0.11/0.15 % Problem : Vampire---4.8_24393 : TPTP v0.0.0. Released v0.0.0. 0.11/0.16 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s 0.16/0.37 % Computer : n009.cluster.edu 0.16/0.37 % Model : x86_64 x86_64 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.16/0.37 % Memory : 8042.1875MB 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64 0.16/0.37 % CPULimit : 1440 0.16/0.37 % WCLimit : 180 0.16/0.37 % DateTime : Mon Jul 3 13:02:26 EDT 2023 0.16/0.37 % CPUTime : 0.16/0.38 This is a THF_ problem 0.16/0.38 Running vampire_rel_static_ahmed-new-hol_6848 --cores 8 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox2/tmp/tmp.6wYljQkmd9/Vampire---4.8_24393 -m 12000 -t 180 0.16/0.41 % (24507)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on Vampire---4 for (1799ds/4Mi) 0.16/0.41 % (24501)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on Vampire---4 for (1799ds/96Mi) 0.16/0.41 % (24503)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=34:si=on:rtra=on_0 on Vampire---4 for (1799ds/34Mi) 0.16/0.41 % (24502)lrs+10_1:2_cnfonf=off:hud=1:inj=on:i=36:si=on:rtra=on_0 on Vampire---4 for (1799ds/36Mi) 0.16/0.41 % (24505)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on Vampire---4 for (1799ds/17Mi) 0.16/0.41 % (24504)lrs+1002_1:1_au=on:s2a=on:s2agt=32:sgt=8:ss=axioms:i=385:si=on:rtra=on_0 on Vampire---4 for (1799ds/385Mi) 0.16/0.41 % (24506)ott+1010_1:1_cnfonf=lazy_gen:fe=off:kws=inv_arity:plsq=on:plsqc=1:plsqr=32,1:prag=on:sp=const_frequency:i=74:si=on:rtra=on_0 on Vampire---4 for (1799ds/74Mi) 0.16/0.41 % (24507)Instruction limit reached! 0.16/0.41 % (24507)------------------------------ 0.16/0.41 % (24507)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.16/0.41 % (24507)Termination reason: Unknown 0.16/0.41 % (24507)Termination phase: shuffling 0.16/0.41 0.16/0.41 % (24507)Memory used [KB]: 1407 0.16/0.41 % (24507)Time elapsed: 0.004 s 0.16/0.41 % (24507)Instructions burned: 5 (million) 0.16/0.41 % (24507)------------------------------ 0.16/0.41 % (24507)------------------------------ 0.16/0.42 % (24508)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=915:si=on:rtra=on_0 on Vampire---4 for (1799ds/915Mi) 0.16/0.42 % (24505)Instruction limit reached! 0.16/0.42 % (24505)------------------------------ 0.16/0.42 % (24505)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.16/0.42 % (24505)Termination reason: Unknown 0.16/0.42 % (24505)Termination phase: shuffling 0.16/0.42 0.16/0.42 % (24505)Memory used [KB]: 1663 0.16/0.42 % (24505)Time elapsed: 0.011 s 0.16/0.42 % (24505)Instructions burned: 18 (million) 0.16/0.42 % (24505)------------------------------ 0.16/0.42 % (24505)------------------------------ 0.16/0.42 % (24509)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on Vampire---4 for (1799ds/21Mi) 0.16/0.43 % (24503)Instruction limit reached! 0.16/0.43 % (24503)------------------------------ 0.16/0.43 % (24503)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.16/0.43 % (24503)Termination reason: Unknown 0.16/0.43 % (24503)Termination phase: Property scanning 0.16/0.43 0.16/0.43 % (24503)Memory used [KB]: 1918 0.16/0.43 % (24503)Time elapsed: 0.019 s 0.16/0.43 % (24503)Instructions burned: 34 (million) 0.16/0.43 % (24503)------------------------------ 0.16/0.43 % (24503)------------------------------ 0.16/0.43 % (24502)Instruction limit reached! 0.16/0.43 % (24502)------------------------------ 0.16/0.43 % (24502)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.16/0.43 % (24502)Termination reason: Unknown 0.16/0.43 % (24502)Termination phase: Property scanning 0.16/0.43 0.16/0.43 % (24502)Memory used [KB]: 1918 0.16/0.43 % (24502)Time elapsed: 0.020 s 0.16/0.43 % (24502)Instructions burned: 37 (million) 0.16/0.43 % (24502)------------------------------ 0.16/0.43 % (24502)------------------------------ 0.16/0.43 % (24509)Instruction limit reached! 0.16/0.43 % (24509)------------------------------ 0.16/0.43 % (24509)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.16/0.43 % (24509)Termination reason: Unknown 0.16/0.43 % (24509)Termination phase: shuffling 0.16/0.43 % (24510)lrs-3_1:1024_cbe=off:chr=on:tnu=1:i=7:si=on:rtra=on_0 on Vampire---4 for (1799ds/7Mi) 0.16/0.43 0.16/0.43 % (24509)Memory used [KB]: 1791 0.16/0.43 % (24509)Time elapsed: 0.011 s 0.16/0.43 % (24509)Instructions burned: 23 (million) 0.16/0.43 % (24509)------------------------------ 0.16/0.43 % (24509)------------------------------ 0.23/0.44 % (24510)Instruction limit reached! 0.23/0.44 % (24510)------------------------------ 0.23/0.44 % (24510)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.23/0.44 % (24510)Termination reason: Unknown 0.23/0.44 % (24510)Termination phase: shuffling 0.23/0.44 0.23/0.44 % (24510)Memory used [KB]: 1407 0.23/0.44 % (24510)Time elapsed: 0.006 s 0.23/0.44 % (24510)Instructions burned: 8 (million) 0.23/0.44 % (24510)------------------------------ 0.23/0.44 % (24510)------------------------------ 0.23/0.44 % (24511)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on Vampire---4 for (1799ds/1021Mi) 0.23/0.44 % (24512)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on Vampire---4 for (1799ds/71Mi) 0.23/0.44 % (24506)Instruction limit reached! 0.23/0.44 % (24506)------------------------------ 0.23/0.44 % (24506)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.23/0.44 % (24506)Termination reason: Unknown 0.23/0.44 % (24506)Termination phase: Function definition elimination 0.23/0.44 0.23/0.44 % (24506)Memory used [KB]: 2174 0.23/0.44 % (24506)Time elapsed: 0.036 s 0.23/0.44 % (24506)Instructions burned: 74 (million) 0.23/0.44 % (24506)------------------------------ 0.23/0.44 % (24506)------------------------------ 0.23/0.45 % (24513)lrs-1010_1:50_au=on:awrs=converge:awrsf=430:bet=on:cbe=off:cha=on:nm=20:sac=on:i=9:si=on:rtra=on_0 on Vampire---4 for (1799ds/9Mi) 0.23/0.45 % (24513)Instruction limit reached! 0.23/0.45 % (24513)------------------------------ 0.23/0.45 % (24513)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.23/0.45 % (24513)Termination reason: Unknown 0.23/0.45 % (24513)Termination phase: shuffling 0.23/0.45 0.23/0.45 % (24513)Memory used [KB]: 1407 0.23/0.45 % (24513)Time elapsed: 0.005 s 0.23/0.45 % (24513)Instructions burned: 9 (million) 0.23/0.45 % (24513)------------------------------ 0.23/0.45 % (24513)------------------------------ 0.23/0.45 % (24514)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=1044:si=on:rtra=on_0 on Vampire---4 for (1799ds/1044Mi) 0.23/0.46 % (24501)Instruction limit reached! 0.23/0.46 % (24501)------------------------------ 0.23/0.46 % (24501)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.23/0.46 % (24501)Termination reason: Unknown 0.23/0.46 % (24501)Termination phase: Saturation 0.23/0.46 0.23/0.46 % (24501)Memory used [KB]: 6652 0.23/0.46 % (24501)Time elapsed: 0.049 s 0.23/0.46 % (24501)Instructions burned: 96 (million) 0.23/0.46 % (24501)------------------------------ 0.23/0.46 % (24501)------------------------------ 0.23/0.46 % (24516)lrs+21_1:1_cond=on:e2e=on:i=61:si=on:rtra=on_0 on Vampire---4 for (1799ds/61Mi) 0.23/0.46 % (24515)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=128:si=on:rtra=on_0 on Vampire---4 for (1799ds/128Mi) 0.23/0.48 % (24512)Instruction limit reached! 0.23/0.48 % (24512)------------------------------ 0.23/0.48 % (24512)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.23/0.48 % (24512)Termination reason: Unknown 0.23/0.48 % (24512)Termination phase: Function definition elimination 0.23/0.48 0.23/0.48 % (24512)Memory used [KB]: 2046 0.23/0.48 % (24512)Time elapsed: 0.036 s 0.23/0.48 % (24512)Instructions burned: 73 (million) 0.23/0.48 % (24512)------------------------------ 0.23/0.48 % (24512)------------------------------ 0.23/0.48 % (24516)Instruction limit reached! 