%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUN085+2 : TPTP v9.0.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 05:22:39 AM UTC 2025
% Result : Theorem 2.66s 2.85s
% Output : Proof 2.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : NUN085+2 : TPTP v9.0.0. Released v7.3.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n013.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Jun 20 02:16:23 EDT 2025
% 0.14/0.36 % CPUTime :
% 2.66/2.85 % SZS status Theorem
% 2.66/2.85 % SZS output start Proof
% 2.66/2.85 tff(tptp_fun_Y24_0_type, type, (
% 2.66/2.85 tptp_fun_Y24_0: $i)).
% 2.66/2.85 tff(tptp_fun_Y21_1_type, type, (
% 2.66/2.85 tptp_fun_Y21_1: $i > $i)).
% 2.66/2.85 tff(tptp_fun_Y4_17_type, type, (
% 2.66/2.85 tptp_fun_Y4_17: $i)).
% 2.66/2.85 tff(tptp_fun_Y1_14_type, type, (
% 2.66/2.85 tptp_fun_Y1_14: $i)).
% 2.66/2.85 tff(r1_type, type, (
% 2.66/2.85 r1: $i > $o)).
% 2.66/2.85 tff(r2_type, type, (
% 2.66/2.85 r2: ( $i * $i ) > $o)).
% 2.66/2.85 tff(tptp_fun_Y2_15_type, type, (
% 2.66/2.85 tptp_fun_Y2_15: $i)).
% 2.66/2.85 tff(r3_type, type, (
% 2.66/2.85 r3: ( $i * $i * $i ) > $o)).
% 2.66/2.85 tff(tptp_fun_Y3_16_type, type, (
% 2.66/2.85 tptp_fun_Y3_16: $i)).
% 2.66/2.85 tff(tptp_fun_Y22_2_type, type, (
% 2.66/2.85 tptp_fun_Y22_2: ( $i * $i ) > $i)).
% 2.66/2.85 tff(tptp_fun_Y15_5_type, type, (
% 2.66/2.85 tptp_fun_Y15_5: ( $i * $i ) > $i)).
% 2.66/2.85 tff(tptp_fun_Y4_4_type, type, (
% 2.66/2.85 tptp_fun_Y4_4: ( $i * $i ) > $i)).
% 2.66/2.85 tff(tptp_fun_Y7_6_type, type, (
% 2.66/2.85 tptp_fun_Y7_6: ( $i * $i ) > $i)).
% 2.66/2.85 tff(tptp_fun_Y16_10_type, type, (
% 2.66/2.85 tptp_fun_Y16_10: $i > $i)).
% 2.66/2.85 tff(1,plain,
% 2.66/2.85 ((r1(Y1!14) & ((~((~r1(Y3!16)) | (~r3(Y3!16, Y2!15, Y1!14)))) & (~((~r1(Y4!17)) | (~r2(Y4!17, Y2!15)))))) <=> (r1(Y1!14) & (~((~r1(Y3!16)) | (~r3(Y3!16, Y2!15, Y1!14)))) & (~((~r1(Y4!17)) | (~r2(Y4!17, Y2!15)))))),
% 2.66/2.85 inference(rewrite,[status(thm)],[])).
% 2.66/2.85 tff(2,plain,
% 2.66/2.85 ((~![Y1: $i] : ((~r1(Y1)) | ![Y2: $i] : (![Y3: $i] : ((~r1(Y3)) | (~r3(Y3, Y2, Y1))) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y2)))))) <=> (~![Y1: $i] : ((~r1(Y1)) | ![Y2: $i] : (![Y3: $i] : ((~r1(Y3)) | (~r3(Y3, Y2, Y1))) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y2))))))),
% 2.66/2.85 inference(rewrite,[status(thm)],[])).
% 2.66/2.85 tff(3,plain,
% 2.66/2.85 ((~![Y1: $i] : (![Y2: $i] : (![Y3: $i] : ((~r1(Y3)) | (~r3(Y3, Y2, Y1))) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y2)))) | ![Y5: $i] : ((~(Y1 = Y5)) | (~r1(Y5))))) <=> (~![Y1: $i] : ((~r1(Y1)) | ![Y2: $i] : (![Y3: $i] : ((~r1(Y3)) | (~r3(Y3, Y2, Y1))) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y2))))))),
% 2.66/2.85 inference(rewrite,[status(thm)],[])).
% 2.66/2.85 tff(4,axiom,(~![Y1: $i] : (![Y2: $i] : (![Y3: $i] : ((~r1(Y3)) | (~r3(Y3, Y2, Y1))) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y2)))) | ![Y5: $i] : ((~(Y1 = Y5)) | (~r1(Y5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','zeroplusoneidzero')).
% 2.66/2.85 tff(5,plain,
% 2.66/2.85 (~![Y1: $i] : ((~r1(Y1)) | ![Y2: $i] : (![Y3: $i] : ((~r1(Y3)) | (~r3(Y3, Y2, Y1))) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y2)))))),
% 2.66/2.85 inference(modus_ponens,[status(thm)],[4, 3])).
% 2.66/2.85 tff(6,plain,
% 2.66/2.85 (~![Y1: $i] : ((~r1(Y1)) | ![Y2: $i] : (![Y3: $i] : ((~r1(Y3)) | (~r3(Y3, Y2, Y1))) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y2)))))),
% 2.66/2.85 inference(modus_ponens,[status(thm)],[5, 2])).
% 2.66/2.85 tff(7,plain,
% 2.66/2.85 (~![Y1: $i] : ((~r1(Y1)) | ![Y2: $i] : (![Y3: $i] : ((~r1(Y3)) | (~r3(Y3, Y2, Y1))) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y2)))))),
% 2.66/2.85 inference(modus_ponens,[status(thm)],[6, 2])).
% 2.66/2.85 tff(8,plain,
% 2.66/2.85 (~![Y1: $i] : ((~r1(Y1)) | ![Y2: $i] : (![Y3: $i] : ((~r1(Y3)) | (~r3(Y3, Y2, Y1))) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y2)))))),
% 2.66/2.85 inference(modus_ponens,[status(thm)],[7, 2])).
% 2.66/2.85 tff(9,plain,
% 2.66/2.85 (r1(Y1!14) & (~((~r1(Y3!16)) | (~r3(Y3!16, Y2!15, Y1!14)))) & (~((~r1(Y4!17)) | (~r2(Y4!17, Y2!15))))),
% 2.66/2.85 inference(modus_ponens,[status(thm)],[8, 1])).
% 2.66/2.85 tff(10,plain,
% 2.66/2.85 (r1(Y1!14)),
% 2.66/2.85 inference(and_elim,[status(thm)],[9])).
% 2.66/2.85 tff(11,plain,
% 2.66/2.85 ((r1(Y1!14) | (Y1!14 = Y24!0)) | (~r1(Y1!14))),
% 2.66/2.85 inference(tautology,[status(thm)],[])).
% 2.66/2.85 tff(12,plain,
% 2.66/2.85 (r1(Y1!14) | (Y1!14 = Y24!0)),
% 2.66/2.85 inference(unit_resolution,[status(thm)],[11, 10])).
% 2.66/2.85 tff(13,plain,
% 2.66/2.85 (^[X19: $i] : refl(((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))) <=> ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))))),
% 2.66/2.85 inference(bind,[status(th)],[])).
% 2.66/2.85 tff(14,plain,
% 2.66/2.85 (![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))) <=> ![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 2.66/2.85 inference(quant_intro,[status(thm)],[13])).
% 2.66/2.85 tff(15,plain,
% 2.66/2.85 (^[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))))))),
% 2.66/2.85 inference(bind,[status(th)],[])).
% 2.66/2.85 tff(16,plain,
% 2.66/2.85 (![X19: $i] : ((r1(X19) & (X19 = Y24!0)) | ((~r1(X19)) & (~(X19 = Y24!0)))) <=> ![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 2.66/2.85 inference(quant_intro,[status(thm)],[15])).
