%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUN087+2 : TPTP v9.0.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 0.11s 0.37s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUN087+2 : TPTP v9.0.0. Released v7.3.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n009.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 02:16:18 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.11/0.37 % SZS status Theorem
% 0.11/0.37 % SZS output start Proof
% 0.11/0.37 tff(r4_type, type, (
% 0.11/0.37 r4: ( $i * $i * $i ) > $o)).
% 0.11/0.37 tff(tptp_fun_Y24_0_type, type, (
% 0.11/0.37 tptp_fun_Y24_0: $i)).
% 0.11/0.37 tff(r1_type, type, (
% 0.11/0.37 r1: $i > $o)).
% 0.11/0.37 tff(tptp_fun_Y8_11_type, type, (
% 0.11/0.37 tptp_fun_Y8_11: $i > $i)).
% 0.11/0.37 tff(tptp_fun_Y17_12_type, type, (
% 0.11/0.37 tptp_fun_Y17_12: $i > $i)).
% 0.11/0.37 tff(1,plain,
% 0.11/0.37 (^[X19: $i] : refl(((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))) <=> ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(2,plain,
% 0.11/0.37 (![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))) <=> ![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.11/0.37 tff(3,plain,
% 0.11/0.37 (^[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))))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(4,plain,
% 0.11/0.37 (![X19: $i] : ((r1(X19) & (X19 = Y24!0)) | ((~r1(X19)) & (~(X19 = Y24!0)))) <=> ![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[3])).
% 0.11/0.37 tff(5,plain,
% 0.11/0.37 (?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24)))) <=> ?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(6,plain,
% 0.11/0.37 (^[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))))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(7,plain,
% 0.11/0.37 (?[Y24: $i] : ![X19: $i] : (((~r1(X19)) & (~(X19 = Y24))) | (r1(X19) & (X19 = Y24))) <=> ?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[6])).
% 0.11/0.37 tff(8,axiom,(?[Y24: $i] : ![X19: $i] : (((~r1(X19)) & (~(X19 = Y24))) | (r1(X19) & (X19 = Y24)))), file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax','axiom_1')).
% 0.11/0.37 tff(9,plain,
% 0.11/0.37 (?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.11/0.37 tff(10,plain,
% 0.11/0.37 (?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.11/0.37 tff(11,plain,(
% 0.11/0.37 $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)))))),
% 0.11/0.37 inference(transitivity,[status(sab)],[10])).
% 0.11/0.37 tff(12,plain,
% 0.11/0.37 (![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.11/0.37 tff(13,plain,
% 0.11/0.37 (![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.11/0.37 tff(14,plain,
% 0.11/0.37 (((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | r1(Y24!0)) <=> ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | r1(Y24!0))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(15,plain,
% 0.11/0.37 ((r1(Y24!0) | $false) <=> r1(Y24!0)),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(16,plain,
% 0.11/0.37 ((~$true) <=> $false),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(17,plain,
% 0.11/0.37 ((r1(Y24!0) | $true) <=> $true),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(18,plain,
% 0.11/0.37 ((Y24!0 = Y24!0) <=> $true),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(19,plain,
% 0.11/0.37 ((r1(Y24!0) | (Y24!0 = Y24!0)) <=> (r1(Y24!0) | $true)),
% 0.11/0.37 inference(monotonicity,[status(thm)],[18])).
% 0.11/0.37 tff(20,plain,
% 0.11/0.37 ((r1(Y24!0) | (Y24!0 = Y24!0)) <=> $true),
% 0.11/0.37 inference(transitivity,[status(thm)],[19, 17])).
% 0.11/0.37 tff(21,plain,
% 0.11/0.37 ((~(r1(Y24!0) | (Y24!0 = Y24!0))) <=> (~$true)),
% 0.11/0.37 inference(monotonicity,[status(thm)],[20])).
