%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUN080+2 : TPTP v9.0.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 05:22:38 AM UTC 2025
% Result : Theorem 0.10s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10 % Problem : NUN080+2 : TPTP v9.0.0. Released v7.3.0.
% 0.06/0.10 % Command : run_E %s %d THM
% 0.10/0.32 % Computer : n011.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Fri Jun 20 02:16:27 EDT 2025
% 0.10/0.32 % CPUTime :
% 0.10/0.37 % SZS status Theorem
% 0.10/0.37 % SZS output start Proof
% 0.10/0.37 tff(r2_type, type, (
% 0.10/0.37 r2: ( $i * $i ) > $o)).
% 0.10/0.37 tff(tptp_fun_Y21_1_type, type, (
% 0.10/0.37 tptp_fun_Y21_1: $i > $i)).
% 0.10/0.37 tff(tptp_fun_Y24_0_type, type, (
% 0.10/0.37 tptp_fun_Y24_0: $i)).
% 0.10/0.37 tff(r1_type, type, (
% 0.10/0.37 r1: $i > $o)).
% 0.10/0.37 tff(tptp_fun_Y15_5_type, type, (
% 0.10/0.37 tptp_fun_Y15_5: ( $i * $i ) > $i)).
% 0.10/0.37 tff(tptp_fun_Y22_2_type, type, (
% 0.10/0.37 tptp_fun_Y22_2: ( $i * $i ) > $i)).
% 0.10/0.37 tff(tptp_fun_Y16_10_type, type, (
% 0.10/0.37 tptp_fun_Y16_10: $i > $i)).
% 0.10/0.37 tff(r3_type, type, (
% 0.10/0.37 r3: ( $i * $i * $i ) > $o)).
% 0.10/0.37 tff(tptp_fun_Y4_4_type, type, (
% 0.10/0.37 tptp_fun_Y4_4: ( $i * $i ) > $i)).
% 0.10/0.37 tff(tptp_fun_Y7_6_type, type, (
% 0.10/0.37 tptp_fun_Y7_6: ( $i * $i ) > $i)).
% 0.10/0.37 tff(1,plain,
% 0.10/0.37 (^[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))))))),
% 0.10/0.37 inference(bind,[status(th)],[])).
% 0.10/0.37 tff(2,plain,
% 0.10/0.37 (![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)))))),
% 0.10/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.10/0.37 tff(3,plain,
% 0.10/0.37 (^[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))))),
% 0.10/0.37 inference(bind,[status(th)],[])).
% 0.10/0.37 tff(4,plain,
% 0.10/0.37 (![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)))),
% 0.10/0.37 inference(quant_intro,[status(thm)],[3])).
% 0.10/0.37 tff(5,plain,
% 0.10/0.37 (![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)))),
% 0.10/0.37 inference(rewrite,[status(thm)],[])).
% 0.10/0.37 tff(6,plain,
% 0.10/0.37 (^[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)))))),
% 0.10/0.37 inference(bind,[status(th)],[])).
% 0.10/0.37 tff(7,plain,
% 0.10/0.37 (![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)))),
% 0.10/0.37 inference(quant_intro,[status(thm)],[6])).
% 0.10/0.37 tff(8,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')).
% 0.10/0.37 tff(9,plain,
% 0.10/0.37 (![X1: $i, X8: $i] : ?[Y4: $i] : (?[Y15: $i] : (r2(X8, Y15) & r3(X1, Y15, Y4)) & ?[Y7: $i] : (r2(Y7, Y4) & r3(X1, X8, Y7)))),
% 0.10/0.38 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.10/0.38 tff(10,plain,
% 0.10/0.38 (![X1: $i, X8: $i] : ?[Y4: $i] : (?[Y15: $i] : (r2(X8, Y15) & r3(X1, Y15, Y4)) & ?[Y7: $i] : (r2(Y7, Y4) & r3(X1, X8, Y7)))),
% 0.10/0.38 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.10/0.38 tff(11,plain,(
% 0.10/0.38 ![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))))),
% 0.10/0.38 inference(skolemize,[status(sab)],[10])).
