0.38 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')).
% 0.12/0.38 tff(7,plain,
% 0.12/0.38 (![X4: $i] : ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.12/0.38 tff(8,plain,
% 0.12/0.38 (![X4: $i] : ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.12/0.38 tff(9,plain,(
% 0.12/0.38 ![X4: $i] : (r1(tptp_fun_Y16_10(X4)) & r3(X4, tptp_fun_Y16_10(X4), X4))),
% 0.12/0.38 inference(skolemize,[status(sab)],[8])).
% 0.12/0.38 tff(10,plain,
% 0.12/0.38 (![X4: $i] : (~((~r1(tptp_fun_Y16_10(X4))) | (~r3(X4, tptp_fun_Y16_10(X4), X4))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.12/0.38 tff(11,plain,
% 0.12/0.38 ((~![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))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(12,plain,
% 0.12/0.38 (~((~r1(tptp_fun_Y16_10(Y24!0))) | (~r3(Y24!0, tptp_fun_Y16_10(Y24!0), Y24!0)))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.12/0.38 tff(13,plain,
% 0.12/0.38 (((~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))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(14,plain,
% 0.12/0.38 (r1(tptp_fun_Y16_10(Y24!0))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[13, 12])).
% 0.12/0.38 tff(15,plain,
% 0.12/0.38 ((r1(tptp_fun_Y16_10(Y24!0)) | (tptp_fun_Y16_10(Y24!0) = Y24!0)) | (~r1(tptp_fun_Y16_10(Y24!0)))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(16,plain,
% 0.12/0.38 (r1(tptp_fun_Y16_10(Y24!0)) | (tptp_fun_Y16_10(Y24!0) = Y24!0)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[15, 14])).
% 0.12/0.38 tff(17,plain,
% 0.12/0.38 (^[X19: $i] : refl(((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))) <=> ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(18,plain,
% 0.12/0.38 (![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))) <=> ![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[17])).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 (^[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))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(20,plain,
% 0.20/0.38 (![X19: $i] : ((r1(X19) & (X19 = Y24!0)) | ((~r1(X19)) & (~(X19 = Y24!0)))) <=> ![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[19])).
% 0.20/0.38 tff(21,plain,
% 0.20/0.38 (?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24)))) <=> ?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(22,plain,
% 0.20/0.38 (^[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))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(23,plain,
% 0.20/0.38 (?[Y24: $i] : ![X19: $i] : (((~r1(X19)) & (~(X19 = Y24))) | (r1(X19) & (X19 = Y24))) <=> ?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[22])).
% 0.20/0.38 tff(24,axiom,(?[Y24: $i] : ![X19: $i] : (((~r1(X19)) & (~(X19 = Y24))) | (r1(X19) & (X19 = Y24)))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax','axiom_1')).
% 0.20/0.38 tff(25,plain,
% 0.20/0.38 (?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.20/0.38 tff(26,plain,
% 0.20/0.38 (?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.20/0.38 tff(27,plain,(
% 0.20/0.38 $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)))))),
% 0.20/0.38 inference(transitivity,[status(sab)],[26])).
% 0.20/0.38 tff(28,plain,
% 0.20/0.38 (![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.20/0.38 tff(29,plain,
% 0.20/0.38 (![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[28, 18])).
% 0.20/0.38 tff(30,plain,
% 0.20/0.38 (((~![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))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(31,plain,
% 0.20/0.38 ((~![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))))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(32,plain,
% 0.20/0.38 ((~![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)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.20/0.38 tff(33,plain,
% 0.20/0.38 (~((~r1(tptp_fun_Y16_10(Y24!0))) | (~(tptp_fun_Y16_10(Y24!0) = Y24!0)))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[32, 29, 16])).
% 0.20/0.38 tff(34,plain,
% 0.20/0.38 (((~r1(tptp_fun_Y16_10(Y24!0))) | (~(tptp_fun_Y16_10(Y24!0) = Y24!0))) | (tptp_fun_Y16_10(Y24!0) = Y24!0)),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(35,plain,
% 0.20/0.38 (tptp_fun_Y16_10(Y24!0) = Y24!0),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[34, 33])).