% 2.66/2.85 tff(17,plain,
% 2.66/2.85 (?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24)))) <=> ?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 2.66/2.85 inference(rewrite,[status(thm)],[])).
% 2.66/2.85 tff(18,plain,
% 2.66/2.85 (^[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))))))),
% 2.66/2.85 inference(bind,[status(th)],[])).
% 2.66/2.85 tff(19,plain,
% 2.66/2.85 (?[Y24: $i] : ![X19: $i] : (((~r1(X19)) & (~(X19 = Y24))) | (r1(X19) & (X19 = Y24))) <=> ?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 2.66/2.85 inference(quant_intro,[status(thm)],[18])).
% 2.66/2.85 tff(20,axiom,(?[Y24: $i] : ![X19: $i] : (((~r1(X19)) & (~(X19 = Y24))) | (r1(X19) & (X19 = Y24)))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax','axiom_1')).
% 2.66/2.85 tff(21,plain,
% 2.66/2.85 (?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 2.66/2.85 inference(modus_ponens,[status(thm)],[20, 19])).
% 2.66/2.85 tff(22,plain,
% 2.66/2.85 (?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 2.66/2.85 inference(modus_ponens,[status(thm)],[21, 17])).
% 2.66/2.85 tff(23,plain,(
% 2.66/2.85 $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)))))),
% 2.66/2.85 inference(transitivity,[status(sab)],[22])).
% 2.66/2.85 tff(24,plain,
% 2.66/2.85 (![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 2.66/2.85 inference(modus_ponens,[status(thm)],[23, 16])).
% 2.66/2.85 tff(25,plain,
% 2.66/2.85 (![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 2.66/2.85 inference(modus_ponens,[status(thm)],[24, 14])).
% 2.66/2.85 tff(26,plain,
% 2.66/2.85 (((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(Y1!14)) | (~(Y1!14 = Y24!0)))) | (~(r1(Y1!14) | (Y1!14 = Y24!0))))) <=> ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~((~r1(Y1!14)) | (~(Y1!14 = Y24!0)))) | (~(r1(Y1!14) | (Y1!14 = Y24!0))))),
% 2.66/2.85 inference(rewrite,[status(thm)],[])).
% 2.66/2.85 tff(27,plain,
% 2.66/2.85 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(Y1!14)) | (~(Y1!14 = Y24!0)))) | (~(r1(Y1!14) | (Y1!14 = Y24!0))))),
% 2.66/2.85 inference(quant_inst,[status(thm)],[])).
% 2.66/2.85 tff(28,plain,
% 2.66/2.85 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~((~r1(Y1!14)) | (~(Y1!14 = Y24!0)))) | (~(r1(Y1!14) | (Y1!14 = Y24!0)))),
% 2.66/2.85 inference(modus_ponens,[status(thm)],[27, 26])).
% 2.66/2.85 tff(29,plain,
% 2.66/2.85 (~((~r1(Y1!14)) | (~(Y1!14 = Y24!0)))),
% 2.66/2.85 inference(unit_resolution,[status(thm)],[28, 25, 12])).
% 2.66/2.85 tff(30,plain,
% 2.66/2.85 (((~r1(Y1!14)) | (~(Y1!14 = Y24!0))) | (Y1!14 = Y24!0)),
% 2.66/2.85 inference(tautology,[status(thm)],[])).
% 2.66/2.85 tff(31,plain,
% 2.66/2.85 (Y1!14 = Y24!0),
% 2.66/2.85 inference(unit_resolution,[status(thm)],[30, 29])).
% 2.66/2.85 tff(32,plain,
% 2.66/2.85 (~((~r1(Y3!16)) | (~r3(Y3!16, Y2!15, Y1!14)))),
% 2.66/2.85 inference(and_elim,[status(thm)],[9])).
% 2.66/2.85 tff(33,plain,
% 2.66/2.85 (r3(Y3!16, Y2!15, Y1!14)),
% 2.66/2.85 inference(or_elim,[status(thm)],[32])).
% 2.66/2.85 tff(34,plain,
% 2.66/2.85 ((r3(Y3!16, Y2!15, Y1!14) | (Y1!14 = tptp_fun_Y22_2(Y2!15, Y3!16))) | (~r3(Y3!16, Y2!15, Y1!14))),
% 2.66/2.85 inference(tautology,[status(thm)],[])).
% 2.66/2.85 tff(35,plain,
% 2.66/2.85 (r3(Y3!16, Y2!15, Y1!14) | (Y1!14 = tptp_fun_Y22_2(Y2!15, Y3!16))),
% 2.66/2.85 inference(unit_resolution,[status(thm)],[34, 33])).
% 2.66/2.85 tff(36,plain,
% 2.66/2.85 (^[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)))))))),
% 2.66/2.85 inference(bind,[status(th)],[])).
% 2.66/2.85 tff(37,plain,
% 2.66/2.85 (![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))))))),
% 2.66/2.85 inference(quant_intro,[status(thm)],[36])).
% 2.66/2.85 tff(38,plain,
% 2.66/2.85 (^[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)))))))),
% 2.66/2.85 inference(bind,[status(th)],[])).
% 2.66/2.85 tff(39,plain,
% 2.66/2.85 (![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))))))),
% 2.66/2.85 inference(quant_intro,[status(thm)],[38])).
% 2.66/2.85 tff(40,plain,
% 2.66/2.85 (![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))))),
% 2.66/2.85 inference(pull_quant,[status(thm)],[])).
% 2.66/2.85 tff(41,plain,
% 2.66/2.85 (![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)))),
% 2.66/2.85 inference(rewrite,[status(thm)],[])).
% 2.66/2.85 tff(42,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')).
% 2.66/2.85 tff(43,plain,
% 2.66/2.85 (![X13: $i, X14: $i] : ?[Y22: $i] : ![X15: $i] : (((~r3(X13, X14, X15)) & (~(X15 = Y22))) | (r3(X13, X14, X15) & (X15 = Y22)))),
% 2.66/2.85 inference(modus_ponens,[status(thm)],[42, 41])).
% 2.66/2.85 tff(44,plain,(
% 2.66/2.85 ![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))))),
% 2.66/2.85 inference(skolemize,[status(sab)],[43])).
% 2.66/2.85 tff(45,plain,
% 2.66/2.85 (![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))))),
% 2.66/2.85 inference(modus_ponens,[status(thm)],[44, 40])).
% 2.66/2.85 tff(46,plain,
% 2.66/2.85 (![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))))))),
% 2.66/2.85 inference(modus_ponens,[status(thm)],[45, 39])).
% 2.66/2.85 tff(47,plain,
% 2.66/2.85 (![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))))))),
% 2.66/2.85 inference(modus_ponens,[status(thm)],[46, 37])).
% 2.66/2.85 tff(48,plain,
% 2.66/2.85 (((~![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(Y3!16, Y2!15, Y1!14) | (Y1!14 = tptp_fun_Y22_2(Y2!15, Y3!16)))) | (~((~r3(Y3!16, Y2!15, Y1!14)) | (~(Y1!14 = tptp_fun_Y22_2(Y2!15, Y3!16))))))) <=> ((~![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(Y3!16, Y2!15, Y1!14) | (Y1!14 = tptp_fun_Y22_2(Y2!15, Y3!16)))) | (~((~r3(Y3!16, Y2!15, Y1!14)) | (~(Y1!14 = tptp_fun_Y22_2(Y2!15, Y3!16))))))),
% 2.66/2.86 inference(rewrite,[status(thm)],[])).
% 2.66/2.86 tff(49,plain,
% 2.66/2.86 ((~![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(Y3!16, Y2!15, Y1!14) | (Y1!14 = tptp_fun_Y22_2(Y2!15, Y3!16)))) | (~((~r3(Y3!16, Y2!15, Y1!14)) | (~(Y1!14 = tptp_fun_Y22_2(Y2!15, Y3!16))))))),
% 2.66/2.86 inference(quant_inst,[status(thm)],[])).