% 0.10/0.38 tff(12,plain,
% 0.10/0.38 (![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)))),
% 0.10/0.38 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.10/0.38 tff(13,plain,
% 0.10/0.38 (![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)))))),
% 0.10/0.38 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.10/0.38 tff(14,plain,
% 0.10/0.38 ((~![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(tptp_fun_Y21_1(Y24!0), tptp_fun_Y15_5(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))) | (~r3(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y15_5(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))) | (~r2(tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))) | (~r3(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0), tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0))))))),
% 0.10/0.38 inference(quant_inst,[status(thm)],[])).
% 0.10/0.38 tff(15,plain,
% 0.10/0.38 (~((~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y15_5(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))) | (~r3(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y15_5(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))) | (~r2(tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))) | (~r3(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0), tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))))),
% 0.10/0.38 inference(unit_resolution,[status(thm)],[14, 13])).
% 0.10/0.38 tff(16,plain,
% 0.10/0.38 (((~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y15_5(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))) | (~r3(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y15_5(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))) | (~r2(tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))) | (~r3(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0), tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0))))) | r3(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y15_5(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))),
% 0.10/0.38 inference(tautology,[status(thm)],[])).
% 0.10/0.38 tff(17,plain,
% 0.10/0.38 (r3(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y15_5(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))),
% 0.10/0.38 inference(unit_resolution,[status(thm)],[16, 15])).
% 0.10/0.38 tff(18,plain,
% 0.10/0.38 (^[Y1: $i, Y2: $i, Y4: $i] : refl(((~r3(Y1, Y4, Y2)) | ![Y5: $i] : ((~r2(Y5, Y4)) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y5))))) <=> ((~r3(Y1, Y4, Y2)) | ![Y5: $i] : ((~r2(Y5, Y4)) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y5))))))),
% 0.10/0.38 inference(bind,[status(th)],[])).
% 0.10/0.38 tff(19,plain,
% 0.10/0.38 (![Y1: $i, Y2: $i, Y4: $i] : ((~r3(Y1, Y4, Y2)) | ![Y5: $i] : ((~r2(Y5, Y4)) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y5))))) <=> ![Y1: $i, Y2: $i, Y4: $i] : ((~r3(Y1, Y4, Y2)) | ![Y5: $i] : ((~r2(Y5, Y4)) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y5)))))),
% 0.10/0.38 inference(quant_intro,[status(thm)],[18])).
% 0.10/0.38 tff(20,plain,
% 0.10/0.38 (^[Y1: $i, Y2: $i, Y4: $i] : rewrite(((~r3(Y1, Y4, Y2)) | ![Y5: $i] : ((~r2(Y5, Y4)) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y5))))) <=> ((~r3(Y1, Y4, Y2)) | ![Y5: $i] : ((~r2(Y5, Y4)) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y5))))))),
% 0.10/0.38 inference(bind,[status(th)],[])).
% 0.10/0.38 tff(21,plain,
% 0.10/0.38 (![Y1: $i, Y2: $i, Y4: $i] : ((~r3(Y1, Y4, Y2)) | ![Y5: $i] : ((~r2(Y5, Y4)) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y5))))) <=> ![Y1: $i, Y2: $i, Y4: $i] : ((~r3(Y1, Y4, Y2)) | ![Y5: $i] : ((~r2(Y5, Y4)) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y5)))))),
% 0.10/0.38 inference(quant_intro,[status(thm)],[20])).
% 0.10/0.38 tff(22,plain,
% 0.10/0.38 (![Y1: $i, Y2: $i, Y4: $i] : ((~r3(Y1, Y4, Y2)) | ![Y5: $i] : ((~r2(Y5, Y4)) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y5))))) <=> ![Y1: $i, Y2: $i, Y4: $i] : ((~r3(Y1, Y4, Y2)) | ![Y5: $i] : ((~r2(Y5, Y4)) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y5)))))),
% 0.10/0.38 inference(transitivity,[status(thm)],[21, 19])).
% 0.10/0.38 tff(23,plain,
% 0.10/0.38 (^[Y1: $i, Y2: $i, Y4: $i] : rewrite(((~r3(Y1, Y4, Y2)) | ![Y5: $i] : ((~r2(Y5, Y4)) | ![Y6: $i] : (~(r1(Y6) & r2(Y6, Y5))))) <=> ((~r3(Y1, Y4, Y2)) | ![Y5: $i] : ((~r2(Y5, Y4)) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y5))))))),
% 0.10/0.38 inference(bind,[status(th)],[])).