% 0.20/0.38 tff(36,plain,
% 0.20/0.38 (r1(tptp_fun_Y16_10(Y24!0)) <=> r1(Y24!0)),
% 0.20/0.38 inference(monotonicity,[status(thm)],[35])).
% 0.20/0.38 tff(37,plain,
% 0.20/0.38 (r1(Y24!0) <=> r1(tptp_fun_Y16_10(Y24!0))),
% 0.20/0.38 inference(symmetry,[status(thm)],[36])).
% 0.20/0.38 tff(38,plain,
% 0.20/0.38 ((~r1(Y24!0)) <=> (~r1(tptp_fun_Y16_10(Y24!0)))),
% 0.20/0.38 inference(monotonicity,[status(thm)],[37])).
% 0.20/0.38 tff(39,plain,
% 0.20/0.38 (^[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))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(40,plain,
% 0.20/0.38 (![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)))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[39])).
% 0.20/0.38 tff(41,plain,
% 0.20/0.38 (^[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))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(42,plain,
% 0.20/0.38 (![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)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[41])).
% 0.20/0.38 tff(43,plain,
% 0.20/0.38 (![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)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(44,plain,
% 0.20/0.38 (^[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)))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(45,plain,
% 0.20/0.38 (![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)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[44])).
% 0.20/0.38 tff(46,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')).
% 0.20/0.38 tff(47,plain,
% 0.20/0.38 (![X1: $i, X8: $i] : ?[Y4: $i] : (?[Y15: $i] : (r2(X8, Y15) & r3(X1, Y15, Y4)) & ?[Y7: $i] : (r2(Y7, Y4) & r3(X1, X8, Y7)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.20/0.38 tff(48,plain,
% 0.20/0.38 (![X1: $i, X8: $i] : ?[Y4: $i] : (?[Y15: $i] : (r2(X8, Y15) & r3(X1, Y15, Y4)) & ?[Y7: $i] : (r2(Y7, Y4) & r3(X1, X8, Y7)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.20/0.38 tff(49,plain,(
% 0.20/0.38 ![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))))),
% 0.20/0.38 inference(skolemize,[status(sab)],[48])).
% 0.20/0.38 tff(50,plain,
% 0.20/0.38 (![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)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[49, 42])).
% 0.20/0.38 tff(51,plain,
% 0.20/0.38 (![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)))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[50, 40])).
% 0.20/0.38 tff(52,plain,
% 0.20/0.38 ((~![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)))))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(53,plain,
% 0.20/0.38 (~((~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))))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.20/0.38 tff(54,plain,
% 0.20/0.38 (((~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))),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(55,plain,
% 0.20/0.38 (r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.20/0.38 tff(56,plain,
% 0.20/0.38 (^[Y1: $i, Y2: $i] : refl(((~r1(Y2)) | (~r2(Y2, Y1))) <=> ((~r1(Y2)) | (~r2(Y2, Y1))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(57,plain,
% 0.20/0.38 (![Y1: $i, Y2: $i] : ((~r1(Y2)) | (~r2(Y2, Y1))) <=> ![Y1: $i, Y2: $i] : ((~r1(Y2)) | (~r2(Y2, Y1)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[56])).
% 0.20/0.38 tff(58,plain,
% 0.20/0.38 (^[Y1: $i, Y2: $i] : trans(monotonicity(rewrite((r1(Y2) & r2(Y2, Y1)) <=> (~((~r1(Y2)) | (~r2(Y2, Y1))))), ((~(r1(Y2) & r2(Y2, Y1))) <=> (~(~((~r1(Y2)) | (~r2(Y2, Y1))))))), rewrite((~(~((~r1(Y2)) | (~r2(Y2, Y1))))) <=> ((~r1(Y2)) | (~r2(Y2, Y1)))), ((~(r1(Y2) & r2(Y2, Y1))) <=> ((~r1(Y2)) | (~r2(Y2, Y1)))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(59,plain,
% 0.20/0.38 (![Y1: $i, Y2: $i] : (~(r1(Y2) & r2(Y2, Y1))) <=> ![Y1: $i, Y2: $i] : ((~r1(Y2)) | (~r2(Y2, Y1)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[58])).
