0.11/0.17 % Problem : Vampire---4.8_17441 : TPTP v0.0.0. Released v0.0.0. 0.18/0.19 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s 0.18/0.40 % Computer : n010.cluster.edu 0.18/0.40 % Model : x86_64 x86_64 0.18/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.18/0.40 % Memory : 8042.1875MB 0.18/0.40 % OS : Linux 3.10.0-693.el7.x86_64 0.18/0.40 % CPULimit : 1440 0.18/0.40 % WCLimit : 180 0.18/0.40 % DateTime : Mon Jul 3 12:46:54 EDT 2023 0.18/0.40 % CPUTime : 0.18/0.40 This is a THF_ problem 0.18/0.40 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/sandbox/tmp/tmp.xuGTqtnLJR/Vampire---4.8_17441 -m 12000 -t 180 0.27/0.44 % (17552)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) 0.27/0.44 % (17549)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on Vampire---4 for (1799ds/96Mi) 0.27/0.44 % (17551)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) 0.27/0.44 % (17550)lrs+10_1:2_cnfonf=off:hud=1:inj=on:i=36:si=on:rtra=on_0 on Vampire---4 for (1799ds/36Mi) 0.27/0.44 % (17553)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on Vampire---4 for (1799ds/17Mi) 0.27/0.44 % (17554)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) 0.27/0.45 % (17555)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) 0.27/0.45 % (17556)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) 0.27/0.45 % (17555)Instruction limit reached! 0.27/0.45 % (17555)------------------------------ 0.27/0.45 % (17555)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.27/0.45 % (17555)Termination reason: Unknown 0.27/0.45 % (17555)Termination phase: shuffling 0.27/0.45 0.27/0.45 % (17555)Memory used [KB]: 1535 0.27/0.45 % (17555)Time elapsed: 0.004 s 0.27/0.45 % (17555)Instructions burned: 4 (million) 0.27/0.45 % (17555)------------------------------ 0.27/0.45 % (17555)------------------------------ 0.27/0.45 % (17553)Instruction limit reached! 0.27/0.45 % (17553)------------------------------ 0.27/0.45 % (17553)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.27/0.45 % (17553)Termination reason: Unknown 0.27/0.45 % (17553)Termination phase: shuffling 0.27/0.45 0.27/0.45 % (17553)Memory used [KB]: 1918 0.27/0.45 % (17553)Time elapsed: 0.011 s 0.27/0.45 % (17553)Instructions burned: 18 (million) 0.27/0.45 % (17553)------------------------------ 0.27/0.45 % (17553)------------------------------ 0.27/0.46 % (17551)Instruction limit reached! 0.27/0.46 % (17551)------------------------------ 0.27/0.46 % (17551)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.27/0.46 % (17551)Termination reason: Unknown 0.27/0.46 % (17551)Termination phase: shuffling 0.27/0.46 0.27/0.46 % (17551)Memory used [KB]: 2174 0.27/0.46 % (17551)Time elapsed: 0.019 s 0.27/0.46 % (17551)Instructions burned: 34 (million) 0.27/0.46 % (17551)------------------------------ 0.27/0.46 % (17551)------------------------------ 0.27/0.46 % (17557)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) 0.27/0.46 % (17550)Instruction limit reached! 0.27/0.46 % (17550)------------------------------ 0.27/0.46 % (17550)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.27/0.46 % (17550)Termination reason: Unknown 0.27/0.46 % (17550)Termination phase: shuffling 0.27/0.46 0.27/0.46 % (17550)Memory used [KB]: 2302 0.27/0.46 % (17550)Time elapsed: 0.021 s 0.27/0.46 % (17550)Instructions burned: 37 (million) 0.27/0.46 % (17550)------------------------------ 0.27/0.46 % (17550)------------------------------ 0.27/0.47 % (17558)lrs-3_1:1024_cbe=off:chr=on:tnu=1:i=7:si=on:rtra=on_0 on Vampire---4 for (1799ds/7Mi) 0.27/0.47 % (17558)Instruction limit reached! 0.27/0.47 % (17558)------------------------------ 0.27/0.47 % (17558)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.27/0.47 % (17558)Termination reason: Unknown 0.27/0.47 % (17558)Termination phase: shuffling 0.27/0.47 0.27/0.47 % (17558)Memory used [KB]: 1535 0.27/0.47 % (17558)Time elapsed: 0.006 s 0.27/0.47 % (17558)Instructions burned: 7 (million) 0.27/0.47 % (17558)------------------------------ 0.27/0.47 % (17558)------------------------------ 0.27/0.47 % (17557)Instruction limit reached! 0.27/0.47 % (17557)------------------------------ 0.27/0.47 % (17557)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.27/0.47 % (17557)Termination reason: Unknown 0.27/0.47 % (17557)Termination phase: shuffling 0.27/0.47 0.27/0.47 % (17557)Memory used [KB]: 1791 0.27/0.47 % (17557)Time elapsed: 0.012 s 0.27/0.47 % (17557)Instructions burned: 21 (million) 0.27/0.47 % (17557)------------------------------ 0.27/0.47 % (17557)------------------------------ 0.27/0.48 % (17559)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) 0.27/0.48 % (17560)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) 0.27/0.48 % (17554)Instruction limit reached! 0.27/0.48 % (17554)------------------------------ 0.27/0.48 % (17554)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.27/0.48 % (17554)Termination reason: Unknown 0.27/0.48 % (17554)Termination phase: Property scanning 0.27/0.48 0.27/0.48 % (17554)Memory used [KB]: 2430 0.27/0.48 % (17554)Time elapsed: 0.038 s 0.27/0.48 % (17554)Instructions burned: 76 (million) 0.27/0.48 % (17554)------------------------------ 0.27/0.48 % (17554)------------------------------ 0.27/0.49 % (17561)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) 0.27/0.49 % (17562)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) 0.27/0.49 % (17549)Instruction limit reached! 0.27/0.49 % (17549)------------------------------ 0.27/0.49 % (17549)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.27/0.49 % (17549)Termination reason: Unknown 0.27/0.49 % (17549)Termination phase: Property scanning 0.27/0.49 0.27/0.49 % (17549)Memory used [KB]: 2686 0.27/0.49 % (17549)Time elapsed: 0.048 s 0.27/0.49 % (17549)Instructions burned: 97 (million) 0.27/0.49 % (17549)------------------------------ 0.27/0.49 % (17549)------------------------------ 0.27/0.49 % (17561)Instruction limit reached! 0.27/0.49 % (17561)------------------------------ 0.27/0.49 % (17561)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.27/0.49 % (17561)Termination reason: Unknown 0.27/0.49 % (17561)Termination phase: shuffling 0.27/0.49 0.27/0.49 % (17561)Memory used [KB]: 1663 0.27/0.49 % (17561)Time elapsed: 0.007 s 0.27/0.49 % (17561)Instructions burned: 9 (million) 0.27/0.49 % (17561)------------------------------ 0.27/0.49 % (17561)------------------------------ 0.27/0.50 % (17563)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) 0.27/0.51 % (17564)lrs+21_1:1_cond=on:e2e=on:i=61:si=on:rtra=on_0 on Vampire---4 for (1799ds/61Mi) 0.27/0.51 % (17565)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=14:si=on:rtra=on_0 on Vampire---4 for (1799ds/14Mi) 0.27/0.51 % (17560)Instruction limit reached! 0.27/0.51 % (17560)------------------------------ 0.27/0.51 % (17560)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.27/0.51 % (17560)Termination reason: Unknown 0.27/0.51 % (17560)Termination phase: Property scanning 0.27/0.51 0.27/0.51 % (17560)Memory used [KB]: 2430 0.27/0.51 % (17560)Time elapsed: 0.037 s 0.27/0.51 % (17560)Instructions burned: 72 (million) 0.27/0.51 % (17560)------------------------------ 0.27/0.51 % (17560)------------------------------ 0.27/0.52 % (17565)Instruction limit reached! 0.27/0.52 % (17565)------------------------------ 0.27/0.52 % (17565)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.27/0.52 % (17565)Termination reason: Unknown 0.27/0.52 % (17565)Termination phase: shuffling 0.27/0.52 0.27/0.52 % (17565)Memory used [KB]: 1791 0.27/0.52 % (17565)Time elapsed: 0.012 s 0.27/0.52 % (17565)Instructions burned: 15 (million) 0.27/0.52 % (17565)------------------------------ 0.27/0.52 % (17565)------------------------------ 0.27/0.53 % (17566)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 (1798ds/2Mi) 0.27/0.53 % (17566)Instruction limit reached! 0.27/0.53 % (17566)------------------------------ 0.27/0.53 % (17566)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.27/0.53 % (17566)Termination reason: Unknown 0.27/0.53 % (17566)Termination phase: shuffling 0.27/0.53 0.27/0.53 % (17566)Memory used [KB]: 1535 0.27/0.53 % (17566)Time elapsed: 0.004 s 0.27/0.53 % (17566)Instructions burned: 3 (million) 0.27/0.53 % (17566)------------------------------ 0.27/0.53 % (17566)------------------------------ 0.27/0.53 % (17567)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 (1798ds/1041Mi) 0.27/0.54 % (17564)Instruction limit reached! 0.27/0.54 % (17564)------------------------------ 0.27/0.54 % (17564)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.27/0.54 % (17564)Termination reason: Unknown 0.27/0.54 % (17564)Termination phase: Preprocessing 3 0.27/0.54 0.27/0.54 % (17564)Memory used [KB]: 2814 0.27/0.54 % (17564)Time elapsed: 0.037 s 0.27/0.54 % (17564)Instructions burned: 61 (million) 0.27/0.54 % (17564)------------------------------ 0.27/0.54 % (17564)------------------------------ 0.27/0.55 % (17568)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 (1798ds/11Mi) 0.27/0.55 % (17568)Instruction limit reached! 