% 0.10/0.38 tff(24,plain,
% 0.10/0.38 (![Y1: $i, Y2: $i, Y4: $i] : ((~r3(Y1, Y4, Y2)) | ![Y5: $i] : ((~r2(Y5, Y4)) | ![Y6: $i] : (~(r1(Y6) & r2(Y6, Y5))))) <=> ![Y1: $i, Y2: $i, Y4: $i] : ((~r3(Y1, Y4, Y2)) | ![Y5: $i] : ((~r2(Y5, Y4)) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y5)))))),
% 0.10/0.38 inference(quant_intro,[status(thm)],[23])).
% 0.10/0.38 tff(25,plain,
% 0.10/0.38 ((~?[Y1: $i, Y2: $i, Y4: $i] : (r3(Y1, Y4, Y2) & ?[Y5: $i] : (r2(Y5, Y4) & ?[Y6: $i] : (r1(Y6) & r2(Y6, Y5))))) <=> (~?[Y1: $i, Y2: $i, Y4: $i] : (r3(Y1, Y4, Y2) & ?[Y5: $i] : (r2(Y5, Y4) & ?[Y6: $i] : (r1(Y6) & r2(Y6, Y5)))))),
% 0.10/0.38 inference(rewrite,[status(thm)],[])).
% 0.10/0.38 tff(26,plain,
% 0.10/0.38 ((~?[Y1: $i, Y2: $i, Y3: $i] : ((Y3 = Y2) & ?[Y4: $i] : (r3(Y1, Y4, Y3) & ?[Y5: $i] : (r2(Y5, Y4) & ?[Y6: $i] : (r1(Y6) & r2(Y6, Y5)))))) <=> (~?[Y1: $i, Y2: $i, Y4: $i] : (r3(Y1, Y4, Y2) & ?[Y5: $i] : (r2(Y5, Y4) & ?[Y6: $i] : (r1(Y6) & r2(Y6, Y5)))))),
% 0.10/0.38 inference(rewrite,[status(thm)],[])).
% 0.10/0.38 tff(27,axiom,(~?[Y1: $i, Y2: $i, Y3: $i] : ((Y3 = Y2) & ?[Y4: $i] : (r3(Y1, Y4, Y3) & ?[Y5: $i] : (r2(Y5, Y4) & ?[Y6: $i] : (r1(Y6) & r2(Y6, Y5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','xplustwoeqy')).
% 0.10/0.38 tff(28,plain,
% 0.10/0.38 (~?[Y1: $i, Y2: $i, Y4: $i] : (r3(Y1, Y4, Y2) & ?[Y5: $i] : (r2(Y5, Y4) & ?[Y6: $i] : (r1(Y6) & r2(Y6, Y5))))),
% 0.10/0.38 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.10/0.38 tff(29,plain,
% 0.10/0.38 (~?[Y1: $i, Y2: $i, Y4: $i] : (r3(Y1, Y4, Y2) & ?[Y5: $i] : (r2(Y5, Y4) & ?[Y6: $i] : (r1(Y6) & r2(Y6, Y5))))),
% 0.10/0.38 inference(modus_ponens,[status(thm)],[28, 25])).
% 0.10/0.38 tff(30,plain,
% 0.10/0.38 (~?[Y1: $i, Y2: $i, Y4: $i] : (r3(Y1, Y4, Y2) & ?[Y5: $i] : (r2(Y5, Y4) & ?[Y6: $i] : (r1(Y6) & r2(Y6, Y5))))),
% 0.10/0.38 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.10/0.38 tff(31,plain,
% 0.10/0.38 (~?[Y1: $i, Y2: $i, Y4: $i] : (r3(Y1, Y4, Y2) & ?[Y5: $i] : (r2(Y5, Y4) & ?[Y6: $i] : (r1(Y6) & r2(Y6, Y5))))),
% 0.10/0.38 inference(modus_ponens,[status(thm)],[30, 25])).