% 2.66/2.86 tff(50,plain,
% 2.66/2.86 ((~![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(Y3!16, Y2!15, Y1!14) | (Y1!14 = tptp_fun_Y22_2(Y2!15, Y3!16)))) | (~((~r3(Y3!16, Y2!15, Y1!14)) | (~(Y1!14 = tptp_fun_Y22_2(Y2!15, Y3!16)))))),
% 2.66/2.86 inference(modus_ponens,[status(thm)],[49, 48])).
% 2.66/2.86 tff(51,plain,
% 2.66/2.86 (~((~r3(Y3!16, Y2!15, Y1!14)) | (~(Y1!14 = tptp_fun_Y22_2(Y2!15, Y3!16))))),
% 2.66/2.86 inference(unit_resolution,[status(thm)],[50, 47, 35])).
% 2.66/2.86 tff(52,plain,
% 2.66/2.86 (((~r3(Y3!16, Y2!15, Y1!14)) | (~(Y1!14 = tptp_fun_Y22_2(Y2!15, Y3!16)))) | (Y1!14 = tptp_fun_Y22_2(Y2!15, Y3!16))),
% 2.66/2.86 inference(tautology,[status(thm)],[])).
% 2.66/2.86 tff(53,plain,
% 2.66/2.86 (Y1!14 = tptp_fun_Y22_2(Y2!15, Y3!16)),
% 2.66/2.86 inference(unit_resolution,[status(thm)],[52, 51])).
% 2.66/2.86 tff(54,plain,
% 2.66/2.86 (tptp_fun_Y22_2(Y2!15, Y3!16) = Y1!14),
% 2.66/2.86 inference(symmetry,[status(thm)],[53])).
% 2.66/2.86 tff(55,plain,
% 2.66/2.86 (r1(Y3!16)),
% 2.66/2.86 inference(or_elim,[status(thm)],[32])).
% 2.66/2.86 tff(56,plain,
% 2.66/2.86 ((r1(Y3!16) | (Y3!16 = Y24!0)) | (~r1(Y3!16))),
% 2.66/2.86 inference(tautology,[status(thm)],[])).
% 2.66/2.86 tff(57,plain,
% 2.66/2.86 (r1(Y3!16) | (Y3!16 = Y24!0)),
% 2.66/2.86 inference(unit_resolution,[status(thm)],[56, 55])).
% 2.66/2.86 tff(58,plain,
% 2.66/2.86 (((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(Y3!16)) | (~(Y3!16 = Y24!0)))) | (~(r1(Y3!16) | (Y3!16 = Y24!0))))) <=> ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~((~r1(Y3!16)) | (~(Y3!16 = Y24!0)))) | (~(r1(Y3!16) | (Y3!16 = Y24!0))))),
% 2.66/2.86 inference(rewrite,[status(thm)],[])).
% 2.66/2.86 tff(59,plain,
% 2.66/2.86 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(Y3!16)) | (~(Y3!16 = Y24!0)))) | (~(r1(Y3!16) | (Y3!16 = Y24!0))))),
% 2.66/2.86 inference(quant_inst,[status(thm)],[])).
% 2.66/2.86 tff(60,plain,
% 2.66/2.86 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~((~r1(Y3!16)) | (~(Y3!16 = Y24!0)))) | (~(r1(Y3!16) | (Y3!16 = Y24!0)))),
% 2.66/2.86 inference(modus_ponens,[status(thm)],[59, 58])).
% 2.66/2.86 tff(61,plain,
% 2.66/2.86 (~((~r1(Y3!16)) | (~(Y3!16 = Y24!0)))),
% 2.66/2.86 inference(unit_resolution,[status(thm)],[60, 25, 57])).
% 2.66/2.86 tff(62,plain,
% 2.66/2.86 (((~r1(Y3!16)) | (~(Y3!16 = Y24!0))) | (Y3!16 = Y24!0)),
% 2.66/2.86 inference(tautology,[status(thm)],[])).
% 2.66/2.86 tff(63,plain,
% 2.66/2.86 (Y3!16 = Y24!0),
% 2.66/2.86 inference(unit_resolution,[status(thm)],[62, 61])).
% 2.66/2.86 tff(64,plain,
% 2.66/2.86 (^[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))))))),
% 2.66/2.86 inference(bind,[status(th)],[])).
% 2.66/2.86 tff(65,plain,
% 2.66/2.86 (![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)))))),
% 2.66/2.86 inference(quant_intro,[status(thm)],[64])).
% 2.66/2.86 tff(66,plain,
% 2.66/2.86 (^[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))))),
% 2.66/2.86 inference(bind,[status(th)],[])).
% 2.66/2.86 tff(67,plain,
% 2.66/2.86 (![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)))),
% 2.66/2.86 inference(quant_intro,[status(thm)],[66])).
% 2.66/2.86 tff(68,plain,
% 2.66/2.86 (![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)))),
% 2.66/2.86 inference(rewrite,[status(thm)],[])).
% 2.66/2.86 tff(69,plain,
% 2.66/2.86 (^[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)))))),
% 2.66/2.86 inference(bind,[status(th)],[])).
% 2.66/2.86 tff(70,plain,
% 2.66/2.86 (![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)))),
% 2.66/2.86 inference(quant_intro,[status(thm)],[69])).
% 2.66/2.86 tff(71,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')).
% 2.66/2.86 tff(72,plain,
% 2.66/2.86 (![X1: $i, X8: $i] : ?[Y4: $i] : (?[Y15: $i] : (r2(X8, Y15) & r3(X1, Y15, Y4)) & ?[Y7: $i] : (r2(Y7, Y4) & r3(X1, X8, Y7)))),
% 2.66/2.86 inference(modus_ponens,[status(thm)],[71, 70])).
% 2.66/2.86 tff(73,plain,
% 2.66/2.86 (![X1: $i, X8: $i] : ?[Y4: $i] : (?[Y15: $i] : (r2(X8, Y15) & r3(X1, Y15, Y4)) & ?[Y7: $i] : (r2(Y7, Y4) & r3(X1, X8, Y7)))),
% 2.66/2.86 inference(modus_ponens,[status(thm)],[72, 68])).
% 2.66/2.86 tff(74,plain,(
% 2.66/2.86 ![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))))),
% 2.66/2.86 inference(skolemize,[status(sab)],[73])).
% 2.66/2.86 tff(75,plain,
% 2.66/2.86 (![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)))),
% 2.66/2.86 inference(modus_ponens,[status(thm)],[74, 67])).
% 2.66/2.86 tff(76,plain,
% 2.66/2.86 (![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)))))),
% 2.66/2.86 inference(modus_ponens,[status(thm)],[75, 65])).
% 2.66/2.86 tff(77,plain,
% 2.66/2.86 (((~![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)))))) | (~((~r3(Y24!0, Y24!0, tptp_fun_Y7_6(Y24!0, 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)))))) <=> ((~![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)))))) | (~((~r3(Y24!0, Y24!0, tptp_fun_Y7_6(Y24!0, 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))))))),
% 2.66/2.86 inference(rewrite,[status(thm)],[])).
% 2.66/2.86 tff(78,plain,
% 2.66/2.86 ((~((~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))) | (~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)))))),
% 2.66/2.86 inference(rewrite,[status(thm)],[])).
% 2.66/2.86 tff(79,plain,
% 2.66/2.86 (((~![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)))))) <=> ((~![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)))))) | (~((~r3(Y24!0, Y24!0, tptp_fun_Y7_6(Y24!0, 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))))))),
% 2.66/2.86 inference(monotonicity,[status(thm)],[78])).
% 2.66/2.86 tff(80,plain,
% 2.66/2.86 (((~![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)))))) <=> ((~![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)))))) | (~((~r3(Y24!0, Y24!0, tptp_fun_Y7_6(Y24!0, 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))))))),
% 2.66/2.86 inference(transitivity,[status(thm)],[79, 77])).
% 2.66/2.86 tff(81,plain,
% 2.66/2.86 ((~![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)))))),
% 2.66/2.86 inference(quant_inst,[status(thm)],[])).