0.27/0.55 % (17568)------------------------------ 0.27/0.55 % (17568)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.27/0.55 % (17568)Termination reason: Unknown 0.27/0.55 % (17568)Termination phase: shuffling 0.27/0.55 0.27/0.55 % (17568)Memory used [KB]: 1663 0.27/0.55 % (17568)Time elapsed: 0.006 s 0.27/0.55 % (17568)Instructions burned: 11 (million) 0.27/0.55 % (17568)------------------------------ 0.27/0.55 % (17568)------------------------------ 0.27/0.55 % (17563)Instruction limit reached! 0.27/0.55 % (17563)------------------------------ 0.27/0.55 % (17563)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.27/0.55 % (17563)Termination reason: Unknown 0.27/0.55 % (17563)Termination phase: Function definition elimination 0.27/0.55 0.27/0.55 % (17563)Memory used [KB]: 2686 0.27/0.55 % (17563)Time elapsed: 0.060 s 0.27/0.55 % (17563)Instructions burned: 130 (million) 0.27/0.55 % (17563)------------------------------ 0.27/0.55 % (17563)------------------------------ 0.27/0.55 % (17569)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) 1.19/0.56 % (17571)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) 1.19/0.56 % (17570)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) 1.30/0.57 % (17570)Instruction limit reached! 1.30/0.57 % (17570)------------------------------ 1.30/0.57 % (17570)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 1.30/0.57 % (17570)Termination reason: Unknown 1.30/0.57 % (17570)Termination phase: shuffling 1.30/0.57 1.30/0.57 % (17570)Memory used [KB]: 1918 1.30/0.57 % (17570)Time elapsed: 0.010 s 1.30/0.57 % (17570)Instructions burned: 28 (million) 1.30/0.57 % (17570)------------------------------ 1.30/0.57 % (17570)------------------------------ 1.30/0.58 % (17571)Instruction limit reached! 1.30/0.58 % (17571)------------------------------ 1.30/0.58 % (17571)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 1.30/0.58 % (17571)Termination reason: Unknown 1.30/0.58 % (17571)Termination phase: Property scanning 1.30/0.58 1.30/0.58 % (17571)Memory used [KB]: 2430 1.30/0.58 % (17571)Time elapsed: 0.018 s 1.30/0.58 % (17571)Instructions burned: 58 (million) 1.30/0.58 % (17571)------------------------------ 1.30/0.58 % (17571)------------------------------ 1.30/0.58 % (17572)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) 1.30/0.58 % (17552)Instruction limit reached! 1.30/0.58 % (17552)------------------------------ 1.30/0.58 % (17552)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 1.30/0.58 % (17552)Termination reason: Unknown 1.30/0.58 % (17552)Termination phase: Saturation 1.30/0.58 1.30/0.58 % (17552)Memory used [KB]: 9338 1.30/0.58 % (17552)Time elapsed: 0.145 s 1.30/0.58 % (17552)Instructions burned: 387 (million) 1.30/0.58 % (17552)------------------------------ 1.30/0.58 % (17552)------------------------------ 1.30/0.59 % (17573)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on Vampire---4 for (1798ds/3Mi) 1.30/0.59 % (17573)Instruction limit reached! 1.30/0.59 % (17573)------------------------------ 1.30/0.59 % (17573)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 1.30/0.59 % (17573)Termination reason: Unknown 1.30/0.59 % (17573)Termination phase: shuffling 1.30/0.59 1.30/0.59 % (17573)Memory used [KB]: 1407 1.30/0.59 % (17573)Time elapsed: 0.002 s 1.30/0.59 % (17573)Instructions burned: 3 (million) 1.30/0.59 % (17573)------------------------------ 1.30/0.59 % (17573)------------------------------ 1.30/0.59 % (17574)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on Vampire---4 for (1798ds/19Mi) 1.30/0.59 % (17569)Instruction limit reached! 1.30/0.59 % (17569)------------------------------ 1.30/0.59 % (17569)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 1.30/0.59 % (17569)Termination reason: Unknown 1.30/0.59 % (17569)Termination phase: Property scanning 1.30/0.59 1.30/0.59 % (17569)Memory used [KB]: 2686 1.30/0.59 % (17569)Time elapsed: 0.040 s 1.30/0.59 % (17569)Instructions burned: 143 (million) 1.30/0.59 % (17569)------------------------------ 1.30/0.59 % (17569)------------------------------ 1.30/0.60 % (17575)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on Vampire---4 for (1798ds/44Mi) 1.30/0.60 % (17574)Instruction limit reached! 1.30/0.60 % (17574)------------------------------ 1.30/0.60 % (17574)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 1.30/0.60 % (17574)Termination reason: Unknown 1.30/0.60 % (17574)Termination phase: shuffling 1.30/0.60 1.30/0.60 % (17574)Memory used [KB]: 1791 1.30/0.60 % (17574)Time elapsed: 0.007 s 1.30/0.60 % (17574)Instructions burned: 20 (million) 1.30/0.60 % (17574)------------------------------ 1.30/0.60 % (17574)------------------------------ 1.30/0.60 % (17576)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=191:si=on:rtra=on_0 on Vampire---4 for (1798ds/191Mi) 1.30/0.61 % (17577)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on Vampire---4 for (1798ds/62Mi) 1.30/0.61 % (17575)Instruction limit reached! 1.30/0.61 % (17575)------------------------------ 1.30/0.61 % (17575)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 1.30/0.61 % (17575)Termination reason: Unknown 1.30/0.61 % (17575)Termination phase: shuffling 1.30/0.61 1.30/0.61 % (17575)Memory used [KB]: 2302 1.30/0.61 % (17575)Time elapsed: 0.014 s 1.30/0.61 % (17575)Instructions burned: 46 (million) 1.30/0.61 % (17575)------------------------------ 1.30/0.61 % (17575)------------------------------ 1.30/0.62 % (17578)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=105:si=on:rtra=on_0 on Vampire---4 for (1798ds/105Mi) 1.30/0.63 % (17577)Instruction limit reached! 1.30/0.63 % (17577)------------------------------ 1.30/0.63 % (17577)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 1.30/0.63 % (17577)Termination reason: Unknown 1.30/0.63 % (17577)Termination phase: Property scanning 1.30/0.63 1.30/0.63 % (17577)Memory used [KB]: 2430 1.30/0.63 % (17577)Time elapsed: 0.019 s 1.30/0.63 % (17577)Instructions burned: 64 (million) 1.30/0.63 % (17577)------------------------------ 1.30/0.63 % (17577)------------------------------ 1.69/0.63 % (17579)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on Vampire---4 for (1797ds/3Mi) 1.69/0.63 % (17579)Instruction limit reached! 1.69/0.63 % (17579)------------------------------ 1.69/0.63 % (17579)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 1.69/0.63 % (17579)Termination reason: Unknown 1.69/0.63 % (17579)Termination phase: shuffling 1.69/0.63 1.69/0.63 % (17579)Memory used [KB]: 1407 1.69/0.63 % (17579)Time elapsed: 0.002 s 1.69/0.63 % (17579)Instructions burned: 3 (million) 1.69/0.63 % (17579)------------------------------ 1.69/0.63 % (17579)------------------------------ 1.69/0.64 % (17556)First to succeed. 1.69/0.64 % (17580)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=238:si=on:rtra=on_0 on Vampire---4 for (1797ds/238Mi) 1.69/0.65 % (17556)Refutation found. Thanks to Tanya! 1.69/0.65 % SZS status Theorem for Vampire---4 1.69/0.65 % SZS output start Proof for Vampire---4 1.69/0.65 thf(func_def_0, type, in: $i > $i > $o). 1.69/0.65 thf(func_def_1, type, exu: ($i > $o) > $o). 1.69/0.65 thf(func_def_6, type, setadjoin: $i > $i > $i). 1.69/0.65 thf(func_def_8, type, powerset: $i > $i). 1.69/0.65 thf(func_def_10, type, setunion: $i > $i). 1.69/0.65 thf(func_def_19, type, descr: ($i > $o) > $i). 1.69/0.65 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i). 1.69/0.65 thf(func_def_26, type, prop2set: $o > $i). 1.69/0.65 thf(func_def_36, type, nonempty: $i > $o). 1.69/0.65 thf(func_def_69, type, set2prop: $i > $o). 1.69/0.65 thf(func_def_88, type, subset: $i > $i > $o). 1.69/0.65 thf(func_def_89, type, disjoint: $i > $i > $o). 1.69/0.65 thf(func_def_90, type, setsmeet: $i > $i > $o). 1.69/0.65 thf(func_def_114, type, binunion: $i > $i > $i). 1.69/0.65 thf(func_def_122, type, binintersect: $i > $i > $i). 1.69/0.65 thf(func_def_135, type, regular: $i > $o). 1.69/0.65 thf(func_def_136, type, setminus: $i > $i > $i). 1.69/0.65 thf(func_def_147, type, symdiff: $i > $i > $i). 1.69/0.65 thf(func_def_153, type, iskpair: $i > $o). 1.69/0.65 thf(func_def_158, type, kpair: $i > $i > $i). 1.69/0.65 thf(func_def_160, type, cartprod: $i > $i > $i). 1.69/0.65 thf(func_def_177, type, singleton: $i > $o). 1.69/0.65 thf(func_def_179, type, ex1: $i > ($i > $o) > $o). 1.69/0.65 thf(func_def_184, type, atmost1p: $i > $o). 1.69/0.65 thf(func_def_185, type, atleast2p: $i > $o). 1.69/0.65 thf(func_def_186, type, atmost2p: $i > $o). 