0.07/0.16 % Problem : Vampire---4.8_23783 : TPTP v0.0.0. Released v0.0.0. 0.15/0.17 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s 0.15/0.39 % Computer : n026.cluster.edu 0.15/0.39 % Model : x86_64 x86_64 0.15/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.15/0.39 % Memory : 8042.1875MB 0.15/0.39 % OS : Linux 3.10.0-693.el7.x86_64 0.15/0.39 % CPULimit : 1440 0.15/0.39 % WCLimit : 180 0.15/0.39 % DateTime : Mon Jul 3 13:07:37 EDT 2023 0.15/0.39 % CPUTime : 0.24/0.39 This is a THF_ problem 0.24/0.39 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.PGvlXuhj1t/Vampire---4.8_23783 -m 12000 -t 180 0.24/0.42 % (23898)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) 0.24/0.42 % (23893)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) 0.24/0.42 % (23894)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) 0.24/0.42 % (23895)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on Vampire---4 for (1799ds/17Mi) 0.24/0.42 % (23896)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) 0.24/0.42 % (23892)lrs+10_1:2_cnfonf=off:hud=1:inj=on:i=36:si=on:rtra=on_0 on Vampire---4 for (1799ds/36Mi) 0.24/0.42 % (23897)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) 0.24/0.42 % (23891)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on Vampire---4 for (1799ds/96Mi) 0.24/0.42 % (23897)Instruction limit reached! 0.24/0.42 % (23897)------------------------------ 0.24/0.42 % (23897)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.24/0.42 % (23897)Termination reason: Unknown 0.24/0.42 % (23897)Termination phase: shuffling 0.24/0.42 0.24/0.42 % (23897)Memory used [KB]: 1279 0.24/0.42 % (23897)Time elapsed: 0.005 s 0.24/0.42 % (23897)Instructions burned: 5 (million) 0.24/0.42 % (23897)------------------------------ 0.24/0.42 % (23897)------------------------------ 0.24/0.43 % (23895)Instruction limit reached! 0.24/0.43 % (23895)------------------------------ 0.24/0.43 % (23895)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.24/0.43 % (23895)Termination reason: Unknown 0.24/0.43 % (23895)Termination phase: shuffling 0.24/0.43 0.24/0.43 % (23895)Memory used [KB]: 1663 0.24/0.43 % (23895)Time elapsed: 0.011 s 0.24/0.43 % (23895)Instructions burned: 18 (million) 0.24/0.43 % (23895)------------------------------ 0.24/0.43 % (23895)------------------------------ 0.24/0.44 % (23893)Instruction limit reached! 0.24/0.44 % (23893)------------------------------ 0.24/0.44 % (23893)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.24/0.44 % (23893)Termination reason: Unknown 0.24/0.44 % (23893)Termination phase: Property scanning 0.24/0.44 0.24/0.44 % (23893)Memory used [KB]: 1663 0.24/0.44 % (23893)Time elapsed: 0.019 s 0.24/0.44 % (23893)Instructions burned: 35 (million) 0.24/0.44 % (23893)------------------------------ 0.24/0.44 % (23893)------------------------------ 0.24/0.44 % (23892)Instruction limit reached! 0.24/0.44 % (23892)------------------------------ 0.24/0.44 % (23892)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.24/0.44 % (23892)Termination reason: Unknown 0.24/0.44 % (23892)Termination phase: Property scanning 0.24/0.44 0.24/0.44 % (23892)Memory used [KB]: 1663 0.24/0.44 % (23892)Time elapsed: 0.019 s 0.24/0.44 % (23892)Instructions burned: 36 (million) 0.24/0.44 % (23892)------------------------------ 0.24/0.44 % (23892)------------------------------ 0.24/0.44 % (23899)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) 0.24/0.44 % (23900)lrs-3_1:1024_cbe=off:chr=on:tnu=1:i=7:si=on:rtra=on_0 on Vampire---4 for (1799ds/7Mi) 0.24/0.45 % (23900)Instruction limit reached! 0.24/0.45 % (23900)------------------------------ 0.24/0.45 % (23900)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.24/0.45 % (23900)Termination reason: Unknown 0.24/0.45 % (23900)Termination phase: shuffling 0.24/0.45 0.24/0.45 % (23900)Memory used [KB]: 1407 0.24/0.45 % (23900)Time elapsed: 0.006 s 0.24/0.45 % (23900)Instructions burned: 8 (million) 0.24/0.45 % (23900)------------------------------ 0.24/0.45 % (23900)------------------------------ 0.24/0.45 % (23899)Instruction limit reached! 0.24/0.45 % (23899)------------------------------ 0.24/0.45 % (23899)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.24/0.45 % (23899)Termination reason: Unknown 0.24/0.45 % (23899)Termination phase: shuffling 0.24/0.45 0.24/0.45 % (23899)Memory used [KB]: 1663 0.24/0.45 % (23899)Time elapsed: 0.013 s 0.24/0.45 % (23899)Instructions burned: 22 (million) 0.24/0.45 % (23899)------------------------------ 0.24/0.45 % (23899)------------------------------ 0.24/0.45 % (23901)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) 0.24/0.45 % (23902)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) 0.24/0.45 % (23896)Instruction limit reached! 0.24/0.45 % (23896)------------------------------ 0.24/0.45 % (23896)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.24/0.45 % (23896)Termination reason: Unknown 0.24/0.45 % (23896)Termination phase: Property scanning 0.24/0.45 0.24/0.45 % (23896)Memory used [KB]: 1791 0.24/0.45 % (23896)Time elapsed: 0.036 s 0.24/0.45 % (23896)Instructions burned: 75 (million) 0.24/0.46 % (23896)------------------------------ 0.24/0.46 % (23896)------------------------------ 0.24/0.46 % (23903)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) 0.24/0.46 % (23904)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) 0.24/0.47 % (23903)Instruction limit reached! 0.24/0.47 % (23903)------------------------------ 0.24/0.47 % (23903)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.24/0.47 % (23903)Termination reason: Unknown 0.24/0.47 % (23903)Termination phase: shuffling 0.24/0.47 0.24/0.47 % (23903)Memory used [KB]: 1407 0.24/0.47 % (23903)Time elapsed: 0.007 s 0.24/0.47 % (23903)Instructions burned: 10 (million) 0.24/0.47 % (23903)------------------------------ 0.24/0.47 % (23903)------------------------------ 0.24/0.47 % (23905)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) 0.24/0.47 % (23891)Instruction limit reached! 0.24/0.47 % (23891)------------------------------ 0.24/0.47 % (23891)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.24/0.47 % (23891)Termination reason: Unknown 0.24/0.47 % (23891)Termination phase: Saturation 0.24/0.47 0.24/0.47 % (23891)Memory used [KB]: 6652 0.24/0.47 % (23891)Time elapsed: 0.052 s 0.24/0.47 % (23891)Instructions burned: 96 (million) 0.24/0.47 % (23891)------------------------------ 0.24/0.47 % (23891)------------------------------ 0.24/0.48 % (23906)lrs+21_1:1_cond=on:e2e=on:i=61:si=on:rtra=on_0 on Vampire---4 for (1799ds/61Mi) 0.24/0.49 % (23902)Instruction limit reached! 0.24/0.49 % (23902)------------------------------ 0.24/0.49 % (23902)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.24/0.49 % (23902)Termination reason: Unknown 0.24/0.49 % (23902)Termination phase: Property scanning 0.24/0.49 0.24/0.49 % (23902)Memory used [KB]: 1918 0.24/0.49 % (23902)Time elapsed: 0.036 s 0.24/0.49 % (23902)Instructions burned: 72 (million) 0.24/0.49 % (23902)------------------------------ 0.24/0.49 % (23902)------------------------------ 0.24/0.50 % (23907)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=14:si=on:rtra=on_0 on Vampire---4 for (1799ds/14Mi) 0.24/0.51 % (23907)Instruction limit reached! 0.24/0.51 % (23907)------------------------------ 0.24/0.51 % (23907)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.24/0.51 % (23907)Termination reason: Unknown 0.24/0.51 % (23907)Termination phase: Property scanning 0.24/0.51 0.24/0.51 % (23907)Memory used [KB]: 1535 0.24/0.51 % (23907)Time elapsed: 0.011 s 0.24/0.51 % (23907)Instructions burned: 14 (million) 0.24/0.51 % (23907)------------------------------ 0.24/0.51 % (23907)------------------------------ 0.24/0.51 % (23908)lrs+2_5:1_cnfonf=lazy_not_be_gen:hud=10:inj=on:ntd=on:tnu=1:i=2:si=on:rtra=on_0 on Vampire---4 for (1799ds/2Mi) 0.24/0.52 % (23906)Instruction limit reached! 0.24/0.52 % (23906)------------------------------ 0.24/0.52 % (23906)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.24/0.52 % (23906)Termination reason: Unknown 0.24/0.52 % (23906)Termination phase: Property scanning 0.24/0.52 0.24/0.52 % (23906)Memory used [KB]: 2814 0.24/0.52 % (23906)Time elapsed: 0.035 s 0.24/0.52 % (23906)Instructions burned: 63 (million) 0.24/0.52 % (23906)------------------------------ 0.24/0.52 % (23906)------------------------------ 0.24/0.52 % (23908)Instruction limit reached! 0.24/0.52 % (23908)------------------------------ 0.24/0.52 % (23908)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.24/0.52 % (23908)Termination reason: Unknown 0.24/0.52 % (23908)Termination phase: shuffling 0.24/0.52 0.24/0.52 % (23908)Memory used [KB]: 1279 0.24/0.52 % (23908)Time elapsed: 0.005 s 0.24/0.52 % (23908)Instructions burned: 2 (million) 0.24/0.52 % (23908)------------------------------ 0.24/0.52 % (23908)------------------------------ 1.06/0.52 % (23909)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) 1.06/0.53 % (23911)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) 1.06/0.53 % (23905)Instruction limit reached! 