% 2.66/2.86 tff(82,plain,
% 2.66/2.86 ((~![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)))))) | (~((~r3(Y24!0, Y24!0, tptp_fun_Y7_6(Y24!0, 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)))))),
% 2.66/2.86 inference(modus_ponens,[status(thm)],[81, 80])).
% 2.66/2.86 tff(83,plain,
% 2.66/2.86 (~((~r3(Y24!0, Y24!0, tptp_fun_Y7_6(Y24!0, 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))))),
% 2.66/2.86 inference(unit_resolution,[status(thm)],[82, 76])).
% 2.66/2.86 tff(84,plain,
% 2.66/2.86 (((~r3(Y24!0, Y24!0, tptp_fun_Y7_6(Y24!0, 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)))) | r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))),
% 2.66/2.86 inference(tautology,[status(thm)],[])).
% 2.66/2.86 tff(85,plain,
% 2.66/2.86 (r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))),
% 2.66/2.86 inference(unit_resolution,[status(thm)],[84, 83])).
% 2.66/2.86 tff(86,plain,
% 2.66/2.86 (((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))) | (~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0)))),
% 2.66/2.86 inference(tautology,[status(thm)],[])).
% 2.66/2.86 tff(87,plain,
% 2.66/2.86 ((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))),
% 2.66/2.86 inference(unit_resolution,[status(thm)],[86, 85])).
% 2.66/2.86 tff(88,plain,
% 2.66/2.86 (^[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)))))))),
% 2.66/2.86 inference(bind,[status(th)],[])).
% 2.66/2.86 tff(89,plain,
% 2.66/2.86 (![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))))))),
% 2.66/2.86 inference(quant_intro,[status(thm)],[88])).
% 2.66/2.86 tff(90,plain,
% 2.66/2.86 (^[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)))))))),
% 2.66/2.86 inference(bind,[status(th)],[])).
% 2.66/2.86 tff(91,plain,
% 2.66/2.86 (![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))))))),
% 2.66/2.86 inference(quant_intro,[status(thm)],[90])).
% 2.66/2.86 tff(92,plain,
% 2.66/2.86 (![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))))),
% 2.66/2.86 inference(pull_quant,[status(thm)],[])).
% 2.66/2.86 tff(93,plain,
% 2.66/2.86 (![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)))),
% 2.66/2.86 inference(rewrite,[status(thm)],[])).
% 2.66/2.86 tff(94,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')).
% 2.66/2.86 tff(95,plain,
% 2.66/2.86 (![X11: $i] : ?[Y21: $i] : ![X12: $i] : (((~r2(X11, X12)) & (~(X12 = Y21))) | (r2(X11, X12) & (X12 = Y21)))),
% 2.66/2.86 inference(modus_ponens,[status(thm)],[94, 93])).
% 2.66/2.86 tff(96,plain,(
% 2.66/2.86 ![X11: $i] : ![X12: $i] : (((~r2(X11, X12)) & (~(X12 = tptp_fun_Y21_1(X11)))) | (r2(X11, X12) & (X12 = tptp_fun_Y21_1(X11))))),
% 2.66/2.86 inference(skolemize,[status(sab)],[95])).
% 2.66/2.86 tff(97,plain,
% 2.66/2.86 (![X11: $i, X12: $i] : (((~r2(X11, X12)) & (~(X12 = tptp_fun_Y21_1(X11)))) | (r2(X11, X12) & (X12 = tptp_fun_Y21_1(X11))))),
% 2.66/2.86 inference(modus_ponens,[status(thm)],[96, 92])).
% 2.66/2.86 tff(98,plain,
% 2.66/2.86 (![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))),
% 2.66/2.86 inference(modus_ponens,[status(thm)],[97, 91])).
% 2.66/2.86 tff(99,plain,
% 2.66/2.86 (![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))),
% 2.66/2.86 inference(modus_ponens,[status(thm)],[98, 89])).
% 2.66/2.86 tff(100,plain,
% 2.66/2.86 (((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | ((~((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)))) | (~((~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))))))) | (~((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)))) | (~((~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))))))),
% 2.66/2.86 inference(rewrite,[status(thm)],[])).
% 2.66/2.86 tff(101,plain,
% 2.66/2.86 (((~(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)))))) <=> ((~((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)))) | (~((~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))))))),
% 2.66/2.86 inference(rewrite,[status(thm)],[])).
% 2.66/2.86 tff(102,plain,
% 2.66/2.86 (((~![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))))))) | ((~((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)))) | (~((~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)))))))),
% 2.66/2.86 inference(monotonicity,[status(thm)],[101])).
% 2.66/2.86 tff(103,plain,
% 2.66/2.86 (((~![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))))))) | (~((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)))) | (~((~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))))))),
% 2.66/2.86 inference(transitivity,[status(thm)],[102, 100])).
% 2.66/2.86 tff(104,plain,
% 2.66/2.86 ((~![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))))))),
% 2.66/2.86 inference(quant_inst,[status(thm)],[])).
% 2.66/2.86 tff(105,plain,
% 2.66/2.86 ((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | (~((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)))) | (~((~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)))))),
% 2.66/2.86 inference(modus_ponens,[status(thm)],[104, 103])).
% 2.66/2.86 tff(106,plain,
% 2.66/2.86 (~((~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))))),
% 2.66/2.86 inference(unit_resolution,[status(thm)],[105, 99, 87])).
% 2.66/2.86 tff(107,plain,
% 2.66/2.86 (((~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))),
% 2.66/2.86 inference(tautology,[status(thm)],[])).
% 2.66/2.86 tff(108,plain,
% 2.66/2.86 (tptp_fun_Y15_5(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0)),
% 2.66/2.86 inference(unit_resolution,[status(thm)],[107, 106])).
% 2.66/2.86 tff(109,plain,
% 2.66/2.86 (tptp_fun_Y21_1(Y24!0) = tptp_fun_Y15_5(Y24!0, Y24!0)),
% 2.66/2.86 inference(symmetry,[status(thm)],[108])).
% 2.66/2.86 tff(110,plain,
% 2.66/2.86 (~((~r1(Y4!17)) | (~r2(Y4!17, Y2!15)))),
% 2.66/2.86 inference(and_elim,[status(thm)],[9])).
% 2.66/2.86 tff(111,plain,
% 2.66/2.86 (r1(Y4!17)),
% 2.66/2.86 inference(or_elim,[status(thm)],[110])).
% 2.66/2.86 tff(112,plain,
% 2.66/2.86 ((r1(Y4!17) | (Y4!17 = Y24!0)) | (~r1(Y4!17))),
% 2.66/2.86 inference(tautology,[status(thm)],[])).
% 2.66/2.86 tff(113,plain,
% 2.66/2.86 (r1(Y4!17) | (Y4!17 = Y24!0)),
% 2.66/2.86 inference(unit_resolution,[status(thm)],[112, 111])).
% 2.66/2.86 tff(114,plain,
% 2.66/2.86 (((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(Y4!17)) | (~(Y4!17 = Y24!0)))) | (~(r1(Y4!17) | (Y4!17 = Y24!0))))) <=> ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~((~r1(Y4!17)) | (~(Y4!17 = Y24!0)))) | (~(r1(Y4!17) | (Y4!17 = Y24!0))))),
% 2.66/2.86 inference(rewrite,[status(thm)],[])).
% 2.66/2.86 tff(115,plain,
% 2.66/2.86 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(Y4!17)) | (~(Y4!17 = Y24!0)))) | (~(r1(Y4!17) | (Y4!17 = Y24!0))))),
% 2.66/2.86 inference(quant_inst,[status(thm)],[])).
% 2.66/2.86 tff(116,plain,
% 2.66/2.86 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~((~r1(Y4!17)) | (~(Y4!17 = Y24!0)))) | (~(r1(Y4!17) | (Y4!17 = Y24!0)))),
% 2.66/2.86 inference(modus_ponens,[status(thm)],[115, 114])).