% 0.10/0.38 tff(32,plain,
% 0.10/0.38 (^[Y1: $i, Y2: $i, Y4: $i] : nnf_neg(refl($oeq((~r3(Y1, Y4, Y2)), (~r3(Y1, Y4, Y2)))), nnf_neg(proof_bind(^[Y5: $i] : nnf_neg(refl($oeq((~r2(Y5, Y4)), (~r2(Y5, Y4)))), nnf_neg(proof_bind(^[Y6: $i] : refl($oeq((~(r1(Y6) & r2(Y6, Y5))), (~(r1(Y6) & r2(Y6, Y5)))))), $oeq((~?[Y6: $i] : (r1(Y6) & r2(Y6, Y5))), ![Y6: $i] : (~(r1(Y6) & r2(Y6, Y5))))), $oeq((~(r2(Y5, Y4) & ?[Y6: $i] : (r1(Y6) & r2(Y6, Y5)))), ((~r2(Y5, Y4)) | ![Y6: $i] : (~(r1(Y6) & r2(Y6, Y5))))))), $oeq((~?[Y5: $i] : (r2(Y5, Y4) & ?[Y6: $i] : (r1(Y6) & r2(Y6, Y5)))), ![Y5: $i] : ((~r2(Y5, Y4)) | ![Y6: $i] : (~(r1(Y6) & r2(Y6, Y5)))))), $oeq((~(r3(Y1, Y4, Y2) & ?[Y5: $i] : (r2(Y5, Y4) & ?[Y6: $i] : (r1(Y6) & r2(Y6, Y5))))), ((~r3(Y1, Y4, Y2)) | ![Y5: $i] : ((~r2(Y5, Y4)) | ![Y6: $i] : (~(r1(Y6) & r2(Y6, Y5)))))))),
% 0.10/0.38 inference(bind,[status(th)],[])).
% 0.10/0.38 tff(33,plain,(
% 0.10/0.38 ![Y1: $i, Y2: $i, Y4: $i] : ((~r3(Y1, Y4, Y2)) | ![Y5: $i] : ((~r2(Y5, Y4)) | ![Y6: $i] : (~(r1(Y6) & r2(Y6, Y5)))))),
% 0.10/0.38 inference(nnf-neg,[status(sab)],[31, 32])).
% 0.10/0.38 tff(34,plain,
% 0.10/0.38 (![Y1: $i, Y2: $i, Y4: $i] : ((~r3(Y1, Y4, Y2)) | ![Y5: $i] : ((~r2(Y5, Y4)) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y5)))))),
% 0.10/0.38 inference(modus_ponens,[status(thm)],[33, 24])).
% 0.10/0.38 tff(35,plain,
% 0.10/0.38 (![Y1: $i, Y2: $i, Y4: $i] : ((~r3(Y1, Y4, Y2)) | ![Y5: $i] : ((~r2(Y5, Y4)) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y5)))))),
% 0.10/0.38 inference(modus_ponens,[status(thm)],[34, 22])).
% 0.10/0.38 tff(36,plain,
% 0.10/0.38 (((~![Y1: $i, Y2: $i, Y4: $i] : ((~r3(Y1, Y4, Y2)) | ![Y5: $i] : ((~r2(Y5, Y4)) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y5)))))) | ((~r3(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y15_5(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))) | ![Y5: $i] : ((~r2(Y5, tptp_fun_Y15_5(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y5)))))) <=> ((~![Y1: $i, Y2: $i, Y4: $i] : ((~r3(Y1, Y4, Y2)) | ![Y5: $i] : ((~r2(Y5, Y4)) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y5)))))) | (~r3(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y15_5(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))) | ![Y5: $i] : ((~r2(Y5, tptp_fun_Y15_5(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y5)))))),
% 0.10/0.38 inference(rewrite,[status(thm)],[])).
% 0.10/0.38 tff(37,plain,
% 0.10/0.38 ((~![Y1: $i, Y2: $i, Y4: $i] : ((~r3(Y1, Y4, Y2)) | ![Y5: $i] : ((~r2(Y5, Y4)) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y5)))))) | ((~r3(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y15_5(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))) | ![Y5: $i] : ((~r2(Y5, tptp_fun_Y15_5(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y5)))))),
% 0.10/0.38 inference(quant_inst,[status(thm)],[])).