1.06/0.53 % (23905)------------------------------ 1.06/0.53 % (23905)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 1.06/0.53 % (23905)Termination reason: Unknown 1.06/0.53 % (23905)Termination phase: Saturation 1.06/0.53 1.06/0.53 % (23905)Memory used [KB]: 6908 1.06/0.53 % (23905)Time elapsed: 0.064 s 1.06/0.53 % (23905)Instructions burned: 129 (million) 1.06/0.53 % (23905)------------------------------ 1.06/0.53 % (23905)------------------------------ 1.06/0.53 % (23910)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) 1.15/0.54 % (23910)Instruction limit reached! 1.15/0.54 % (23910)------------------------------ 1.15/0.54 % (23910)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 1.15/0.54 % (23910)Termination reason: Unknown 1.15/0.54 % (23910)Termination phase: shuffling 1.15/0.54 1.15/0.54 % (23910)Memory used [KB]: 1407 1.15/0.54 % (23910)Time elapsed: 0.006 s 1.15/0.54 % (23910)Instructions burned: 11 (million) 1.15/0.54 % (23910)------------------------------ 1.15/0.54 % (23910)------------------------------ 1.15/0.54 % (23912)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) 1.15/0.55 % (23913)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) 1.15/0.55 % (23912)Instruction limit reached! 1.15/0.55 % (23912)------------------------------ 1.15/0.55 % (23912)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 1.15/0.55 % (23912)Termination reason: Unknown 1.15/0.55 % (23912)Termination phase: Property scanning 1.15/0.55 1.15/0.55 % (23912)Memory used [KB]: 1791 1.15/0.55 % (23912)Time elapsed: 0.011 s 1.15/0.55 % (23912)Instructions burned: 29 (million) 1.15/0.55 % (23912)------------------------------ 1.15/0.55 % (23912)------------------------------ 1.15/0.56 % (23914)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) 1.15/0.57 % (23913)Instruction limit reached! 1.15/0.57 % (23913)------------------------------ 1.15/0.57 % (23913)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 1.15/0.57 % (23913)Termination reason: Unknown 1.15/0.57 % (23913)Termination phase: Function definition elimination 1.15/0.57 1.15/0.57 % (23913)Memory used [KB]: 1791 1.15/0.57 % (23913)Time elapsed: 0.017 s 1.15/0.57 % (23913)Instructions burned: 56 (million) 1.15/0.57 % (23913)------------------------------ 1.15/0.57 % (23913)------------------------------ 1.15/0.57 % (23911)Instruction limit reached! 1.15/0.57 % (23911)------------------------------ 1.15/0.57 % (23911)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 1.15/0.57 % (23911)Termination reason: Unknown 1.15/0.57 % (23911)Termination phase: Saturation 1.15/0.57 1.15/0.57 % (23911)Memory used [KB]: 6652 1.15/0.57 % (23911)Time elapsed: 0.043 s 1.15/0.57 % (23911)Instructions burned: 140 (million) 1.15/0.57 % (23911)------------------------------ 1.15/0.57 % (23911)------------------------------ 1.15/0.57 % (23915)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) 1.15/0.58 % (23915)Instruction limit reached! 1.15/0.58 % (23915)------------------------------ 1.15/0.58 % (23915)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 1.15/0.58 % (23915)Termination reason: Unknown 1.15/0.58 % (23915)Termination phase: shuffling 1.15/0.58 1.15/0.58 % (23915)Memory used [KB]: 1279 1.15/0.58 % (23915)Time elapsed: 0.003 s 1.15/0.58 % (23915)Instructions burned: 6 (million) 1.15/0.58 % (23915)------------------------------ 1.15/0.58 % (23915)------------------------------ 1.15/0.58 % (23916)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) 1.15/0.58 % (23916)Instruction limit reached! 1.15/0.58 % (23916)------------------------------ 1.15/0.58 % (23916)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 1.15/0.58 % (23916)Termination reason: Unknown 1.15/0.58 % (23916)Termination phase: shuffling 1.15/0.58 1.15/0.58 % (23916)Memory used [KB]: 1663 1.15/0.58 % (23916)Time elapsed: 0.007 s 1.15/0.58 % (23916)Instructions burned: 21 (million) 1.15/0.58 % (23916)------------------------------ 1.15/0.58 % (23916)------------------------------ 1.15/0.58 % (23917)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) 1.15/0.59 % (23918)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) 1.15/0.60 % (23917)Instruction limit reached! 1.15/0.60 % (23917)------------------------------ 1.15/0.60 % (23917)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 1.15/0.60 % (23917)Termination reason: Unknown 1.15/0.60 % (23917)Termination phase: SInE selection 1.15/0.60 1.15/0.60 % (23917)Memory used [KB]: 1791 1.15/0.60 % (23917)Time elapsed: 0.013 s 1.15/0.60 % (23917)Instructions burned: 44 (million) 1.15/0.60 % (23917)------------------------------ 1.15/0.60 % (23917)------------------------------ 1.15/0.60 % (23894)Instruction limit reached! 1.15/0.60 % (23894)------------------------------ 1.15/0.60 % (23894)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 1.15/0.60 % (23894)Termination reason: Unknown 1.15/0.60 % (23894)Termination phase: Saturation 1.15/0.60 1.15/0.60 % (23894)Memory used [KB]: 7931 1.15/0.60 % (23894)Time elapsed: 0.179 s 1.15/0.60 % (23894)Instructions burned: 385 (million) 1.15/0.60 % (23894)------------------------------ 1.15/0.60 % (23894)------------------------------ 1.15/0.60 % (23919)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) 1.15/0.61 % (23920)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) 1.15/0.62 % (23919)Instruction limit reached! 1.15/0.62 % (23919)------------------------------ 1.15/0.62 % (23919)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 1.15/0.62 % (23919)Termination reason: Unknown 1.15/0.62 % (23919)Termination phase: Property scanning 1.15/0.62 1.15/0.62 % (23919)Memory used [KB]: 1918 1.15/0.62 % (23919)Time elapsed: 0.018 s 1.15/0.62 % (23919)Instructions burned: 65 (million) 1.15/0.62 % (23919)------------------------------ 1.15/0.62 % (23919)------------------------------ 1.15/0.63 % (23921)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 % (23921)Instruction limit reached! 1.69/0.63 % (23921)------------------------------ 1.69/0.63 % (23921)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 1.69/0.63 % (23921)Termination reason: Unknown 1.69/0.63 % (23921)Termination phase: shuffling 1.69/0.63 1.69/0.63 % (23921)Memory used [KB]: 1279 1.69/0.63 % (23921)Time elapsed: 0.003 s 1.69/0.63 % (23921)Instructions burned: 4 (million) 1.69/0.63 % (23921)------------------------------ 1.69/0.63 % (23921)------------------------------ 1.69/0.64 % (23920)Instruction limit reached! 1.69/0.64 % (23920)------------------------------ 1.69/0.64 % (23920)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 1.69/0.64 % (23920)Termination reason: Unknown 1.69/0.64 % (23920)Termination phase: Saturation 1.69/0.64 1.69/0.64 % (23920)Memory used [KB]: 6652 1.69/0.64 % (23920)Time elapsed: 0.031 s 1.69/0.64 % (23920)Instructions burned: 106 (million) 1.69/0.64 % (23920)------------------------------ 1.69/0.64 % (23920)------------------------------ 1.69/0.64 % (23922)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 % (23923)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on Vampire---4 for (1797ds/3Mi) 1.69/0.65 % (23923)Instruction limit reached! 1.69/0.65 % (23923)------------------------------ 1.69/0.65 % (23923)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 1.69/0.65 % (23923)Termination reason: Unknown 1.69/0.65 % (23923)Termination phase: shuffling 1.69/0.65 1.69/0.65 % (23923)Memory used [KB]: 1279 1.69/0.65 % (23923)Time elapsed: 0.002 s 1.69/0.65 % (23923)Instructions burned: 3 (million) 1.69/0.65 % (23923)------------------------------ 1.69/0.65 % (23923)------------------------------ 1.69/0.65 % (23918)Instruction limit reached! 1.69/0.65 % (23918)------------------------------ 1.69/0.65 % (23918)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 1.69/0.65 % (23918)Termination reason: Unknown 1.69/0.65 % (23918)Termination phase: Saturation 1.69/0.65 1.69/0.65 % (23918)Memory used [KB]: 7419 1.69/0.65 % (23918)Time elapsed: 0.057 s 1.69/0.65 % (23918)Instructions burned: 193 (million) 1.69/0.65 % (23918)------------------------------ 1.69/0.65 % (23918)------------------------------ 1.69/0.65 % (23914)Instruction limit reached! 