1.69/0.65 thf(func_def_187, type, upairsetp: $i > $o). 1.69/0.65 thf(func_def_191, type, kfst: $i > $i). 1.69/0.65 thf(func_def_203, type, ksnd: $i > $i). 1.69/0.65 thf(func_def_213, type, breln: $i > $i > $i > $o). 1.69/0.65 thf(func_def_214, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i). 1.69/0.65 thf(func_def_222, type, func: $i > $i > $i > $o). 1.69/0.65 thf(func_def_223, type, funcSet: $i > $i > $i). 1.69/0.65 thf(func_def_226, type, ap: $i > $i > $i > $i > $i). 1.69/0.65 thf(func_def_232, type, lam: $i > $i > ($i > $i) > $i). 1.69/0.65 thf(func_def_259, type, if: $i > $o > $i > $i > $i). 1.69/0.65 thf(func_def_325, type, sP1: $i > $i > $i > $i > $o). 1.69/0.65 thf(func_def_327, type, sP3: $i > $i > $o). 1.69/0.65 thf(func_def_328, type, sP4: $i > $o). 1.69/0.65 thf(func_def_329, type, sP5: $i > $i > $o). 1.69/0.65 thf(func_def_330, type, sP6: $i > $i > $o). 1.69/0.65 thf(func_def_332, type, sP8: $i > $i > $i > $o). 1.69/0.65 thf(func_def_334, type, sP10: $o > $i > $i > $i > $o). 1.69/0.65 thf(func_def_337, type, sK13: ($i > $o) > ($i > $o) > $i > $i > $i). 1.69/0.65 thf(func_def_338, type, sK14: ($i > $o) > ($i > $o) > $i > $i > $i). 1.69/0.65 thf(func_def_341, type, sK17: $i > $o). 1.69/0.65 thf(func_def_342, type, sK18: $i > $o). 1.69/0.65 thf(func_def_344, type, sK20: $i > $o). 1.69/0.65 thf(func_def_346, type, sK22: ($i > $o) > $i > $i). 1.69/0.65 thf(func_def_353, type, sK29: $i > $i > $i). 1.69/0.65 thf(func_def_354, type, sK30: $i > $i > $i). 1.69/0.65 thf(func_def_368, type, sK44: $i > $o). 1.69/0.65 thf(func_def_383, type, sK59: $i > $i > $i). 1.69/0.65 thf(func_def_391, type, sK67: $i > $o). 1.69/0.65 thf(func_def_409, type, sK85: $i > $i). 1.69/0.65 thf(func_def_411, type, sK87: $i > $i). 1.69/0.65 thf(func_def_416, type, sK92: $i > $o). 1.69/0.65 thf(func_def_418, type, sK94: ($i > $o) > $i > $i). 1.69/0.65 thf(func_def_419, type, sK95: ($i > $o) > $i > $i). 1.69/0.65 thf(func_def_436, type, sK112: $i > $i > $i > $i > $i). 1.69/0.65 thf(func_def_437, type, sK113: $i > $i > $i > $i > $i). 1.69/0.65 thf(func_def_438, type, sK114: $i > $i > $i > $i > $i). 1.69/0.65 thf(func_def_439, type, sK115: $i > $i > $i > $i > $i). 1.69/0.65 thf(func_def_451, type, sK127: $i > $o). 1.69/0.65 thf(func_def_454, type, sK130: $i > ($i > $o) > $i). 1.69/0.65 thf(func_def_460, type, sK136: $i > $i > $o). 1.69/0.65 thf(func_def_464, type, sK140: $i > $i > $i). 1.69/0.65 thf(func_def_468, type, sK144: ($i > $i) > $i > $i > $i). 1.69/0.65 thf(func_def_471, type, sK147: $i > $i). 1.69/0.65 thf(func_def_482, type, sK158: $i > $o). 1.69/0.65 thf(func_def_496, type, sK172: ($i > $i) > $i > $i > $i). 1.69/0.65 thf(func_def_499, type, sK175: $i > $i). 1.69/0.65 thf(func_def_501, type, sK177: $i > $o). 1.69/0.65 thf(func_def_512, type, sK188: $i > $o). 1.69/0.65 thf(func_def_514, type, sK190: ($i > $o) > $i > $i > $i > $i). 1.69/0.65 thf(func_def_515, type, sK191: ($i > $o) > $i > $i > $i > $i). 1.69/0.65 thf(func_def_536, type, sK212: $i > $i > $i). 1.69/0.65 thf(func_def_537, type, sK213: $i > $i > $i). 1.69/0.65 thf(func_def_538, type, sK214: $i > $i > $i). 1.69/0.65 thf(func_def_539, type, sK215: $i > $i > $i). 1.69/0.65 thf(func_def_540, type, sK216: $i > $i > $i > $i). 1.69/0.65 thf(func_def_541, type, sK217: $i > $i). 1.69/0.65 thf(func_def_542, type, sK218: $i > $i). 1.69/0.65 thf(func_def_543, type, sK219: $i > $i). 1.69/0.65 thf(func_def_544, type, sK220: $i > $i). 1.69/0.65 thf(func_def_545, type, sK221: $i > $i > $i > $i). 1.69/0.65 thf(func_def_546, type, sK222: $i > $i > $i > $i). 1.69/0.65 thf(func_def_547, type, sK223: $i > $i > $i). 1.69/0.65 thf(func_def_548, type, sK224: $i > $i > $i). 1.69/0.65 thf(func_def_549, type, sK225: $i > $i > $i). 1.69/0.65 thf(func_def_551, type, sK227: $i > $i). 1.69/0.65 thf(func_def_552, type, sK228: $i > $i). 1.69/0.65 thf(func_def_553, type, sK229: $i > $i). 1.69/0.65 thf(func_def_554, type, sK230: $i > $i > $i). 1.69/0.65 thf(func_def_555, type, sK231: $i > $i > ($i > $i) > $i). 1.69/0.65 thf(func_def_556, type, sK232: $i > $i). 1.69/0.65 thf(func_def_577, type, sK253: $i > $i > $o). 1.69/0.65 thf(func_def_583, type, sK259: $i > $o). 1.69/0.65 thf(func_def_586, type, sK262: $i > ($i > $o) > $i). 1.69/0.65 thf(func_def_587, type, sK263: $i > ($i > $o) > $i). 1.69/0.65 thf(func_def_594, type, sK270: $i > $i). 1.69/0.65 thf(func_def_597, type, sK273: ($i > $o) > $i). 1.69/0.65 thf(func_def_598, type, sK274: ($i > $o) > $i). 1.69/0.65 thf(func_def_599, type, sK275: $i > $o). 1.69/0.65 thf(func_def_633, type, sK309: $i > $i > $i). 1.69/0.65 thf(func_def_638, type, sK314: ($i > $i) > $i > $i > $i). 1.69/0.65 thf(func_def_641, type, sK317: $i > $i). 1.69/0.65 thf(func_def_665, type, sK341: $i > $i). 1.69/0.65 thf(func_def_686, type, sK362: $i > $i > $i). 1.69/0.65 thf(func_def_712, type, sK388: $i > $o). 1.69/0.65 thf(func_def_714, type, sK390: ($i > $o) > $i > $i > $i > $i). 1.69/0.65 thf(func_def_715, type, sK391: ($i > $o) > $i > $i > $i > $i). 1.69/0.65 thf(func_def_716, type, sK392: ($i > $i) > $i > $i > $i). 1.69/0.65 thf(func_def_719, type, sK395: $i > $i). 1.69/0.65 thf(func_def_720, type, sK396: ($i > $o) > $i). 1.69/0.65 thf(func_def_721, type, sK397: $i > $o). 1.69/0.65 thf(func_def_722, type, sK398: $i > $i). 1.69/0.65 thf(func_def_741, type, sK417: $i > $o). 1.69/0.65 thf(func_def_744, type, sK420: $i > $o). 1.69/0.65 thf(func_def_746, type, sK422: ($i > $o) > $i > $i). 1.69/0.65 thf(func_def_760, type, sK436: $i > $i > $i). 1.69/0.65 thf(func_def_766, type, sK442: $i > $o). 1.69/0.65 thf(func_def_774, type, sK450: $i > $i). 1.69/0.65 thf(func_def_779, type, sK455: $i > $i > $i > $i). 1.69/0.65 thf(func_def_780, type, sK456: $i > $i > $i > $i). 1.69/0.65 thf(func_def_802, type, sK478: $i > $o). 1.69/0.65 thf(func_def_811, type, sK487: $i > $o). 1.69/0.65 thf(func_def_816, type, sK492: $i > $i > $i). 1.69/0.65 thf(func_def_817, type, sK493: $i > $i > $i > $i > $i). 1.69/0.65 thf(func_def_818, type, sK494: $i > $i > $i > $i > $i). 1.69/0.65 thf(func_def_823, type, sK499: $i > $o). 1.69/0.65 thf(func_def_840, type, sK516: $i > $i > $o). 1.69/0.65 thf(func_def_865, type, sK541: $i > $i > $o). 1.69/0.65 thf(func_def_867, type, sK543: $i > $o). 1.69/0.65 thf(func_def_869, type, sK545: $i > ($i > $o) > $i). 1.69/0.65 thf(func_def_879, type, sK555: $i > $o). 1.69/0.65 thf(func_def_896, type, sK572: $i > $o). 1.69/0.65 thf(func_def_898, type, sK574: $i > ($i > $o) > $i). 1.69/0.65 thf(func_def_899, type, sK575: $o > $i > $i > $i). 1.69/0.65 thf(func_def_920, type, sK596: $i > $o). 1.69/0.65 thf(func_def_923, type, sK599: $i > ($i > $o) > $i). 1.69/0.65 thf(func_def_924, type, sK600: $i > ($i > $o) > $i). 1.69/0.65 thf(func_def_925, type, sK601: $i > $o). 1.69/0.65 thf(func_def_928, type, sK604: $i > $i > $i). 1.69/0.65 thf(func_def_945, type, sK621: ($i > $o) > $i). 1.69/0.65 thf(func_def_946, type, sK622: $i > $o). 1.69/0.65 thf(func_def_947, type, sK623: $i > $i). 1.69/0.65 thf(func_def_948, type, sK624: $i > $o). 1.69/0.65 thf(func_def_949, type, sK625: ($i > $o) > $i). 1.69/0.65 thf(func_def_952, type, sK628: $i > $i > $i > $i). 1.69/0.65 thf(func_def_960, type, sK636: $i > $i > $i). 1.69/0.65 thf(func_def_972, type, sK648: $i > $i > $i > $i). 1.69/0.65 thf(func_def_973, type, sK649: $i > $i > $i > $i). 1.69/0.65 thf(func_def_978, type, sK654: $i > $i > $i > $i > $i). 1.69/0.65 thf(func_def_996, type, sK672: $i > $i > $i > $i > $i). 1.69/0.65 thf(func_def_1022, type, sK698: $i > $o). 1.69/0.65 thf(func_def_1023, type, sK699: ($i > $o) > $i > $i > $i). 1.69/0.65 thf(func_def_1035, type, sK711: $i > $o). 1.69/0.65 thf(func_def_1043, type, sK719: $i > $o). 1.69/0.65 thf(func_def_1044, type, sK720: ($i > $o) > $i > $i). 1.69/0.65 thf(func_def_1046, type, sK722: $i > $o). 1.69/0.65 thf(func_def_1048, type, sK724: ($i > $o) > $i > $i). 1.69/0.65 thf(func_def_1069, type, sK745: $i > $i > $o). 1.69/0.65 thf(func_def_1074, type, sK750: $i > $i > $o). 1.69/0.65 thf(func_def_1076, type, sK752: ($i > $o) > ($i > $o) > $i). 1.69/0.65 thf(func_def_1077, type, sK753: ($i > $o) > ($i > $o) > $i). 1.69/0.65 thf(func_def_1078, type, sK754: $i > $o). 1.69/0.65 thf(func_def_1079, type, sK755: $i > $o). 1.69/0.65 thf(func_def_1088, type, sK764: ($i > $i) > $i > $i > $i). 1.69/0.65 thf(func_def_1091, type, sK767: $i > $i). 1.69/0.65 thf(func_def_1130, type, sK806: $i > $o). 1.69/0.65 thf(func_def_1139, type, sK815: $i > $i > $o). 1.69/0.65 thf(func_def_1144, type, sK820: $i > $o). 1.69/0.65 thf(func_def_1148, type, sK824: $i > $i). 1.69/0.65 thf(func_def_1149, type, sK825: $i > $o). 1.69/0.65 thf(func_def_1150, type, sK826: $i > $o). 1.69/0.65 thf(func_def_1151, type, sK827: ($i > $o) > ($i > $o) > $i). 