0.23/0.48 % (24516)------------------------------ 0.23/0.48 % (24516)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.23/0.48 % (24516)Termination reason: Unknown 0.23/0.48 % (24516)Termination phase: Preprocessing 3 0.23/0.48 0.23/0.48 % (24516)Memory used [KB]: 3070 0.23/0.48 % (24516)Time elapsed: 0.020 s 0.23/0.48 % (24516)Instructions burned: 62 (million) 0.23/0.48 % (24516)------------------------------ 0.23/0.48 % (24516)------------------------------ 0.23/0.48 % (24517)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=14:si=on:rtra=on_0 on Vampire---4 for (1799ds/14Mi) 0.23/0.48 % (24519)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on Vampire---4 for (1799ds/1041Mi) 0.23/0.49 % (24517)Instruction limit reached! 0.23/0.49 % (24517)------------------------------ 0.23/0.49 % (24517)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.23/0.49 % (24517)Termination reason: Unknown 0.23/0.49 % (24517)Termination phase: shuffling 0.23/0.49 0.23/0.49 % (24517)Memory used [KB]: 1663 0.23/0.49 % (24517)Time elapsed: 0.011 s 0.23/0.49 % (24517)Instructions burned: 14 (million) 0.23/0.49 % (24517)------------------------------ 0.23/0.49 % (24517)------------------------------ 0.23/0.50 % (24518)lrs+2_5:1_cnfonf=lazy_not_be_gen:hud=10:inj=on:ntd=on:tnu=1:i=2:si=on:rtra=on_0 on Vampire---4 for (1799ds/2Mi) 0.23/0.50 % (24518)Instruction limit reached! 0.23/0.50 % (24518)------------------------------ 0.23/0.50 % (24518)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.23/0.50 % (24518)Termination reason: Unknown 0.23/0.50 % (24518)Termination phase: shuffling 0.23/0.50 0.23/0.50 % (24518)Memory used [KB]: 1279 0.23/0.50 % (24518)Time elapsed: 0.003 s 0.23/0.50 % (24518)Instructions burned: 3 (million) 0.23/0.50 % (24518)------------------------------ 0.23/0.50 % (24518)------------------------------ 0.23/0.50 % (24515)Instruction limit reached! 0.23/0.50 % (24515)------------------------------ 0.23/0.50 % (24515)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.23/0.50 % (24515)Termination reason: Unknown 0.23/0.50 % (24515)Termination phase: Saturation 0.23/0.50 0.23/0.50 % (24515)Memory used [KB]: 6908 0.23/0.50 % (24515)Time elapsed: 0.044 s 0.23/0.50 % (24515)Instructions burned: 130 (million) 0.23/0.50 % (24515)------------------------------ 0.23/0.50 % (24515)------------------------------ 0.23/0.50 % (24520)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on Vampire---4 for (1799ds/11Mi) 0.23/0.51 % (24522)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=26:si=on:rtra=on_0 on Vampire---4 for (1798ds/26Mi) 0.23/0.51 % (24520)Instruction limit reached! 0.23/0.51 % (24520)------------------------------ 0.23/0.51 % (24520)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.23/0.51 % (24520)Termination reason: Unknown 0.23/0.51 % (24520)Termination phase: shuffling 0.23/0.51 0.23/0.51 % (24520)Memory used [KB]: 1535 0.23/0.51 % (24520)Time elapsed: 0.008 s 0.23/0.51 % (24520)Instructions burned: 12 (million) 0.23/0.51 % (24520)------------------------------ 0.23/0.51 % (24520)------------------------------ 0.23/0.51 % (24521)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on Vampire---4 for (1798ds/140Mi) 0.23/0.52 % (24522)Instruction limit reached! 0.23/0.52 % (24522)------------------------------ 0.23/0.52 % (24522)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.23/0.52 % (24522)Termination reason: Unknown 0.23/0.52 % (24522)Termination phase: shuffling 0.23/0.52 0.23/0.52 % (24522)Memory used [KB]: 1791 0.23/0.52 % (24522)Time elapsed: 0.009 s 0.23/0.52 % (24522)Instructions burned: 28 (million) 0.23/0.52 % (24522)------------------------------ 0.23/0.52 % (24522)------------------------------ 0.23/0.52 % (24523)lrs+1002_1:4_au=on:av=off:bsr=on:cbe=off:nm=2:i=56:si=on:rtra=on_0 on Vampire---4 for (1798ds/56Mi) 0.23/0.52 % (24524)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on Vampire---4 for (1798ds/275Mi) 0.23/0.54 % (24508)First to succeed. 0.23/0.54 % (24508)Refutation found. Thanks to Tanya! 0.23/0.54 % SZS status Theorem for Vampire---4 0.23/0.54 % SZS output start Proof for Vampire---4 0.23/0.54 thf(func_def_0, type, in: $i > $i > $o). 0.23/0.54 thf(func_def_1, type, exu: ($i > $o) > $o). 0.23/0.54 thf(func_def_6, type, setadjoin: $i > $i > $i). 0.23/0.54 thf(func_def_8, type, powerset: $i > $i). 0.23/0.54 thf(func_def_10, type, setunion: $i > $i). 0.23/0.54 thf(func_def_19, type, descr: ($i > $o) > $i). 0.23/0.54 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i). 0.23/0.54 thf(func_def_26, type, prop2set: $o > $i). 0.23/0.54 thf(func_def_36, type, nonempty: $i > $o). 0.23/0.54 thf(func_def_69, type, set2prop: $i > $o). 0.23/0.54 thf(func_def_88, type, subset: $i > $i > $o). 0.23/0.54 thf(func_def_89, type, disjoint: $i > $i > $o). 0.23/0.54 thf(func_def_90, type, setsmeet: $i > $i > $o). 0.23/0.54 thf(func_def_114, type, binunion: $i > $i > $i). 0.23/0.54 thf(func_def_122, type, binintersect: $i > $i > $i). 0.23/0.54 thf(func_def_135, type, regular: $i > $o). 0.23/0.54 thf(func_def_136, type, setminus: $i > $i > $i). 0.23/0.54 thf(func_def_147, type, symdiff: $i > $i > $i). 0.23/0.54 thf(func_def_153, type, iskpair: $i > $o). 0.23/0.54 thf(func_def_158, type, kpair: $i > $i > $i). 0.23/0.54 thf(func_def_160, type, cartprod: $i > $i > $i). 0.23/0.54 thf(func_def_177, type, singleton: $i > $o). 0.23/0.54 thf(func_def_179, type, ex1: $i > ($i > $o) > $o). 0.23/0.54 thf(func_def_184, type, atmost1p: $i > $o). 0.23/0.54 thf(func_def_185, type, atleast2p: $i > $o). 0.23/0.54 thf(func_def_186, type, atmost2p: $i > $o). 0.23/0.54 thf(func_def_187, type, upairsetp: $i > $o). 0.23/0.54 thf(func_def_191, type, kfst: $i > $i). 0.23/0.54 thf(func_def_203, type, ksnd: $i > $i). 0.23/0.54 thf(func_def_213, type, breln: $i > $i > $i > $o). 0.23/0.54 thf(func_def_214, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i). 0.23/0.54 thf(func_def_235, type, sP0: $i > $i > $i > $o > $o). 0.23/0.54 thf(func_def_239, type, sP4: $i > $i > $o). 0.23/0.54 thf(func_def_240, type, sP5: $i > $o). 0.23/0.54 thf(func_def_241, type, sP6: $i > $i > $o). 0.23/0.54 thf(func_def_242, type, sP7: $i > $i > $o). 0.23/0.54 thf(func_def_245, type, sK10: $i > $o). 0.23/0.54 thf(func_def_246, type, sK11: ($i > $o) > $i > $i > $i). 0.23/0.54 thf(func_def_250, type, sK15: $i > $i > $i > $i). 0.23/0.54 thf(func_def_251, type, sK16: $i > $i > $i > $i). 0.23/0.54 thf(func_def_304, type, sK69: $i > $i). 0.23/0.54 thf(func_def_308, type, sK73: $i > $i > $o). 0.23/0.54 thf(func_def_317, type, sK82: $i > $o). 0.23/0.54 thf(func_def_330, type, sK95: $i > $o). 0.23/0.54 thf(func_def_333, type, sK98: $i > ($i > $o) > $i). 0.23/0.54 thf(func_def_334, type, sK99: $i > ($i > $o) > $i). 0.23/0.54 thf(func_def_335, type, sK100: $i > $o). 0.23/0.54 thf(func_def_336, type, sK101: $i > $i). 0.23/0.54 thf(func_def_337, type, sK102: ($i > $o) > $i). 0.23/0.54 thf(func_def_343, type, sK108: $i > $o). 0.23/0.54 thf(func_def_345, type, sK110: ($i > $o) > $i > $i). 0.23/0.54 thf(func_def_346, type, sK111: ($i > $o) > $i > $i). 0.23/0.54 thf(func_def_365, type, sK130: $i > $i > $i). 0.23/0.54 thf(func_def_370, type, sK135: $o > $i > $i > $i). 0.23/0.54 thf(func_def_390, type, sK155: $i > $i > $o). 0.23/0.54 thf(func_def_391, type, sK156: $i > $i). 