1.69/0.65 % (23914)------------------------------ 1.69/0.65 % (23914)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 1.69/0.65 % (23914)Termination reason: Unknown 1.69/0.65 % (23914)Termination phase: Saturation 1.69/0.65 1.69/0.65 % (23914)Memory used [KB]: 8187 1.69/0.65 % (23914)Time elapsed: 0.093 s 1.69/0.65 % (23914)Instructions burned: 275 (million) 1.69/0.65 % (23914)------------------------------ 1.69/0.65 % (23914)------------------------------ 1.69/0.65 % (23924)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on Vampire---4 for (1797ds/4Mi) 1.69/0.66 % (23924)Instruction limit reached! 1.69/0.66 % (23924)------------------------------ 1.69/0.66 % (23924)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 1.69/0.66 % (23924)Termination reason: Unknown 1.69/0.66 % (23924)Termination phase: shuffling 1.69/0.66 % (23925)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on Vampire---4 for (1797ds/149Mi) 1.69/0.66 1.69/0.66 % (23924)Memory used [KB]: 1279 1.69/0.66 % (23924)Time elapsed: 0.003 s 1.69/0.66 % (23924)Instructions burned: 6 (million) 1.69/0.66 % (23924)------------------------------ 1.69/0.66 % (23924)------------------------------ 1.69/0.66 % (23926)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on Vampire---4 for (1797ds/150Mi) 1.69/0.66 % (23927)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=199:si=on:rtra=on_0 on Vampire---4 for (1797ds/199Mi) 2.09/0.70 % (23922)Instruction limit reached! 2.09/0.70 % (23922)------------------------------ 2.09/0.70 % (23922)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 2.09/0.70 % (23922)Termination reason: Unknown 2.09/0.70 % (23922)Termination phase: Saturation 2.09/0.70 2.09/0.70 % (23922)Memory used [KB]: 6652 2.09/0.70 % (23922)Time elapsed: 0.060 s 2.09/0.70 % (23922)Instructions burned: 238 (million) 2.09/0.70 % (23922)------------------------------ 2.09/0.70 % (23922)------------------------------ 2.09/0.70 % (23925)Instruction limit reached! 2.09/0.70 % (23925)------------------------------ 2.09/0.70 % (23925)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 2.09/0.70 % (23925)Termination reason: Unknown 2.09/0.70 % (23925)Termination phase: Saturation 2.09/0.70 2.09/0.70 % (23925)Memory used [KB]: 7164 2.09/0.70 % (23925)Time elapsed: 0.047 s 2.09/0.70 % (23925)Instructions burned: 149 (million) 2.09/0.70 % (23925)------------------------------ 2.09/0.70 % (23925)------------------------------ 2.09/0.71 % (23928)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on Vampire---4 for (1796ds/39Mi) 2.09/0.71 % (23926)Instruction limit reached! 2.09/0.71 % (23926)------------------------------ 2.09/0.71 % (23926)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 2.09/0.71 % (23926)Termination reason: Unknown 2.09/0.71 % (23926)Termination phase: Saturation 2.09/0.71 2.09/0.71 % (23926)Memory used [KB]: 7803 2.09/0.71 % (23926)Time elapsed: 0.049 s 2.09/0.71 % (23926)Instructions burned: 152 (million) 2.09/0.71 % (23926)------------------------------ 2.09/0.71 % (23926)------------------------------ 2.09/0.71 % (23929)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=721:si=on:rtra=on_0 on Vampire---4 for (1796ds/721Mi) 2.09/0.72 % (23930)lrs+1002_1:8_av=off:fd=off:hud=5:tnu=1:i=3:si=on:rtra=on_0 on Vampire---4 for (1796ds/3Mi) 2.09/0.72 % (23928)Instruction limit reached! 2.09/0.72 % (23928)------------------------------ 2.09/0.72 % (23928)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 2.09/0.72 % (23928)Termination reason: Unknown 2.09/0.72 % (23928)Termination phase: Property scanning 2.09/0.72 2.09/0.72 % (23928)Memory used [KB]: 1918 2.09/0.72 % (23928)Time elapsed: 0.013 s 2.09/0.72 % (23928)Instructions burned: 40 (million) 2.09/0.72 % (23928)------------------------------ 2.09/0.72 % (23928)------------------------------ 2.09/0.72 % (23930)Instruction limit reached! 2.09/0.72 % (23930)------------------------------ 2.09/0.72 % (23930)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 2.09/0.72 % (23930)Termination reason: Unknown 2.09/0.72 % (23930)Termination phase: shuffling 2.09/0.72 2.09/0.72 % (23930)Memory used [KB]: 1279 2.09/0.72 % (23930)Time elapsed: 0.003 s 2.09/0.72 % (23930)Instructions burned: 5 (million) 2.09/0.72 % (23930)------------------------------ 2.09/0.72 % (23930)------------------------------ 2.09/0.73 % (23931)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on Vampire---4 for (1796ds/18Mi) 2.09/0.73 % (23927)Instruction limit reached! 2.09/0.73 % (23927)------------------------------ 2.09/0.73 % (23927)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 2.09/0.73 % (23927)Termination reason: Unknown 2.09/0.73 % (23927)Termination phase: Saturation 2.09/0.73 2.09/0.73 % (23927)Memory used [KB]: 6908 2.09/0.73 % (23927)Time elapsed: 0.066 s 2.09/0.73 % (23927)Instructions burned: 201 (million) 2.09/0.73 % (23927)------------------------------ 2.09/0.73 % (23927)------------------------------ 2.09/0.73 % (23932)lrs+10_1:1_au=on:c=on:sac=on:slsq=on:slsqc=2:i=218:si=on:rtra=on_0 on Vampire---4 for (1796ds/218Mi) 2.09/0.73 % (23931)Instruction limit reached! 2.09/0.73 % (23931)------------------------------ 2.09/0.73 % (23931)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 2.09/0.73 % (23931)Termination reason: Unknown 2.09/0.73 % (23931)Termination phase: shuffling 2.09/0.73 2.09/0.73 % (23931)Memory used [KB]: 1663 2.09/0.73 % (23931)Time elapsed: 0.007 s 2.09/0.73 % (23931)Instructions burned: 20 (million) 2.09/0.73 % (23931)------------------------------ 2.09/0.73 % (23931)------------------------------ 2.09/0.74 % (23933)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on Vampire---4 for (1796ds/448Mi) 2.09/0.74 % (23934)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on Vampire---4 for (1796ds/6Mi) 2.09/0.74 % (23934)Instruction limit reached! 2.09/0.74 % (23934)------------------------------ 2.09/0.74 % (23934)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 2.09/0.74 % (23934)Termination reason: Unknown 2.09/0.74 % (23934)Termination phase: shuffling 2.09/0.74 2.09/0.74 % (23934)Memory used [KB]: 1279 2.09/0.74 % (23934)Time elapsed: 0.003 s 2.09/0.74 % (23934)Instructions burned: 6 (million) 2.09/0.74 % (23934)------------------------------ 2.09/0.74 % (23934)------------------------------ 2.59/0.75 % (23935)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=9:si=on:rtra=on_0 on Vampire---4 for (1796ds/9Mi) 2.59/0.76 % (23935)Instruction limit reached! 2.59/0.76 % (23935)------------------------------ 2.59/0.76 % (23935)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 2.59/0.76 % (23935)Termination reason: Unknown 2.59/0.76 % (23935)Termination phase: shuffling 2.59/0.76 2.59/0.76 % (23935)Memory used [KB]: 1407 2.59/0.76 % (23935)Time elapsed: 0.005 s 2.59/0.76 % (23935)Instructions burned: 11 (million) 2.59/0.76 % (23935)------------------------------ 2.59/0.76 % (23935)------------------------------ 2.63/0.77 % (23936)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on Vampire---4 for (1796ds/16Mi) 2.63/0.77 % (23936)Instruction limit reached! 2.63/0.77 % (23936)------------------------------ 2.63/0.77 % (23936)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 2.63/0.77 % (23936)Termination reason: Unknown 2.63/0.77 % (23936)Termination phase: shuffling 2.63/0.77 2.63/0.77 % (23936)Memory used [KB]: 1535 2.63/0.77 % (23936)Time elapsed: 0.007 s 2.63/0.77 % (23936)Instructions burned: 18 (million) 2.63/0.77 % (23936)------------------------------ 2.63/0.77 % (23936)------------------------------ 2.63/0.78 % (23937)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=40:si=on:rtra=on_0 on Vampire---4 for (1796ds/40Mi) 2.63/0.79 % (23909)Instruction limit reached! 2.63/0.79 % (23909)------------------------------ 2.63/0.79 % (23909)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 2.63/0.79 % (23909)Termination reason: Unknown 2.63/0.79 % (23909)Termination phase: Saturation 2.63/0.79 2.63/0.79 % (23909)Memory used [KB]: 9466 2.63/0.79 % (23909)Time elapsed: 0.270 s 2.63/0.79 % (23909)Instructions burned: 1044 (million) 2.63/0.79 % (23909)------------------------------ 2.63/0.79 % (23909)------------------------------ 2.63/0.79 % (23932)Instruction limit reached! 2.63/0.79 % (23932)------------------------------ 2.63/0.79 % (23932)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 2.63/0.79 % (23932)Termination reason: Unknown 2.63/0.79 % (23932)Termination phase: Saturation 2.63/0.79 2.63/0.79 % (23932)Memory used [KB]: 7547 2.63/0.79 % (23932)Time elapsed: 0.066 s 2.63/0.79 % (23932)Instructions burned: 219 (million) 2.63/0.79 % (23932)------------------------------ 2.63/0.79 % (23932)------------------------------ 2.63/0.80 % (23937)Instruction limit reached! 