1.69/0.65 thf(func_def_1152, type, sK828: ($i > $o) > ($i > $o) > $i). 1.69/0.65 thf(func_def_1157, type, sK833: $i > $i > $i > $i). 1.69/0.65 thf(func_def_1178, type, sK854: $i > $i). 1.69/0.65 thf(func_def_1186, type, sK862: $i > $i > $i > $i > $i). 1.69/0.65 thf(func_def_1199, type, sK875: $i > $i > $o). 1.69/0.65 thf(func_def_1200, type, sK876: $i > $i). 1.69/0.65 thf(func_def_1201, type, sK877: $i > $i). 1.69/0.65 thf(func_def_1202, type, sK878: ($i > $i > $o) > $i > $i). 1.69/0.65 thf(func_def_1203, type, sK879: ($i > $i > $o) > $i > $i). 1.69/0.65 thf(func_def_1204, type, sK880: $i > ($i > $i > $o) > $i > $i). 1.69/0.65 thf(func_def_1206, type, ph882: !>[X0: $tType]:(X0)). 1.69/0.65 thf(f4610,plain,( 1.69/0.65 $false), 1.69/0.65 inference(avatar_sat_refutation,[],[f4503,f4564,f4608])). 1.69/0.65 thf(f4608,plain,( 1.69/0.65 ~spl881_10), 1.69/0.65 inference(avatar_contradiction_clause,[],[f4607])). 1.69/0.65 thf(f4607,plain,( 1.69/0.65 $false | ~spl881_10), 1.69/0.65 inference(subsumption_resolution,[],[f4606,f4498])). 1.69/0.65 thf(f4498,plain,( 1.69/0.65 ($true = (in @ sK304 @ sK303)) | ~spl881_10), 1.69/0.65 inference(avatar_component_clause,[],[f4496])). 1.69/0.65 thf(f4496,plain,( 1.69/0.65 spl881_10 <=> ($true = (in @ sK304 @ sK303))), 1.69/0.65 introduced(avatar_definition,[new_symbols(naming,[spl881_10])])). 1.69/0.65 thf(f4606,plain,( 1.69/0.65 ($true != (in @ sK304 @ sK303))), 1.69/0.65 inference(subsumption_resolution,[],[f4587,f3225])). 1.69/0.65 thf(f3225,plain,( 1.69/0.65 (setminusER = $true)), 1.69/0.65 inference(cnf_transformation,[],[f1674])). 1.69/0.65 thf(f1674,plain,( 1.69/0.65 (symdiffIneg1 = $true) & (sepSubset = $true) & (ex1E1 = $true) & (inPowerset = $true) & (subsetRefl = $true) & (kfstpairEq = $true) & (funcGraphProp4 = $true) & (setunionE2 = $true) & (demorgan2a = $true) & (iffalseProp1 = $true) & (complementTcontraSubset = $true) & (singletonsubset = $true) & (inIntersectImpInUnion2 = $true) & (setminusER = $true) & (inIntersectImpInUnion = $true) & (demorgan1b = $true) & (subsetTI = $true) & (dpsetconstrER = $true) & (emptyset__Cong = $true) & (setukpairIR = $true) & (setunionsingleton2 = $true) & (ifp = $true) & (notequalI1 = $true) & (setminusELneg = $true) & (notdallE = $true) & (theprop = $true) & (vacuousDall = $true) & (funcGraphProp3 = $true) & (ap2apEq1 = $true) & (setminusSubset2 = $true) & (setukpairinjR2 = $true) & (subbreln = $true) & (doubleComplementE1 = $true) & (binintersectSubset1 = $true) & (setminusIRneg = $true) & (omegaSAx = $true) & (prop2set2propI = $true) & (setadjoinSub = $true) & (demorgan2a2 = $true) & (emptysetimpfalse = $true) & (ex1I = $true) & (nonemptyE1 = $true) & (upairequniteq = $true) & (binintersectSubset5 = $true) & (kfstsingleton = $true) & (apProp = $true) & (intersectInPowersetIntersectUnions = $true) & (binunionLsub = $true) & (omegaIndAx = $true) & (complementInPowersetComplementIntersect = $true) & (setbeta = $true) & (wellorderingAx = $true) & (secondinupair = $true) & (brelnall1 = $true) & (in__Cong = $true) & (emptyI = $true) & (notinsingleton = $true) & (setukpairinjL = $true) & (eqinunit = $true) & (cartprodsndpairEq = $true) & (funcextLem = $true) & (upairset2E = $true) & (demorgan1a = $true) & (setminusT_lem = $true) & (upairset2IR = $true) & (exuE3u = $true) & (binunionEcases = $true) & (upairsetIL = $true) & (descr__Cong = $true) & (complementT_lem = $true) & (dpsetconstrI = $true) & (setadjoinOr = $true) & (iffalse = $true) & (emptyE1 = $true) & (binunionTILcontra = $true) & (subsetE2 = $true) & (dsetconstrEL = $true) & (binintersectTERcontra = $true) & (sepInPowerset = $true) & (setadjoinIL = $true) & (notsubsetI = $true) & (ex1E2 = $true) & (setminusILneg = $true) & (eta1 = $true) & (funcinfuncset = $true) & (setminusSubset1 = $true) & (beta1 = $true) & (emptyinunitempty = $true) & (ubforcartprodlem3 = $true) & (inIntersectImpInIntersectUnions = $true) & (complementUnionInPowersetComplement = $true) & (exuE3e = $true) & (eqimpsubset1 = $true) & (emptyinPowerset = $true) & (eqimpsubset2 = $true) & (exuE1 = $true) & (complementTE1 = $true) & (complementTnotintersectT = $true) & (cartprodmempaircEq = $true) & (cartprodsndin = $true) & (ap2apEq2 = $true) & (kpairp = $true) & (quantDeMorgan2 = $true) & (dsetconstrI = $true) & (contrasubsetT1 = $true) & (omega0Ax = $true) & (cartprodpairmemEL = $true) & (iftrue = $true) & (singletoninpowerset = $true) & (singletonsuniq = $true) & (inComplementUnionImpInComplement1 = $true) & (nonemptyI = $true) & (notdexE = $true) & (singletonsswitch = $true) & (iftrueProp1 = $true) & (powersetT_lem = $true) & (complementImpComplementIntersect = $true) & (theeq = $true) & (binunionIR = $true) & (setminusI = $true) & (complementTI1 = $true) & (binintersectRsub = $true) & (setunion__Cong = $true) & (setextAx = $true) & (symdiffIneg2 = $true) & (cartprodpairsurjEq = $true) & (app = $true) & (upairsubunion = $true) & (powersetI1 = $true) & (binintersectER = $true) & (nonemptyI1 = $true) & (emptysetAx = $true) & (cartprodfstin = $true) & (doubleComplementSub2 = $true) & (replAx = $true) & (setminusEL = $true) & (contrasubsetT = $true) & (contrasubsetT2 = $true) & (inCongP = $true) & (setoftrueEq = $true) & (setextsub = $true) & (setadjoin__Cong = $true) & (foundationAx = $true) & (notequalI2 = $true) & (setadjoinAx = $true) & (dpsetconstrEL1 = $true) & (doubleComplementSub1 = $true) & (emptysetE = $true) & (demorgan1 = $true) & (funcext2 = $true) & (binunionTE = $true) & (binunionIL = $true) & (setukpairinjR1 = $true) & (kpairiskpair = $true) & (setunionAx = $true) & (dpsetconstrSub = $true) & (binintersectT_lem = $true) & (lam2p = $true) & (exuEu = $true) & (setminusLsub = $true) & (prop2setE = $true) & (doubleComplementI1 = $true) & (powersetTI1 = $true) & (cartprodmempair1 = $true) & (powersetE1 = $true) & (quantDeMorgan1 = $true) & (uniqinunit = $true) & (powersetTE1 = $true) & (infuncsetfunc = $true) & (funcext = $true) & (iftrueorfalse = $true) & (demorgan2a1 = $true) & (kpairsurjEq = $true) & (funcGraphProp1 = $true) & (brelnall2 = $true) & (symdiffE = $true) & (powersetsubset = $true) & (setadjoinIR = $true) & (subsetI2 = $true) & (eta2 = $true) & (powersetAx = $true) & (ap2p = $true) & (setOfPairsIsBReln = $true) & (powersetI = $true) & (subsetI1 = $true) & (setunionI = $true) & (funcGraphProp2 = $true) & (cartprodmempair = $true) & (setukpairinjL2 = $true) & (binintersectTELcontra = $true) & (binunionTEcontra = $true) & (binintersectSubset3 = $true) & (ifSingleton = $true) & (setukpairinjL1 = $true) & (funcImageSingleton = $true) & (doubleComplementEq = $true) & (setukpairinjR11 = $true) & (setunionE = $true) & (binintersectSubset4 = $true) & (symdiffI2 = $true) & (upairsetIR = $true) & (singletonprop = $true) & (dpsetconstrERa = $true) & (disjointsetsI1 = $true) & (dsetconstr__Cong = $true) & (dpsetconstrEL2 = $true) & (cartprodfstpairEq = $true) & (cartprodpairmemER = $true) & (quantDeMorgan4 = $true) & (cartprodpairin = $true) & (setunionsingleton1 = $true) & (binintersectI = $true) & (beta2 = $true) & (exuE2 = $true) & (exuI2 = $true) & (setadjoinSub2 = $true) & (emptyInPowerset = $true) & (binunionRsub = $true) & (contrasubsetT3 = $true) & (exuI1 = $true) & (iftrueProp2 = $true) & (dsetconstrER = $true) & (subset2powerset = $true) & (ubforcartprodlem2 = $true) & (lamProp = $true) & (setextT = $true) & (setukpairinjR = $true) & (notinemptyset = $true) & (upairinpowunion = $true) & (setminusERneg = $true) & (powerset__Cong = $true) & (exu__Cong = $true) & (upairsetE = $true) & (noeltsimpempty = $true) & (subPowSU = $true) & (binintersectLsub = $true) & (lam2lamEq = $true) & (binunionTIRcontra = $true) & (singletoninpowunion = $true) & (setukpairinjR12 = $true) & (demorgan2b2 = $true) & (ksndpairEq = $true) & (ksndsingleton = $true) & (lamp = $true) & (setadjoinE = $true) & (subsetE = $true) & (descrp = $true) & (subsetTrans = $true) & (ex1I2 = $true) & (symdiffI1 = $true) & (binintersectEL = $true) & (setukpairIL = $true) & (setunionsingleton = $true) & (nonemptyImpWitness = $true) & (eqbreln = $true) & (binunionT_lem = $true) & (quantDeMorgan3 = $true) & (subsetemptysetimpeq = $true) & (iffalseProp2 = $true) & (ubforcartprodlem1 = $true) & ((($true = (in @ sK303 @ (powerset @ sK302))) & (((in @ sK304 @ sK302) = $true) & ((in @ sK304 @ (setminus @ sK302 @ (binunion @ sK301 @ sK303))) != $true) & ($true = (in @ sK304 @ (binintersect @ (setminus @ sK302 @ sK301) @ (setminus @ sK302 @ sK303)))))) & ((in @ sK301 @ (powerset @ sK302)) = $true)) & (emptysetsubset = $true) & (bs114d = $true) & (prop2setI = $true) & (omega__Cong = $true) & (setext = $true) & (binintersectSubset2 = $true) & (complementSubsetComplementIntersect = $true) & (inComplementUnionImpNotIn1 = $true) & (binunionE = $true) & (exuI3 = $true) & (contraSubsetComplement = $true) & (powersetE = $true)), 1.69/0.65 inference(skolemisation,[status(esa),new_symbols(skolem,[sK301,sK302,sK303,sK304])],[f915,f1673,f1672,f1671])). 