% 2.66/2.86 tff(117,plain,
% 2.66/2.86 (~((~r1(Y4!17)) | (~(Y4!17 = Y24!0)))),
% 2.66/2.86 inference(unit_resolution,[status(thm)],[116, 25, 113])).
% 2.66/2.86 tff(118,plain,
% 2.66/2.86 (((~r1(Y4!17)) | (~(Y4!17 = Y24!0))) | (Y4!17 = Y24!0)),
% 2.66/2.86 inference(tautology,[status(thm)],[])).
% 2.66/2.86 tff(119,plain,
% 2.66/2.86 (Y4!17 = Y24!0),
% 2.66/2.86 inference(unit_resolution,[status(thm)],[118, 117])).
% 2.66/2.86 tff(120,plain,
% 2.66/2.86 (Y24!0 = Y4!17),
% 2.66/2.86 inference(symmetry,[status(thm)],[119])).
% 2.66/2.86 tff(121,plain,
% 2.66/2.86 (tptp_fun_Y21_1(Y24!0) = tptp_fun_Y21_1(Y4!17)),
% 2.66/2.86 inference(monotonicity,[status(thm)],[120])).
% 2.66/2.86 tff(122,plain,
% 2.66/2.86 (tptp_fun_Y21_1(Y4!17) = tptp_fun_Y21_1(Y24!0)),
% 2.66/2.86 inference(symmetry,[status(thm)],[121])).
% 2.66/2.86 tff(123,plain,
% 2.66/2.86 (r2(Y4!17, Y2!15)),
% 2.66/2.86 inference(or_elim,[status(thm)],[110])).
% 2.66/2.86 tff(124,plain,
% 2.66/2.86 ((r2(Y4!17, Y2!15) | (Y2!15 = tptp_fun_Y21_1(Y4!17))) | (~r2(Y4!17, Y2!15))),
% 2.66/2.86 inference(tautology,[status(thm)],[])).
% 2.66/2.86 tff(125,plain,
% 2.66/2.86 (r2(Y4!17, Y2!15) | (Y2!15 = tptp_fun_Y21_1(Y4!17))),
% 2.66/2.86 inference(unit_resolution,[status(thm)],[124, 123])).
% 2.66/2.86 tff(126,plain,
% 2.66/2.86 (((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | ((~(r2(Y4!17, Y2!15) | (Y2!15 = tptp_fun_Y21_1(Y4!17)))) | (~((~r2(Y4!17, Y2!15)) | (~(Y2!15 = tptp_fun_Y21_1(Y4!17))))))) <=> ((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | (~(r2(Y4!17, Y2!15) | (Y2!15 = tptp_fun_Y21_1(Y4!17)))) | (~((~r2(Y4!17, Y2!15)) | (~(Y2!15 = tptp_fun_Y21_1(Y4!17))))))),
% 2.66/2.86 inference(rewrite,[status(thm)],[])).
% 2.66/2.86 tff(127,plain,
% 2.66/2.86 ((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | ((~(r2(Y4!17, Y2!15) | (Y2!15 = tptp_fun_Y21_1(Y4!17)))) | (~((~r2(Y4!17, Y2!15)) | (~(Y2!15 = tptp_fun_Y21_1(Y4!17))))))),
% 2.66/2.86 inference(quant_inst,[status(thm)],[])).
% 2.66/2.86 tff(128,plain,
% 2.66/2.86 ((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | (~(r2(Y4!17, Y2!15) | (Y2!15 = tptp_fun_Y21_1(Y4!17)))) | (~((~r2(Y4!17, Y2!15)) | (~(Y2!15 = tptp_fun_Y21_1(Y4!17)))))),
% 2.66/2.86 inference(modus_ponens,[status(thm)],[127, 126])).
% 2.66/2.86 tff(129,plain,
% 2.66/2.86 (~((~r2(Y4!17, Y2!15)) | (~(Y2!15 = tptp_fun_Y21_1(Y4!17))))),
% 2.66/2.86 inference(unit_resolution,[status(thm)],[128, 99, 125])).
% 2.66/2.86 tff(130,plain,
% 2.66/2.86 (((~r2(Y4!17, Y2!15)) | (~(Y2!15 = tptp_fun_Y21_1(Y4!17)))) | (Y2!15 = tptp_fun_Y21_1(Y4!17))),
% 2.66/2.86 inference(tautology,[status(thm)],[])).
% 2.66/2.86 tff(131,plain,
% 2.66/2.86 (Y2!15 = tptp_fun_Y21_1(Y4!17)),
% 2.66/2.86 inference(unit_resolution,[status(thm)],[130, 129])).
% 2.66/2.86 tff(132,plain,
% 2.66/2.86 (Y2!15 = tptp_fun_Y15_5(Y24!0, Y24!0)),
% 2.66/2.86 inference(transitivity,[status(thm)],[131, 122, 109])).
% 2.66/2.86 tff(133,plain,
% 2.66/2.86 (tptp_fun_Y22_2(Y2!15, Y3!16) = tptp_fun_Y22_2(tptp_fun_Y15_5(Y24!0, Y24!0), Y24!0)),
% 2.66/2.86 inference(monotonicity,[status(thm)],[132, 63])).
% 2.66/2.86 tff(134,plain,
% 2.66/2.86 (tptp_fun_Y22_2(tptp_fun_Y15_5(Y24!0, Y24!0), Y24!0) = tptp_fun_Y22_2(Y2!15, Y3!16)),
% 2.66/2.86 inference(symmetry,[status(thm)],[133])).
% 2.66/2.86 tff(135,plain,
% 2.66/2.86 (((~r3(Y24!0, Y24!0, tptp_fun_Y7_6(Y24!0, 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)))) | r3(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))),
% 2.66/2.86 inference(tautology,[status(thm)],[])).
% 2.66/2.86 tff(136,plain,
% 2.66/2.86 (r3(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))),
% 2.66/2.86 inference(unit_resolution,[status(thm)],[135, 83])).
% 2.66/2.86 tff(137,plain,
% 2.66/2.86 ((r3(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)) | (tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y22_2(tptp_fun_Y15_5(Y24!0, Y24!0), Y24!0))) | (~r3(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)))),
% 2.66/2.86 inference(tautology,[status(thm)],[])).
% 2.66/2.86 tff(138,plain,
% 2.66/2.86 (r3(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)) | (tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y22_2(tptp_fun_Y15_5(Y24!0, Y24!0), Y24!0))),
% 2.66/2.86 inference(unit_resolution,[status(thm)],[137, 136])).
% 2.66/2.86 tff(139,plain,
% 2.66/2.86 (((~![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_Y15_5(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)) | (tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y22_2(tptp_fun_Y15_5(Y24!0, Y24!0), Y24!0)))) | (~((~r3(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y22_2(tptp_fun_Y15_5(Y24!0, 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_Y15_5(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)) | (tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y22_2(tptp_fun_Y15_5(Y24!0, Y24!0), Y24!0)))) | (~((~r3(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y22_2(tptp_fun_Y15_5(Y24!0, Y24!0), Y24!0))))))),
% 2.66/2.86 inference(rewrite,[status(thm)],[])).
% 2.66/2.86 tff(140,plain,
% 2.66/2.86 ((~![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_Y15_5(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)) | (tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y22_2(tptp_fun_Y15_5(Y24!0, Y24!0), Y24!0)))) | (~((~r3(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y22_2(tptp_fun_Y15_5(Y24!0, Y24!0), Y24!0))))))),
% 2.66/2.86 inference(quant_inst,[status(thm)],[])).
% 2.66/2.86 tff(141,plain,
% 2.66/2.86 ((~![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_Y15_5(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)) | (tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y22_2(tptp_fun_Y15_5(Y24!0, Y24!0), Y24!0)))) | (~((~r3(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y22_2(tptp_fun_Y15_5(Y24!0, Y24!0), Y24!0)))))),
% 2.66/2.86 inference(modus_ponens,[status(thm)],[140, 139])).