% 0.10/0.38 tff(38,plain,
% 0.10/0.38 ((~![Y1: $i, Y2: $i, Y4: $i] : ((~r3(Y1, Y4, Y2)) | ![Y5: $i] : ((~r2(Y5, Y4)) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y5)))))) | (~r3(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y15_5(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))) | ![Y5: $i] : ((~r2(Y5, tptp_fun_Y15_5(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y5))))),
% 0.10/0.38 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.10/0.38 tff(39,plain,
% 0.10/0.38 (![Y5: $i] : ((~r2(Y5, tptp_fun_Y15_5(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y5))))),
% 0.10/0.38 inference(unit_resolution,[status(thm)],[38, 35, 17])).
% 0.10/0.38 tff(40,plain,
% 0.10/0.38 (((~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y15_5(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))) | (~r3(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y15_5(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))) | (~r2(tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))) | (~r3(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0), tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0))))) | r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y15_5(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))),
% 0.10/0.38 inference(tautology,[status(thm)],[])).
% 0.10/0.38 tff(41,plain,
% 0.10/0.38 (r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y15_5(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))),
% 0.10/0.38 inference(unit_resolution,[status(thm)],[40, 15])).
% 0.10/0.38 tff(42,plain,
% 0.10/0.38 (((~![Y5: $i] : ((~r2(Y5, tptp_fun_Y15_5(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y5))))) | ((~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y15_5(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, tptp_fun_Y21_1(Y24!0)))))) <=> ((~![Y5: $i] : ((~r2(Y5, tptp_fun_Y15_5(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y5))))) | (~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y15_5(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, tptp_fun_Y21_1(Y24!0)))))),
% 0.10/0.38 inference(rewrite,[status(thm)],[])).
% 0.10/0.38 tff(43,plain,
% 0.10/0.38 ((~![Y5: $i] : ((~r2(Y5, tptp_fun_Y15_5(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y5))))) | ((~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y15_5(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, tptp_fun_Y21_1(Y24!0)))))),
% 0.10/0.38 inference(quant_inst,[status(thm)],[])).
% 0.10/0.38 tff(44,plain,
% 0.10/0.38 ((~![Y5: $i] : ((~r2(Y5, tptp_fun_Y15_5(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y5))))) | (~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y15_5(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, tptp_fun_Y21_1(Y24!0))))),
% 0.10/0.38 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.10/0.38 tff(45,plain,
% 0.10/0.38 (![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, tptp_fun_Y21_1(Y24!0))))),
% 0.10/0.38 inference(unit_resolution,[status(thm)],[44, 41, 39])).
% 0.10/0.38 tff(46,plain,
% 0.10/0.38 (^[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)))))),
% 0.10/0.38 inference(bind,[status(th)],[])).
% 0.10/0.38 tff(47,plain,
% 0.10/0.38 (![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))))),
% 0.10/0.38 inference(quant_intro,[status(thm)],[46])).
% 0.10/0.38 tff(48,plain,
% 0.10/0.38 (![X4: $i] : ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4)) <=> ![X4: $i] : ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4))),
% 0.10/0.38 inference(rewrite,[status(thm)],[])).
% 0.10/0.38 tff(49,plain,
% 0.10/0.38 (^[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))))),
% 0.10/0.38 inference(bind,[status(th)],[])).
% 0.10/0.38 tff(50,plain,
% 0.10/0.38 (![X4: $i] : ?[Y9: $i] : (?[Y16: $i] : (r1(Y16) & r3(X4, Y16, Y9)) & (Y9 = X4)) <=> ![X4: $i] : ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4))),
% 0.10/0.38 inference(quant_intro,[status(thm)],[49])).
% 0.10/0.38 tff(51,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')).
% 0.10/0.38 tff(52,plain,
% 0.10/0.38 (![X4: $i] : ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4))),
% 0.10/0.38 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.10/0.38 tff(53,plain,
% 0.10/0.38 (![X4: $i] : ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4))),
% 0.10/0.38 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.10/0.38 tff(54,plain,(
% 0.10/0.38 ![X4: $i] : (r1(tptp_fun_Y16_10(X4)) & r3(X4, tptp_fun_Y16_10(X4), X4))),
% 0.10/0.38 inference(skolemize,[status(sab)],[53])).