1.69/0.65 thf(f1671,plain,( 1.69/0.65 ? [X0,X1] : (? [X2] : (($true = (in @ X2 @ (powerset @ X1))) & ? [X3] : (((in @ X3 @ X1) = $true) & ($true != (in @ X3 @ (setminus @ X1 @ (binunion @ X0 @ X2)))) & ((in @ X3 @ (binintersect @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2))) = $true))) & ((in @ X0 @ (powerset @ X1)) = $true)) => (? [X2] : (($true = (in @ X2 @ (powerset @ sK302))) & ? [X3] : (((in @ X3 @ sK302) = $true) & ($true != (in @ X3 @ (setminus @ sK302 @ (binunion @ sK301 @ X2)))) & ($true = (in @ X3 @ (binintersect @ (setminus @ sK302 @ sK301) @ (setminus @ sK302 @ X2)))))) & ((in @ sK301 @ (powerset @ sK302)) = $true))), 1.69/0.65 introduced(choice_axiom,[])). 1.69/0.65 thf(f1672,plain,( 1.69/0.65 ? [X2] : (($true = (in @ X2 @ (powerset @ sK302))) & ? [X3] : (((in @ X3 @ sK302) = $true) & ($true != (in @ X3 @ (setminus @ sK302 @ (binunion @ sK301 @ X2)))) & ($true = (in @ X3 @ (binintersect @ (setminus @ sK302 @ sK301) @ (setminus @ sK302 @ X2)))))) => (($true = (in @ sK303 @ (powerset @ sK302))) & ? [X3] : (((in @ X3 @ sK302) = $true) & ($true != (in @ X3 @ (setminus @ sK302 @ (binunion @ sK301 @ sK303)))) & ($true = (in @ X3 @ (binintersect @ (setminus @ sK302 @ sK301) @ (setminus @ sK302 @ sK303))))))), 1.69/0.65 introduced(choice_axiom,[])). 1.69/0.65 thf(f1673,plain,( 1.69/0.65 ? [X3] : (((in @ X3 @ sK302) = $true) & ($true != (in @ X3 @ (setminus @ sK302 @ (binunion @ sK301 @ sK303)))) & ($true = (in @ X3 @ (binintersect @ (setminus @ sK302 @ sK301) @ (setminus @ sK302 @ sK303))))) => (((in @ sK304 @ sK302) = $true) & ((in @ sK304 @ (setminus @ sK302 @ (binunion @ sK301 @ sK303))) != $true) & ($true = (in @ sK304 @ (binintersect @ (setminus @ sK302 @ sK301) @ (setminus @ sK302 @ sK303)))))), 1.69/0.65 introduced(choice_axiom,[])). 1.69/0.65 thf(f915,plain,( 1.69/0.65 (symdiffIneg1 = $true) & (sepSubset = $true) & (ex1E1 = $true) & (inPowerset = $true) & (subsetRefl = $true) & (kfstpairEq = $true) & (funcGraphProp4 = $true) & (setunionE2 = $true) & (demorgan2a = $true) & (iffalseProp1 = $true) & (complementTcontraSubset = $true) & (singletonsubset = $true) & (inIntersectImpInUnion2 = $true) & (setminusER = $true) & (inIntersectImpInUnion = $true) & (demorgan1b = $true) & (subsetTI = $true) & (dpsetconstrER = $true) & (emptyset__Cong = $true) & (setukpairIR = $true) & (setunionsingleton2 = $true) & (ifp = $true) & (notequalI1 = $true) & (setminusELneg = $true) & (notdallE = $true) & (theprop = $true) & (vacuousDall = $true) & (funcGraphProp3 = $true) & (ap2apEq1 = $true) & (setminusSubset2 = $true) & (setukpairinjR2 = $true) & (subbreln = $true) & (doubleComplementE1 = $true) & (binintersectSubset1 = $true) & (setminusIRneg = $true) & (omegaSAx = $true) & (prop2set2propI = $true) & (setadjoinSub = $true) & (demorgan2a2 = $true) & (emptysetimpfalse = $true) & (ex1I = $true) & (nonemptyE1 = $true) & (upairequniteq = $true) & (binintersectSubset5 = $true) & (kfstsingleton = $true) & (apProp = $true) & (intersectInPowersetIntersectUnions = $true) & (binunionLsub = $true) & (omegaIndAx = $true) & (complementInPowersetComplementIntersect = $true) & (setbeta = $true) & (wellorderingAx = $true) & (secondinupair = $true) & (brelnall1 = $true) & (in__Cong = $true) & (emptyI = $true) & (notinsingleton = $true) & (setukpairinjL = $true) & (eqinunit = $true) & (cartprodsndpairEq = $true) & (funcextLem = $true) & (upairset2E = $true) & (demorgan1a = $true) & (setminusT_lem = $true) & (upairset2IR = $true) & (exuE3u = $true) & (binunionEcases = $true) & (upairsetIL = $true) & (descr__Cong = $true) & (complementT_lem = $true) & (dpsetconstrI = $true) & (setadjoinOr = $true) & (iffalse = $true) & (emptyE1 = $true) & (binunionTILcontra = $true) & (subsetE2 = $true) & (dsetconstrEL = $true) & (binintersectTERcontra = $true) & (sepInPowerset = $true) & (setadjoinIL = $true) & (notsubsetI = $true) & (ex1E2 = $true) & (setminusILneg = $true) & (eta1 = $true) & (funcinfuncset = $true) & (setminusSubset1 = $true) & (beta1 = $true) & (emptyinunitempty = $true) & (ubforcartprodlem3 = $true) & (inIntersectImpInIntersectUnions = $true) & (complementUnionInPowersetComplement = $true) & (exuE3e = $true) & (eqimpsubset1 = $true) & (emptyinPowerset = $true) & (eqimpsubset2 = $true) & (exuE1 = $true) & (complementTE1 = $true) & (complementTnotintersectT = $true) & (cartprodmempaircEq = $true) & (cartprodsndin = $true) & (ap2apEq2 = $true) & (kpairp = $true) & (quantDeMorgan2 = $true) & (dsetconstrI = $true) & (contrasubsetT1 = $true) & (omega0Ax = $true) & (cartprodpairmemEL = $true) & (iftrue = $true) & (singletoninpowerset = $true) & (singletonsuniq = $true) & (inComplementUnionImpInComplement1 = $true) & (nonemptyI = $true) & (notdexE = $true) & (singletonsswitch = $true) & (iftrueProp1 = $true) & (powersetT_lem = $true) & (complementImpComplementIntersect = $true) & (theeq = $true) & (binunionIR = $true) & (setminusI = $true) & (complementTI1 = $true) & (binintersectRsub = $true) & (setunion__Cong = $true) & (setextAx = $true) & (symdiffIneg2 = $true) & (cartprodpairsurjEq = $true) & (app = $true) & (upairsubunion = $true) & (powersetI1 = $true) & (binintersectER = $true) & (nonemptyI1 = $true) & (emptysetAx = $true) & (cartprodfstin = $true) & (doubleComplementSub2 = $true) & (replAx = $true) & (setminusEL = $true) & (contrasubsetT = $true) & (contrasubsetT2 = $true) & (inCongP = $true) & (setoftrueEq = $true) & (setextsub = $true) & (setadjoin__Cong = $true) & (foundationAx = $true) & (notequalI2 = $true) & (setadjoinAx = $true) & (dpsetconstrEL1 = $true) & (doubleComplementSub1 = $true) & (emptysetE = $true) & (demorgan1 = $true) & (funcext2 = $true) & (binunionTE = $true) & (binunionIL = $true) & (setukpairinjR1 = $true) & (kpairiskpair = $true) & (setunionAx = $true) & (dpsetconstrSub = $true) & (binintersectT_lem = $true) & (lam2p = $true) & (exuEu = $true) & (setminusLsub = $true) & (prop2setE = $true) & (doubleComplementI1 = $true) & (powersetTI1 = $true) & (cartprodmempair1 = $true) & (powersetE1 = $true) & (quantDeMorgan1 = $true) & (uniqinunit = $true) & (powersetTE1 = $true) & (infuncsetfunc = $true) & (funcext = $true) & (iftrueorfalse = $true) & (demorgan2a1 = $true) & (kpairsurjEq = $true) & (funcGraphProp1 = $true) & (brelnall2 = $true) & (symdiffE = $true) & (powersetsubset = $true) & (setadjoinIR = $true) & (subsetI2 = $true) & (eta2 = $true) & (powersetAx = $true) & (ap2p = $true) & (setOfPairsIsBReln = $true) & (powersetI = $true) & (subsetI1 = $true) & (setunionI = $true) & (funcGraphProp2 = $true) & (cartprodmempair = $true) & (setukpairinjL2 = $true) & (binintersectTELcontra = $true) & (binunionTEcontra = $true) & (binintersectSubset3 = $true) & (ifSingleton = $true) & (setukpairinjL1 = $true) & (funcImageSingleton = $true) & (doubleComplementEq = $true) & (setukpairinjR11 = $true) & (setunionE = $true) & (binintersectSubset4 = $true) & (symdiffI2 = $true) & (upairsetIR = $true) & (singletonprop = $true) & (dpsetconstrERa = $true) & (disjointsetsI1 = $true) & (dsetconstr__Cong = $true) & (dpsetconstrEL2 = $true) & (cartprodfstpairEq = $true) & (cartprodpairmemER = $true) & (quantDeMorgan4 = $true) & (cartprodpairin = $true) & (setunionsingleton1 = $true) & (binintersectI = $true) & (beta2 = $true) & (exuE2 = $true) & (exuI2 = $true) & (setadjoinSub2 = $true) & (emptyInPowerset = $true) & (binunionRsub = $true) & (contrasubsetT3 = $true) & (exuI1 = $true) & (iftrueProp2 = $true) & (dsetconstrER = $true) & (subset2powerset = $true) & (ubforcartprodlem2 = $true) & (lamProp = $true) & (setextT = $true) & (setukpairinjR = $true) & (notinemptyset = $true) & (upairinpowunion = $true) & (setminusERneg = $true) & (powerset__Cong = $true) & (exu__Cong = $true) & (upairsetE = $true) & (noeltsimpempty = $true) & (subPowSU = $true) & (binintersectLsub = $true) & (lam2lamEq = $true) & (binunionTIRcontra = $true) & (singletoninpowunion = $true) & (setukpairinjR12 = $true) & (demorgan2b2 = $true) & (ksndpairEq = $true) & (ksndsingleton = $true) & (lamp = $true) & (setadjoinE = $true) & (subsetE = $true) & (descrp = $true) & (subsetTrans = $true) & (ex1I2 = $true) & (symdiffI1 = $true) & (binintersectEL = $true) & (setukpairIL = $true) & (setunionsingleton = $true) & (nonemptyImpWitness = $true) & (eqbreln = $true) & (binunionT_lem = $true) & (quantDeMorgan3 = $true) & (subsetemptysetimpeq = $true) & (iffalseProp2 = $true) & (ubforcartprodlem1 = $true) & ? [X0,X1] : (? [X2] : (($true = (in @ X2 @ (powerset @ X1))) & ? [X3] : (((in @ X3 @ X1) = $true) & ($true != (in @ X3 @ (setminus @ X1 @ (binunion @ X0 @ X2)))) & ((in @ X3 @ (binintersect @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2))) = $true))) & ((in @ X0 @ (powerset @ X1)) = $true)) & (emptysetsubset = $true) & (bs114d = $true) & (prop2setI = $true) & (omega__Cong = $true) & (setext = $true) & (binintersectSubset2 = $true) & (complementSubsetComplementIntersect = $true) & (inComplementUnionImpNotIn1 = $true) & (binunionE = $true) & (exuI3 = $true) & (contraSubsetComplement = $true) & (powersetE = $true)), 1.69/0.65 inference(flattening,[],[f914])). 