% 2.66/2.86 tff(142,plain,
% 2.66/2.86 (~((~r3(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y22_2(tptp_fun_Y15_5(Y24!0, Y24!0), Y24!0))))),
% 2.66/2.86 inference(unit_resolution,[status(thm)],[141, 47, 138])).
% 2.66/2.86 tff(143,plain,
% 2.66/2.86 (((~r3(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y22_2(tptp_fun_Y15_5(Y24!0, Y24!0), Y24!0)))) | (tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y22_2(tptp_fun_Y15_5(Y24!0, Y24!0), Y24!0))),
% 2.66/2.86 inference(tautology,[status(thm)],[])).
% 2.66/2.86 tff(144,plain,
% 2.66/2.86 (tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y22_2(tptp_fun_Y15_5(Y24!0, Y24!0), Y24!0)),
% 2.66/2.86 inference(unit_resolution,[status(thm)],[143, 142])).
% 2.66/2.86 tff(145,plain,
% 2.66/2.86 (((~r3(Y24!0, Y24!0, tptp_fun_Y7_6(Y24!0, 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)))) | r2(tptp_fun_Y7_6(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))),
% 2.66/2.86 inference(tautology,[status(thm)],[])).
% 2.66/2.86 tff(146,plain,
% 2.66/2.86 (r2(tptp_fun_Y7_6(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))),
% 2.66/2.86 inference(unit_resolution,[status(thm)],[145, 83])).
% 2.66/2.86 tff(147,plain,
% 2.66/2.86 ((r2(tptp_fun_Y7_6(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)) | (tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y21_1(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)))),
% 2.66/2.86 inference(tautology,[status(thm)],[])).
% 2.66/2.86 tff(148,plain,
% 2.66/2.86 (r2(tptp_fun_Y7_6(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)) | (tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y21_1(tptp_fun_Y7_6(Y24!0, Y24!0)))),
% 2.66/2.86 inference(unit_resolution,[status(thm)],[147, 146])).
% 2.66/2.86 tff(149,plain,
% 2.66/2.86 (((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | ((~(r2(tptp_fun_Y7_6(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)) | (tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y21_1(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))) | (~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y21_1(tptp_fun_Y7_6(Y24!0, Y24!0)))))))) <=> ((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | (~(r2(tptp_fun_Y7_6(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)) | (tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y21_1(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))) | (~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y21_1(tptp_fun_Y7_6(Y24!0, Y24!0)))))))),
% 2.66/2.86 inference(rewrite,[status(thm)],[])).
% 2.66/2.86 tff(150,plain,
% 2.66/2.86 ((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | ((~(r2(tptp_fun_Y7_6(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)) | (tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y21_1(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))) | (~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y21_1(tptp_fun_Y7_6(Y24!0, Y24!0)))))))),
% 2.66/2.86 inference(quant_inst,[status(thm)],[])).
% 2.66/2.86 tff(151,plain,
% 2.66/2.86 ((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | (~(r2(tptp_fun_Y7_6(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)) | (tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y21_1(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))) | (~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y21_1(tptp_fun_Y7_6(Y24!0, Y24!0))))))),
% 2.66/2.86 inference(modus_ponens,[status(thm)],[150, 149])).
% 2.66/2.86 tff(152,plain,
% 2.66/2.86 (~((~r2(tptp_fun_Y7_6(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y21_1(tptp_fun_Y7_6(Y24!0, Y24!0)))))),
% 2.66/2.86 inference(unit_resolution,[status(thm)],[151, 99, 148])).
% 2.66/2.86 tff(153,plain,
% 2.66/2.86 (((~r2(tptp_fun_Y7_6(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y21_1(tptp_fun_Y7_6(Y24!0, Y24!0))))) | (tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y21_1(tptp_fun_Y7_6(Y24!0, Y24!0)))),
% 2.66/2.86 inference(tautology,[status(thm)],[])).
% 2.66/2.86 tff(154,plain,
% 2.66/2.86 (tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y21_1(tptp_fun_Y7_6(Y24!0, Y24!0))),
% 2.66/2.86 inference(unit_resolution,[status(thm)],[153, 152])).
% 2.66/2.86 tff(155,plain,
% 2.66/2.86 (tptp_fun_Y21_1(tptp_fun_Y7_6(Y24!0, Y24!0)) = tptp_fun_Y4_4(Y24!0, Y24!0)),
% 2.66/2.86 inference(symmetry,[status(thm)],[154])).
% 2.66/2.86 tff(156,plain,
% 2.66/2.86 (^[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)))))),
% 2.66/2.87 inference(bind,[status(th)],[])).
% 2.66/2.87 tff(157,plain,
% 2.66/2.87 (![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))))),
% 2.66/2.87 inference(quant_intro,[status(thm)],[156])).
% 2.66/2.87 tff(158,plain,
% 2.66/2.87 (![X4: $i] : ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4)) <=> ![X4: $i] : ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4))),
% 2.66/2.87 inference(rewrite,[status(thm)],[])).
% 2.66/2.87 tff(159,plain,
% 2.66/2.87 (^[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))))),
% 2.66/2.87 inference(bind,[status(th)],[])).
% 2.66/2.87 tff(160,plain,
% 2.66/2.87 (![X4: $i] : ?[Y9: $i] : (?[Y16: $i] : (r1(Y16) & r3(X4, Y16, Y9)) & (Y9 = X4)) <=> ![X4: $i] : ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4))),
% 2.66/2.87 inference(quant_intro,[status(thm)],[159])).
% 2.66/2.87 tff(161,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')).
% 2.66/2.87 tff(162,plain,
% 2.66/2.87 (![X4: $i] : ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4))),
% 2.66/2.87 inference(modus_ponens,[status(thm)],[161, 160])).
% 2.66/2.87 tff(163,plain,
% 2.66/2.87 (![X4: $i] : ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4))),
% 2.66/2.87 inference(modus_ponens,[status(thm)],[162, 158])).
% 2.66/2.87 tff(164,plain,(
% 2.66/2.87 ![X4: $i] : (r1(tptp_fun_Y16_10(X4)) & r3(X4, tptp_fun_Y16_10(X4), X4))),
% 2.66/2.87 inference(skolemize,[status(sab)],[163])).
% 2.66/2.87 tff(165,plain,
% 2.66/2.87 (![X4: $i] : (~((~r1(tptp_fun_Y16_10(X4))) | (~r3(X4, tptp_fun_Y16_10(X4), X4))))),
% 2.66/2.87 inference(modus_ponens,[status(thm)],[164, 157])).
% 2.66/2.87 tff(166,plain,
% 2.66/2.87 ((~![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))))),
% 2.66/2.87 inference(quant_inst,[status(thm)],[])).
% 2.66/2.87 tff(167,plain,
% 2.66/2.87 (~((~r1(tptp_fun_Y16_10(Y24!0))) | (~r3(Y24!0, tptp_fun_Y16_10(Y24!0), Y24!0)))),
% 2.66/2.87 inference(unit_resolution,[status(thm)],[166, 165])).
% 2.66/2.87 tff(168,plain,
% 2.66/2.87 (((~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)),
% 2.66/2.87 inference(tautology,[status(thm)],[])).
% 2.66/2.87 tff(169,plain,
% 2.66/2.87 (r3(Y24!0, tptp_fun_Y16_10(Y24!0), Y24!0)),
% 2.66/2.87 inference(unit_resolution,[status(thm)],[168, 167])).
% 2.66/2.87 tff(170,plain,
% 2.66/2.87 ((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))),
% 2.66/2.87 inference(tautology,[status(thm)],[])).
% 2.66/2.87 tff(171,plain,
% 2.66/2.87 (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))),
% 2.66/2.87 inference(unit_resolution,[status(thm)],[170, 169])).
% 2.66/2.87 tff(172,plain,
% 2.66/2.87 (((~![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))))))),
% 2.66/2.87 inference(rewrite,[status(thm)],[])).
% 2.66/2.87 tff(173,plain,
% 2.66/2.87 ((~![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))))))),
% 2.66/2.87 inference(quant_inst,[status(thm)],[])).