% 0.11/0.37 tff(22,plain,
% 0.11/0.37 ((~(r1(Y24!0) | (Y24!0 = Y24!0))) <=> $false),
% 0.11/0.37 inference(transitivity,[status(thm)],[21, 16])).
% 0.11/0.37 tff(23,plain,
% 0.11/0.37 ((~(~r1(Y24!0))) <=> r1(Y24!0)),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(24,plain,
% 0.11/0.37 (((~r1(Y24!0)) | $false) <=> (~r1(Y24!0))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(25,plain,
% 0.11/0.37 ((~(Y24!0 = Y24!0)) <=> (~$true)),
% 0.11/0.37 inference(monotonicity,[status(thm)],[18])).
% 0.11/0.37 tff(26,plain,
% 0.11/0.37 ((~(Y24!0 = Y24!0)) <=> $false),
% 0.11/0.37 inference(transitivity,[status(thm)],[25, 16])).
% 0.11/0.37 tff(27,plain,
% 0.11/0.37 (((~r1(Y24!0)) | (~(Y24!0 = Y24!0))) <=> ((~r1(Y24!0)) | $false)),
% 0.11/0.37 inference(monotonicity,[status(thm)],[26])).
% 0.11/0.37 tff(28,plain,
% 0.11/0.37 (((~r1(Y24!0)) | (~(Y24!0 = Y24!0))) <=> (~r1(Y24!0))),
% 0.11/0.37 inference(transitivity,[status(thm)],[27, 24])).
% 0.11/0.37 tff(29,plain,
% 0.11/0.37 ((~((~r1(Y24!0)) | (~(Y24!0 = Y24!0)))) <=> (~(~r1(Y24!0)))),
% 0.11/0.37 inference(monotonicity,[status(thm)],[28])).
% 0.11/0.37 tff(30,plain,
% 0.11/0.37 ((~((~r1(Y24!0)) | (~(Y24!0 = Y24!0)))) <=> r1(Y24!0)),
% 0.11/0.37 inference(transitivity,[status(thm)],[29, 23])).
% 0.11/0.37 tff(31,plain,
% 0.11/0.37 (((~((~r1(Y24!0)) | (~(Y24!0 = Y24!0)))) | (~(r1(Y24!0) | (Y24!0 = Y24!0)))) <=> (r1(Y24!0) | $false)),
% 0.11/0.37 inference(monotonicity,[status(thm)],[30, 22])).
% 0.11/0.37 tff(32,plain,
% 0.11/0.37 (((~((~r1(Y24!0)) | (~(Y24!0 = Y24!0)))) | (~(r1(Y24!0) | (Y24!0 = Y24!0)))) <=> r1(Y24!0)),
% 0.11/0.37 inference(transitivity,[status(thm)],[31, 15])).
% 0.11/0.37 tff(33,plain,
% 0.11/0.37 (((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(Y24!0)) | (~(Y24!0 = Y24!0)))) | (~(r1(Y24!0) | (Y24!0 = Y24!0))))) <=> ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | r1(Y24!0))),
% 0.11/0.37 inference(monotonicity,[status(thm)],[32])).
% 0.11/0.37 tff(34,plain,
% 0.11/0.37 (((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(Y24!0)) | (~(Y24!0 = Y24!0)))) | (~(r1(Y24!0) | (Y24!0 = Y24!0))))) <=> ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | r1(Y24!0))),
% 0.11/0.37 inference(transitivity,[status(thm)],[33, 14])).
% 0.11/0.37 tff(35,plain,
% 0.11/0.37 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(Y24!0)) | (~(Y24!0 = Y24!0)))) | (~(r1(Y24!0) | (Y24!0 = Y24!0))))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(36,plain,
% 0.11/0.37 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | r1(Y24!0)),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.11/0.37 tff(37,plain,
% 0.11/0.37 (r1(Y24!0)),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[36, 13])).