0.23/0.54 thf(func_def_392, type, sK157: $i > $i). 0.23/0.54 thf(func_def_393, type, sK158: ($i > $i > $o) > $i > $i). 0.23/0.54 thf(func_def_394, type, sK159: ($i > $i > $o) > $i > $i). 0.23/0.54 thf(func_def_395, type, sK160: $i > ($i > $i > $o) > $i > $i). 0.23/0.54 thf(func_def_408, type, sK173: $i > $o). 0.23/0.54 thf(func_def_417, type, sK182: $i > $i > $o). 0.23/0.54 thf(func_def_429, type, sK194: $i > $o). 0.23/0.54 thf(func_def_431, type, sK196: ($i > $o) > $i > $i). 0.23/0.54 thf(func_def_439, type, sK204: $i > $o). 0.23/0.54 thf(func_def_446, type, sK211: $i > $o). 0.23/0.54 thf(func_def_447, type, sK212: $i > $o). 0.23/0.54 thf(func_def_450, type, sK215: $i > ($i > $o) > $i). 0.23/0.54 thf(func_def_453, type, sK218: $i > $i > $i). 0.23/0.54 thf(func_def_464, type, sK229: $i > $o). 0.23/0.54 thf(func_def_465, type, sK230: ($i > $o) > $i). 0.23/0.54 thf(func_def_469, type, sK234: $i > $o). 0.23/0.54 thf(func_def_478, type, sK243: $i > $i > $o). 0.23/0.54 thf(func_def_484, type, sK249: $i > $o). 0.23/0.54 thf(func_def_486, type, sK251: $i > ($i > $o) > $i). 0.23/0.54 thf(func_def_504, type, sK269: ($i > $o) > $i > $i). 0.23/0.54 thf(func_def_506, type, sK271: $i > $o). 0.23/0.54 thf(func_def_509, type, sK274: $i > $o). 0.23/0.54 thf(func_def_511, type, sK276: ($i > $o) > $i > $i). 0.23/0.54 thf(func_def_515, type, sK280: $i > $i > $i). 0.23/0.54 thf(func_def_518, type, sK283: $i > $i > $o). 0.23/0.54 thf(func_def_531, type, sK296: $i > $o). 0.23/0.54 thf(func_def_534, type, sK299: $i > $o). 0.23/0.54 thf(func_def_536, type, sK301: $i > $i > $o). 0.23/0.54 thf(func_def_538, type, sK303: ($i > $o) > $i > $i). 0.23/0.54 thf(func_def_540, type, sK305: $i > $o). 0.23/0.54 thf(func_def_541, type, sK306: ($i > $o) > ($i > $o) > $i). 0.23/0.54 thf(func_def_542, type, sK307: ($i > $o) > ($i > $o) > $i). 0.23/0.54 thf(func_def_543, type, sK308: $i > $o). 0.23/0.54 thf(func_def_544, type, sK309: $i > $o). 0.23/0.54 thf(func_def_545, type, sK310: $i > $o). 0.23/0.54 thf(func_def_547, type, sK312: ($i > $o) > $i). 0.23/0.54 thf(func_def_548, type, sK313: ($i > $o) > $i). 0.23/0.54 thf(func_def_566, type, sK331: $i > $i > $i). 0.23/0.54 thf(func_def_569, type, sK334: $i > $i > $i). 0.23/0.54 thf(func_def_581, type, sK346: ($i > $o) > ($i > $o) > $i > $i > $i). 0.23/0.54 thf(func_def_582, type, sK347: ($i > $o) > ($i > $o) > $i > $i > $i). 0.23/0.54 thf(func_def_585, type, sK350: $i > $o). 0.23/0.54 thf(func_def_586, type, sK351: $i > $o). 0.23/0.54 thf(func_def_590, type, sK355: $i > $i > $i). 0.23/0.54 thf(func_def_593, type, sK358: $i > $i > $i). 0.23/0.54 thf(func_def_600, type, sK365: $i > $o). 0.23/0.54 thf(func_def_602, type, sK367: ($i > $o) > $i > $i). 0.23/0.54 thf(func_def_617, type, sK382: $i > $i > $i). 0.23/0.54 thf(func_def_618, type, sK383: $i > $i > $i). 0.23/0.54 thf(func_def_625, type, sK390: $i > ($i > $o) > $i). 0.23/0.54 thf(func_def_626, type, sK391: $i > $o). 0.23/0.54 thf(func_def_630, type, sK395: $i > $o). 0.23/0.54 thf(func_def_633, type, sK398: $i > $i > $i). 0.23/0.54 thf(func_def_634, type, sK399: $i > $i > $i). 0.23/0.54 thf(func_def_635, type, sK400: $i > $i > $i). 0.23/0.54 thf(func_def_636, type, sK401: $i > $i > $i). 0.23/0.54 thf(func_def_637, type, sK402: $i > $i > $i > $i). 0.23/0.54 thf(func_def_638, type, sK403: $i > $i). 0.23/0.54 thf(func_def_639, type, sK404: $i > $i). 0.23/0.54 thf(func_def_640, type, sK405: $i > $i). 0.23/0.54 thf(func_def_641, type, sK406: $i > $i). 0.23/0.54 thf(func_def_642, type, sK407: $i > $i > $i). 0.23/0.54 thf(func_def_643, type, sK408: $i > $i > $i > $i). 0.23/0.54 thf(func_def_644, type, sK409: $i > $i > $i > $i). 0.23/0.54 thf(func_def_645, type, sK410: $i > $i > $i). 0.23/0.54 thf(func_def_646, type, sK411: $i > $i > $i). 0.23/0.54 thf(func_def_648, type, sK413: $i > $i). 0.23/0.54 thf(func_def_649, type, sK414: $i > $i). 0.23/0.54 thf(func_def_650, type, sK415: $i > $i). 0.23/0.54 thf(func_def_651, type, sK416: $i > $i > $i). 0.23/0.54 thf(func_def_657, type, sK422: $i > $i). 0.23/0.54 thf(func_def_663, type, sK428: ($i > $o) > $i). 0.23/0.54 thf(func_def_664, type, sK429: $i > $o). 0.23/0.54 thf(func_def_665, type, sK430: $i > $i). 0.23/0.54 thf(func_def_674, type, sK439: $i > $i). 0.23/0.54 thf(func_def_687, type, sK452: $i > $i > $i). 0.23/0.54 thf(func_def_692, type, sK457: $i > $i). 0.23/0.54 thf(func_def_694, type, sK459: $i > $i). 0.23/0.54 thf(func_def_699, type, sK464: $i > $o). 0.23/0.54 thf(func_def_703, type, sK468: $i > $i). 0.23/0.54 thf(func_def_704, type, sK469: $i > $i). 0.23/0.54 thf(func_def_708, type, sK473: $i > $o). 0.23/0.54 thf(func_def_715, type, sK480: ($i > $o) > ($i > $o) > $i). 0.23/0.54 thf(func_def_716, type, sK481: ($i > $o) > ($i > $o) > $i). 0.23/0.54 thf(func_def_717, type, sK482: $i > $o). 0.23/0.54 thf(func_def_718, type, sK483: $i > $o). 0.23/0.54 thf(func_def_730, type, sK495: $i > $o). 0.23/0.54 thf(func_def_736, type, sK501: $i > $o). 0.23/0.54 thf(func_def_738, type, sK503: $i > ($i > $o) > $i). 0.23/0.54 thf(func_def_747, type, sK512: $i > $o). 0.23/0.54 thf(func_def_757, type, sK522: $i > $i > $o). 0.23/0.54 thf(func_def_763, type, sK528: $i > $i > $o). 0.23/0.54 thf(func_def_776, type, ph541: !>[X0: $tType]:(X0)). 0.23/0.54 thf(f2745,plain,( 0.23/0.54 $false), 0.23/0.54 inference(avatar_sat_refutation,[],[f2740,f2742,f2744])). 0.23/0.54 thf(f2744,plain,( 0.23/0.54 spl540_2), 0.23/0.54 inference(avatar_contradiction_clause,[],[f2743])). 0.23/0.54 thf(f2743,plain,( 0.23/0.54 $false | spl540_2), 0.23/0.54 inference(subsumption_resolution,[],[f2739,f2724])). 0.23/0.54 thf(f2724,plain,( 0.23/0.54 ($true = (in @ sK181 @ sK178))), 0.23/0.54 inference(subsumption_resolution,[],[f2718,f2019])). 0.23/0.54 thf(f2019,plain,( 0.23/0.54 (dpsetconstrEL1 = $true)), 0.23/0.54 inference(cnf_transformation,[],[f1098])). 0.23/0.54 thf(f1098,plain,( 0.23/0.54 (emptyInPowerset = $true) & (uniqinunit = $true) & (inCongP = $true) & (setminusILneg = $true) & (dpsetconstrI = $true) & (exuE1 = $true) & (dsetconstrEL = $true) & (noeltsimpempty = $true) & (subsetI1 = $true) & (prop2set2propI = $true) & (replAx = $true) & (powersetE1 = $true) & (ex1I = $true) & (binunionIL = $true) & (ksndsingleton = $true) & (binunionRsub = $true) & (quantDeMorgan1 = $true) & (upairsetIR = $true) & (descrp = $true) & (kfstsingleton = $true) & (exuE3e = $true) & (sepSubset = $true) & (setadjoinSub2 = $true) & (bs114d = $true) & (setunionE = $true) & (kfstpairEq = $true) & (binintersectSubset3 = $true) & (notdexE = $true) & (setukpairinjR11 = $true) & (setadjoin__Cong = $true) & (emptysetimpfalse = $true) & (cartprodpairin = $true) & (setminusI = $true) & (exuE3u = $true) & (setoftrueEq = $true) & (binintersectSubset4 = $true) & (notinsingleton = $true) & (ubforcartprodlem1 = $true) & (notsubsetI = $true) & (subsetE2 = $true) & (cartprodsndin = $true) & (emptysetE = $true) & (setadjoinE = $true) & (cartprodsndpairEq = $true) & (powersetE = $true) & (cartprodpairmemER = $true) & (ubforcartprodlem3 = $true) & (binintersectSubset2 = $true) & (nonemptyI1 = $true) & (sepInPowerset = $true) & (vacuousDall = $true) & (kpairsurjEq = $true) & (setukpairinjR1 = $true) & (upairsetE = $true) & (dsetconstrER = $true) & (prop2setE = $true) & (emptyI = $true) & (nonemptyImpWitness = $true) & (inPowerset = $true) & (setukpairinjL1 = $true) & (nonemptyE1 = $true) & (setukpairinjR12 = $true) & (omega__Cong = $true) & (foundationAx = $true) & (subsetRefl = $true) & (exuE2 = $true) & (descr__Cong = $true) & (setminusER = $true) & (binintersectEL = $true) & (setextsub = $true) & (singletoninpowunion = $true) & (exuI2 = $true) & (subsetemptysetimpeq = $true) & (dsetconstrI = $true) & (setunion__Cong = $true) & (emptyE1 = $true) & (powersetI = $true) & (setukpairinjL = $true) & (setbeta = $true) & (setminusERneg = $true) & (nonemptyI = $true) & (setminusIRneg = $true) & (quantDeMorgan4 = $true) & (cartprodpairmemEL = $true) & (eqimpsubset1 = $true) & (setukpairinjR = $true) & (setukpairinjL2 = $true) & (singletonsuniq = $true) & (singletonsswitch = $true) & (powersetAx = $true) & (symdiffIneg1 = $true) & (emptyinunitempty = $true) & (upairsubunion = $true) & (cartprodpairsurjEq = $true) & (exuEu = $true) & (dpsetconstrEL1 = $true) & (setunionsingleton2 = $true) & (symdiffI2 = $true) & (setminusSubset2 = $true) & (setunionAx = $true) & (ex1I2 = $true) & (ubforcartprodlem2 = $true) & (emptyinPowerset = $true) & (subsetTrans = $true) & (exu__Cong = $true) & (setminusSubset1 = $true) & (singletoninpowerset = $true) & (upairequniteq = $true) & (omegaSAx = $true) & (upairsetIL = $true) & (setextAx = $true) & (binintersectSubset1 = $true) & (symdiffE = $true) & (binunionLsub = $true) & (disjointsetsI1 = $true) & (binintersectI = $true) & (quantDeMorgan2 = $true) & (subsetE = $true) & (secondinupair = $true) & (upairset2E = $true) & (singletonprop = $true) & (binintersectLsub = $true) & (prop2setI = $true) & (eqimpsubset2 = $true) & (binintersectSubset5 = $true) & (setunionsingleton1 = $true) & (setunionsingleton = $true) & (eqinunit = $true) & (binintersectRsub = $true) & (subsetI2 = $true) & (binunionE = $true) & (exuI1 = $true) & (cartprodmempair1 = $true) & (setukpairIR = $true) & (symdiffI1 = $true) & (omega0Ax = $true) & (setadjoinIL = $true) & (kpairiskpair = $true) & (exuI3 = $true) & (notequalI1 = $true) & (subset2powerset = $true) & (binunionEcases = $true) & (upairset2IR = $true) & (cartprodfstpairEq = $true) & (setOfPairsIsBReln = $true) & (omegaIndAx = $true) & (($true != (sK182 @ sK181 @ sK180)) & ((in @ (kpair @ sK181 @ sK180) @ (dpsetconstr @ sK178 @ sK179 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK182 @ Y0 @ Y1)))))) = $true)) & (symdiffIneg2 = $true) & (in__Cong = $true) & (ksndpairEq = $true) & (setminusELneg = $true) & (emptysetsubset = $true) & (setadjoinIR = $true) & (notinemptyset = $true) & (ex1E1 = $true) & (binunionIR = $true) & (setukpairIL = $true) & (setadjoinAx = $true) & (dpsetconstrSub = $true) & (subPowSU = $true) & (powersetI1 = $true) & (kpairp = $true) & (setminusLsub = $true) & (setext = $true) & (theprop = $true) & (setadjoinOr = $true) & (powerset__Cong = $true) & (notdallE = $true) & (dpsetconstrERa = $true) & (setukpairinjR2 = $true) & (cartprodmempaircEq = $true) & (dpsetconstrEL2 = $true) & (dsetconstr__Cong = $true) & (upairinpowunion = $true) & (notequalI2 = $true) & (singletonsubset = $true) & (setminusEL = $true) & (setadjoinSub = $true) & (cartprodmempair = $true) & (binintersectER = $true) & (cartprodfstin = $true) & (setunionE2 = $true) & (quantDeMorgan3 = $true) & (emptyset__Cong = $true) & (emptysetAx = $true) & (wellorderingAx = $true) & (setunionI = $true) & (powersetsubset = $true)), 0.23/0.54 inference(skolemisation,[status(esa),new_symbols(skolem,[sK178,sK179,sK180,sK181,sK182])],[f634,f1097])). 0.23/0.54 thf(f1097,plain,( 0.23/0.54 ? [X0,X1,X2,X3,X4 : $i > $i > $o] : (($true != (X4 @ X3 @ X2)) & ($true = (in @ (kpair @ X3 @ X2) @ (dpsetconstr @ X0 @ X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X4 @ Y0 @ Y1)))))))) => (($true != (sK182 @ sK181 @ sK180)) & ((in @ (kpair @ sK181 @ sK180) @ (dpsetconstr @ sK178 @ sK179 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK182 @ Y0 @ Y1)))))) = $true))), 0.23/0.54 introduced(choice_axiom,[])). 0.23/0.54 thf(f634,plain,( 0.23/0.54 (emptyInPowerset = $true) & (uniqinunit = $true) & (inCongP = $true) & (setminusILneg = $true) & (dpsetconstrI = $true) & (exuE1 = $true) & (dsetconstrEL = $true) & (noeltsimpempty = $true) & (subsetI1 = $true) & (prop2set2propI = $true) & (replAx = $true) & (powersetE1 = $true) & (ex1I = $true) & (binunionIL = $true) & (ksndsingleton = $true) & (binunionRsub = $true) & (quantDeMorgan1 = $true) & (upairsetIR = $true) & (descrp = $true) & (kfstsingleton = $true) & (exuE3e = $true) & (sepSubset = $true) & (setadjoinSub2 = $true) & (bs114d = $true) & (setunionE = $true) & (kfstpairEq = $true) & (binintersectSubset3 = $true) & (notdexE = $true) & (setukpairinjR11 = $true) & (setadjoin__Cong = $true) & (emptysetimpfalse = $true) & (cartprodpairin = $true) & (setminusI = $true) & (exuE3u = $true) & (setoftrueEq = $true) & (binintersectSubset4 = $true) & (notinsingleton = $true) & (ubforcartprodlem1 = $true) & (notsubsetI = $true) & (subsetE2 = $true) & (cartprodsndin = $true) & (emptysetE = $true) & (setadjoinE = $true) & (cartprodsndpairEq = $true) & (powersetE = $true) & (cartprodpairmemER = $true) & (ubforcartprodlem3 = $true) & (binintersectSubset2 = $true) & (nonemptyI1 = $true) & (sepInPowerset = $true) & (vacuousDall = $true) & (kpairsurjEq = $true) & (setukpairinjR1 = $true) & (upairsetE = $true) & (dsetconstrER = $true) & (prop2setE = $true) & (emptyI = $true) & (nonemptyImpWitness = $true) & (inPowerset = $true) & (setukpairinjL1 = $true) & (nonemptyE1 = $true) & (setukpairinjR12 = $true) & (omega__Cong = $true) & (foundationAx = $true) & (subsetRefl = $true) & (exuE2 = $true) & (descr__Cong = $true) & (setminusER = $true) & (binintersectEL = $true) & (setextsub = $true) & (singletoninpowunion = $true) & (exuI2 = $true) & (subsetemptysetimpeq = $true) & (dsetconstrI = $true) & (setunion__Cong = $true) & (emptyE1 = $true) & (powersetI = $true) & (setukpairinjL = $true) & (setbeta = $true) & (setminusERneg = $true) & (nonemptyI = $true) & (setminusIRneg = $true) & (quantDeMorgan4 = $true) & (cartprodpairmemEL = $true) & (eqimpsubset1 = $true) & (setukpairinjR = $true) & (setukpairinjL2 = $true) & (singletonsuniq = $true) & (singletonsswitch = $true) & (powersetAx = $true) & (symdiffIneg1 = $true) & (emptyinunitempty = $true) & (upairsubunion = $true) & (cartprodpairsurjEq = $true) & (exuEu = $true) & (dpsetconstrEL1 = $true) & (setunionsingleton2 = $true) & (symdiffI2 = $true) & (setminusSubset2 = $true) & (setunionAx = $true) & (ex1I2 = $true) & (ubforcartprodlem2 = $true) & (emptyinPowerset = $true) & (subsetTrans = $true) & (exu__Cong = $true) & (setminusSubset1 = $true) & (singletoninpowerset = $true) & (upairequniteq = $true) & (omegaSAx = $true) & (upairsetIL = $true) & (setextAx = $true) & (binintersectSubset1 = $true) & (symdiffE = $true) & (binunionLsub = $true) & (disjointsetsI1 = $true) & (binintersectI = $true) & (quantDeMorgan2 = $true) & (subsetE = $true) & (secondinupair = $true) & (upairset2E = $true) & (singletonprop = $true) & (binintersectLsub = $true) & (prop2setI = $true) & (eqimpsubset2 = $true) & (binintersectSubset5 = $true) & (setunionsingleton1 = $true) & (setunionsingleton = $true) & (eqinunit = $true) & (binintersectRsub = $true) & (subsetI2 = $true) & (binunionE = $true) & (exuI1 = $true) & (cartprodmempair1 = $true) & (setukpairIR = $true) & (symdiffI1 = $true) & (omega0Ax = $true) & (setadjoinIL = $true) & (kpairiskpair = $true) & (exuI3 = $true) & (notequalI1 = $true) & (subset2powerset = $true) & (binunionEcases = $true) & (upairset2IR = $true) & (cartprodfstpairEq = $true) & (setOfPairsIsBReln = $true) & (omegaIndAx = $true) & ? [X0,X1,X2,X3,X4 : $i > $i > $o] : (($true != (X4 @ X3 @ X2)) & ($true = (in @ (kpair @ X3 @ X2) @ (dpsetconstr @ X0 @ X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X4 @ Y0 @ Y1)))))))) & (symdiffIneg2 = $true) & (in__Cong = $true) & (ksndpairEq = $true) & (setminusELneg = $true) & (emptysetsubset = $true) & (setadjoinIR = $true) & (notinemptyset = $true) & (ex1E1 = $true) & (binunionIR = $true) & (setukpairIL = $true) & (setadjoinAx = $true) & (dpsetconstrSub = $true) & (subPowSU = $true) & (powersetI1 = $true) & (kpairp = $true) & (setminusLsub = $true) & (setext = $true) & (theprop = $true) & (setadjoinOr = $true) & (powerset__Cong = $true) & (notdallE = $true) & (dpsetconstrERa = $true) & (setukpairinjR2 = $true) & (cartprodmempaircEq = $true) & (dpsetconstrEL2 = $true) & (dsetconstr__Cong = $true) & (upairinpowunion = $true) & (notequalI2 = $true) & (singletonsubset = $true) & (setminusEL = $true) & (setadjoinSub = $true) & (cartprodmempair = $true) & (binintersectER = $true) & (cartprodfstin = $true) & (setunionE2 = $true) & (quantDeMorgan3 = $true) & (emptyset__Cong = $true) & (emptysetAx = $true) & (wellorderingAx = $true) & (setunionI = $true) & (powersetsubset = $true)), 0.23/0.54 inference(flattening,[],[f633])). 