2.63/0.80 % (23937)------------------------------ 2.63/0.80 % (23937)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 2.63/0.80 % (23937)Termination reason: Unknown 2.63/0.80 % (23937)Termination phase: SInE selection 2.63/0.80 2.63/0.80 % (23937)Memory used [KB]: 1791 2.63/0.80 % (23937)Time elapsed: 0.018 s 2.63/0.80 % (23937)Instructions burned: 43 (million) 2.63/0.80 % (23937)------------------------------ 2.63/0.80 % (23937)------------------------------ 3.15/0.80 % (23938)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on Vampire---4 for (1796ds/2Mi) 3.15/0.80 % (23939)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on Vampire---4 for (1796ds/98Mi) 3.15/0.80 % (23938)Instruction limit reached! 3.15/0.80 % (23938)------------------------------ 3.15/0.80 % (23938)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 3.15/0.80 % (23938)Termination reason: Unknown 3.15/0.80 % (23938)Termination phase: shuffling 3.15/0.80 3.15/0.80 % (23938)Memory used [KB]: 1151 3.15/0.80 % (23938)Time elapsed: 0.002 s 3.15/0.80 % (23938)Instructions burned: 2 (million) 3.15/0.80 % (23938)------------------------------ 3.15/0.80 % (23938)------------------------------ 3.15/0.81 % (23898)Instruction limit reached! 3.15/0.81 % (23898)------------------------------ 3.15/0.81 % (23898)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 3.15/0.81 % (23898)Termination reason: Unknown 3.15/0.81 % (23898)Termination phase: Saturation 3.15/0.81 3.15/0.81 % (23898)Memory used [KB]: 9722 3.15/0.81 % (23898)Time elapsed: 0.388 s 3.15/0.81 % (23898)Instructions burned: 916 (million) 3.15/0.81 % (23898)------------------------------ 3.15/0.81 % (23898)------------------------------ 3.15/0.81 % (23940)lrs+1004_1:1_chr=on:prag=on:i=8:si=on:rtra=on_0 on Vampire---4 for (1796ds/8Mi) 3.15/0.81 % (23940)Instruction limit reached! 3.15/0.81 % (23940)------------------------------ 3.15/0.81 % (23940)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 3.15/0.81 % (23940)Termination reason: Unknown 3.15/0.81 % (23940)Termination phase: shuffling 3.15/0.81 3.15/0.81 % (23940)Memory used [KB]: 1407 3.15/0.81 % (23940)Time elapsed: 0.004 s 3.15/0.81 % (23940)Instructions burned: 9 (million) 3.15/0.81 % (23940)------------------------------ 3.15/0.81 % (23940)------------------------------ 3.15/0.81 % (23942)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on Vampire---4 for (1795ds/3Mi) 3.15/0.82 % (23941)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on Vampire---4 for (1795ds/86Mi) 3.15/0.82 % (23942)Instruction limit reached! 3.15/0.82 % (23942)------------------------------ 3.15/0.82 % (23942)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 3.15/0.82 % (23942)Termination reason: Unknown 3.15/0.82 % (23942)Termination phase: shuffling 3.15/0.82 3.15/0.82 % (23942)Memory used [KB]: 1279 3.15/0.82 % (23942)Time elapsed: 0.003 s 3.15/0.82 % (23942)Instructions burned: 4 (million) 3.15/0.82 % (23942)------------------------------ 3.15/0.82 % (23942)------------------------------ 3.15/0.82 % (23943)lrs+1010_1:1024_au=on:hud=10:ntd=on:ss=included:i=294:si=on:rtra=on_0 on Vampire---4 for (1795ds/294Mi) 3.15/0.82 % (23944)lrs+1010_1:6_au=on:cnfonf=conj_eager:nwc=10.0:pe=on:prag=on:s2a=on:ss=axioms:st=1.5:i=274:si=on:rtra=on_0 on Vampire---4 for (1795ds/274Mi) 3.15/0.83 % (23939)Instruction limit reached! 3.15/0.83 % (23939)------------------------------ 3.15/0.83 % (23939)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 3.15/0.83 % (23939)Termination reason: Unknown 3.15/0.83 % (23939)Termination phase: Saturation 3.15/0.83 3.15/0.83 % (23939)Memory used [KB]: 2046 3.15/0.83 % (23939)Time elapsed: 0.027 s 3.15/0.83 % (23939)Instructions burned: 98 (million) 3.15/0.83 % (23939)------------------------------ 3.15/0.83 % (23939)------------------------------ 3.29/0.84 % (23945)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on Vampire---4 for (1795ds/47Mi) 3.29/0.84 % (23933)Instruction limit reached! 3.29/0.84 % (23933)------------------------------ 3.29/0.84 % (23933)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 3.29/0.84 % (23933)Termination reason: Unknown 3.29/0.84 % (23933)Termination phase: Saturation 3.29/0.84 3.29/0.84 % (23933)Memory used [KB]: 6652 3.29/0.84 % (23933)Time elapsed: 0.106 s 3.29/0.84 % (23933)Instructions burned: 449 (million) 3.29/0.84 % (23933)------------------------------ 3.29/0.84 % (23933)------------------------------ 3.29/0.85 % (23945)Instruction limit reached! 3.29/0.85 % (23945)------------------------------ 3.29/0.85 % (23945)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 3.29/0.85 % (23945)Termination reason: Unknown 3.29/0.85 % (23945)Termination phase: Property scanning 3.29/0.85 3.29/0.85 % (23945)Memory used [KB]: 1918 3.29/0.85 % (23945)Time elapsed: 0.015 s 3.29/0.85 % (23945)Instructions burned: 49 (million) 3.29/0.85 % (23945)------------------------------ 3.29/0.85 % (23945)------------------------------ 3.29/0.85 % (23946)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on Vampire---4 for (1795ds/37Mi) 3.29/0.86 % (23941)Instruction limit reached! 3.29/0.86 % (23941)------------------------------ 3.29/0.86 % (23941)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 3.29/0.86 % (23941)Termination reason: Unknown 3.29/0.86 % (23941)Termination phase: Saturation 3.29/0.86 3.29/0.86 % (23941)Memory used [KB]: 6524 3.29/0.86 % (23941)Time elapsed: 0.028 s 3.29/0.86 % (23941)Instructions burned: 87 (million) 3.29/0.86 % (23941)------------------------------ 3.29/0.86 % (23941)------------------------------ 3.29/0.86 % (23947)lrs+1002_1:16_av=off:e2e=on:fe=axiom:prag=on:sos=on:ss=axioms:i=3:si=on:rtra=on_0 on Vampire---4 for (1795ds/3Mi) 3.29/0.86 % (23947)Instruction limit reached! 3.29/0.86 % (23947)------------------------------ 3.29/0.86 % (23947)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 3.29/0.86 % (23947)Termination reason: Unknown 3.29/0.86 % (23947)Termination phase: shuffling 3.29/0.86 3.29/0.86 % (23947)Memory used [KB]: 1279 3.29/0.86 % (23947)Time elapsed: 0.002 s 3.29/0.86 % (23947)Instructions burned: 3 (million) 3.29/0.86 % (23947)------------------------------ 3.29/0.86 % (23947)------------------------------ 3.29/0.86 % (23946)Instruction limit reached! 3.29/0.86 % (23946)------------------------------ 3.29/0.86 % (23946)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 3.29/0.86 % (23946)Termination reason: Unknown 3.29/0.86 % (23946)Termination phase: Property scanning 3.29/0.86 3.29/0.86 % (23946)Memory used [KB]: 1791 3.29/0.86 % (23946)Time elapsed: 0.012 s 3.29/0.86 % (23946)Instructions burned: 39 (million) 3.29/0.86 % (23946)------------------------------ 3.29/0.86 % (23946)------------------------------ 3.29/0.87 % (23953)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:i=5:si=on:rtra=on_0 on Vampire---4 for (1795ds/5Mi) 3.29/0.87 % (23901)Instruction limit reached! 3.29/0.87 % (23901)------------------------------ 3.29/0.87 % (23901)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 3.29/0.87 % (23901)Termination reason: Unknown 3.29/0.87 % (23901)Termination phase: Saturation 3.29/0.87 3.29/0.87 % (23901)Memory used [KB]: 10362 3.29/0.87 % (23901)Time elapsed: 0.420 s 3.29/0.87 % (23901)Instructions burned: 1021 (million) 3.29/0.87 % (23901)------------------------------ 3.29/0.87 % (23901)------------------------------ 3.29/0.87 % (23953)Instruction limit reached! 3.29/0.87 % (23953)------------------------------ 3.29/0.87 % (23953)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 3.29/0.87 % (23953)Termination reason: Unknown 3.29/0.87 % (23953)Termination phase: shuffling 3.29/0.87 3.29/0.87 % (23953)Memory used [KB]: 1279 3.29/0.87 % (23953)Time elapsed: 0.003 s 3.29/0.87 % (23953)Instructions burned: 6 (million) 3.29/0.87 % (23953)------------------------------ 3.29/0.87 % (23953)------------------------------ 3.29/0.87 % (23954)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=44:si=on:rtra=on_0 on Vampire---4 for (1795ds/44Mi) 3.29/0.87 % (23952)lrs+10_8:1_au=on:e2e=on:hfsq=on:hfsqc=1:ins=3:s2a=on:s2at=3.0:ss=axioms:i=19:si=on:rtra=on_0 on Vampire---4 for (1795ds/19Mi) 3.29/0.88 % (23955)ott+21_1:3_bd=off:cnfonf=lazy_gen:fe=off:hfsq=on:hfsqc=3:hud=10:ixr=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=450:si=on:rtra=on_0 on Vampire---4 for (1795ds/450Mi) 3.29/0.88 % (23956)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=102:si=on:rtra=on_0 on Vampire---4 for (1795ds/102Mi) 3.29/0.88 % (23952)Instruction limit reached! 3.29/0.88 % (23952)------------------------------ 3.29/0.88 % (23952)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 3.29/0.88 % (23952)Termination reason: Unknown 3.29/0.88 % (23952)Termination phase: Property scanning 3.29/0.88 3.29/0.88 % (23952)Memory used [KB]: 1535 3.29/0.88 % (23952)Time elapsed: 0.010 s 3.29/0.88 % (23952)Instructions burned: 19 (million) 3.29/0.88 % (23952)------------------------------ 3.29/0.88 % (23952)------------------------------ 3.29/0.88 % (23954)Instruction limit reached! 