% 0.11/0.37 tff(38,plain,
% 0.11/0.37 (^[Y1: $i] : refl(((~r1(Y1)) | ![Y2: $i] : ((~r1(Y2)) | (~r4(Y2, Y2, Y1)))) <=> ((~r1(Y1)) | ![Y2: $i] : ((~r1(Y2)) | (~r4(Y2, Y2, Y1)))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(39,plain,
% 0.11/0.37 (![Y1: $i] : ((~r1(Y1)) | ![Y2: $i] : ((~r1(Y2)) | (~r4(Y2, Y2, Y1)))) <=> ![Y1: $i] : ((~r1(Y1)) | ![Y2: $i] : ((~r1(Y2)) | (~r4(Y2, Y2, Y1))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[38])).
% 0.11/0.37 tff(40,plain,
% 0.11/0.37 (^[Y1: $i] : rewrite(((~r1(Y1)) | ![Y2: $i] : ((~r1(Y2)) | (~r4(Y2, Y2, Y1)))) <=> ((~r1(Y1)) | ![Y2: $i] : ((~r1(Y2)) | (~r4(Y2, Y2, Y1)))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(41,plain,
% 0.11/0.37 (![Y1: $i] : ((~r1(Y1)) | ![Y2: $i] : ((~r1(Y2)) | (~r4(Y2, Y2, Y1)))) <=> ![Y1: $i] : ((~r1(Y1)) | ![Y2: $i] : ((~r1(Y2)) | (~r4(Y2, Y2, Y1))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[40])).
% 0.11/0.37 tff(42,plain,
% 0.11/0.37 (![Y1: $i] : ((~r1(Y1)) | ![Y2: $i] : ((~r1(Y2)) | (~r4(Y2, Y2, Y1)))) <=> ![Y1: $i] : ((~r1(Y1)) | ![Y2: $i] : ((~r1(Y2)) | (~r4(Y2, Y2, Y1))))),
% 0.11/0.37 inference(transitivity,[status(thm)],[41, 39])).
% 0.11/0.37 tff(43,plain,
% 0.11/0.37 (^[Y1: $i] : rewrite(((~r1(Y1)) | ![Y2: $i] : (~(r1(Y2) & r4(Y2, Y2, Y1)))) <=> ((~r1(Y1)) | ![Y2: $i] : ((~r1(Y2)) | (~r4(Y2, Y2, Y1)))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(44,plain,
% 0.11/0.37 (![Y1: $i] : ((~r1(Y1)) | ![Y2: $i] : (~(r1(Y2) & r4(Y2, Y2, Y1)))) <=> ![Y1: $i] : ((~r1(Y1)) | ![Y2: $i] : ((~r1(Y2)) | (~r4(Y2, Y2, Y1))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[43])).
% 0.11/0.37 tff(45,plain,
% 0.11/0.37 (^[Y1: $i] : rewrite((![Y2: $i] : (~(r1(Y2) & r4(Y2, Y2, Y1))) | (~r1(Y1))) <=> ((~r1(Y1)) | ![Y2: $i] : (~(r1(Y2) & r4(Y2, Y2, Y1)))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(46,plain,
% 0.11/0.37 (![Y1: $i] : (![Y2: $i] : (~(r1(Y2) & r4(Y2, Y2, Y1))) | (~r1(Y1))) <=> ![Y1: $i] : ((~r1(Y1)) | ![Y2: $i] : (~(r1(Y2) & r4(Y2, Y2, Y1))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[45])).
% 0.11/0.37 tff(47,plain,
% 0.11/0.37 ((~?[Y1: $i] : (?[Y2: $i] : (r1(Y2) & r4(Y2, Y2, Y1)) & r1(Y1))) <=> (~?[Y1: $i] : (?[Y2: $i] : (r1(Y2) & r4(Y2, Y2, Y1)) & r1(Y1)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(48,plain,
% 0.11/0.37 ((~?[Y1: $i] : (?[Y2: $i] : (r1(Y2) & r4(Y2, Y2, Y1)) & ?[Y3: $i] : (r1(Y3) & (Y1 = Y3)))) <=> (~?[Y1: $i] : (?[Y2: $i] : (r1(Y2) & r4(Y2, Y2, Y1)) & r1(Y1)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(49,axiom,(~?[Y1: $i] : (?[Y2: $i] : (r1(Y2) & r4(Y2, Y2, Y1)) & ?[Y3: $i] : (r1(Y3) & (Y1 = Y3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','zerotimeszeroeqzero')).