0.23/0.54 thf(f633,plain,( 0.23/0.54 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0,X1,X2,X3,X4 : $i > $i > $o] : (($true != (X4 @ X3 @ X2)) & ($true = (in @ (kpair @ X3 @ X2) @ (dpsetconstr @ X0 @ X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X4 @ Y0 @ Y1)))))))) & (dpsetconstrEL2 = $true)) & (dpsetconstrEL1 = $true)) & (dpsetconstrERa = $true)) & (setOfPairsIsBReln = $true)) & (dpsetconstrSub = $true)) & (dpsetconstrI = $true)) & (cartprodpairsurjEq = $true)) & (cartprodsndpairEq = $true)) & (cartprodfstpairEq = $true)) & (cartprodmempaircEq = $true)) & (cartprodpairmemER = $true)) & (cartprodpairmemEL = $true)) & (cartprodsndin = $true)) & (kpairsurjEq = $true)) & (ksndpairEq = $true)) & (ksndsingleton = $true)) & (setukpairinjR = $true)) & (setukpairinjR2 = $true)) & (upairequniteq = $true)) & (setukpairinjR1 = $true)) & (setukpairinjR12 = $true)) & (setukpairinjR11 = $true)) & (setukpairinjL = $true)) & (setukpairinjL2 = $true)) & (cartprodfstin = $true)) & (kfstpairEq = $true)) & (theprop = $true)) & (kfstsingleton = $true)) & (setukpairinjL1 = $true)) & (singletonsuniq = $true)) & (ex1I2 = $true)) & (ex1I = $true)) & (ex1E1 = $true)) & (singletonprop = $true)) & (setunionsingleton = $true)) & (setunionsingleton2 = $true)) & (setunionsingleton1 = $true)) & (setunionE2 = $true)) & (cartprodmempair = $true)) & (cartprodmempair1 = $true)) & (cartprodpairin = $true)) & (ubforcartprodlem3 = $true)) & (ubforcartprodlem2 = $true)) & (ubforcartprodlem1 = $true)) & (upairinpowunion = $true)) & (upairsubunion = $true)) & (upairset2E = $true)) & (singletoninpowunion = $true)) & (singletoninpowerset = $true)) & (singletonsubset = $true)) & (kpairp = $true)) & (kpairiskpair = $true)) & (setukpairIR = $true)) & (setukpairIL = $true)) & (secondinupair = $true)) & (symdiffIneg2 = $true)) & (symdiffIneg1 = $true)) & (symdiffI2 = $true)) & (symdiffI1 = $true)) & (symdiffE = $true)) & (setminusSubset1 = $true)) & (setminusLsub = $true)) & (setminusIRneg = $true)) & (setminusILneg = $true)) & (setminusELneg = $true)) & (setminusERneg = $true)) & (setminusSubset2 = $true)) & (setminusER = $true)) & (setminusEL = $true)) & (setminusI = $true)) & (bs114d = $true)) & (binintersectSubset1 = $true)) & (binintersectSubset4 = $true)) & (binintersectRsub = $true)) & (disjointsetsI1 = $true)) & (binintersectER = $true)) & (binintersectSubset3 = $true)) & (binintersectSubset2 = $true)) & (binintersectLsub = $true)) & (binintersectEL = $true)) & (binintersectSubset5 = $true)) & (binintersectI = $true)) & (binunionRsub = $true)) & (binunionLsub = $true)) & (binunionE = $true)) & (binunionEcases = $true)) & (binunionIR = $true)) & (upairset2IR = $true)) & (binunionIL = $true)) & (sepSubset = $true)) & (sepInPowerset = $true)) & (powersetsubset = $true)) & (inPowerset = $true)) & (powersetE1 = $true)) & (powersetI1 = $true)) & (subsetemptysetimpeq = $true)) & (setextsub = $true)) & (subset2powerset = $true)) & (setadjoinSub2 = $true)) & (setadjoinSub = $true)) & (subsetTrans = $true)) & (subsetRefl = $true)) & (notequalI2 = $true)) & (notequalI1 = $true)) & (notsubsetI = $true)) & (subsetE2 = $true)) & (subsetE = $true)) & (emptysetsubset = $true)) & (subsetI2 = $true)) & (eqimpsubset1 = $true)) & (eqimpsubset2 = $true)) & (subsetI1 = $true)) & (dsetconstr__Cong = $true)) & (descr__Cong = $true)) & (exuEu = $true)) & (omega__Cong = $true)) & (setunion__Cong = $true)) & (powerset__Cong = $true)) & (setadjoin__Cong = $true)) & (emptyset__Cong = $true)) & (exu__Cong = $true)) & (exuE3u = $true)) & (in__Cong = $true)) & (inCongP = $true)) & (exuI2 = $true)) & (exuI3 = $true)) & (exuI1 = $true)) & (notdallE = $true)) & (notdexE = $true)) & (prop2set2propI = $true)) & (prop2setI = $true)) & (quantDeMorgan4 = $true)) & (quantDeMorgan3 = $true)) & (quantDeMorgan2 = $true)) & (quantDeMorgan1 = $true)) & (vacuousDall = $true)) & (emptyE1 = $true)) & (upairsetIR = $true)) & (upairsetIL = $true)) & (upairsetE = $true)) & (singletonsswitch = $true)) & (eqinunit = $true)) & (notinsingleton = $true)) & (uniqinunit = $true)) & (nonemptyImpWitness = $true)) & (exuE2 = $true)) & (subPowSU = $true)) & (setunionE = $true)) & (setunionI = $true)) & (powersetE = $true)) & (emptyInPowerset = $true)) & (emptyinPowerset = $true)) & (powersetI = $true)) & (setoftrueEq = $true)) & (setadjoinOr = $true)) & (setadjoinE = $true)) & (setadjoinIR = $true)) & (emptyinunitempty = $true)) & (setadjoinIL = $true)) & (nonemptyI1 = $true)) & (nonemptyI = $true)) & (nonemptyE1 = $true)) & (setbeta = $true)) & (noeltsimpempty = $true)) & (emptyI = $true)) & (setext = $true)) & (exuE3e = $true)) & (notinemptyset = $true)) & (emptysetimpfalse = $true)) & (emptysetE = $true)) & (prop2setE = $true)) & (exuE1 = $true)) & (dsetconstrER = $true)) & (dsetconstrEL = $true)) & (dsetconstrI = $true)) & (descrp = $true)) & (wellorderingAx = $true)) & (foundationAx = $true)) & (replAx = $true)) & (omegaIndAx = $true)) & (omegaSAx = $true)) & (omega0Ax = $true)) & (setunionAx = $true)) & (powersetAx = $true)) & (setadjoinAx = $true)) & (emptysetAx = $true)) & (setextAx = $true)), 0.23/0.54 inference(ennf_transformation,[],[f204])). 0.23/0.54 thf(f204,plain,( 0.23/0.54 ~((setextAx = $true) => ((emptysetAx = $true) => ((setadjoinAx = $true) => ((powersetAx = $true) => ((setunionAx = $true) => ((omega0Ax = $true) => ((omegaSAx = $true) => ((omegaIndAx = $true) => ((replAx = $true) => ((foundationAx = $true) => ((wellorderingAx = $true) => ((descrp = $true) => ((dsetconstrI = $true) => ((dsetconstrEL = $true) => ((dsetconstrER = $true) => ((exuE1 = $true) => ((prop2setE = $true) => ((emptysetE = $true) => ((emptysetimpfalse = $true) => ((notinemptyset = $true) => ((exuE3e = $true) => ((setext = $true) => ((emptyI = $true) => ((noeltsimpempty = $true) => ((setbeta = $true) => ((nonemptyE1 = $true) => ((nonemptyI = $true) => ((nonemptyI1 = $true) => ((setadjoinIL = $true) => ((emptyinunitempty = $true) => ((setadjoinIR = $true) => ((setadjoinE = $true) => ((setadjoinOr = $true) => ((setoftrueEq = $true) => ((powersetI = $true) => ((emptyinPowerset = $true) => ((emptyInPowerset = $true) => ((powersetE = $true) => ((setunionI = $true) => ((setunionE = $true) => ((subPowSU = $true) => ((exuE2 = $true) => ((nonemptyImpWitness = $true) => ((uniqinunit = $true) => ((notinsingleton = $true) => ((eqinunit = $true) => ((singletonsswitch = $true) => ((upairsetE = $true) => ((upairsetIL = $true) => ((upairsetIR = $true) => ((emptyE1 = $true) => ((vacuousDall = $true) => ((quantDeMorgan1 = $true) => ((quantDeMorgan2 = $true) => ((quantDeMorgan3 = $true) => ((quantDeMorgan4 = $true) => ((prop2setI = $true) => ((prop2set2propI = $true) => ((notdexE = $true) => ((notdallE = $true) => ((exuI1 = $true) => ((exuI3 = $true) => ((exuI2 = $true) => ((inCongP = $true) => ((in__Cong = $true) => ((exuE3u = $true) => ((exu__Cong = $true) => ((emptyset__Cong = $true) => ((setadjoin__Cong = $true) => ((powerset__Cong = $true) => ((setunion__Cong = $true) => ((omega__Cong = $true) => ((exuEu = $true) => ((descr__Cong = $true) => ((dsetconstr__Cong = $true) => ((subsetI1 = $true) => ((eqimpsubset2 = $true) => ((eqimpsubset1 = $true) => ((subsetI2 = $true) => ((emptysetsubset = $true) => ((subsetE = $true) => ((subsetE2 = $true) => ((notsubsetI = $true) => ((notequalI1 = $true) => ((notequalI2 = $true) => ((subsetRefl = $true) => ((subsetTrans = $true) => ((setadjoinSub = $true) => ((setadjoinSub2 = $true) => ((subset2powerset = $true) => ((setextsub = $true) => ((subsetemptysetimpeq = $true) => ((powersetI1 = $true) => ((powersetE1 = $true) => ((inPowerset = $true) => ((powersetsubset = $true) => ((sepInPowerset = $true) => ((sepSubset = $true) => ((binunionIL = $true) => ((upairset2IR = $true) => ((binunionIR = $true) => ((binunionEcases = $true) => ((binunionE = $true) => ((binunionLsub = $true) => ((binunionRsub = $true) => ((binintersectI = $true) => ((binintersectSubset5 = $true) => ((binintersectEL = $true) => ((binintersectLsub = $true) => ((binintersectSubset2 = $true) => ((binintersectSubset3 = $true) => ((binintersectER = $true) => ((disjointsetsI1 = $true) => ((binintersectRsub = $true) => ((binintersectSubset4 = $true) => ((binintersectSubset1 = $true) => ((bs114d = $true) => ((setminusI = $true) => ((setminusEL = $true) => ((setminusER = $true) => ((setminusSubset2 = $true) => ((setminusERneg = $true) => ((setminusELneg = $true) => ((setminusILneg = $true) => ((setminusIRneg = $true) => ((setminusLsub = $true) => ((setminusSubset1 = $true) => ((symdiffE = $true) => ((symdiffI1 = $true) => ((symdiffI2 = $true) => ((symdiffIneg1 = $true) => ((symdiffIneg2 = $true) => ((secondinupair = $true) => ((setukpairIL = $true) => ((setukpairIR = $true) => ((kpairiskpair = $true) => ((kpairp = $true) => ((singletonsubset = $true) => ((singletoninpowerset = $true) => ((singletoninpowunion = $true) => ((upairset2E = $true) => ((upairsubunion = $true) => ((upairinpowunion = $true) => ((ubforcartprodlem1 = $true) => ((ubforcartprodlem2 = $true) => ((ubforcartprodlem3 = $true) => ((cartprodpairin = $true) => ((cartprodmempair1 = $true) => ((cartprodmempair = $true) => ((setunionE2 = $true) => ((setunionsingleton1 = $true) => ((setunionsingleton2 = $true) => ((setunionsingleton = $true) => ((singletonprop = $true) => ((ex1E1 = $true) => ((ex1I = $true) => ((ex1I2 = $true) => ((singletonsuniq = $true) => ((setukpairinjL1 = $true) => ((kfstsingleton = $true) => ((theprop = $true) => ((kfstpairEq = $true) => ((cartprodfstin = $true) => ((setukpairinjL2 = $true) => ((setukpairinjL = $true) => ((setukpairinjR11 = $true) => ((setukpairinjR12 = $true) => ((setukpairinjR1 = $true) => ((upairequniteq = $true) => ((setukpairinjR2 = $true) => ((setukpairinjR = $true) => ((ksndsingleton = $true) => ((ksndpairEq = $true) => ((kpairsurjEq = $true) => ((cartprodsndin = $true) => ((cartprodpairmemEL = $true) => ((cartprodpairmemER = $true) => ((cartprodmempaircEq = $true) => ((cartprodfstpairEq = $true) => ((cartprodsndpairEq = $true) => ((cartprodpairsurjEq = $true) => ((dpsetconstrI = $true) => ((dpsetconstrSub = $true) => ((setOfPairsIsBReln = $true) => ((dpsetconstrERa = $true) => ((dpsetconstrEL1 = $true) => ((dpsetconstrEL2 = $true) => ! [X0,X1,X2,X3,X4 : $i > $i > $o] : (($true = (in @ (kpair @ X3 @ X2) @ (dpsetconstr @ X0 @ X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X4 @ Y0 @ Y1))))))) => ($true = (X4 @ X3 @ X2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 0.23/0.54 inference(fool_elimination,[],[f203])). 0.23/0.54 thf(f203,plain,( 0.23/0.54 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => ! [X0,X1,X2,X3,X4 : $i > $i > $o] : ((in @ (kpair @ X3 @ X2) @ (dpsetconstr @ X0 @ X1 @ (^[X5 : $i, X6 : $i] : (X4 @ X5 @ X6)))) => (X4 @ X3 @ X2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 0.23/0.54 inference(rectify,[],[f195])). 0.23/0.54 thf(f195,negated_conjecture,( 0.23/0.54 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => ! [X3,X4,X2,X1,X0 : $i > $i > $o] : ((in @ (kpair @ X1 @ X2) @ (dpsetconstr @ X3 @ X4 @ (^[X8 : $i, X10 : $i] : (X0 @ X8 @ X10)))) => (X0 @ X1 @ X2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 0.23/0.54 inference(negated_conjecture,[],[f194])). 0.23/0.54 thf(f194,conjecture,( 0.23/0.54 setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => ! [X3,X4,X2,X1,X0 : $i > $i > $o] : ((in @ (kpair @ X1 @ X2) @ (dpsetconstr @ X3 @ X4 @ (^[X8 : $i, X10 : $i] : (X0 @ X8 @ X10)))) => (X0 @ X1 @ X2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 0.23/0.54 file('/export/starexec/sandbox2/tmp/tmp.6wYljQkmd9/Vampire---4.8_24393',dpsetconstrER)). 0.23/0.54 thf(f2718,plain,( 0.23/0.54 (dpsetconstrEL1 != $true) | ($true = (in @ sK181 @ sK178))), 0.23/0.54 inference(trivial_inequality_removal,[],[f2714])). 0.23/0.54 thf(f2714,plain,( 0.23/0.54 ($true != $true) | ($true = (in @ sK181 @ sK178)) | (dpsetconstrEL1 != $true)), 0.23/0.54 inference(superposition,[],[f2692,f2712])). 0.23/0.54 thf(f2712,plain,( 0.23/0.54 ($true = (in @ (kpair @ sK181 @ sK180) @ (dpsetconstr @ sK178 @ sK179 @ sK182)))), 0.23/0.54 inference(beta_eta_normalization,[],[f1967])). 0.23/0.54 thf(f1967,plain,( 0.23/0.54 ((in @ (kpair @ sK181 @ sK180) @ (dpsetconstr @ sK178 @ sK179 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK182 @ Y0 @ Y1)))))) = $true)), 0.23/0.54 inference(cnf_transformation,[],[f1098])). 0.23/0.54 thf(f2692,plain,( 0.23/0.54 ( ! [X2 : $i,X3 : $i > $i > $o,X0 : $i,X1 : $i,X4 : $i] : (($true != (in @ (kpair @ X4 @ X2) @ (dpsetconstr @ X0 @ X1 @ X3))) | (dpsetconstrEL1 != $true) | ($true = (in @ X4 @ X0))) )), 0.23/0.54 inference(beta_eta_normalization,[],[f1779])). 0.23/0.54 thf(f1779,plain,( 0.23/0.54 ( ! [X2 : $i,X3 : $i > $i > $o,X0 : $i,X1 : $i,X4 : $i] : (($true != (in @ (kpair @ X4 @ X2) @ (dpsetconstr @ X0 @ X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X3 @ Y0 @ Y1))))))) | (dpsetconstrEL1 != $true) | ($true = (in @ X4 @ X0))) )), 0.23/0.54 inference(cnf_transformation,[],[f936])). 0.23/0.54 thf(f936,plain,( 0.23/0.54 (! [X0,X1,X2,X3 : $i > $i > $o,X4] : (($true = (in @ X4 @ X0)) | ($true != (in @ (kpair @ X4 @ X2) @ (dpsetconstr @ X0 @ X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X3 @ Y0 @ Y1)))))))) | (dpsetconstrEL1 != $true)) & ((dpsetconstrEL1 = $true) | (($true != (in @ sK74 @ sK70)) & ((in @ (kpair @ sK74 @ sK72) @ (dpsetconstr @ sK70 @ sK71 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK73 @ Y0 @ Y1)))))) = $true)))), 0.23/0.54 inference(skolemisation,[status(esa),new_symbols(skolem,[sK70,sK71,sK72,sK73,sK74])],[f934,f935])). 0.23/0.54 thf(f935,plain,( 0.23/0.54 ? [X5,X6,X7,X8 : $i > $i > $o,X9] : (($true != (in @ X9 @ X5)) & ($true = (in @ (kpair @ X9 @ X7) @ (dpsetconstr @ X5 @ X6 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X8 @ Y0 @ Y1)))))))) => (($true != (in @ sK74 @ sK70)) & ((in @ (kpair @ sK74 @ sK72) @ (dpsetconstr @ sK70 @ sK71 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK73 @ Y0 @ Y1)))))) = $true))), 0.23/0.54 introduced(choice_axiom,[])). 