3.29/0.88 % (23954)------------------------------ 3.29/0.88 % (23954)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 3.29/0.88 % (23954)Termination reason: Unknown 3.29/0.88 % (23954)Termination phase: Property scanning 3.29/0.88 3.29/0.88 % (23954)Memory used [KB]: 1791 3.29/0.88 % (23954)Time elapsed: 0.013 s 3.29/0.88 % (23954)Instructions burned: 47 (million) 3.29/0.88 % (23954)------------------------------ 3.29/0.88 % (23954)------------------------------ 3.29/0.89 % (23958)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on Vampire---4 for (1795ds/204Mi) 3.29/0.89 % (23957)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on Vampire---4 for (1795ds/134Mi) 3.29/0.90 % (23904)Refutation not found, non-redundant clauses discarded% (23904)------------------------------ 3.29/0.90 % (23904)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 3.29/0.90 % (23904)Termination reason: Refutation not found, non-redundant clauses discarded 3.29/0.90 3.29/0.90 % (23904)Memory used [KB]: 8443 3.29/0.90 % (23904)Time elapsed: 0.435 s 3.29/0.90 % (23904)Instructions burned: 1013 (million) 3.29/0.90 % (23904)------------------------------ 3.29/0.90 % (23904)------------------------------ 3.29/0.90 % (23944)Instruction limit reached! 3.29/0.90 % (23944)------------------------------ 3.29/0.90 % (23944)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 3.29/0.90 % (23944)Termination reason: Unknown 3.29/0.90 % (23944)Termination phase: Saturation 3.29/0.90 3.29/0.90 % (23944)Memory used [KB]: 7036 3.29/0.90 % (23944)Time elapsed: 0.080 s 3.29/0.90 % (23944)Instructions burned: 276 (million) 3.29/0.90 % (23944)------------------------------ 3.29/0.90 % (23944)------------------------------ 3.29/0.91 % (23956)Instruction limit reached! 3.29/0.91 % (23956)------------------------------ 3.29/0.91 % (23956)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 3.29/0.91 % (23956)Termination reason: Unknown 3.29/0.91 % (23956)Termination phase: Saturation 3.29/0.91 3.29/0.91 % (23956)Memory used [KB]: 7547 3.29/0.91 % (23956)Time elapsed: 0.030 s 3.29/0.91 % (23956)Instructions burned: 104 (million) 3.29/0.91 % (23956)------------------------------ 3.29/0.91 % (23956)------------------------------ 3.29/0.91 % (23943)Instruction limit reached! 3.29/0.91 % (23943)------------------------------ 3.29/0.91 % (23943)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 3.29/0.91 % (23943)Termination reason: Unknown 3.29/0.91 % (23943)Termination phase: Saturation 3.29/0.91 3.29/0.91 % (23943)Memory used [KB]: 7803 3.29/0.91 % (23943)Time elapsed: 0.090 s 3.29/0.91 % (23943)Instructions burned: 295 (million) 3.29/0.91 % (23943)------------------------------ 3.29/0.91 % (23943)------------------------------ 3.29/0.91 % (23959)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on Vampire---4 for (1795ds/154Mi) 3.29/0.91 % (23960)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=424:si=on:rtra=on_0 on Vampire---4 for (1795ds/424Mi) 3.29/0.92 % (23961)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on Vampire---4 for (1795ds/41Mi) 3.29/0.92 % (23962)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on Vampire---4 for (1795ds/231Mi) 3.29/0.93 % (23961)Instruction limit reached! 3.29/0.93 % (23961)------------------------------ 3.29/0.93 % (23961)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 3.29/0.93 % (23961)Termination reason: Unknown 3.29/0.93 % (23961)Termination phase: Property scanning 3.29/0.93 3.29/0.93 % (23961)Memory used [KB]: 1791 3.29/0.93 % (23961)Time elapsed: 0.012 s 3.29/0.93 % (23961)Instructions burned: 42 (million) 3.29/0.93 % (23961)------------------------------ 3.29/0.93 % (23961)------------------------------ 3.87/0.93 % (23963)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=70:si=on:rtra=on_0 on Vampire---4 for (1794ds/70Mi) 3.87/0.95 % (23958)Instruction limit reached! 3.87/0.95 % (23958)------------------------------ 3.87/0.95 % (23958)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 3.87/0.95 % (23958)Termination reason: Unknown 3.87/0.95 % (23958)Termination phase: Saturation 3.87/0.95 3.87/0.95 % (23958)Memory used [KB]: 7419 3.87/0.95 % (23958)Time elapsed: 0.057 s 3.87/0.95 % (23958)Instructions burned: 206 (million) 3.87/0.95 % (23958)------------------------------ 3.87/0.95 % (23958)------------------------------ 3.87/0.95 % (23959)Instruction limit reached! 3.87/0.95 % (23959)------------------------------ 3.87/0.95 % (23959)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 3.87/0.95 % (23959)Termination reason: Unknown 3.87/0.95 % (23959)Termination phase: Saturation 3.87/0.95 3.87/0.95 % (23959)Memory used [KB]: 6524 3.87/0.95 % (23959)Time elapsed: 0.038 s 3.87/0.95 % (23959)Instructions burned: 156 (million) 3.87/0.95 % (23959)------------------------------ 3.87/0.95 % (23959)------------------------------ 3.87/0.95 % (23929)Instruction limit reached! 3.87/0.95 % (23929)------------------------------ 3.87/0.95 % (23929)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 3.87/0.95 % (23929)Termination reason: Unknown 3.87/0.95 % (23929)Termination phase: Saturation 3.87/0.95 3.87/0.95 % (23929)Memory used [KB]: 9722 3.87/0.95 % (23929)Time elapsed: 0.240 s 3.87/0.95 % (23929)Instructions burned: 722 (million) 3.87/0.95 % (23929)------------------------------ 3.87/0.95 % (23929)------------------------------ 3.87/0.95 % (23957)Instruction limit reached! 3.87/0.95 % (23957)------------------------------ 3.87/0.95 % (23957)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 3.87/0.95 % (23957)Termination reason: Unknown 3.87/0.95 % (23957)Termination phase: Saturation 3.87/0.95 3.87/0.95 % (23957)Memory used [KB]: 6908 3.87/0.95 % (23957)Time elapsed: 0.059 s 3.87/0.95 % (23957)Instructions burned: 135 (million) 3.87/0.95 % (23957)------------------------------ 3.87/0.95 % (23957)------------------------------ 3.87/0.95 % (23963)Instruction limit reached! 3.87/0.95 % (23963)------------------------------ 3.87/0.95 % (23963)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 3.87/0.95 % (23963)Termination reason: Unknown 3.87/0.95 % (23963)Termination phase: Property scanning 3.87/0.95 3.87/0.95 % (23963)Memory used [KB]: 1918 3.87/0.95 % (23963)Time elapsed: 0.019 s 3.87/0.95 % (23963)Instructions burned: 73 (million) 3.87/0.95 % (23963)------------------------------ 3.87/0.95 % (23963)------------------------------ 3.87/0.95 % (23964)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=297:si=on:rtra=on_0 on Vampire---4 for (1794ds/297Mi) 3.87/0.95 % (23965)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on Vampire---4 for (1794ds/182Mi) 3.87/0.96 % (23966)lrs+1010_1:1024_au=on:fe=axiom:lwlo=on:nm=0:ntd=on:nwc=10.0:spb=non_intro:uhcvi=on:i=130:si=on:rtra=on_0 on Vampire---4 for (1794ds/130Mi) 3.87/0.96 % (23968)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on Vampire---4 for (1794ds/297Mi) 3.87/0.96 % (23967)lrs+21_1:16_au=on:cbe=off:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=7,4:i=570:si=on:rtra=on_0 on Vampire---4 for (1794ds/570Mi) 3.87/0.98 % (23962)Instruction limit reached! 3.87/0.98 % (23962)------------------------------ 3.87/0.98 % (23962)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 3.87/0.98 % (23962)Termination reason: Unknown 3.87/0.98 % (23962)Termination phase: Saturation 3.87/0.98 3.87/0.98 % (23962)Memory used [KB]: 10874 3.87/0.98 % (23962)Time elapsed: 0.067 s 3.87/0.98 % (23962)Instructions burned: 231 (million) 3.87/0.98 % (23962)------------------------------ 3.87/0.98 % (23962)------------------------------ 4.40/0.99 % (23969)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=190:si=on:rtra=on_0 on Vampire---4 for (1794ds/190Mi) 4.40/0.99 % (23966)Instruction limit reached! 4.40/0.99 % (23966)------------------------------ 4.40/0.99 % (23966)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 4.40/0.99 % (23966)Termination reason: Unknown 4.40/0.99 % (23966)Termination phase: Saturation 4.40/0.99 4.40/0.99 % (23966)Memory used [KB]: 6908 4.40/0.99 % (23966)Time elapsed: 0.035 s 4.40/0.99 % (23966)Instructions burned: 132 (million) 4.40/0.99 % (23966)------------------------------ 4.40/0.99 % (23966)------------------------------ 4.40/1.00 % (23970)dis+1003_1:64_cha=on:cnfonf=lazy_gen:hud=9:nwc=8.0:prag=on:i=96:si=on:rtra=on_0 on Vampire---4 for (1794ds/96Mi) 4.40/1.00 % (23955)Instruction limit reached! 4.40/1.00 % (23955)------------------------------ 4.40/1.00 % (23955)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 4.40/1.00 % (23955)Termination reason: Unknown 4.40/1.00 % (23955)Termination phase: Saturation 4.40/1.00 4.40/1.00 % (23955)Memory used [KB]: 7675 4.40/1.00 % (23955)Time elapsed: 0.123 s 4.40/1.00 % (23955)Instructions burned: 451 (million) 4.40/1.00 % (23955)------------------------------ 4.40/1.00 % (23955)------------------------------ 4.40/1.00 % (23965)Instruction limit reached! 