1.69/0.65 thf(f914,plain,( 1.69/0.65 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0,X1] : (? [X2] : (? [X3] : ((($true != (in @ X3 @ (setminus @ X1 @ (binunion @ X0 @ X2)))) & ((in @ X3 @ (binintersect @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2))) = $true)) & ((in @ X3 @ X1) = $true)) & ($true = (in @ X2 @ (powerset @ X1)))) & ((in @ X0 @ (powerset @ X1)) = $true)) & (demorgan2b2 = $true)) & (demorgan2a = $true)) & (demorgan1 = $true)) & (demorgan1b = $true)) & (demorgan1a = $true)) & (demorgan2a2 = $true)) & (complementUnionInPowersetComplement = $true)) & (demorgan2a1 = $true)) & (binunionTEcontra = $true)) & (binunionTE = $true)) & (inComplementUnionImpInComplement1 = $true)) & (inComplementUnionImpNotIn1 = $true)) & (intersectInPowersetIntersectUnions = $true)) & (inIntersectImpInIntersectUnions = $true)) & (inIntersectImpInUnion2 = $true)) & (inIntersectImpInUnion = $true)) & (binunionTIRcontra = $true)) & (binunionTILcontra = $true)) & (complementTcontraSubset = $true)) & (contraSubsetComplement = $true)) & (complementInPowersetComplementIntersect = $true)) & (complementSubsetComplementIntersect = $true)) & (complementImpComplementIntersect = $true)) & (complementTnotintersectT = $true)) & (doubleComplementEq = $true)) & (doubleComplementSub2 = $true)) & (doubleComplementSub1 = $true)) & (doubleComplementE1 = $true)) & (doubleComplementI1 = $true)) & (contrasubsetT3 = $true)) & (contrasubsetT2 = $true)) & (contrasubsetT1 = $true)) & (contrasubsetT = $true)) & (binintersectTERcontra = $true)) & (binintersectTELcontra = $true)) & (complementTE1 = $true)) & (complementTI1 = $true)) & (powersetTE1 = $true)) & (powersetTI1 = $true)) & (subsetTI = $true)) & (setextT = $true)) & (complementT_lem = $true)) & (setminusT_lem = $true)) & (powersetT_lem = $true)) & (binunionT_lem = $true)) & (binintersectT_lem = $true)) & (iftrueorfalse = $true)) & (iffalse = $true)) & (iftrue = $true)) & (theeq = $true)) & (ifp = $true)) & (ifSingleton = $true)) & (iftrueProp2 = $true)) & (iftrueProp1 = $true)) & (iffalseProp2 = $true)) & (iffalseProp1 = $true)) & (eta2 = $true)) & (beta2 = $true)) & (lam2lamEq = $true)) & (eta1 = $true)) & (beta1 = $true)) & (ap2apEq2 = $true)) & (ap2apEq1 = $true)) & (funcext2 = $true)) & (funcext = $true)) & (eqbreln = $true)) & (subbreln = $true)) & (funcGraphProp4 = $true)) & (funcextLem = $true)) & (funcGraphProp2 = $true)) & (funcGraphProp3 = $true)) & (funcGraphProp1 = $true)) & (ex1E2 = $true)) & (brelnall2 = $true)) & (brelnall1 = $true)) & (lam2p = $true)) & (lamp = $true)) & (lamProp = $true)) & (funcinfuncset = $true)) & (ap2p = $true)) & (infuncsetfunc = $true)) & (app = $true)) & (apProp = $true)) & (funcImageSingleton = $true)) & (dpsetconstrER = $true)) & (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)), 1.69/0.65 inference(ennf_transformation,[],[f301])). 1.69/0.65 thf(f301,plain,( 1.69/0.65 ~((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) => ((dpsetconstrER = $true) => ((funcImageSingleton = $true) => ((apProp = $true) => ((app = $true) => ((infuncsetfunc = $true) => ((ap2p = $true) => ((funcinfuncset = $true) => ((lamProp = $true) => ((lamp = $true) => ((lam2p = $true) => ((brelnall1 = $true) => ((brelnall2 = $true) => ((ex1E2 = $true) => ((funcGraphProp1 = $true) => ((funcGraphProp3 = $true) => ((funcGraphProp2 = $true) => ((funcextLem = $true) => ((funcGraphProp4 = $true) => ((subbreln = $true) => ((eqbreln = $true) => ((funcext = $true) => ((funcext2 = $true) => ((ap2apEq1 = $true) => ((ap2apEq2 = $true) => ((beta1 = $true) => ((eta1 = $true) => ((lam2lamEq = $true) => ((beta2 = $true) => ((eta2 = $true) => ((iffalseProp1 = $true) => ((iffalseProp2 = $true) => ((iftrueProp1 = $true) => ((iftrueProp2 = $true) => ((ifSingleton = $true) => ((ifp = $true) => ((theeq = $true) => ((iftrue = $true) => ((iffalse = $true) => ((iftrueorfalse = $true) => ((binintersectT_lem = $true) => ((binunionT_lem = $true) => ((powersetT_lem = $true) => ((setminusT_lem = $true) => ((complementT_lem = $true) => ((setextT = $true) => ((subsetTI = $true) => ((powersetTI1 = $true) => ((powersetTE1 = $true) => ((complementTI1 = $true) => ((complementTE1 = $true) => ((binintersectTELcontra = $true) => ((binintersectTERcontra = $true) => ((contrasubsetT = $true) => ((contrasubsetT1 = $true) => ((contrasubsetT2 = $true) => ((contrasubsetT3 = $true) => ((doubleComplementI1 = $true) => ((doubleComplementE1 = $true) => ((doubleComplementSub1 = $true) => ((doubleComplementSub2 = $true) => ((doubleComplementEq = $true) => ((complementTnotintersectT = $true) => ((complementImpComplementIntersect = $true) => ((complementSubsetComplementIntersect = $true) => ((complementInPowersetComplementIntersect = $true) => ((contraSubsetComplement = $true) => ((complementTcontraSubset = $true) => ((binunionTILcontra = $true) => ((binunionTIRcontra = $true) => ((inIntersectImpInUnion = $true) => ((inIntersectImpInUnion2 = $true) => ((inIntersectImpInIntersectUnions = $true) => ((intersectInPowersetIntersectUnions = $true) => ((inComplementUnionImpNotIn1 = $true) => ((inComplementUnionImpInComplement1 = $true) => ((binunionTE = $true) => ((binunionTEcontra = $true) => ((demorgan2a1 = $true) => ((complementUnionInPowersetComplement = $true) => ((demorgan2a2 = $true) => ((demorgan1a = $true) => ((demorgan1b = $true) => ((demorgan1 = $true) => ((demorgan2a = $true) => ((demorgan2b2 = $true) => ! [X0,X1] : (((in @ X0 @ (powerset @ X1)) = $true) => ! [X2] : (($true = (in @ X2 @ (powerset @ X1))) => ! [X3] : (((in @ X3 @ X1) = $true) => (((in @ X3 @ (binintersect @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2))) = $true) => ($true = (in @ X3 @ (setminus @ X1 @ (binunion @ X0 @ X2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1.69/0.65 inference(fool_elimination,[],[f300])). 1.69/0.65 thf(f300,plain,( 1.69/0.65 ~(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 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => ! [X0,X1] : ((in @ X0 @ (powerset @ X1)) => ! [X2] : ((in @ X2 @ (powerset @ X1)) => ! [X3] : ((in @ X3 @ X1) => ((in @ X3 @ (binintersect @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2))) => (in @ X3 @ (setminus @ X1 @ (binunion @ X0 @ X2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1.69/0.65 inference(rectify,[],[f278])). 1.69/0.65 thf(f278,negated_conjecture,( 1.69/0.65 ~(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 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => ! [X11,X3] : ((in @ X11 @ (powerset @ X3)) => ! [X16] : ((in @ X16 @ (powerset @ X3)) => ! [X1] : ((in @ X1 @ X3) => ((in @ X1 @ (binintersect @ (setminus @ X3 @ X11) @ (setminus @ X3 @ X16))) => (in @ X1 @ (setminus @ X3 @ (binunion @ X11 @ X16)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1.69/0.65 inference(negated_conjecture,[],[f277])). 1.69/0.65 thf(f277,conjecture,( 1.69/0.65 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 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => ! [X11,X3] : ((in @ X11 @ (powerset @ X3)) => ! [X16] : ((in @ X16 @ (powerset @ X3)) => ! [X1] : ((in @ X1 @ X3) => ((in @ X1 @ (binintersect @ (setminus @ X3 @ X11) @ (setminus @ X3 @ X16))) => (in @ X1 @ (setminus @ X3 @ (binunion @ X11 @ X16))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1.69/0.65 file('/export/starexec/sandbox/tmp/tmp.xuGTqtnLJR/Vampire---4.8_17441',demorgan2b)). 1.69/0.65 thf(f4587,plain,( 1.69/0.65 (setminusER != $true) | ($true != (in @ sK304 @ sK303))), 1.69/0.65 inference(trivial_inequality_removal,[],[f4580])). 1.69/0.65 thf(f4580,plain,( 1.69/0.65 ($true != $true) | (setminusER != $true) | ($true != (in @ sK304 @ sK303))), 1.69/0.65 inference(superposition,[],[f2936,f4540])). 1.69/0.65 thf(f4540,plain,( 1.69/0.65 ((in @ sK304 @ (setminus @ sK302 @ sK303)) = $true)), 1.69/0.65 inference(subsumption_resolution,[],[f4529,f3109])). 1.69/0.65 thf(f3109,plain,( 1.69/0.65 (binintersectER = $true)), 1.69/0.65 inference(cnf_transformation,[],[f1674])). 1.69/0.65 thf(f4529,plain,( 1.69/0.65 (binintersectER != $true) | ((in @ sK304 @ (setminus @ sK302 @ sK303)) = $true)), 1.69/0.65 inference(trivial_inequality_removal,[],[f4523])). 