0.23/0.54 thf(f934,plain,( 0.23/0.54 (! [X0,X1,X2,X3 : $i > $i > $o,X4] : (($true = (in @ X4 @ X0)) | ($true != (in @ (kpair @ X4 @ X2) @ (dpsetconstr @ X0 @ X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X3 @ Y0 @ Y1)))))))) | (dpsetconstrEL1 != $true)) & ((dpsetconstrEL1 = $true) | ? [X5,X6,X7,X8 : $i > $i > $o,X9] : (($true != (in @ X9 @ X5)) & ($true = (in @ (kpair @ X9 @ X7) @ (dpsetconstr @ X5 @ X6 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X8 @ Y0 @ Y1)))))))))), 0.23/0.54 inference(rectify,[],[f933])). 0.23/0.54 thf(f933,plain,( 0.23/0.54 (! [X0,X1,X2,X3 : $i > $i > $o,X4] : (($true = (in @ X4 @ X0)) | ($true != (in @ (kpair @ X4 @ X2) @ (dpsetconstr @ X0 @ X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X3 @ Y0 @ Y1)))))))) | (dpsetconstrEL1 != $true)) & ((dpsetconstrEL1 = $true) | ? [X0,X1,X2,X3 : $i > $i > $o,X4] : (($true != (in @ X4 @ X0)) & ($true = (in @ (kpair @ X4 @ X2) @ (dpsetconstr @ X0 @ X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X3 @ Y0 @ Y1)))))))))), 0.23/0.54 inference(nnf_transformation,[],[f807])). 0.23/0.54 thf(f807,plain,( 0.23/0.54 ! [X0,X1,X2,X3 : $i > $i > $o,X4] : (($true = (in @ X4 @ X0)) | ($true != (in @ (kpair @ X4 @ X2) @ (dpsetconstr @ X0 @ X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X3 @ Y0 @ Y1)))))))) <=> (dpsetconstrEL1 = $true)), 0.23/0.54 inference(ennf_transformation,[],[f206])). 0.23/0.54 thf(f206,plain,( 0.23/0.54 ! [X0,X1,X2,X3 : $i > $i > $o,X4] : (($true = (in @ (kpair @ X4 @ X2) @ (dpsetconstr @ X0 @ X1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X3 @ Y0 @ Y1))))))) => ($true = (in @ X4 @ X0))) <=> (dpsetconstrEL1 = $true)), 0.23/0.54 inference(fool_elimination,[],[f205])). 0.23/0.54 thf(f205,plain,( 0.23/0.54 (! [X0,X1,X2,X3 : $i > $i > $o,X4] : ((in @ (kpair @ X4 @ X2) @ (dpsetconstr @ X0 @ X1 @ (^[X5 : $i, X6 : $i] : (X3 @ X5 @ X6)))) => (in @ X4 @ X0)) = dpsetconstrEL1)), 0.23/0.54 inference(rectify,[],[f192])). 0.23/0.54 thf(f192,axiom,( 0.23/0.54 (! [X3,X4,X2,X0 : $i > $i > $o,X1] : ((in @ (kpair @ X1 @ X2) @ (dpsetconstr @ X3 @ X4 @ (^[X8 : $i, X10 : $i] : (X0 @ X8 @ X10)))) => (in @ X1 @ X3)) = dpsetconstrEL1)), 0.23/0.54 file('/export/starexec/sandbox2/tmp/tmp.6wYljQkmd9/Vampire---4.8_24393',dpsetconstrEL1)). 0.23/0.54 thf(f2739,plain,( 0.23/0.54 ($true != (in @ sK181 @ sK178)) | spl540_2), 0.23/0.54 inference(avatar_component_clause,[],[f2737])). 0.23/0.54 thf(f2737,plain,( 0.23/0.54 spl540_2 <=> ($true = (in @ sK181 @ sK178))), 0.23/0.54 introduced(avatar_definition,[new_symbols(naming,[spl540_2])])). 0.23/0.54 thf(f2742,plain,( 0.23/0.54 spl540_1), 0.23/0.54 inference(avatar_contradiction_clause,[],[f2741])). 0.23/0.54 thf(f2741,plain,( 0.23/0.54 $false | spl540_1), 0.23/0.54 inference(subsumption_resolution,[],[f2735,f2725])). 0.23/0.54 thf(f2725,plain,( 0.23/0.54 ($true = (in @ sK180 @ sK179))), 0.23/0.54 inference(subsumption_resolution,[],[f2717,f1942])). 0.23/0.54 thf(f1942,plain,( 0.23/0.54 (dpsetconstrEL2 = $true)), 0.23/0.54 inference(cnf_transformation,[],[f1098])). 0.23/0.54 thf(f2717,plain,( 0.23/0.54 (dpsetconstrEL2 != $true) | ($true = (in @ sK180 @ sK179))), 0.23/0.54 inference(trivial_inequality_removal,[],[f2713])). 0.23/0.54 thf(f2713,plain,( 0.23/0.54 (dpsetconstrEL2 != $true) | ($true != $true) | ($true = (in @ sK180 @ sK179))), 0.23/0.54 inference(superposition,[],[f2704,f2712])). 0.23/0.54 thf(f2704,plain,( 0.23/0.54 ( ! [X8 : $i,X6 : $i,X9 : $i,X7 : $i > $i > $o,X5 : $i] : (($true != (in @ (kpair @ X5 @ X6) @ (dpsetconstr @ X9 @ X8 @ X7))) | (dpsetconstrEL2 != $true) | ($true = (in @ X6 @ X8))) )), 0.23/0.54 inference(beta_eta_normalization,[],[f2238])). 0.23/0.54 thf(f2238,plain,( 0.23/0.54 ( ! [X8 : $i,X6 : $i,X9 : $i,X7 : $i > $i > $o,X5 : $i] : (($true != (in @ (kpair @ X5 @ X6) @ (dpsetconstr @ X9 @ X8 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X7 @ Y0 @ Y1))))))) | (dpsetconstrEL2 != $true) | ($true = (in @ X6 @ X8))) )), 0.23/0.54 inference(cnf_transformation,[],[f1257])). 0.23/0.54 thf(f1257,plain,( 0.23/0.54 ((dpsetconstrEL2 = $true) | (($true = (in @ (kpair @ sK281 @ sK282) @ (dpsetconstr @ sK285 @ sK284 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK283 @ Y0 @ Y1))))))) & ($true != (in @ sK282 @ sK284)))) & (! [X5,X6,X7 : $i > $i > $o,X8,X9] : (($true != (in @ (kpair @ X5 @ X6) @ (dpsetconstr @ X9 @ X8 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X7 @ Y0 @ Y1))))))) | ($true = (in @ X6 @ X8))) | (dpsetconstrEL2 != $true))), 0.23/0.54 inference(skolemisation,[status(esa),new_symbols(skolem,[sK281,sK282,sK283,sK284,sK285])],[f1255,f1256])). 0.23/0.54 thf(f1256,plain,( 0.23/0.54 ? [X0,X1,X2 : $i > $i > $o,X3,X4] : (($true = (in @ (kpair @ X0 @ X1) @ (dpsetconstr @ X4 @ X3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X2 @ Y0 @ Y1))))))) & ((in @ X1 @ X3) != $true)) => (($true = (in @ (kpair @ sK281 @ sK282) @ (dpsetconstr @ sK285 @ sK284 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK283 @ Y0 @ Y1))))))) & ($true != (in @ sK282 @ sK284)))), 0.23/0.54 introduced(choice_axiom,[])). 0.23/0.54 thf(f1255,plain,( 0.23/0.54 ((dpsetconstrEL2 = $true) | ? [X0,X1,X2 : $i > $i > $o,X3,X4] : (($true = (in @ (kpair @ X0 @ X1) @ (dpsetconstr @ X4 @ X3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X2 @ Y0 @ Y1))))))) & ((in @ X1 @ X3) != $true))) & (! [X5,X6,X7 : $i > $i > $o,X8,X9] : (($true != (in @ (kpair @ X5 @ X6) @ (dpsetconstr @ X9 @ X8 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X7 @ Y0 @ Y1))))))) | ($true = (in @ X6 @ X8))) | (dpsetconstrEL2 != $true))), 0.23/0.54 inference(rectify,[],[f1254])). 0.23/0.54 thf(f1254,plain,( 0.23/0.54 ((dpsetconstrEL2 = $true) | ? [X0,X1,X2 : $i > $i > $o,X3,X4] : (($true = (in @ (kpair @ X0 @ X1) @ (dpsetconstr @ X4 @ X3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X2 @ Y0 @ Y1))))))) & ((in @ X1 @ X3) != $true))) & (! [X0,X1,X2 : $i > $i > $o,X3,X4] : (($true != (in @ (kpair @ X0 @ X1) @ (dpsetconstr @ X4 @ X3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X2 @ Y0 @ Y1))))))) | ((in @ X1 @ X3) = $true)) | (dpsetconstrEL2 != $true))), 0.23/0.54 inference(nnf_transformation,[],[f781])). 0.23/0.54 thf(f781,plain,( 0.23/0.54 (dpsetconstrEL2 = $true) <=> ! [X0,X1,X2 : $i > $i > $o,X3,X4] : (($true != (in @ (kpair @ X0 @ X1) @ (dpsetconstr @ X4 @ X3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X2 @ Y0 @ Y1))))))) | ((in @ X1 @ X3) = $true))), 0.23/0.54 inference(ennf_transformation,[],[f255])). 0.23/0.54 thf(f255,plain,( 0.23/0.54 ! [X0,X1,X2 : $i > $i > $o,X3,X4] : (($true = (in @ (kpair @ X0 @ X1) @ (dpsetconstr @ X4 @ X3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X2 @ Y0 @ Y1))))))) => ((in @ X1 @ X3) = $true)) <=> (dpsetconstrEL2 = $true)), 0.23/0.54 inference(fool_elimination,[],[f254])). 0.23/0.54 thf(f254,plain,( 0.23/0.54 (dpsetconstrEL2 = ! [X0,X1,X2 : $i > $i > $o,X3,X4] : ((in @ (kpair @ X0 @ X1) @ (dpsetconstr @ X4 @ X3 @ (^[X5 : $i, X6 : $i] : (X2 @ X5 @ X6)))) => (in @ X1 @ X3)))), 0.23/0.54 inference(rectify,[],[f193])). 0.23/0.54 thf(f193,axiom,( 0.23/0.54 (dpsetconstrEL2 = ! [X1,X2,X0 : $i > $i > $o,X4,X3] : ((in @ (kpair @ X1 @ X2) @ (dpsetconstr @ X3 @ X4 @ (^[X8 : $i, X10 : $i] : (X0 @ X8 @ X10)))) => (in @ X2 @ X4)))), 0.23/0.54 file('/export/starexec/sandbox2/tmp/tmp.6wYljQkmd9/Vampire---4.8_24393',dpsetconstrEL2)). 0.23/0.54 thf(f2735,plain,( 0.23/0.54 ($true != (in @ sK180 @ sK179)) | spl540_1), 0.23/0.54 inference(avatar_component_clause,[],[f2733])). 0.23/0.54 thf(f2733,plain,( 0.23/0.54 spl540_1 <=> ($true = (in @ sK180 @ sK179))), 0.23/0.54 introduced(avatar_definition,[new_symbols(naming,[spl540_1])])). 