% 2.66/2.87 tff(174,plain,
% 2.66/2.87 ((~![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)))))),
% 2.66/2.87 inference(modus_ponens,[status(thm)],[173, 172])).
% 2.66/2.87 tff(175,plain,
% 2.66/2.87 (~((~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))))),
% 2.66/2.87 inference(unit_resolution,[status(thm)],[174, 47, 171])).
% 2.66/2.87 tff(176,plain,
% 2.66/2.87 (((~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))),
% 2.66/2.87 inference(tautology,[status(thm)],[])).
% 2.66/2.87 tff(177,plain,
% 2.66/2.87 (Y24!0 = tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)),
% 2.66/2.87 inference(unit_resolution,[status(thm)],[176, 175])).
% 2.66/2.87 tff(178,plain,
% 2.66/2.87 (tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0) = Y24!0),
% 2.66/2.87 inference(symmetry,[status(thm)],[177])).
% 2.66/2.87 tff(179,plain,
% 2.66/2.87 (((~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))),
% 2.66/2.87 inference(tautology,[status(thm)],[])).
% 2.66/2.87 tff(180,plain,
% 2.66/2.87 (r1(tptp_fun_Y16_10(Y24!0))),
% 2.66/2.87 inference(unit_resolution,[status(thm)],[179, 167])).
% 2.66/2.87 tff(181,plain,
% 2.66/2.87 ((r1(tptp_fun_Y16_10(Y24!0)) | (tptp_fun_Y16_10(Y24!0) = Y24!0)) | (~r1(tptp_fun_Y16_10(Y24!0)))),
% 2.66/2.87 inference(tautology,[status(thm)],[])).
% 2.66/2.87 tff(182,plain,
% 2.66/2.87 (r1(tptp_fun_Y16_10(Y24!0)) | (tptp_fun_Y16_10(Y24!0) = Y24!0)),
% 2.66/2.87 inference(unit_resolution,[status(thm)],[181, 180])).
% 2.66/2.87 tff(183,plain,
% 2.66/2.87 (((~![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)))))),
% 2.66/2.87 inference(rewrite,[status(thm)],[])).
% 2.66/2.87 tff(184,plain,
% 2.66/2.87 (((~((~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)))) <=> ((~(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)))))),
% 2.66/2.87 inference(rewrite,[status(thm)],[])).
% 2.66/2.87 tff(185,plain,
% 2.66/2.87 (((~![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))))))),
% 2.66/2.87 inference(monotonicity,[status(thm)],[184])).
% 2.66/2.87 tff(186,plain,
% 2.66/2.87 (((~![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)))))),
% 2.66/2.87 inference(transitivity,[status(thm)],[185, 183])).
% 2.66/2.87 tff(187,plain,
% 2.66/2.87 ((~![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))))),
% 2.66/2.87 inference(quant_inst,[status(thm)],[])).
% 2.66/2.87 tff(188,plain,
% 2.66/2.87 ((~![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))))),
% 2.66/2.87 inference(modus_ponens,[status(thm)],[187, 186])).
% 2.66/2.87 tff(189,plain,
% 2.66/2.87 (~((~r1(tptp_fun_Y16_10(Y24!0))) | (~(tptp_fun_Y16_10(Y24!0) = Y24!0)))),
% 2.66/2.87 inference(unit_resolution,[status(thm)],[188, 25, 182])).
% 2.66/2.87 tff(190,plain,
% 2.66/2.87 (((~r1(tptp_fun_Y16_10(Y24!0))) | (~(tptp_fun_Y16_10(Y24!0) = Y24!0))) | (tptp_fun_Y16_10(Y24!0) = Y24!0)),
% 2.66/2.87 inference(tautology,[status(thm)],[])).
% 2.66/2.87 tff(191,plain,
% 2.66/2.87 (tptp_fun_Y16_10(Y24!0) = Y24!0),
% 2.66/2.87 inference(unit_resolution,[status(thm)],[190, 189])).
% 2.66/2.87 tff(192,plain,
% 2.66/2.87 (Y24!0 = tptp_fun_Y16_10(Y24!0)),
% 2.66/2.87 inference(symmetry,[status(thm)],[191])).
% 2.66/2.87 tff(193,plain,
% 2.66/2.87 (tptp_fun_Y22_2(Y24!0, Y24!0) = tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)),
% 2.66/2.87 inference(monotonicity,[status(thm)],[192])).
% 2.66/2.87 tff(194,plain,
% 2.66/2.87 (((~r3(Y24!0, Y24!0, tptp_fun_Y7_6(Y24!0, 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)))) | r3(Y24!0, Y24!0, tptp_fun_Y7_6(Y24!0, Y24!0))),
% 2.66/2.87 inference(tautology,[status(thm)],[])).
% 2.66/2.87 tff(195,plain,
% 2.66/2.87 (r3(Y24!0, Y24!0, tptp_fun_Y7_6(Y24!0, Y24!0))),
% 2.66/2.87 inference(unit_resolution,[status(thm)],[194, 83])).
% 2.66/2.87 tff(196,plain,
% 2.66/2.87 ((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)))),
% 2.66/2.87 inference(tautology,[status(thm)],[])).
% 2.66/2.87 tff(197,plain,
% 2.66/2.87 (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))),
% 2.66/2.87 inference(unit_resolution,[status(thm)],[196, 195])).
% 2.66/2.87 tff(198,plain,
% 2.66/2.87 (((~![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))))))),
% 2.66/2.87 inference(rewrite,[status(thm)],[])).
% 2.66/2.87 tff(199,plain,
% 2.66/2.87 ((~![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))))))),
% 2.66/2.87 inference(quant_inst,[status(thm)],[])).
% 2.66/2.87 tff(200,plain,
% 2.66/2.87 ((~![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)))))),
% 2.66/2.87 inference(modus_ponens,[status(thm)],[199, 198])).
% 2.66/2.87 tff(201,plain,
% 2.66/2.87 (~((~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))))),
% 2.66/2.87 inference(unit_resolution,[status(thm)],[200, 47, 197])).
% 2.66/2.87 tff(202,plain,
% 2.66/2.87 (((~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))),
% 2.66/2.87 inference(tautology,[status(thm)],[])).
% 2.66/2.87 tff(203,plain,
% 2.66/2.87 (tptp_fun_Y7_6(Y24!0, Y24!0) = tptp_fun_Y22_2(Y24!0, Y24!0)),
% 2.66/2.87 inference(unit_resolution,[status(thm)],[202, 201])).
% 2.66/2.87 tff(204,plain,
% 2.66/2.87 (tptp_fun_Y7_6(Y24!0, Y24!0) = Y4!17),
% 2.66/2.87 inference(transitivity,[status(thm)],[203, 193, 178, 120])).
% 2.66/2.87 tff(205,plain,
% 2.66/2.87 (tptp_fun_Y21_1(tptp_fun_Y7_6(Y24!0, Y24!0)) = tptp_fun_Y21_1(Y4!17)),
% 2.66/2.87 inference(monotonicity,[status(thm)],[204])).
% 2.66/2.87 tff(206,plain,
% 2.66/2.87 (tptp_fun_Y21_1(Y4!17) = tptp_fun_Y21_1(tptp_fun_Y7_6(Y24!0, Y24!0))),
% 2.66/2.87 inference(symmetry,[status(thm)],[205])).
% 2.66/2.87 tff(207,plain,
% 2.66/2.87 (tptp_fun_Y21_1(Y4!17) = Y24!0),
% 2.66/2.87 inference(transitivity,[status(thm)],[206, 155, 144, 134, 54, 31])).
% 2.66/2.87 tff(208,plain,
% 2.66/2.87 (tptp_fun_Y21_1(Y4!17) = Y2!15),
% 2.66/2.87 inference(symmetry,[status(thm)],[131])).
% 2.66/2.87 tff(209,plain,
% 2.66/2.87 (r1(tptp_fun_Y21_1(Y4!17)) <=> r1(Y2!15)),
% 2.66/2.87 inference(monotonicity,[status(thm)],[208])).