4.40/1.00 % (23965)------------------------------ 4.40/1.00 % (23965)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 4.40/1.00 % (23965)Termination reason: Unknown 4.40/1.00 % (23965)Termination phase: Saturation 4.40/1.00 4.40/1.00 % (23965)Memory used [KB]: 7419 4.40/1.00 % (23965)Time elapsed: 0.050 s 4.40/1.00 % (23965)Instructions burned: 183 (million) 4.40/1.00 % (23965)------------------------------ 4.40/1.00 % (23965)------------------------------ 4.40/1.01 % (23972)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on Vampire---4 for (1793ds/368Mi) 4.40/1.01 % (23971)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on Vampire---4 for (1793ds/182Mi) 4.40/1.02 % (23970)Instruction limit reached! 4.40/1.02 % (23970)------------------------------ 4.40/1.02 % (23970)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 4.40/1.02 % (23970)Termination reason: Unknown 4.40/1.02 % (23970)Termination phase: Saturation 4.40/1.02 4.40/1.02 % (23970)Memory used [KB]: 6524 4.40/1.02 % (23970)Time elapsed: 0.025 s 4.40/1.02 % (23970)Instructions burned: 99 (million) 4.40/1.02 % (23970)------------------------------ 4.40/1.02 % (23970)------------------------------ 4.40/1.03 % (23968)Instruction limit reached! 4.40/1.03 % (23968)------------------------------ 4.40/1.03 % (23968)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 4.40/1.03 % (23968)Termination reason: Unknown 4.40/1.03 % (23968)Termination phase: Saturation 4.40/1.03 4.40/1.03 % (23968)Memory used [KB]: 8443 4.40/1.03 % (23968)Time elapsed: 0.069 s 4.40/1.03 % (23968)Instructions burned: 297 (million) 4.40/1.03 % (23968)------------------------------ 4.40/1.03 % (23968)------------------------------ 4.40/1.03 % (23973)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=390:si=on:rtra=on_0 on Vampire---4 for (1793ds/390Mi) 4.40/1.03 % (23974)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on Vampire---4 for (1793ds/192Mi) 4.40/1.04 % (23964)Instruction limit reached! 4.40/1.04 % (23964)------------------------------ 4.40/1.04 % (23964)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 4.40/1.04 % (23964)Termination reason: Unknown 4.40/1.04 % (23964)Termination phase: Saturation 4.40/1.04 4.40/1.04 % (23964)Memory used [KB]: 7803 4.40/1.04 % (23964)Time elapsed: 0.085 s 4.40/1.04 % (23964)Instructions burned: 297 (million) 4.40/1.04 % (23964)------------------------------ 4.40/1.04 % (23964)------------------------------ 4.40/1.04 % (23969)Instruction limit reached! 4.40/1.04 % (23969)------------------------------ 4.40/1.04 % (23969)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 4.40/1.04 % (23969)Termination reason: Unknown 4.40/1.04 % (23969)Termination phase: Saturation 4.40/1.04 4.40/1.04 % (23960)Instruction limit reached! 4.40/1.04 % (23960)------------------------------ 4.40/1.04 % (23960)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 4.40/1.04 % (23969)Memory used [KB]: 8059 4.40/1.04 % (23969)Time elapsed: 0.056 s 4.40/1.04 % (23969)Instructions burned: 190 (million) 4.40/1.04 % (23969)------------------------------ 4.40/1.04 % (23969)------------------------------ 4.40/1.04 % (23960)Termination reason: Unknown 4.40/1.04 % (23960)Termination phase: Saturation 4.40/1.04 4.40/1.04 % (23960)Memory used [KB]: 8827 4.40/1.04 % (23960)Time elapsed: 0.136 s 4.40/1.04 % (23960)Instructions burned: 426 (million) 4.40/1.04 % (23960)------------------------------ 4.40/1.04 % (23960)------------------------------ 4.40/1.05 % (23975)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=279:si=on:rtra=on_0 on Vampire---4 for (1793ds/279Mi) 4.40/1.05 % (23976)lrs+1010_1:1024_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:ixr=off:i=25:si=on:rtra=on_0 on Vampire---4 for (1793ds/25Mi) 5.02/1.05 % (23977)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=940:si=on:rtra=on_0 on Vampire---4 for (1793ds/940Mi) 5.02/1.06 % (23976)Instruction limit reached! 5.02/1.06 % (23976)------------------------------ 5.02/1.06 % (23976)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 5.02/1.06 % (23976)Termination reason: Unknown 5.02/1.06 % (23976)Termination phase: shuffling 5.02/1.06 5.02/1.06 % (23976)Memory used [KB]: 1663 5.02/1.06 % (23976)Time elapsed: 0.008 s 5.02/1.06 % (23976)Instructions burned: 25 (million) 5.02/1.06 % (23976)------------------------------ 5.02/1.06 % (23976)------------------------------ 5.38/1.08 % (23978)lrs+2_1:1_bd=off:e2e=on:fde=none:kws=inv_precedence:plsq=on:plsqr=32,1:sos=on:i=422:si=on:rtra=on_0 on Vampire---4 for (1793ds/422Mi) 5.38/1.09 % (23974)Instruction limit reached! 5.38/1.09 % (23974)------------------------------ 5.38/1.09 % (23974)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 5.38/1.09 % (23974)Termination reason: Unknown 5.38/1.09 % (23974)Termination phase: Saturation 5.38/1.09 5.38/1.09 % (23974)Memory used [KB]: 7547 5.38/1.09 % (23974)Time elapsed: 0.053 s 5.38/1.09 % (23974)Instructions burned: 192 (million) 5.38/1.09 % (23974)------------------------------ 5.38/1.09 % (23974)------------------------------ 5.38/1.09 % (23967)Instruction limit reached! 5.38/1.09 % (23967)------------------------------ 5.38/1.09 % (23967)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 5.38/1.09 % (23967)Termination reason: Unknown 5.38/1.09 % (23967)Termination phase: Saturation 5.38/1.09 5.38/1.09 % (23967)Memory used [KB]: 9594 5.38/1.09 % (23967)Time elapsed: 0.133 s 5.38/1.09 % (23967)Instructions burned: 571 (million) 5.38/1.09 % (23967)------------------------------ 5.38/1.09 % (23967)------------------------------ 5.38/1.09 % (23979)lrs+10_1:1_cnfonf=lazy_gen:hud=7:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=103:si=on:rtra=on_0 on Vampire---4 for (1793ds/103Mi) 5.38/1.10 % (23980)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on Vampire---4 for (1793ds/182Mi) 5.38/1.10 % (23971)Instruction limit reached! 5.38/1.10 % (23971)------------------------------ 5.38/1.10 % (23971)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 5.38/1.10 % (23971)Termination reason: Unknown 5.38/1.10 % (23971)Termination phase: Saturation 5.38/1.10 5.38/1.10 % (23971)Memory used [KB]: 9594 5.38/1.10 % (23971)Time elapsed: 0.091 s 5.38/1.10 % (23971)Instructions burned: 183 (million) 5.38/1.10 % (23971)------------------------------ 5.38/1.10 % (23971)------------------------------ 5.38/1.11 % (23975)Instruction limit reached! 5.38/1.11 % (23975)------------------------------ 5.38/1.11 % (23975)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 5.38/1.11 % (23975)Termination reason: Unknown 5.38/1.11 % (23975)Termination phase: Saturation 5.38/1.11 5.38/1.11 % (23975)Memory used [KB]: 6652 5.38/1.11 % (23975)Time elapsed: 0.066 s 5.38/1.11 % (23975)Instructions burned: 280 (million) 5.38/1.11 % (23975)------------------------------ 5.38/1.11 % (23975)------------------------------ 5.65/1.12 % (23981)lrs+10_1:5_av=off:bd=off:fd=off:kws=precedence:nwc=3.0:prag=on:rawr=on:sos=all:sp=reverse_frequency:i=230:si=on:rtra=on_0 on Vampire---4 for (1792ds/230Mi) 5.65/1.12 % (23982)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on Vampire---4 for (1792ds/83Mi) 5.65/1.12 % (23979)Instruction limit reached! 5.65/1.12 % (23979)------------------------------ 5.65/1.12 % (23979)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 5.65/1.12 % (23979)Termination reason: Unknown 5.65/1.12 % (23979)Termination phase: Saturation 5.65/1.12 5.65/1.12 % (23979)Memory used [KB]: 6524 5.65/1.12 % (23979)Time elapsed: 0.026 s 5.65/1.12 % (23979)Instructions burned: 103 (million) 5.65/1.12 % (23979)------------------------------ 5.65/1.12 % (23979)------------------------------ 5.65/1.12 % (23972)Instruction limit reached! 5.65/1.12 % (23972)------------------------------ 5.65/1.12 % (23972)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 5.65/1.12 % (23972)Termination reason: Unknown 5.65/1.12 % (23972)Termination phase: Saturation 5.65/1.12 5.65/1.12 % (23972)Memory used [KB]: 7931 5.65/1.12 % (23972)Time elapsed: 0.113 s 5.65/1.12 % (23972)Instructions burned: 371 (million) 5.65/1.12 % (23972)------------------------------ 5.65/1.12 % (23972)------------------------------ 5.65/1.13 % (23983)lrs+1002_1:1_anc=all:cbe=off:cnfonf=lazy_not_gen_be_off:fe=off:hud=5:nwc=10.0:plsq=on:plsqr=32,1:prag=on:sp=unary_first:i=202:si=on:rtra=on_0 on Vampire---4 for (1792ds/202Mi) 5.65/1.13 % (23985)lrs+1010_1:1_cbe=off:cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=148:si=on:rtra=on_0 on Vampire---4 for (1792ds/148Mi) 5.65/1.14 % (23982)Instruction limit reached! 