0.23/0.54 thf(f2740,plain,( 0.23/0.54 ~spl540_1 | ~spl540_2), 0.23/0.54 inference(avatar_split_clause,[],[f2723,f2737,f2733])). 0.23/0.54 thf(f2723,plain,( 0.23/0.54 ($true != (in @ sK181 @ sK178)) | ($true != (in @ sK180 @ sK179))), 0.23/0.54 inference(subsumption_resolution,[],[f2722,f1945])). 0.23/0.54 thf(f1945,plain,( 0.23/0.54 (dpsetconstrERa = $true)), 0.23/0.54 inference(cnf_transformation,[],[f1098])). 0.23/0.54 thf(f2722,plain,( 0.23/0.54 ($true != (in @ sK180 @ sK179)) | ($true != (in @ sK181 @ sK178)) | (dpsetconstrERa != $true)), 0.23/0.54 inference(subsumption_resolution,[],[f2719,f1968])). 0.23/0.54 thf(f1968,plain,( 0.23/0.54 ($true != (sK182 @ sK181 @ sK180))), 0.23/0.54 inference(cnf_transformation,[],[f1098])). 0.23/0.54 thf(f2719,plain,( 0.23/0.54 ($true = (sK182 @ sK181 @ sK180)) | (dpsetconstrERa != $true) | ($true != (in @ sK181 @ sK178)) | ($true != (in @ sK180 @ sK179))), 0.23/0.54 inference(trivial_inequality_removal,[],[f2715])). 0.23/0.54 thf(f2715,plain,( 0.23/0.54 ($true != $true) | ($true != (in @ sK180 @ sK179)) | (dpsetconstrERa != $true) | ($true = (sK182 @ sK181 @ sK180)) | ($true != (in @ sK181 @ sK178))), 0.23/0.54 inference(superposition,[],[f2672,f2712])). 0.23/0.54 thf(f2672,plain,( 0.23/0.54 ( ! [X8 : $i,X6 : $i,X9 : $i,X7 : $i > $i > $o,X5 : $i] : (($true != (in @ (kpair @ X8 @ X9) @ (dpsetconstr @ X6 @ X5 @ X7))) | ($true != (in @ X9 @ X5)) | ($true = (X7 @ X8 @ X9)) | ($true != (in @ X8 @ X6)) | (dpsetconstrERa != $true)) )), 0.23/0.54 inference(beta_eta_normalization,[],[f2186])). 0.23/0.54 thf(f2186,plain,( 0.23/0.54 ( ! [X8 : $i,X6 : $i,X9 : $i,X7 : $i > $i > $o,X5 : $i] : (($true = (X7 @ X8 @ X9)) | ($true != (in @ X9 @ X5)) | ((in @ (kpair @ X8 @ X9) @ (dpsetconstr @ X6 @ X5 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X7 @ Y0 @ Y1)))))) != $true) | ($true != (in @ X8 @ X6)) | (dpsetconstrERa != $true)) )), 0.23/0.54 inference(cnf_transformation,[],[f1195])). 0.23/0.54 thf(f1195,plain,( 0.23/0.54 ((dpsetconstrERa = $true) | (($true = (in @ sK244 @ sK242)) & (($true = (in @ sK245 @ sK241)) & ((in @ (kpair @ sK244 @ sK245) @ (dpsetconstr @ sK242 @ sK241 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK243 @ Y0 @ Y1)))))) = $true) & ($true != (sK243 @ sK244 @ sK245))))) & (! [X5,X6,X7 : $i > $i > $o,X8] : (($true != (in @ X8 @ X6)) | ! [X9] : (($true != (in @ X9 @ X5)) | ((in @ (kpair @ X8 @ X9) @ (dpsetconstr @ X6 @ X5 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X7 @ Y0 @ Y1)))))) != $true) | ($true = (X7 @ X8 @ X9)))) | (dpsetconstrERa != $true))), 0.23/0.54 inference(skolemisation,[status(esa),new_symbols(skolem,[sK241,sK242,sK243,sK244,sK245])],[f1192,f1194,f1193])). 0.23/0.54 thf(f1193,plain,( 0.23/0.54 ? [X0,X1,X2 : $i > $i > $o,X3] : (((in @ X3 @ X1) = $true) & ? [X4] : (($true = (in @ X4 @ X0)) & ($true = (in @ (kpair @ X3 @ X4) @ (dpsetconstr @ X1 @ X0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X2 @ Y0 @ Y1))))))) & ((X2 @ X3 @ X4) != $true))) => (($true = (in @ sK244 @ sK242)) & ? [X4] : (($true = (in @ X4 @ sK241)) & ($true = (in @ (kpair @ sK244 @ X4) @ (dpsetconstr @ sK242 @ sK241 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK243 @ Y0 @ Y1))))))) & ($true != (sK243 @ sK244 @ X4))))), 0.23/0.54 introduced(choice_axiom,[])). 0.23/0.54 thf(f1194,plain,( 0.23/0.54 ? [X4] : (($true = (in @ X4 @ sK241)) & ($true = (in @ (kpair @ sK244 @ X4) @ (dpsetconstr @ sK242 @ sK241 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK243 @ Y0 @ Y1))))))) & ($true != (sK243 @ sK244 @ X4))) => (($true = (in @ sK245 @ sK241)) & ((in @ (kpair @ sK244 @ sK245) @ (dpsetconstr @ sK242 @ sK241 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK243 @ Y0 @ Y1)))))) = $true) & ($true != (sK243 @ sK244 @ sK245)))), 0.23/0.54 introduced(choice_axiom,[])). 0.23/0.54 thf(f1192,plain,( 0.23/0.54 ((dpsetconstrERa = $true) | ? [X0,X1,X2 : $i > $i > $o,X3] : (((in @ X3 @ X1) = $true) & ? [X4] : (($true = (in @ X4 @ X0)) & ($true = (in @ (kpair @ X3 @ X4) @ (dpsetconstr @ X1 @ X0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X2 @ Y0 @ Y1))))))) & ((X2 @ X3 @ X4) != $true)))) & (! [X5,X6,X7 : $i > $i > $o,X8] : (($true != (in @ X8 @ X6)) | ! [X9] : (($true != (in @ X9 @ X5)) | ((in @ (kpair @ X8 @ X9) @ (dpsetconstr @ X6 @ X5 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X7 @ Y0 @ Y1)))))) != $true) | ($true = (X7 @ X8 @ X9)))) | (dpsetconstrERa != $true))), 0.23/0.54 inference(rectify,[],[f1191])). 0.23/0.54 thf(f1191,plain,( 0.23/0.54 ((dpsetconstrERa = $true) | ? [X0,X1,X2 : $i > $i > $o,X3] : (((in @ X3 @ X1) = $true) & ? [X4] : (($true = (in @ X4 @ X0)) & ($true = (in @ (kpair @ X3 @ X4) @ (dpsetconstr @ X1 @ X0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X2 @ Y0 @ Y1))))))) & ((X2 @ X3 @ X4) != $true)))) & (! [X0,X1,X2 : $i > $i > $o,X3] : (((in @ X3 @ X1) != $true) | ! [X4] : (($true != (in @ X4 @ X0)) | ($true != (in @ (kpair @ X3 @ X4) @ (dpsetconstr @ X1 @ X0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X2 @ Y0 @ Y1))))))) | ((X2 @ X3 @ X4) = $true))) | (dpsetconstrERa != $true))), 0.23/0.54 inference(nnf_transformation,[],[f663])). 0.23/0.54 thf(f663,plain,( 0.23/0.54 (dpsetconstrERa = $true) <=> ! [X0,X1,X2 : $i > $i > $o,X3] : (((in @ X3 @ X1) != $true) | ! [X4] : (($true != (in @ X4 @ X0)) | ($true != (in @ (kpair @ X3 @ X4) @ (dpsetconstr @ X1 @ X0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X2 @ Y0 @ Y1))))))) | ((X2 @ X3 @ X4) = $true)))), 0.23/0.54 inference(flattening,[],[f662])). 0.23/0.54 thf(f662,plain,( 0.23/0.54 ! [X0,X1,X2 : $i > $i > $o,X3] : (! [X4] : ((((X2 @ X3 @ X4) = $true) | ($true != (in @ (kpair @ X3 @ X4) @ (dpsetconstr @ X1 @ X0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X2 @ Y0 @ Y1)))))))) | ($true != (in @ X4 @ X0))) | ((in @ X3 @ X1) != $true)) <=> (dpsetconstrERa = $true)), 0.23/0.54 inference(ennf_transformation,[],[f568])). 0.23/0.54 thf(f568,plain,( 0.23/0.54 ! [X0,X1,X2 : $i > $i > $o,X3] : (((in @ X3 @ X1) = $true) => ! [X4] : (($true = (in @ X4 @ X0)) => (($true = (in @ (kpair @ X3 @ X4) @ (dpsetconstr @ X1 @ X0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X2 @ Y0 @ Y1))))))) => ((X2 @ X3 @ X4) = $true)))) <=> (dpsetconstrERa = $true)), 0.23/0.54 inference(fool_elimination,[],[f567])). 0.23/0.54 thf(f567,plain,( 0.23/0.54 (dpsetconstrERa = ! [X0,X1,X2 : $i > $i > $o,X3] : ((in @ X3 @ X1) => ! [X4] : ((in @ X4 @ X0) => ((in @ (kpair @ X3 @ X4) @ (dpsetconstr @ X1 @ X0 @ (^[X5 : $i, X6 : $i] : (X2 @ X5 @ X6)))) => (X2 @ X3 @ X4)))))), 0.23/0.54 inference(rectify,[],[f191])). 0.23/0.54 thf(f191,axiom,( 0.23/0.54 (dpsetconstrERa = ! [X4,X3,X0 : $i > $i > $o,X1] : ((in @ X1 @ X3) => ! [X2] : ((in @ X2 @ X4) => ((in @ (kpair @ X1 @ X2) @ (dpsetconstr @ X3 @ X4 @ (^[X8 : $i, X10 : $i] : (X0 @ X8 @ X10)))) => (X0 @ X1 @ X2)))))), 0.23/0.54 file('/export/starexec/sandbox2/tmp/tmp.6wYljQkmd9/Vampire---4.8_24393',dpsetconstrERa)). 0.23/0.54 % SZS output end Proof for Vampire---4 0.23/0.54 % (24508)------------------------------ 0.23/0.54 % (24508)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.23/0.54 % (24508)Termination reason: Refutation 0.23/0.54 0.23/0.54 % (24508)Memory used [KB]: 8827 0.23/0.54 % (24508)Time elapsed: 0.123 s 0.23/0.54 % (24508)Instructions burned: 213 (million) 0.23/0.54 % (24508)------------------------------ 0.23/0.54 % (24508)------------------------------ 0.23/0.54 % (24500)Success in time 0.147 s 0.23/0.54 % Vampire---4.8 exiting 0.23/0.54 EOF