% 2.66/2.87 tff(210,plain,
% 2.66/2.87 (r1(Y2!15) <=> r1(tptp_fun_Y21_1(Y4!17))),
% 2.66/2.87 inference(symmetry,[status(thm)],[209])).
% 2.66/2.87 tff(211,plain,
% 2.66/2.87 ((~r1(Y2!15)) <=> (~r1(tptp_fun_Y21_1(Y4!17)))),
% 2.66/2.87 inference(monotonicity,[status(thm)],[210])).
% 2.66/2.87 tff(212,plain,
% 2.66/2.87 (^[X7: $i, Y10: $i] : refl(((~r1(Y10)) | (~r2(X7, Y10))) <=> ((~r1(Y10)) | (~r2(X7, Y10))))),
% 2.66/2.87 inference(bind,[status(th)],[])).
% 2.66/2.87 tff(213,plain,
% 2.66/2.87 (![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10))) <=> ![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))),
% 2.66/2.87 inference(quant_intro,[status(thm)],[212])).
% 2.66/2.87 tff(214,plain,
% 2.66/2.87 (![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10))) <=> ![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))),
% 2.66/2.87 inference(rewrite,[status(thm)],[])).
% 2.66/2.87 tff(215,plain,
% 2.66/2.87 (^[X7: $i, Y10: $i] : rewrite((![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))) | (~r2(X7, Y10))) <=> ((~r1(Y10)) | (~r2(X7, Y10))))),
% 2.66/2.87 inference(bind,[status(th)],[])).
% 2.66/2.87 tff(216,plain,
% 2.66/2.87 (![X7: $i, Y10: $i] : (![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))) | (~r2(X7, Y10))) <=> ![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))),
% 2.66/2.87 inference(quant_intro,[status(thm)],[215])).
% 2.66/2.87 tff(217,axiom,(![X7: $i, Y10: $i] : (![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))) | (~r2(X7, Y10)))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax','axiom_7a')).
% 2.66/2.87 tff(218,plain,
% 2.66/2.87 (![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))),
% 2.66/2.87 inference(modus_ponens,[status(thm)],[217, 216])).
% 2.66/2.87 tff(219,plain,
% 2.66/2.87 (![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))),
% 2.66/2.87 inference(modus_ponens,[status(thm)],[218, 214])).
% 2.66/2.87 tff(220,plain,(
% 2.66/2.87 ![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))),
% 2.66/2.87 inference(skolemize,[status(sab)],[219])).
% 2.66/2.87 tff(221,plain,
% 2.66/2.87 (![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))),
% 2.66/2.87 inference(modus_ponens,[status(thm)],[220, 213])).
% 2.66/2.87 tff(222,plain,
% 2.66/2.87 (((~![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))) | ((~r1(Y2!15)) | (~r2(Y4!17, Y2!15)))) <=> ((~![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))) | (~r1(Y2!15)) | (~r2(Y4!17, Y2!15)))),
% 2.66/2.87 inference(rewrite,[status(thm)],[])).
% 2.66/2.87 tff(223,plain,
% 2.66/2.87 ((~![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))) | ((~r1(Y2!15)) | (~r2(Y4!17, Y2!15)))),
% 2.66/2.87 inference(quant_inst,[status(thm)],[])).
% 2.66/2.87 tff(224,plain,
% 2.66/2.87 ((~![X7: $i, Y10: $i] : ((~r1(Y10)) | (~r2(X7, Y10)))) | (~r1(Y2!15)) | (~r2(Y4!17, Y2!15))),
% 2.66/2.87 inference(modus_ponens,[status(thm)],[223, 222])).
% 2.66/2.87 tff(225,plain,
% 2.66/2.87 (~r1(Y2!15)),
% 2.66/2.87 inference(unit_resolution,[status(thm)],[224, 221, 123])).
% 2.66/2.87 tff(226,plain,
% 2.66/2.87 (~r1(tptp_fun_Y21_1(Y4!17))),
% 2.66/2.87 inference(modus_ponens,[status(thm)],[225, 211])).
% 2.66/2.87 tff(227,plain,
% 2.66/2.87 (((~r1(tptp_fun_Y21_1(Y4!17))) | (~(tptp_fun_Y21_1(Y4!17) = Y24!0))) | r1(tptp_fun_Y21_1(Y4!17))),
% 2.66/2.87 inference(tautology,[status(thm)],[])).
% 2.66/2.87 tff(228,plain,
% 2.66/2.87 ((~r1(tptp_fun_Y21_1(Y4!17))) | (~(tptp_fun_Y21_1(Y4!17) = Y24!0))),
% 2.66/2.87 inference(unit_resolution,[status(thm)],[227, 226])).
% 2.66/2.87 tff(229,plain,
% 2.66/2.87 (((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(tptp_fun_Y21_1(Y4!17))) | (~(tptp_fun_Y21_1(Y4!17) = Y24!0)))) | (~(r1(tptp_fun_Y21_1(Y4!17)) | (tptp_fun_Y21_1(Y4!17) = Y24!0))))) <=> ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~((~r1(tptp_fun_Y21_1(Y4!17))) | (~(tptp_fun_Y21_1(Y4!17) = Y24!0)))) | (~(r1(tptp_fun_Y21_1(Y4!17)) | (tptp_fun_Y21_1(Y4!17) = Y24!0))))),
% 2.66/2.87 inference(rewrite,[status(thm)],[])).
% 2.66/2.87 tff(230,plain,
% 2.66/2.87 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(tptp_fun_Y21_1(Y4!17))) | (~(tptp_fun_Y21_1(Y4!17) = Y24!0)))) | (~(r1(tptp_fun_Y21_1(Y4!17)) | (tptp_fun_Y21_1(Y4!17) = Y24!0))))),
% 2.66/2.87 inference(quant_inst,[status(thm)],[])).
% 2.66/2.87 tff(231,plain,
% 2.66/2.87 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~((~r1(tptp_fun_Y21_1(Y4!17))) | (~(tptp_fun_Y21_1(Y4!17) = Y24!0)))) | (~(r1(tptp_fun_Y21_1(Y4!17)) | (tptp_fun_Y21_1(Y4!17) = Y24!0)))),
% 2.66/2.87 inference(modus_ponens,[status(thm)],[230, 229])).
% 2.66/2.87 tff(232,plain,
% 2.66/2.87 ((~((~r1(tptp_fun_Y21_1(Y4!17))) | (~(tptp_fun_Y21_1(Y4!17) = Y24!0)))) | (~(r1(tptp_fun_Y21_1(Y4!17)) | (tptp_fun_Y21_1(Y4!17) = Y24!0)))),
% 2.66/2.87 inference(unit_resolution,[status(thm)],[231, 25])).
% 2.66/2.87 tff(233,plain,
% 2.66/2.87 (~(r1(tptp_fun_Y21_1(Y4!17)) | (tptp_fun_Y21_1(Y4!17) = Y24!0))),
% 2.66/2.87 inference(unit_resolution,[status(thm)],[232, 228])).
% 2.66/2.87 tff(234,plain,
% 2.66/2.87 ((r1(tptp_fun_Y21_1(Y4!17)) | (tptp_fun_Y21_1(Y4!17) = Y24!0)) | (~(tptp_fun_Y21_1(Y4!17) = Y24!0))),
% 2.66/2.87 inference(tautology,[status(thm)],[])).
% 2.66/2.87 tff(235,plain,
% 2.66/2.87 (~(tptp_fun_Y21_1(Y4!17) = Y24!0)),
% 2.66/2.87 inference(unit_resolution,[status(thm)],[234, 233])).
% 2.66/2.87 tff(236,plain,
% 2.66/2.87 ($false),
% 2.66/2.87 inference(unit_resolution,[status(thm)],[235, 207])).
% 2.66/2.87 % SZS output end Proof
% 2.66/2.87 % E exiting
%------------------------------------------------------------------------------