% 0.11/0.37 tff(50,plain,
% 0.11/0.37 (~?[Y1: $i] : (?[Y2: $i] : (r1(Y2) & r4(Y2, Y2, Y1)) & r1(Y1))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.11/0.37 tff(51,plain,
% 0.11/0.37 (~?[Y1: $i] : (?[Y2: $i] : (r1(Y2) & r4(Y2, Y2, Y1)) & r1(Y1))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[50, 47])).
% 0.11/0.37 tff(52,plain,
% 0.11/0.37 (~?[Y1: $i] : (?[Y2: $i] : (r1(Y2) & r4(Y2, Y2, Y1)) & r1(Y1))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.11/0.37 tff(53,plain,
% 0.11/0.37 (~?[Y1: $i] : (?[Y2: $i] : (r1(Y2) & r4(Y2, Y2, Y1)) & r1(Y1))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[52, 47])).
% 0.11/0.37 tff(54,plain,
% 0.11/0.37 (^[Y1: $i] : nnf_neg(nnf_neg(proof_bind(^[Y2: $i] : refl($oeq((~(r1(Y2) & r4(Y2, Y2, Y1))), (~(r1(Y2) & r4(Y2, Y2, Y1)))))), $oeq((~?[Y2: $i] : (r1(Y2) & r4(Y2, Y2, Y1))), ![Y2: $i] : (~(r1(Y2) & r4(Y2, Y2, Y1))))), refl($oeq((~r1(Y1)), (~r1(Y1)))), $oeq((~(?[Y2: $i] : (r1(Y2) & r4(Y2, Y2, Y1)) & r1(Y1))), (![Y2: $i] : (~(r1(Y2) & r4(Y2, Y2, Y1))) | (~r1(Y1)))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(55,plain,(
% 0.11/0.37 ![Y1: $i] : (![Y2: $i] : (~(r1(Y2) & r4(Y2, Y2, Y1))) | (~r1(Y1)))),
% 0.11/0.37 inference(nnf-neg,[status(sab)],[53, 54])).
% 0.11/0.37 tff(56,plain,
% 0.11/0.37 (![Y1: $i] : ((~r1(Y1)) | ![Y2: $i] : (~(r1(Y2) & r4(Y2, Y2, Y1))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[55, 46])).
% 0.11/0.37 tff(57,plain,
% 0.11/0.37 (![Y1: $i] : ((~r1(Y1)) | ![Y2: $i] : ((~r1(Y2)) | (~r4(Y2, Y2, Y1))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[56, 44])).
% 0.11/0.37 tff(58,plain,
% 0.11/0.37 (![Y1: $i] : ((~r1(Y1)) | ![Y2: $i] : ((~r1(Y2)) | (~r4(Y2, Y2, Y1))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[57, 42])).