% 0.10/0.38 tff(55,plain,
% 0.10/0.38 (![X4: $i] : (~((~r1(tptp_fun_Y16_10(X4))) | (~r3(X4, tptp_fun_Y16_10(X4), X4))))),
% 0.10/0.38 inference(modus_ponens,[status(thm)],[54, 47])).
% 0.10/0.38 tff(56,plain,
% 0.10/0.38 ((~![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))))),
% 0.10/0.39 inference(quant_inst,[status(thm)],[])).
% 0.10/0.39 tff(57,plain,
% 0.10/0.39 (~((~r1(tptp_fun_Y16_10(Y24!0))) | (~r3(Y24!0, tptp_fun_Y16_10(Y24!0), Y24!0)))),
% 0.10/0.39 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.10/0.39 tff(58,plain,
% 0.10/0.39 (((~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))),
% 0.10/0.39 inference(tautology,[status(thm)],[])).
% 0.10/0.39 tff(59,plain,
% 0.10/0.39 (r1(tptp_fun_Y16_10(Y24!0))),
% 0.10/0.39 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.10/0.39 tff(60,plain,
% 0.10/0.39 ((r1(tptp_fun_Y16_10(Y24!0)) | (tptp_fun_Y16_10(Y24!0) = Y24!0)) | (~r1(tptp_fun_Y16_10(Y24!0)))),
% 0.10/0.39 inference(tautology,[status(thm)],[])).
% 0.10/0.39 tff(61,plain,
% 0.10/0.39 (r1(tptp_fun_Y16_10(Y24!0)) | (tptp_fun_Y16_10(Y24!0) = Y24!0)),
% 0.10/0.39 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.10/0.39 tff(62,plain,
% 0.10/0.39 (^[X19: $i] : refl(((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))) <=> ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))))),
% 0.10/0.39 inference(bind,[status(th)],[])).
% 0.10/0.39 tff(63,plain,
% 0.10/0.39 (![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))) <=> ![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.10/0.39 inference(quant_intro,[status(thm)],[62])).
% 0.10/0.39 tff(64,plain,
% 0.10/0.39 (^[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))))))),
% 0.10/0.39 inference(bind,[status(th)],[])).
% 0.10/0.39 tff(65,plain,
% 0.10/0.39 (![X19: $i] : ((r1(X19) & (X19 = Y24!0)) | ((~r1(X19)) & (~(X19 = Y24!0)))) <=> ![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.10/0.39 inference(quant_intro,[status(thm)],[64])).
% 0.10/0.39 tff(66,plain,
% 0.10/0.39 (?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24)))) <=> ?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.10/0.39 inference(rewrite,[status(thm)],[])).
% 0.10/0.39 tff(67,plain,
% 0.10/0.39 (^[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))))))),
% 0.10/0.39 inference(bind,[status(th)],[])).
% 0.10/0.39 tff(68,plain,
% 0.10/0.39 (?[Y24: $i] : ![X19: $i] : (((~r1(X19)) & (~(X19 = Y24))) | (r1(X19) & (X19 = Y24))) <=> ?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.10/0.39 inference(quant_intro,[status(thm)],[67])).
% 0.10/0.39 tff(69,axiom,(?[Y24: $i] : ![X19: $i] : (((~r1(X19)) & (~(X19 = Y24))) | (r1(X19) & (X19 = Y24)))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax','axiom_1')).
% 0.10/0.39 tff(70,plain,
% 0.10/0.39 (?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.10/0.39 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.10/0.39 tff(71,plain,
% 0.10/0.39 (?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.10/0.39 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.10/0.39 tff(72,plain,(
% 0.10/0.39 $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)))))),
% 0.10/0.39 inference(transitivity,[status(sab)],[71])).
% 0.10/0.39 tff(73,plain,
% 0.10/0.39 (![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.10/0.39 inference(modus_ponens,[status(thm)],[72, 65])).
% 0.10/0.39 tff(74,plain,
% 0.10/0.39 (![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.10/0.39 inference(modus_ponens,[status(thm)],[73, 63])).
% 0.10/0.39 tff(75,plain,
% 0.10/0.39 (((~![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))))),
% 0.10/0.39 inference(rewrite,[status(thm)],[])).