1.69/0.65 thf(f4523,plain,( 1.69/0.65 ((in @ sK304 @ (setminus @ sK302 @ sK303)) = $true) | ($true != $true) | (binintersectER != $true)), 1.69/0.65 inference(superposition,[],[f3616,f2975])). 1.69/0.65 thf(f2975,plain,( 1.69/0.65 ($true = (in @ sK304 @ (binintersect @ (setminus @ sK302 @ sK301) @ (setminus @ sK302 @ sK303))))), 1.69/0.65 inference(cnf_transformation,[],[f1674])). 1.69/0.65 thf(f3616,plain,( 1.69/0.65 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ (binintersect @ X5 @ X4)) != $true) | ((in @ X3 @ X4) = $true) | (binintersectER != $true)) )), 1.69/0.65 inference(cnf_transformation,[],[f2123])). 1.69/0.65 thf(f2123,plain,( 1.69/0.65 ((binintersectER = $true) | (((in @ sK584 @ sK585) != $true) & ($true = (in @ sK584 @ (binintersect @ sK586 @ sK585))))) & (! [X3,X4,X5] : (((in @ X3 @ X4) = $true) | ((in @ X3 @ (binintersect @ X5 @ X4)) != $true)) | (binintersectER != $true))), 1.69/0.65 inference(skolemisation,[status(esa),new_symbols(skolem,[sK584,sK585,sK586])],[f2121,f2122])). 1.69/0.65 thf(f2122,plain,( 1.69/0.65 ? [X0,X1,X2] : (($true != (in @ X0 @ X1)) & ((in @ X0 @ (binintersect @ X2 @ X1)) = $true)) => (((in @ sK584 @ sK585) != $true) & ($true = (in @ sK584 @ (binintersect @ sK586 @ sK585))))), 1.69/0.65 introduced(choice_axiom,[])). 1.69/0.65 thf(f2121,plain,( 1.69/0.65 ((binintersectER = $true) | ? [X0,X1,X2] : (($true != (in @ X0 @ X1)) & ((in @ X0 @ (binintersect @ X2 @ X1)) = $true))) & (! [X3,X4,X5] : (((in @ X3 @ X4) = $true) | ((in @ X3 @ (binintersect @ X5 @ X4)) != $true)) | (binintersectER != $true))), 1.69/0.65 inference(rectify,[],[f2120])). 1.69/0.65 thf(f2120,plain,( 1.69/0.65 ((binintersectER = $true) | ? [X0,X1,X2] : (($true != (in @ X0 @ X1)) & ((in @ X0 @ (binintersect @ X2 @ X1)) = $true))) & (! [X0,X1,X2] : (($true = (in @ X0 @ X1)) | ((in @ X0 @ (binintersect @ X2 @ X1)) != $true)) | (binintersectER != $true))), 1.69/0.65 inference(nnf_transformation,[],[f1066])). 1.69/0.65 thf(f1066,plain,( 1.69/0.65 (binintersectER = $true) <=> ! [X0,X1,X2] : (($true = (in @ X0 @ X1)) | ((in @ X0 @ (binintersect @ X2 @ X1)) != $true))), 1.69/0.65 inference(ennf_transformation,[],[f669])). 1.69/0.65 thf(f669,plain,( 1.69/0.65 ! [X0,X1,X2] : (((in @ X0 @ (binintersect @ X2 @ X1)) = $true) => ($true = (in @ X0 @ X1))) <=> (binintersectER = $true)), 1.69/0.65 inference(fool_elimination,[],[f668])). 1.69/0.65 thf(f668,plain,( 1.69/0.65 (! [X0,X1,X2] : ((in @ X0 @ (binintersect @ X2 @ X1)) => (in @ X0 @ X1)) = binintersectER)), 1.69/0.65 inference(rectify,[],[f114])). 1.69/0.65 thf(f114,axiom,( 1.69/0.65 (! [X1,X4,X3] : ((in @ X1 @ (binintersect @ X3 @ X4)) => (in @ X1 @ X4)) = binintersectER)), 1.69/0.65 file('/export/starexec/sandbox/tmp/tmp.xuGTqtnLJR/Vampire---4.8_17441',binintersectER)). 1.69/0.65 thf(f2936,plain,( 1.69/0.65 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X4 @ (setminus @ X3 @ X5)) != $true) | ((in @ X4 @ X5) != $true) | (setminusER != $true)) )), 1.69/0.65 inference(cnf_transformation,[],[f1642])). 1.69/0.65 thf(f1642,plain,( 1.69/0.65 ((setminusER = $true) | (($true = (in @ sK280 @ (setminus @ sK279 @ sK281))) & ((in @ sK280 @ sK281) = $true))) & (! [X3,X4,X5] : (((in @ X4 @ (setminus @ X3 @ X5)) != $true) | ((in @ X4 @ X5) != $true)) | (setminusER != $true))), 1.69/0.65 inference(skolemisation,[status(esa),new_symbols(skolem,[sK279,sK280,sK281])],[f1640,f1641])). 1.69/0.65 thf(f1641,plain,( 1.69/0.65 ? [X0,X1,X2] : (($true = (in @ X1 @ (setminus @ X0 @ X2))) & ($true = (in @ X1 @ X2))) => (($true = (in @ sK280 @ (setminus @ sK279 @ sK281))) & ((in @ sK280 @ sK281) = $true))), 1.69/0.65 introduced(choice_axiom,[])). 1.69/0.65 thf(f1640,plain,( 1.69/0.65 ((setminusER = $true) | ? [X0,X1,X2] : (($true = (in @ X1 @ (setminus @ X0 @ X2))) & ($true = (in @ X1 @ X2)))) & (! [X3,X4,X5] : (((in @ X4 @ (setminus @ X3 @ X5)) != $true) | ((in @ X4 @ X5) != $true)) | (setminusER != $true))), 1.69/0.65 inference(rectify,[],[f1639])). 1.69/0.65 thf(f1639,plain,( 1.69/0.65 ((setminusER = $true) | ? [X0,X1,X2] : (($true = (in @ X1 @ (setminus @ X0 @ X2))) & ($true = (in @ X1 @ X2)))) & (! [X0,X1,X2] : (($true != (in @ X1 @ (setminus @ X0 @ X2))) | ($true != (in @ X1 @ X2))) | (setminusER != $true))), 1.69/0.65 inference(nnf_transformation,[],[f1043])). 1.69/0.65 thf(f1043,plain,( 1.69/0.65 (setminusER = $true) <=> ! [X0,X1,X2] : (($true != (in @ X1 @ (setminus @ X0 @ X2))) | ($true != (in @ X1 @ X2)))), 1.69/0.65 inference(ennf_transformation,[],[f844])). 1.69/0.65 thf(f844,plain,( 1.69/0.65 (setminusER = $true) <=> ! [X0,X1,X2] : (($true = (in @ X1 @ (setminus @ X0 @ X2))) => ($true != (in @ X1 @ X2)))), 1.69/0.65 inference(flattening,[],[f438])). 1.69/0.65 thf(f438,plain,( 1.69/0.65 (setminusER = $true) <=> ! [X0,X1,X2] : (($true = (in @ X1 @ (setminus @ X0 @ X2))) => ~($true = (in @ X1 @ X2)))), 1.69/0.65 inference(fool_elimination,[],[f437])). 1.69/0.65 thf(f437,plain,( 1.69/0.65 (setminusER = ! [X0,X1,X2] : ((in @ X1 @ (setminus @ X0 @ X2)) => ~(in @ X1 @ X2)))), 1.69/0.65 inference(rectify,[],[f122])). 1.69/0.65 thf(f122,axiom,( 1.69/0.65 (setminusER = ! [X3,X1,X4] : ((in @ X1 @ (setminus @ X3 @ X4)) => ~(in @ X1 @ X4)))), 1.69/0.65 file('/export/starexec/sandbox/tmp/tmp.xuGTqtnLJR/Vampire---4.8_17441',setminusER)). 1.69/0.65 thf(f4564,plain,( 1.69/0.65 ~spl881_11), 1.69/0.65 inference(avatar_split_clause,[],[f4561,f4500])). 1.69/0.65 thf(f4500,plain,( 1.69/0.65 spl881_11 <=> ((in @ sK304 @ sK301) = $true)), 1.69/0.65 introduced(avatar_definition,[new_symbols(naming,[spl881_11])])). 1.69/0.65 thf(f4561,plain,( 1.69/0.65 ((in @ sK304 @ sK301) != $true)), 1.69/0.65 inference(subsumption_resolution,[],[f4556,f3225])). 1.69/0.65 thf(f4556,plain,( 1.69/0.65 ((in @ sK304 @ sK301) != $true) | (setminusER != $true)), 1.69/0.65 inference(trivial_inequality_removal,[],[f4544])). 1.69/0.65 thf(f4544,plain,( 1.69/0.65 ($true != $true) | ((in @ sK304 @ sK301) != $true) | (setminusER != $true)), 1.69/0.65 inference(superposition,[],[f2936,f4536])). 1.69/0.65 thf(f4536,plain,( 1.69/0.65 ($true = (in @ sK304 @ (setminus @ sK302 @ sK301)))), 1.69/0.65 inference(subsumption_resolution,[],[f4533,f2988])). 1.69/0.65 thf(f2988,plain,( 1.69/0.65 (binintersectEL = $true)), 1.69/0.65 inference(cnf_transformation,[],[f1674])). 1.69/0.65 thf(f4533,plain,( 1.69/0.65 ($true = (in @ sK304 @ (setminus @ sK302 @ sK301))) | (binintersectEL != $true)), 1.69/0.65 inference(trivial_inequality_removal,[],[f4526])). 1.69/0.65 thf(f4526,plain,( 1.69/0.65 (binintersectEL != $true) | ($true != $true) | ($true = (in @ sK304 @ (setminus @ sK302 @ sK301)))), 1.69/0.65 inference(superposition,[],[f3374,f2975])). 1.69/0.65 thf(f3374,plain,( 1.69/0.65 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ (binintersect @ X0 @ X1)) != $true) | (binintersectEL != $true) | ($true = (in @ X2 @ X0))) )), 1.69/0.65 inference(cnf_transformation,[],[f1848])). 1.69/0.65 thf(f1848,plain,( 1.69/0.65 (! [X0,X1,X2] : (($true = (in @ X2 @ X0)) | ((in @ X2 @ (binintersect @ X0 @ X1)) != $true)) | (binintersectEL != $true)) & ((binintersectEL = $true) | (($true != (in @ sK415 @ sK413)) & ((in @ sK415 @ (binintersect @ sK413 @ sK414)) = $true)))), 1.69/0.65 inference(skolemisation,[status(esa),new_symbols(skolem,[sK413,sK414,sK415])],[f1846,f1847])). 1.69/0.65 thf(f1847,plain,( 1.69/0.65 ? [X3,X4,X5] : (($true != (in @ X5 @ X3)) & ((in @ X5 @ (binintersect @ X3 @ X4)) = $true)) => (($true != (in @ sK415 @ sK413)) & ((in @ sK415 @ (binintersect @ sK413 @ sK414)) = $true))), 1.69/0.65 introduced(choice_axiom,[])). 1.69/0.65 thf(f1846,plain,( 1.69/0.65 (! [X0,X1,X2] : (($true = (in @ X2 @ X0)) | ((in @ X2 @ (binintersect @ X0 @ X1)) != $true)) | (binintersectEL != $true)) & ((binintersectEL = $true) | ? [X3,X4,X5] : (($true != (in @ X5 @ X3)) & ((in @ X5 @ (binintersect @ X3 @ X4)) = $true)))), 1.69/0.65 inference(rectify,[],[f1845])). 1.69/0.65 thf(f1845,plain,( 1.69/0.65 (! [X0,X1,X2] : (($true = (in @ X2 @ X0)) | ((in @ X2 @ (binintersect @ X0 @ X1)) != $true)) | (binintersectEL != $true)) & ((binintersectEL = $true) | ? [X0,X1,X2] : (($true != (in @ X2 @ X0)) & ((in @ X2 @ (binintersect @ X0 @ X1)) = $true)))), 1.69/0.65 inference(nnf_transformation,[],[f1010])). 1.69/0.65 thf(f1010,plain,( 1.69/0.65 ! [X0,X1,X2] : (($true = (in @ X2 @ X0)) | ((in @ X2 @ (binintersect @ X0 @ X1)) != $true)) <=> (binintersectEL = $true)), 1.69/0.65 inference(ennf_transformation,[],[f620])). 1.69/0.65 thf(f620,plain,( 1.69/0.65 (binintersectEL = $true) <=> ! [X0,X1,X2] : (((in @ X2 @ (binintersect @ X0 @ X1)) = $true) => ($true = (in @ X2 @ X0)))), 1.69/0.65 inference(fool_elimination,[],[f619])). 1.69/0.65 thf(f619,plain,( 1.69/0.65 (binintersectEL = ! [X0,X1,X2] : ((in @ X2 @ (binintersect @ X0 @ X1)) => (in @ X2 @ X0)))), 1.69/0.65 inference(rectify,[],[f110])). 