5.65/1.14 % (23982)------------------------------ 5.65/1.14 % (23982)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 5.65/1.14 % (23982)Termination reason: Unknown 5.65/1.14 % (23982)Termination phase: Property scanning 5.65/1.14 5.65/1.14 % (23982)Memory used [KB]: 1918 5.65/1.14 % (23982)Time elapsed: 0.022 s 5.65/1.14 % (23982)Instructions burned: 84 (million) 5.65/1.14 % (23982)------------------------------ 5.65/1.14 % (23982)------------------------------ 5.65/1.14 % (23980)Instruction limit reached! 5.65/1.14 % (23980)------------------------------ 5.65/1.14 % (23980)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 5.65/1.14 % (23980)Termination reason: Unknown 5.65/1.14 % (23980)Termination phase: Saturation 5.65/1.14 5.65/1.14 % (23980)Memory used [KB]: 6652 5.65/1.14 % (23980)Time elapsed: 0.043 s 5.65/1.14 % (23980)Instructions burned: 182 (million) 5.65/1.14 % (23980)------------------------------ 5.65/1.14 % (23980)------------------------------ 5.65/1.15 % (23986)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on Vampire---4 for (1792ds/104Mi) 5.65/1.15 % (23973)Instruction limit reached! 5.65/1.15 % (23973)------------------------------ 5.65/1.15 % (23973)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 5.65/1.15 % (23973)Termination reason: Unknown 5.65/1.15 % (23973)Termination phase: Saturation 5.65/1.15 5.65/1.15 % (23973)Memory used [KB]: 8059 5.65/1.15 % (23973)Time elapsed: 0.117 s 5.65/1.15 % (23973)Instructions burned: 390 (million) 5.65/1.15 % (23973)------------------------------ 5.65/1.15 % (23973)------------------------------ 5.87/1.15 % (23987)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on Vampire---4 for (1792ds/6Mi) 5.87/1.15 % (23987)Instruction limit reached! 5.87/1.15 % (23987)------------------------------ 5.87/1.15 % (23987)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 5.87/1.15 % (23987)Termination reason: Unknown 5.87/1.15 % (23987)Termination phase: shuffling 5.87/1.15 5.87/1.15 % (23987)Memory used [KB]: 1279 5.87/1.15 % (23987)Time elapsed: 0.003 s 5.87/1.15 % (23987)Instructions burned: 6 (million) 5.87/1.15 % (23987)------------------------------ 5.87/1.15 % (23987)------------------------------ 5.87/1.15 % (23988)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1200:si=on:rtra=on_0 on Vampire---4 for (1792ds/1200Mi) 5.87/1.16 % (23989)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on Vampire---4 for (1792ds/90Mi) 5.87/1.17 % (23985)Instruction limit reached! 5.87/1.17 % (23985)------------------------------ 5.87/1.17 % (23985)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 5.87/1.17 % (23985)Termination reason: Unknown 5.87/1.17 % (23985)Termination phase: Saturation 5.87/1.17 5.87/1.17 % (23985)Memory used [KB]: 6524 5.87/1.17 % (23985)Time elapsed: 0.037 s 5.87/1.17 % (23985)Instructions burned: 152 (million) 5.87/1.17 % (23985)------------------------------ 5.87/1.17 % (23985)------------------------------ 5.87/1.17 % (23986)Instruction limit reached! 5.87/1.17 % (23986)------------------------------ 5.87/1.17 % (23986)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 5.87/1.17 % (23986)Termination reason: Unknown 5.87/1.17 % (23986)Termination phase: Saturation 5.87/1.17 5.87/1.17 % (23986)Memory used [KB]: 6780 5.87/1.17 % (23986)Time elapsed: 0.028 s 5.87/1.17 % (23986)Instructions burned: 105 (million) 5.87/1.17 % (23986)------------------------------ 5.87/1.17 % (23986)------------------------------ 5.87/1.17 % (23983)Instruction limit reached! 5.87/1.17 % (23983)------------------------------ 5.87/1.17 % (23983)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 5.87/1.17 % (23983)Termination reason: Unknown 5.87/1.17 % (23983)Termination phase: Saturation 5.87/1.17 5.87/1.17 % (23983)Memory used [KB]: 6652 5.87/1.17 % (23983)Time elapsed: 0.048 s 5.87/1.17 % (23983)Instructions burned: 205 (million) 5.87/1.17 % (23983)------------------------------ 5.87/1.17 % (23983)------------------------------ 5.87/1.17 % (23990)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on Vampire---4 for (1792ds/164Mi) 5.87/1.18 % (23991)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=392:si=on:rtra=on_0 on Vampire---4 for (1792ds/392Mi) 5.87/1.18 % (23992)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on Vampire---4 for (1792ds/279Mi) 5.87/1.18 % (23989)Instruction limit reached! 5.87/1.18 % (23989)------------------------------ 5.87/1.18 % (23989)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 5.87/1.18 % (23989)Termination reason: Unknown 5.87/1.18 % (23989)Termination phase: Saturation 5.87/1.18 5.87/1.18 % (23989)Memory used [KB]: 6908 5.87/1.18 % (23989)Time elapsed: 0.025 s 5.87/1.18 % (23989)Instructions burned: 93 (million) 5.87/1.18 % (23989)------------------------------ 5.87/1.18 % (23989)------------------------------ 5.87/1.19 % (23993)lrs+1010_1:128_au=on:av=off:bd=preordered:bs=on:chr=on:cnfonf=lazy_not_gen:ntd=on:piset=and:i=59:si=on:rtra=on_0 on Vampire---4 for (1792ds/59Mi) 5.87/1.20 % (23993)Instruction limit reached! 5.87/1.20 % (23993)------------------------------ 5.87/1.20 % (23993)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 5.87/1.20 % (23993)Termination reason: Unknown 5.87/1.20 % (23993)Termination phase: Function definition elimination 5.87/1.20 5.87/1.20 % (23993)Memory used [KB]: 1791 5.87/1.20 % (23993)Time elapsed: 0.016 s 5.87/1.20 % (23993)Instructions burned: 59 (million) 5.87/1.20 % (23993)------------------------------ 5.87/1.20 % (23993)------------------------------ 5.87/1.21 % (23994)lrs+10_1:1_au=on:sd=1:sgt=32:sos=on:ss=axioms:i=141:si=on:rtra=on_0 on Vampire---4 for (1791ds/141Mi) 5.87/1.21 % (23978)Refutation not found, non-redundant clauses discarded% (23978)------------------------------ 5.87/1.21 % (23978)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 5.87/1.21 % (23978)Termination reason: Refutation not found, non-redundant clauses discarded 5.87/1.21 5.87/1.21 % (23978)Memory used [KB]: 9594 5.87/1.21 % (23978)Time elapsed: 0.138 s 5.87/1.21 % (23978)Instructions burned: 419 (million) 5.87/1.21 % (23978)------------------------------ 5.87/1.21 % (23978)------------------------------ 5.87/1.22 % (23990)Instruction limit reached! 5.87/1.22 % (23990)------------------------------ 5.87/1.22 % (23990)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 5.87/1.22 % (23990)Termination reason: Unknown 5.87/1.22 % (23990)Termination phase: Saturation 5.87/1.22 5.87/1.22 % (23990)Memory used [KB]: 2430 5.87/1.22 % (23990)Time elapsed: 0.045 s 5.87/1.22 % (23990)Instructions burned: 165 (million) 5.87/1.22 % (23990)------------------------------ 5.87/1.22 % (23990)------------------------------ 5.87/1.22 % (23981)Instruction limit reached! 5.87/1.22 % (23981)------------------------------ 5.87/1.22 % (23981)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 5.87/1.22 % (23981)Termination reason: Unknown 5.87/1.22 % (23981)Termination phase: Saturation 5.87/1.22 5.87/1.22 % (23981)Memory used [KB]: 2942 5.87/1.22 % (23981)Time elapsed: 0.104 s 5.87/1.22 % (23981)Instructions burned: 231 (million) 5.87/1.22 % (23981)------------------------------ 5.87/1.22 % (23981)------------------------------ 5.87/1.22 % (23995)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=389:si=on:rtra=on_0 on Vampire---4 for (1791ds/389Mi) 5.87/1.23 % (23996)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on Vampire---4 for (1791ds/593Mi) 5.87/1.23 % (23997)ott+1010_1:20_cnfonf=lazy_pi_sigma_gen:fe=axiom:plsq=on:plsqc=2:plsqr=32,1:sac=on:sos=all:i=4759:si=on:rtra=on_0 on Vampire---4 for (1791ds/4759Mi) 6.45/1.24 % (23992)Instruction limit reached! 6.45/1.24 % (23992)------------------------------ 6.45/1.24 % (23992)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 6.45/1.24 % (23992)Termination reason: Unknown 6.45/1.24 % (23992)Termination phase: Saturation 6.45/1.24 6.45/1.24 % (23992)Memory used [KB]: 6652 6.45/1.24 % (23992)Time elapsed: 0.063 s 6.45/1.24 % (23992)Instructions burned: 281 (million) 6.45/1.24 % (23992)------------------------------ 6.45/1.24 % (23992)------------------------------ 6.45/1.25 % (23994)Instruction limit reached! 6.45/1.25 % (23994)------------------------------ 6.45/1.25 % (23994)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 6.45/1.25 % (23994)Termination reason: Unknown 6.45/1.25 % (23994)Termination phase: Saturation 6.45/1.25 6.45/1.25 % (23994)Memory used [KB]: 7036 6.45/1.25 % (23994)Time elapsed: 0.040 s 6.45/1.25 % (23998)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on Vampire---4 for (1791ds/906Mi) 6.45/1.25 % (23994)Instructions burned: 142 (million) 6.45/1.25 % (23994)------------------------------ 6.45/1.25 % (23994)------------------------------ 6.45/1.26 % (23977)Instruction limit reached! 