% 0.11/0.37 tff(59,plain,
% 0.11/0.37 (((~![Y1: $i] : ((~r1(Y1)) | ![Y2: $i] : ((~r1(Y2)) | (~r4(Y2, Y2, Y1))))) | ((~r1(Y24!0)) | ![Y2: $i] : ((~r1(Y2)) | (~r4(Y2, Y2, Y24!0))))) <=> ((~![Y1: $i] : ((~r1(Y1)) | ![Y2: $i] : ((~r1(Y2)) | (~r4(Y2, Y2, Y1))))) | (~r1(Y24!0)) | ![Y2: $i] : ((~r1(Y2)) | (~r4(Y2, Y2, Y24!0))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(60,plain,
% 0.11/0.37 ((~![Y1: $i] : ((~r1(Y1)) | ![Y2: $i] : ((~r1(Y2)) | (~r4(Y2, Y2, Y1))))) | ((~r1(Y24!0)) | ![Y2: $i] : ((~r1(Y2)) | (~r4(Y2, Y2, Y24!0))))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(61,plain,
% 0.11/0.37 ((~![Y1: $i] : ((~r1(Y1)) | ![Y2: $i] : ((~r1(Y2)) | (~r4(Y2, Y2, Y1))))) | (~r1(Y24!0)) | ![Y2: $i] : ((~r1(Y2)) | (~r4(Y2, Y2, Y24!0)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.11/0.37 tff(62,plain,
% 0.11/0.37 (![Y2: $i] : ((~r1(Y2)) | (~r4(Y2, Y2, Y24!0)))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[61, 58, 37])).
% 0.11/0.37 tff(63,plain,
% 0.11/0.37 (^[X5: $i] : rewrite((r1(tptp_fun_Y17_12(X5)) & r4(X5, tptp_fun_Y17_12(X5), tptp_fun_Y8_11(X5)) & r1(tptp_fun_Y8_11(X5))) <=> (~((~r1(tptp_fun_Y17_12(X5))) | (~r4(X5, tptp_fun_Y17_12(X5), tptp_fun_Y8_11(X5))) | (~r1(tptp_fun_Y8_11(X5))))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(64,plain,
% 0.11/0.37 (![X5: $i] : (r1(tptp_fun_Y17_12(X5)) & r4(X5, tptp_fun_Y17_12(X5), tptp_fun_Y8_11(X5)) & r1(tptp_fun_Y8_11(X5))) <=> ![X5: $i] : (~((~r1(tptp_fun_Y17_12(X5))) | (~r4(X5, tptp_fun_Y17_12(X5), tptp_fun_Y8_11(X5))) | (~r1(tptp_fun_Y8_11(X5)))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[63])).
% 0.11/0.38 tff(65,plain,
% 0.11/0.38 (^[X5: $i] : rewrite(((r1(tptp_fun_Y17_12(X5)) & r4(X5, tptp_fun_Y17_12(X5), tptp_fun_Y8_11(X5))) & r1(tptp_fun_Y8_11(X5))) <=> (r1(tptp_fun_Y17_12(X5)) & r4(X5, tptp_fun_Y17_12(X5), tptp_fun_Y8_11(X5)) & r1(tptp_fun_Y8_11(X5))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(66,plain,
% 0.11/0.38 (![X5: $i] : ((r1(tptp_fun_Y17_12(X5)) & r4(X5, tptp_fun_Y17_12(X5), tptp_fun_Y8_11(X5))) & r1(tptp_fun_Y8_11(X5))) <=> ![X5: $i] : (r1(tptp_fun_Y17_12(X5)) & r4(X5, tptp_fun_Y17_12(X5), tptp_fun_Y8_11(X5)) & r1(tptp_fun_Y8_11(X5)))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[65])).
% 0.11/0.38 tff(67,plain,
% 0.11/0.38 (![X5: $i] : ?[Y8: $i] : (?[Y17: $i] : (r1(Y17) & r4(X5, Y17, Y8)) & r1(Y8)) <=> ![X5: $i] : ?[Y8: $i] : (?[Y17: $i] : (r1(Y17) & r4(X5, Y17, Y8)) & r1(Y8))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(68,plain,
% 0.11/0.38 (^[X5: $i] : quant_intro(proof_bind(^[Y8: $i] : rewrite((?[Y17: $i] : (r1(Y17) & r4(X5, Y17, Y8)) & ?[Y18: $i] : (r1(Y18) & (Y8 = Y18))) <=> (?[Y17: $i] : (r1(Y17) & r4(X5, Y17, Y8)) & r1(Y8)))), (?[Y8: $i] : (?[Y17: $i] : (r1(Y17) & r4(X5, Y17, Y8)) & ?[Y18: $i] : (r1(Y18) & (Y8 = Y18))) <=> ?[Y8: $i] : (?[Y17: $i] : (r1(Y17) & r4(X5, Y17, Y8)) & r1(Y8))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(69,plain,
% 0.11/0.38 (![X5: $i] : ?[Y8: $i] : (?[Y17: $i] : (r1(Y17) & r4(X5, Y17, Y8)) & ?[Y18: $i] : (r1(Y18) & (Y8 = Y18))) <=> ![X5: $i] : ?[Y8: $i] : (?[Y17: $i] : (r1(Y17) & r4(X5, Y17, Y8)) & r1(Y8))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[68])).