% 0.10/0.39 tff(76,plain,
% 0.10/0.39 ((~![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))))),
% 0.10/0.39 inference(quant_inst,[status(thm)],[])).
% 0.10/0.39 tff(77,plain,
% 0.10/0.39 ((~![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)))),
% 0.10/0.39 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.10/0.39 tff(78,plain,
% 0.10/0.39 (~((~r1(tptp_fun_Y16_10(Y24!0))) | (~(tptp_fun_Y16_10(Y24!0) = Y24!0)))),
% 0.10/0.39 inference(unit_resolution,[status(thm)],[77, 74, 61])).
% 0.10/0.39 tff(79,plain,
% 0.10/0.39 (((~r1(tptp_fun_Y16_10(Y24!0))) | (~(tptp_fun_Y16_10(Y24!0) = Y24!0))) | (tptp_fun_Y16_10(Y24!0) = Y24!0)),
% 0.10/0.39 inference(tautology,[status(thm)],[])).
% 0.10/0.39 tff(80,plain,
% 0.10/0.39 (tptp_fun_Y16_10(Y24!0) = Y24!0),
% 0.10/0.39 inference(unit_resolution,[status(thm)],[79, 78])).
% 0.10/0.39 tff(81,plain,
% 0.10/0.39 (Y24!0 = tptp_fun_Y16_10(Y24!0)),
% 0.10/0.39 inference(symmetry,[status(thm)],[80])).
% 0.10/0.39 tff(82,plain,
% 0.10/0.39 (((~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)),
% 0.10/0.39 inference(tautology,[status(thm)],[])).
% 0.10/0.39 tff(83,plain,
% 0.10/0.39 (r3(Y24!0, tptp_fun_Y16_10(Y24!0), Y24!0)),
% 0.10/0.39 inference(unit_resolution,[status(thm)],[82, 57])).
% 0.10/0.39 tff(84,plain,
% 0.10/0.39 ((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))),
% 0.10/0.39 inference(tautology,[status(thm)],[])).
% 0.10/0.39 tff(85,plain,
% 0.10/0.39 (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))),
% 0.10/0.39 inference(unit_resolution,[status(thm)],[84, 83])).
% 0.10/0.39 tff(86,plain,
% 0.10/0.39 (^[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)))))))),
% 0.10/0.39 inference(bind,[status(th)],[])).
% 0.10/0.39 tff(87,plain,
% 0.10/0.39 (![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))))))),
% 0.10/0.39 inference(quant_intro,[status(thm)],[86])).
% 0.10/0.39 tff(88,plain,
% 0.10/0.39 (^[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)))))))),
% 0.10/0.39 inference(bind,[status(th)],[])).
% 0.10/0.39 tff(89,plain,
% 0.10/0.39 (![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))))))),
% 0.10/0.39 inference(quant_intro,[status(thm)],[88])).
% 0.10/0.39 tff(90,plain,
% 0.10/0.39 (![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(91,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(92,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')).
% 0.19/0.39 tff(93,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)],[92, 91])).
% 0.19/0.39 tff(94,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)],[93])).
% 0.19/0.39 tff(95,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)],[94, 90])).
% 0.19/0.39 tff(96,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)],[95, 89])).
% 0.19/0.39 tff(97,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)],[96, 87])).
% 0.19/0.39 tff(98,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(99,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(100,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)],[99, 98])).
% 0.19/0.39 tff(101,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)],[100, 97, 85])).
% 0.19/0.39 tff(102,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(103,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)],[102, 101])).
% 0.19/0.39 tff(104,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)],[103])).
% 0.19/0.39 tff(105,plain,
% 0.19/0.39 (tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0) = tptp_fun_Y16_10(Y24!0)),
% 0.19/0.39 inference(transitivity,[status(thm)],[104, 81])).
% 0.19/0.39 tff(106,plain,
% 0.19/0.39 (r1(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)) <=> r1(tptp_fun_Y16_10(Y24!0))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[105])).
% 0.19/0.39 tff(107,plain,
% 0.19/0.39 (r1(tptp_fun_Y16_10(Y24!0)) <=> r1(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0))),
% 0.19/0.39 inference(symmetry,[status(thm)],[106])).