1.69/0.65 thf(f110,axiom,( 1.69/0.65 (binintersectEL = ! [X3,X4,X1] : ((in @ X1 @ (binintersect @ X3 @ X4)) => (in @ X1 @ X3)))), 1.69/0.65 file('/export/starexec/sandbox/tmp/tmp.xuGTqtnLJR/Vampire---4.8_17441',binintersectEL)). 1.69/0.65 thf(f4503,plain,( 1.69/0.65 spl881_10 | spl881_11), 1.69/0.65 inference(avatar_split_clause,[],[f4376,f4500,f4496])). 1.69/0.65 thf(f4376,plain,( 1.69/0.65 ((in @ sK304 @ sK301) = $true) | ($true = (in @ sK304 @ sK303))), 1.69/0.65 inference(subsumption_resolution,[],[f4369,f2965])). 1.69/0.65 thf(f2965,plain,( 1.69/0.65 (binunionE = $true)), 1.69/0.65 inference(cnf_transformation,[],[f1674])). 1.69/0.65 thf(f4369,plain,( 1.69/0.65 ($true = (in @ sK304 @ sK303)) | ((in @ sK304 @ sK301) = $true) | (binunionE != $true)), 1.69/0.65 inference(trivial_inequality_removal,[],[f4363])). 1.69/0.65 thf(f4363,plain,( 1.69/0.65 ($true = (in @ sK304 @ sK303)) | (binunionE != $true) | ((in @ sK304 @ sK301) = $true) | ($true != $true)), 1.69/0.65 inference(superposition,[],[f3787,f4333])). 1.69/0.65 thf(f4333,plain,( 1.69/0.65 ((in @ sK304 @ (binunion @ sK301 @ sK303)) = $true)), 1.69/0.65 inference(subsumption_resolution,[],[f4332,f3119])). 1.69/0.65 thf(f3119,plain,( 1.69/0.65 (setminusI = $true)), 1.69/0.65 inference(cnf_transformation,[],[f1674])). 1.69/0.65 thf(f4332,plain,( 1.69/0.65 ((in @ sK304 @ (binunion @ sK301 @ sK303)) = $true) | (setminusI != $true)), 1.69/0.65 inference(subsumption_resolution,[],[f4331,f2977])). 1.69/0.65 thf(f2977,plain,( 1.69/0.65 ((in @ sK304 @ sK302) = $true)), 1.69/0.65 inference(cnf_transformation,[],[f1674])). 1.69/0.65 thf(f4331,plain,( 1.69/0.65 ((in @ sK304 @ (binunion @ sK301 @ sK303)) = $true) | ((in @ sK304 @ sK302) != $true) | (setminusI != $true)), 1.69/0.65 inference(trivial_inequality_removal,[],[f4315])). 1.69/0.65 thf(f4315,plain,( 1.69/0.65 ((in @ sK304 @ (binunion @ sK301 @ sK303)) = $true) | (setminusI != $true) | ($true != $true) | ((in @ sK304 @ sK302) != $true)), 1.69/0.65 inference(superposition,[],[f2976,f2788])). 1.69/0.65 thf(f2788,plain,( 1.69/0.65 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (in @ X1 @ (setminus @ X0 @ X2))) | (setminusI != $true) | ($true = (in @ X1 @ X2)) | ($true != (in @ X1 @ X0))) )), 1.69/0.65 inference(cnf_transformation,[],[f1477])). 1.69/0.65 thf(f1477,plain,( 1.69/0.65 (! [X0,X1,X2] : (($true != (in @ X1 @ X0)) | ($true = (in @ X1 @ X2)) | ($true = (in @ X1 @ (setminus @ X0 @ X2)))) | (setminusI != $true)) & ((setminusI = $true) | (($true = (in @ sK170 @ sK169)) & ((in @ sK170 @ sK171) != $true) & ((in @ sK170 @ (setminus @ sK169 @ sK171)) != $true)))), 1.69/0.65 inference(skolemisation,[status(esa),new_symbols(skolem,[sK169,sK170,sK171])],[f1475,f1476])). 1.69/0.65 thf(f1476,plain,( 1.69/0.65 ? [X3,X4,X5] : (((in @ X4 @ X3) = $true) & ((in @ X4 @ X5) != $true) & ((in @ X4 @ (setminus @ X3 @ X5)) != $true)) => (($true = (in @ sK170 @ sK169)) & ((in @ sK170 @ sK171) != $true) & ((in @ sK170 @ (setminus @ sK169 @ sK171)) != $true))), 1.69/0.65 introduced(choice_axiom,[])). 1.69/0.65 thf(f1475,plain,( 1.69/0.65 (! [X0,X1,X2] : (($true != (in @ X1 @ X0)) | ($true = (in @ X1 @ X2)) | ($true = (in @ X1 @ (setminus @ X0 @ X2)))) | (setminusI != $true)) & ((setminusI = $true) | ? [X3,X4,X5] : (((in @ X4 @ X3) = $true) & ((in @ X4 @ X5) != $true) & ((in @ X4 @ (setminus @ X3 @ X5)) != $true)))), 1.69/0.65 inference(rectify,[],[f1474])). 1.69/0.65 thf(f1474,plain,( 1.69/0.65 (! [X0,X1,X2] : (($true != (in @ X1 @ X0)) | ($true = (in @ X1 @ X2)) | ($true = (in @ X1 @ (setminus @ X0 @ X2)))) | (setminusI != $true)) & ((setminusI = $true) | ? [X0,X1,X2] : (($true = (in @ X1 @ X0)) & ($true != (in @ X1 @ X2)) & ($true != (in @ X1 @ (setminus @ X0 @ X2)))))), 1.69/0.65 inference(nnf_transformation,[],[f1195])). 1.69/0.65 thf(f1195,plain,( 1.69/0.65 ! [X0,X1,X2] : (($true != (in @ X1 @ X0)) | ($true = (in @ X1 @ X2)) | ($true = (in @ X1 @ (setminus @ X0 @ X2)))) <=> (setminusI = $true)), 1.69/0.65 inference(flattening,[],[f1194])). 1.69/0.65 thf(f1194,plain,( 1.69/0.65 ! [X0,X1,X2] : ((($true = (in @ X1 @ (setminus @ X0 @ X2))) | ($true = (in @ X1 @ X2))) | ($true != (in @ X1 @ X0))) <=> (setminusI = $true)), 1.69/0.65 inference(ennf_transformation,[],[f828])). 1.69/0.65 thf(f828,plain,( 1.69/0.65 ! [X0,X1,X2] : (($true = (in @ X1 @ X0)) => (($true != (in @ X1 @ X2)) => ($true = (in @ X1 @ (setminus @ X0 @ X2))))) <=> (setminusI = $true)), 1.69/0.65 inference(flattening,[],[f289])). 1.69/0.65 thf(f289,plain,( 1.69/0.65 ! [X0,X1,X2] : (($true = (in @ X1 @ X0)) => (~($true = (in @ X1 @ X2)) => ($true = (in @ X1 @ (setminus @ X0 @ X2))))) <=> (setminusI = $true)), 1.69/0.65 inference(fool_elimination,[],[f288])). 1.69/0.65 thf(f288,plain,( 1.69/0.65 (! [X0,X1,X2] : ((in @ X1 @ X0) => (~(in @ X1 @ X2) => (in @ X1 @ (setminus @ X0 @ X2)))) = setminusI)), 1.69/0.65 inference(rectify,[],[f120])). 1.69/0.65 thf(f120,axiom,( 1.69/0.65 (! [X3,X1,X4] : ((in @ X1 @ X3) => (~(in @ X1 @ X4) => (in @ X1 @ (setminus @ X3 @ X4)))) = setminusI)), 1.69/0.65 file('/export/starexec/sandbox/tmp/tmp.xuGTqtnLJR/Vampire---4.8_17441',setminusI)). 1.69/0.65 thf(f2976,plain,( 1.69/0.65 ((in @ sK304 @ (setminus @ sK302 @ (binunion @ sK301 @ sK303))) != $true)), 1.69/0.65 inference(cnf_transformation,[],[f1674])). 1.69/0.65 thf(f3787,plain,( 1.69/0.65 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ (binunion @ X0 @ X1)) != $true) | (binunionE != $true) | ($true = (in @ X2 @ X0)) | ((in @ X2 @ X1) = $true)) )), 1.69/0.65 inference(cnf_transformation,[],[f2298])). 1.69/0.65 thf(f2298,plain,( 1.69/0.65 (! [X0,X1,X2] : (((in @ X2 @ X1) = $true) | ((in @ X2 @ (binunion @ X0 @ X1)) != $true) | ($true = (in @ X2 @ X0))) | (binunionE != $true)) & ((binunionE = $true) | (($true != (in @ sK702 @ sK701)) & ((in @ sK702 @ (binunion @ sK700 @ sK701)) = $true) & ((in @ sK702 @ sK700) != $true)))), 1.69/0.65 inference(skolemisation,[status(esa),new_symbols(skolem,[sK700,sK701,sK702])],[f2296,f2297])). 1.69/0.65 thf(f2297,plain,( 1.69/0.65 ? [X3,X4,X5] : (((in @ X5 @ X4) != $true) & ($true = (in @ X5 @ (binunion @ X3 @ X4))) & ($true != (in @ X5 @ X3))) => (($true != (in @ sK702 @ sK701)) & ((in @ sK702 @ (binunion @ sK700 @ sK701)) = $true) & ((in @ sK702 @ sK700) != $true))), 1.69/0.65 introduced(choice_axiom,[])). 1.69/0.65 thf(f2296,plain,( 1.69/0.65 (! [X0,X1,X2] : (((in @ X2 @ X1) = $true) | ((in @ X2 @ (binunion @ X0 @ X1)) != $true) | ($true = (in @ X2 @ X0))) | (binunionE != $true)) & ((binunionE = $true) | ? [X3,X4,X5] : (((in @ X5 @ X4) != $true) & ($true = (in @ X5 @ (binunion @ X3 @ X4))) & ($true != (in @ X5 @ X3))))), 1.69/0.65 inference(rectify,[],[f2295])). 1.69/0.65 thf(f2295,plain,( 1.69/0.65 (! [X0,X1,X2] : (((in @ X2 @ X1) = $true) | ((in @ X2 @ (binunion @ X0 @ X1)) != $true) | ($true = (in @ X2 @ X0))) | (binunionE != $true)) & ((binunionE = $true) | ? [X0,X1,X2] : (((in @ X2 @ X1) != $true) & ((in @ X2 @ (binunion @ X0 @ X1)) = $true) & ($true != (in @ X2 @ X0))))), 1.69/0.65 inference(nnf_transformation,[],[f889])). 1.69/0.65 thf(f889,plain,( 1.69/0.65 ! [X0,X1,X2] : (((in @ X2 @ X1) = $true) | ((in @ X2 @ (binunion @ X0 @ X1)) != $true) | ($true = (in @ X2 @ X0))) <=> (binunionE = $true)), 1.69/0.65 inference(flattening,[],[f888])). 1.69/0.65 thf(f888,plain,( 1.69/0.65 (binunionE = $true) <=> ! [X0,X1,X2] : ((($true = (in @ X2 @ X0)) | ((in @ X2 @ X1) = $true)) | ((in @ X2 @ (binunion @ X0 @ X1)) != $true))), 1.69/0.65 inference(ennf_transformation,[],[f460])). 1.69/0.65 thf(f460,plain,( 1.69/0.65 (binunionE = $true) <=> ! [X0,X1,X2] : (((in @ X2 @ (binunion @ X0 @ X1)) = $true) => (($true = (in @ X2 @ X0)) | ((in @ X2 @ X1) = $true)))), 1.69/0.65 inference(fool_elimination,[],[f459])). 1.69/0.65 thf(f459,plain,( 1.69/0.65 (! [X0,X1,X2] : ((in @ X2 @ (binunion @ X0 @ X1)) => ((in @ X2 @ X0) | (in @ X2 @ X1))) = binunionE)), 1.69/0.65 inference(rectify,[],[f105])). 1.69/0.65 thf(f105,axiom,( 1.69/0.65 (! [X3,X4,X1] : ((in @ X1 @ (binunion @ X3 @ X4)) => ((in @ X1 @ X3) | (in @ X1 @ X4))) = binunionE)), 1.69/0.65 file('/export/starexec/sandbox/tmp/tmp.xuGTqtnLJR/Vampire---4.8_17441',binunionE)). 1.69/0.65 % SZS output end Proof for Vampire---4 1.69/0.65 % (17556)------------------------------ 1.69/0.65 % (17556)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 1.69/0.65 % (17556)Termination reason: Refutation 1.69/0.65 1.69/0.65 % (17556)Memory used [KB]: 11257 1.69/0.65 % (17556)Time elapsed: 0.202 s 1.69/0.65 % (17556)Instructions burned: 508 (million) 1.69/0.65 % (17556)------------------------------ 1.69/0.65 % (17556)------------------------------ 1.69/0.65 % (17548)Success in time 0.226 s 1.69/0.65 % Vampire---4.8 exiting 1.69/0.65 EOF