% 0.11/0.38 tff(70,axiom,(![X5: $i] : ?[Y8: $i] : (?[Y17: $i] : (r1(Y17) & r4(X5, Y17, Y8)) & ?[Y18: $i] : (r1(Y18) & (Y8 = Y18)))), file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax','axiom_5a')).
% 0.11/0.38 tff(71,plain,
% 0.11/0.38 (![X5: $i] : ?[Y8: $i] : (?[Y17: $i] : (r1(Y17) & r4(X5, Y17, Y8)) & r1(Y8))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.11/0.38 tff(72,plain,
% 0.11/0.38 (![X5: $i] : ?[Y8: $i] : (?[Y17: $i] : (r1(Y17) & r4(X5, Y17, Y8)) & r1(Y8))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.11/0.38 tff(73,plain,(
% 0.11/0.38 ![X5: $i] : ((r1(tptp_fun_Y17_12(X5)) & r4(X5, tptp_fun_Y17_12(X5), tptp_fun_Y8_11(X5))) & r1(tptp_fun_Y8_11(X5)))),
% 0.11/0.38 inference(skolemize,[status(sab)],[72])).
% 0.11/0.38 tff(74,plain,
% 0.11/0.38 (![X5: $i] : (r1(tptp_fun_Y17_12(X5)) & r4(X5, tptp_fun_Y17_12(X5), tptp_fun_Y8_11(X5)) & r1(tptp_fun_Y8_11(X5)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[73, 66])).
% 0.11/0.38 tff(75,plain,
% 0.11/0.38 (![X5: $i] : (~((~r1(tptp_fun_Y17_12(X5))) | (~r4(X5, tptp_fun_Y17_12(X5), tptp_fun_Y8_11(X5))) | (~r1(tptp_fun_Y8_11(X5)))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[74, 64])).
% 0.11/0.38 tff(76,plain,
% 0.11/0.38 ((~![X5: $i] : (~((~r1(tptp_fun_Y17_12(X5))) | (~r4(X5, tptp_fun_Y17_12(X5), tptp_fun_Y8_11(X5))) | (~r1(tptp_fun_Y8_11(X5)))))) | (~((~r1(tptp_fun_Y17_12(Y24!0))) | (~r4(Y24!0, tptp_fun_Y17_12(Y24!0), tptp_fun_Y8_11(Y24!0))) | (~r1(tptp_fun_Y8_11(Y24!0)))))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(77,plain,
% 0.11/0.38 (~((~r1(tptp_fun_Y17_12(Y24!0))) | (~r4(Y24!0, tptp_fun_Y17_12(Y24!0), tptp_fun_Y8_11(Y24!0))) | (~r1(tptp_fun_Y8_11(Y24!0))))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[76, 75])).