% 0.19/0.39 tff(108,plain,
% 0.19/0.39 (r1(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[59, 107])).
% 0.19/0.39 tff(109,plain,
% 0.19/0.39 ((~![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)))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(110,plain,
% 0.19/0.39 (~((~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))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[109, 13])).
% 0.19/0.39 tff(111,plain,
% 0.19/0.39 (((~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)))) | r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(112,plain,
% 0.19/0.39 (r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[111, 110])).
% 0.19/0.39 tff(113,plain,
% 0.19/0.39 ((r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0)) | (tptp_fun_Y15_5(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0))) | (~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0)))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(114,plain,
% 0.19/0.39 (r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0)) | (tptp_fun_Y15_5(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[113, 112])).
% 0.19/0.39 tff(115,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(116,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)],[115])).
% 0.19/0.39 tff(117,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(118,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)],[117])).
% 0.19/0.39 tff(119,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(120,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)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(121,axiom,(![X11: $i] : ?[Y21: $i] : ![X12: $i] : (((~r2(X11, X12)) & (~(X12 = Y21))) | (r2(X11, X12) & (X12 = Y21)))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax','axiom_2')).
% 0.19/0.40 tff(122,plain,
% 0.19/0.40 (![X11: $i] : ?[Y21: $i] : ![X12: $i] : (((~r2(X11, X12)) & (~(X12 = Y21))) | (r2(X11, X12) & (X12 = Y21)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.19/0.40 tff(123,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))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[122])).
% 0.19/0.40 tff(124,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))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[123, 119])).
% 0.19/0.40 tff(125,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))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[124, 118])).
% 0.19/0.40 tff(126,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))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[125, 116])).
% 0.19/0.40 tff(127,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(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0)) | (tptp_fun_Y15_5(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0)))) | (~((~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))) | (~(tptp_fun_Y15_5(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, tptp_fun_Y15_5(Y24!0, Y24!0)) | (tptp_fun_Y15_5(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0)))) | (~((~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))) | (~(tptp_fun_Y15_5(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(128,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(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0)) | (tptp_fun_Y15_5(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0)))) | (~((~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))) | (~(tptp_fun_Y15_5(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0))))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(129,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(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0)) | (tptp_fun_Y15_5(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0)))) | (~((~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))) | (~(tptp_fun_Y15_5(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.19/0.40 tff(130,plain,
% 0.19/0.40 (~((~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))) | (~(tptp_fun_Y15_5(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[129, 126, 114])).
% 0.19/0.40 tff(131,plain,
% 0.19/0.40 (((~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))) | (~(tptp_fun_Y15_5(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0)))) | (tptp_fun_Y15_5(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(132,plain,
% 0.19/0.40 (tptp_fun_Y15_5(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[131, 130])).
% 0.19/0.40 tff(133,plain,
% 0.19/0.40 (tptp_fun_Y21_1(Y24!0) = tptp_fun_Y15_5(Y24!0, Y24!0)),
% 0.19/0.40 inference(symmetry,[status(thm)],[132])).
% 0.19/0.40 tff(134,plain,
% 0.19/0.40 (r2(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) <=> r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[104, 133])).
% 0.19/0.40 tff(135,plain,
% 0.19/0.40 (r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0)) <=> r2(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))),
% 0.19/0.40 inference(symmetry,[status(thm)],[134])).
% 0.19/0.40 tff(136,plain,
% 0.19/0.40 (r2(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[112, 135])).
% 0.19/0.40 tff(137,plain,
% 0.19/0.40 (((~![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, tptp_fun_Y21_1(Y24!0))))) | ((~r1(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0))) | (~r2(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))))) <=> ((~![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, tptp_fun_Y21_1(Y24!0))))) | (~r1(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0))) | (~r2(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(138,plain,
% 0.19/0.40 ((~![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, tptp_fun_Y21_1(Y24!0))))) | ((~r1(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0))) | (~r2(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(139,plain,
% 0.19/0.40 ((~![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, tptp_fun_Y21_1(Y24!0))))) | (~r1(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0))) | (~r2(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.19/0.40 tff(140,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[139, 136, 108, 45])).
% 0.19/0.40 % SZS output end Proof
% 0.19/0.40 % E exiting
%------------------------------------------------------------------------------