% 0.20/0.38 tff(60,plain,
% 0.20/0.38 ((~?[Y1: $i, Y2: $i] : (r1(Y2) & r2(Y2, Y1))) <=> (~?[Y1: $i, Y2: $i] : (r1(Y2) & r2(Y2, Y1)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(61,plain,
% 0.20/0.38 ((~?[Y1: $i] : ((Y1 = Y1) & ?[Y2: $i] : (r1(Y2) & r2(Y2, Y1)))) <=> (~?[Y1: $i, Y2: $i] : (r1(Y2) & r2(Y2, Y1)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(62,axiom,(~?[Y1: $i] : ((Y1 = Y1) & ?[Y2: $i] : (r1(Y2) & r2(Y2, Y1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','oneeqone')).
% 0.20/0.38 tff(63,plain,
% 0.20/0.38 (~?[Y1: $i, Y2: $i] : (r1(Y2) & r2(Y2, Y1))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.20/0.38 tff(64,plain,
% 0.20/0.38 (~?[Y1: $i, Y2: $i] : (r1(Y2) & r2(Y2, Y1))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[63, 60])).
% 0.20/0.38 tff(65,plain,
% 0.20/0.38 (~?[Y1: $i, Y2: $i] : (r1(Y2) & r2(Y2, Y1))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.20/0.38 tff(66,plain,
% 0.20/0.38 (~?[Y1: $i, Y2: $i] : (r1(Y2) & r2(Y2, Y1))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[65, 60])).
% 0.20/0.38 tff(67,plain,
% 0.20/0.38 (^[Y1: $i, Y2: $i] : refl($oeq((~(r1(Y2) & r2(Y2, Y1))), (~(r1(Y2) & r2(Y2, Y1)))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(68,plain,(
% 0.20/0.38 ![Y1: $i, Y2: $i] : (~(r1(Y2) & r2(Y2, Y1)))),
% 0.20/0.38 inference(nnf-neg,[status(sab)],[66, 67])).
% 0.20/0.38 tff(69,plain,
% 0.20/0.38 (![Y1: $i, Y2: $i] : ((~r1(Y2)) | (~r2(Y2, Y1)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[68, 59])).
% 0.20/0.38 tff(70,plain,
% 0.20/0.38 (![Y1: $i, Y2: $i] : ((~r1(Y2)) | (~r2(Y2, Y1)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[69, 57])).
% 0.20/0.38 tff(71,plain,
% 0.20/0.38 (((~![Y1: $i, Y2: $i] : ((~r1(Y2)) | (~r2(Y2, Y1)))) | ((~r1(Y24!0)) | (~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))))) <=> ((~![Y1: $i, Y2: $i] : ((~r1(Y2)) | (~r2(Y2, Y1)))) | (~r1(Y24!0)) | (~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(72,plain,
% 0.20/0.38 ((~![Y1: $i, Y2: $i] : ((~r1(Y2)) | (~r2(Y2, Y1)))) | ((~r1(Y24!0)) | (~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(73,plain,
% 0.20/0.38 ((~![Y1: $i, Y2: $i] : ((~r1(Y2)) | (~r2(Y2, Y1)))) | (~r1(Y24!0)) | (~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.20/0.38 tff(74,plain,
% 0.20/0.38 (~r1(Y24!0)),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[73, 70, 55])).
% 0.20/0.38 tff(75,plain,
% 0.20/0.38 (~r1(tptp_fun_Y16_10(Y24!0))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[74, 38])).
% 0.20/0.38 tff(76,plain,
% 0.20/0.38 ($false),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[14, 75])).
% 0.20/0.38 % SZS output end Proof
% 0.20/0.39 % E exiting
%------------------------------------------------------------------------------