% 0.11/0.38 tff(78,plain,
% 0.11/0.38 (((~r1(tptp_fun_Y17_12(Y24!0))) | (~r4(Y24!0, tptp_fun_Y17_12(Y24!0), tptp_fun_Y8_11(Y24!0))) | (~r1(tptp_fun_Y8_11(Y24!0)))) | r1(tptp_fun_Y8_11(Y24!0))),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(79,plain,
% 0.11/0.38 (r1(tptp_fun_Y8_11(Y24!0))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.11/0.38 tff(80,plain,
% 0.11/0.38 ((r1(tptp_fun_Y8_11(Y24!0)) | (tptp_fun_Y8_11(Y24!0) = Y24!0)) | (~r1(tptp_fun_Y8_11(Y24!0)))),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(81,plain,
% 0.11/0.38 (r1(tptp_fun_Y8_11(Y24!0)) | (tptp_fun_Y8_11(Y24!0) = Y24!0)),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[80, 79])).
% 0.11/0.38 tff(82,plain,
% 0.11/0.38 (((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(tptp_fun_Y8_11(Y24!0))) | (~(tptp_fun_Y8_11(Y24!0) = Y24!0)))) | (~(r1(tptp_fun_Y8_11(Y24!0)) | (tptp_fun_Y8_11(Y24!0) = Y24!0))))) <=> ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~((~r1(tptp_fun_Y8_11(Y24!0))) | (~(tptp_fun_Y8_11(Y24!0) = Y24!0)))) | (~(r1(tptp_fun_Y8_11(Y24!0)) | (tptp_fun_Y8_11(Y24!0) = Y24!0))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(83,plain,
% 0.11/0.38 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(tptp_fun_Y8_11(Y24!0))) | (~(tptp_fun_Y8_11(Y24!0) = Y24!0)))) | (~(r1(tptp_fun_Y8_11(Y24!0)) | (tptp_fun_Y8_11(Y24!0) = Y24!0))))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(84,plain,
% 0.11/0.38 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~((~r1(tptp_fun_Y8_11(Y24!0))) | (~(tptp_fun_Y8_11(Y24!0) = Y24!0)))) | (~(r1(tptp_fun_Y8_11(Y24!0)) | (tptp_fun_Y8_11(Y24!0) = Y24!0)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.11/0.38 tff(85,plain,
% 0.11/0.38 (~((~r1(tptp_fun_Y8_11(Y24!0))) | (~(tptp_fun_Y8_11(Y24!0) = Y24!0)))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[84, 13, 81])).
% 0.11/0.38 tff(86,plain,
% 0.11/0.38 (((~r1(tptp_fun_Y8_11(Y24!0))) | (~(tptp_fun_Y8_11(Y24!0) = Y24!0))) | (tptp_fun_Y8_11(Y24!0) = Y24!0)),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(87,plain,
% 0.11/0.38 (tptp_fun_Y8_11(Y24!0) = Y24!0),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.11/0.38 tff(88,plain,
% 0.11/0.38 (((~r1(tptp_fun_Y17_12(Y24!0))) | (~r4(Y24!0, tptp_fun_Y17_12(Y24!0), tptp_fun_Y8_11(Y24!0))) | (~r1(tptp_fun_Y8_11(Y24!0)))) | r1(tptp_fun_Y17_12(Y24!0))),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(89,plain,
% 0.11/0.38 (r1(tptp_fun_Y17_12(Y24!0))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[88, 77])).
% 0.11/0.38 tff(90,plain,
% 0.11/0.38 ((r1(tptp_fun_Y17_12(Y24!0)) | (tptp_fun_Y17_12(Y24!0) = Y24!0)) | (~r1(tptp_fun_Y17_12(Y24!0)))),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(91,plain,
% 0.11/0.38 (r1(tptp_fun_Y17_12(Y24!0)) | (tptp_fun_Y17_12(Y24!0) = Y24!0)),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[90, 89])).
% 0.11/0.38 tff(92,plain,
% 0.11/0.38 (((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(tptp_fun_Y17_12(Y24!0))) | (~(tptp_fun_Y17_12(Y24!0) = Y24!0)))) | (~(r1(tptp_fun_Y17_12(Y24!0)) | (tptp_fun_Y17_12(Y24!0) = Y24!0))))) <=> ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~((~r1(tptp_fun_Y17_12(Y24!0))) | (~(tptp_fun_Y17_12(Y24!0) = Y24!0)))) | (~(r1(tptp_fun_Y17_12(Y24!0)) | (tptp_fun_Y17_12(Y24!0) = Y24!0))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(93,plain,
% 0.11/0.38 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(tptp_fun_Y17_12(Y24!0))) | (~(tptp_fun_Y17_12(Y24!0) = Y24!0)))) | (~(r1(tptp_fun_Y17_12(Y24!0)) | (tptp_fun_Y17_12(Y24!0) = Y24!0))))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(94,plain,
% 0.11/0.38 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~((~r1(tptp_fun_Y17_12(Y24!0))) | (~(tptp_fun_Y17_12(Y24!0) = Y24!0)))) | (~(r1(tptp_fun_Y17_12(Y24!0)) | (tptp_fun_Y17_12(Y24!0) = Y24!0)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.11/0.38 tff(95,plain,
% 0.11/0.38 (~((~r1(tptp_fun_Y17_12(Y24!0))) | (~(tptp_fun_Y17_12(Y24!0) = Y24!0)))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[94, 13, 91])).
% 0.11/0.38 tff(96,plain,
% 0.11/0.38 (((~r1(tptp_fun_Y17_12(Y24!0))) | (~(tptp_fun_Y17_12(Y24!0) = Y24!0))) | (tptp_fun_Y17_12(Y24!0) = Y24!0)),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(97,plain,
% 0.11/0.38 (tptp_fun_Y17_12(Y24!0) = Y24!0),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[96, 95])).
% 0.11/0.38 tff(98,plain,
% 0.11/0.38 (r4(Y24!0, tptp_fun_Y17_12(Y24!0), tptp_fun_Y8_11(Y24!0)) <=> r4(Y24!0, Y24!0, Y24!0)),
% 0.11/0.38 inference(monotonicity,[status(thm)],[97, 87])).
% 0.11/0.38 tff(99,plain,
% 0.11/0.38 (((~r1(tptp_fun_Y17_12(Y24!0))) | (~r4(Y24!0, tptp_fun_Y17_12(Y24!0), tptp_fun_Y8_11(Y24!0))) | (~r1(tptp_fun_Y8_11(Y24!0)))) | r4(Y24!0, tptp_fun_Y17_12(Y24!0), tptp_fun_Y8_11(Y24!0))),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(100,plain,
% 0.11/0.38 (r4(Y24!0, tptp_fun_Y17_12(Y24!0), tptp_fun_Y8_11(Y24!0))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[99, 77])).
% 0.11/0.38 tff(101,plain,
% 0.11/0.38 (r4(Y24!0, Y24!0, Y24!0)),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[100, 98])).
% 0.11/0.38 tff(102,plain,
% 0.11/0.38 (((~![Y2: $i] : ((~r1(Y2)) | (~r4(Y2, Y2, Y24!0)))) | ((~r1(Y24!0)) | (~r4(Y24!0, Y24!0, Y24!0)))) <=> ((~![Y2: $i] : ((~r1(Y2)) | (~r4(Y2, Y2, Y24!0)))) | (~r1(Y24!0)) | (~r4(Y24!0, Y24!0, Y24!0)))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(103,plain,
% 0.11/0.38 ((~![Y2: $i] : ((~r1(Y2)) | (~r4(Y2, Y2, Y24!0)))) | ((~r1(Y24!0)) | (~r4(Y24!0, Y24!0, Y24!0)))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(104,plain,
% 0.11/0.38 ((~![Y2: $i] : ((~r1(Y2)) | (~r4(Y2, Y2, Y24!0)))) | (~r1(Y24!0)) | (~r4(Y24!0, Y24!0, Y24!0))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.11/0.38 tff(105,plain,
% 0.11/0.38 ($false),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[104, 37, 101, 62])).
% 0.11/0.38 % SZS output end Proof
% 0.11/0.38 % E exiting
%------------------------------------------------------------------------------