6.45/1.26 % (23977)------------------------------ 6.45/1.26 % (23977)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 6.45/1.26 % (23977)Termination reason: Unknown 6.45/1.26 % (23977)Termination phase: Saturation 6.45/1.26 6.45/1.26 % (23977)Memory used [KB]: 6780 6.45/1.26 % (23977)Time elapsed: 0.205 s 6.45/1.26 % (23977)Instructions burned: 941 (million) 6.45/1.26 % (23977)------------------------------ 6.45/1.26 % (23977)------------------------------ 6.45/1.26 % (23999)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=668:si=on:rtra=on_0 on Vampire---4 for (1791ds/668Mi) 6.45/1.27 % (24000)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=1670:si=on:rtra=on_0 on Vampire---4 for (1791ds/1670Mi) 6.45/1.27 % (23991)Instruction limit reached! 6.45/1.27 % (23991)------------------------------ 6.45/1.27 % (23991)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 6.45/1.27 % (23991)Termination reason: Unknown 6.45/1.27 % (23991)Termination phase: Saturation 6.45/1.27 6.45/1.27 % (23991)Memory used [KB]: 10106 6.45/1.27 % (23991)Time elapsed: 0.092 s 6.45/1.27 % (23991)Instructions burned: 395 (million) 6.45/1.27 % (23991)------------------------------ 6.45/1.27 % (23991)------------------------------ 6.71/1.28 % (24001)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on Vampire---4 for (1791ds/794Mi) 6.71/1.35 % (23995)Instruction limit reached! 6.71/1.35 % (23995)------------------------------ 6.71/1.35 % (23995)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 6.71/1.35 % (23995)Termination reason: Unknown 6.71/1.35 % (23995)Termination phase: Saturation 6.71/1.35 6.71/1.35 % (23995)Memory used [KB]: 8827 6.71/1.35 % (23995)Time elapsed: 0.125 s 6.71/1.35 % (23995)Instructions burned: 391 (million) 6.71/1.35 % (23995)------------------------------ 6.71/1.35 % (23995)------------------------------ 6.71/1.35 % (24002)lrs+1010_1:1_cnfonf=lazy_pi_sigma_gen:fd=off:ntd=on:sd=1:sgt=32:sos=on:ss=axioms:i=294:si=on:rtra=on_0 on Vampire---4 for (1790ds/294Mi) 6.84/1.41 % (23999)Instruction limit reached! 6.84/1.41 % (23999)------------------------------ 6.84/1.41 % (23999)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 6.84/1.41 % (23999)Termination reason: Unknown 6.84/1.41 % (23999)Termination phase: Saturation 6.84/1.41 6.84/1.41 % (23999)Memory used [KB]: 13944 6.84/1.41 % (23999)Time elapsed: 0.149 s 6.84/1.41 % (23999)Instructions burned: 668 (million) 6.84/1.41 % (23999)------------------------------ 6.84/1.41 % (23999)------------------------------ 6.84/1.41 % (23996)Instruction limit reached! 6.84/1.41 % (23996)------------------------------ 6.84/1.41 % (23996)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 6.84/1.41 % (23996)Termination reason: Unknown 6.84/1.41 % (23996)Termination phase: Saturation 6.84/1.41 6.84/1.41 % (23996)Memory used [KB]: 8187 6.84/1.41 % (23996)Time elapsed: 0.185 s 6.84/1.41 % (23996)Instructions burned: 594 (million) 6.84/1.41 % (23996)------------------------------ 6.84/1.41 % (23996)------------------------------ 7.18/1.42 % (24004)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=970:si=on:rtra=on_0 on Vampire---4 for (1790ds/970Mi) 7.18/1.43 % (24005)ott+10_1:1024_anc=none:bd=off:e2e=on:fde=none:fsr=off:hud=10:ixr=off:nm=4:nwc=5.0:spb=goal:i=383:si=on:rtra=on_0 on Vampire---4 for (1789ds/383Mi) 7.18/1.45 % (24002)Instruction limit reached! 7.18/1.45 % (24002)------------------------------ 7.18/1.45 % (24002)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 7.18/1.45 % (24002)Termination reason: Unknown 7.18/1.45 % (24002)Termination phase: Saturation 7.18/1.45 7.18/1.45 % (24002)Memory used [KB]: 6652 7.18/1.45 % (24002)Time elapsed: 0.094 s 7.18/1.45 % (24002)Instructions burned: 294 (million) 7.18/1.45 % (24002)------------------------------ 7.18/1.45 % (24002)------------------------------ 7.28/1.46 % (24006)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=961:si=on:rtra=on_0 on Vampire---4 for (1789ds/961Mi) 7.28/1.53 % (24001)Instruction limit reached! 7.28/1.53 % (24001)------------------------------ 7.28/1.53 % (24001)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 7.28/1.53 % (24001)Termination reason: Unknown 7.28/1.53 % (24001)Termination phase: Saturation 7.28/1.53 7.28/1.53 % (24001)Memory used [KB]: 4221 7.28/1.53 % (24001)Time elapsed: 0.250 s 7.28/1.53 % (24001)Instructions burned: 795 (million) 7.28/1.53 % (24001)------------------------------ 7.28/1.53 % (24001)------------------------------ 7.28/1.53 % (23998)Instruction limit reached! 7.28/1.53 % (23998)------------------------------ 7.28/1.53 % (23998)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 7.28/1.53 % (23998)Termination reason: Unknown 7.28/1.53 % (23998)Termination phase: Saturation 7.28/1.53 7.28/1.53 % (23998)Memory used [KB]: 9210 7.28/1.53 % (23998)Time elapsed: 0.279 s 7.28/1.53 % (23998)Instructions burned: 907 (million) 7.28/1.53 % (23998)------------------------------ 7.28/1.53 % (23998)------------------------------ 7.83/1.54 % (24007)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=1083:si=on:rtra=on_0 on Vampire---4 for (1788ds/1083Mi) 7.83/1.54 % (24008)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=1398:si=on:rtra=on_0 on Vampire---4 for (1788ds/1398Mi) 7.83/1.54 % (23988)Instruction limit reached! 7.83/1.54 % (23988)------------------------------ 7.83/1.54 % (23988)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 7.83/1.54 % (23988)Termination reason: Unknown 7.83/1.54 % (23988)Termination phase: Saturation 7.83/1.54 7.83/1.54 % (23988)Memory used [KB]: 10874 7.83/1.54 % (23988)Time elapsed: 0.389 s 7.83/1.54 % (23988)Instructions burned: 1201 (million) 7.83/1.54 % (23988)------------------------------ 7.83/1.54 % (23988)------------------------------ 7.83/1.55 % (24009)lrs+1010_1:3_cnfonf=conj_eager:fsr=off:prag=on:sd=4:sgt=10:ss=axioms:i=562:si=on:rtra=on_0 on Vampire---4 for (1788ds/562Mi) 8.22/1.62 % (24004)Instruction limit reached! 8.22/1.62 % (24004)------------------------------ 8.22/1.62 % (24004)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 8.22/1.62 % (24004)Termination reason: Unknown 8.22/1.62 % (24004)Termination phase: Saturation 8.22/1.62 8.22/1.62 % (24004)Memory used [KB]: 9210 8.22/1.62 % (24004)Time elapsed: 0.210 s 8.22/1.62 % (24004)Instructions burned: 972 (million) 8.22/1.62 % (24004)------------------------------ 8.22/1.62 % (24004)------------------------------ 8.22/1.63 % (24005)Instruction limit reached! 8.22/1.63 % (24005)------------------------------ 8.22/1.63 % (24005)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 8.22/1.63 % (24005)Termination reason: Unknown 8.22/1.63 % (24005)Termination phase: Saturation 8.22/1.63 8.22/1.63 % (24005)Memory used [KB]: 9722 8.22/1.63 % (24005)Time elapsed: 0.221 s 8.22/1.63 % (24005)Instructions burned: 384 (million) 8.22/1.63 % (24005)------------------------------ 8.22/1.63 % (24005)------------------------------ 8.22/1.63 % (24010)lrs+1010_1:2_au=on:e2e=on:sd=3:ss=axioms:st=3.0:i=1208:si=on:rtra=on_0 on Vampire---4 for (1787ds/1208Mi) 8.22/1.64 % (24011)lrs+1010_1:7_bd=off:cnfonf=lazy_not_be_gen:fe=off:hud=10:tnu=1:i=348:si=on:rtra=on_0 on Vampire---4 for (1787ds/348Mi) 10.14/1.68 % (24000)Instruction limit reached! 10.14/1.68 % (24000)------------------------------ 10.14/1.68 % (24000)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 10.14/1.68 % (24000)Termination reason: Unknown 10.14/1.68 % (24000)Termination phase: Saturation 10.14/1.68 10.14/1.68 % (24000)Memory used [KB]: 10234 10.14/1.68 % (24000)Time elapsed: 0.411 s 10.14/1.68 % (24000)Instructions burned: 1671 (million) 10.14/1.68 % (24000)------------------------------ 10.14/1.68 % (24000)------------------------------ 10.14/1.69 % (24012)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on Vampire---4 for (1787ds/343Mi) 10.14/1.72 % (24009)Instruction limit reached! 10.14/1.72 % (24009)------------------------------ 10.14/1.72 % (24009)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 10.14/1.72 % (24009)Termination reason: Unknown 10.14/1.72 % (24009)Termination phase: Saturation 10.14/1.72 10.14/1.72 % (24009)Memory used [KB]: 7931 10.14/1.72 % (24009)Time elapsed: 0.167 s 10.14/1.72 % (24009)Instructions burned: 563 (million) 10.14/1.72 % (24009)------------------------------ 10.14/1.72 % (24009)------------------------------ 10.54/1.72 % (24013)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=1655:si=on:rtra=on_0 on Vampire---4 for (1786ds/1655Mi) 10.70/1.77 % (24006)Instruction limit reached! 10.70/1.77 % (24006)------------------------------ 10.70/1.77 % (24006)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 10.70/1.77 % (24006)Termination reason: Unknown 10.70/1.77 % (24006)Termination phase: Saturation 10.70/1.77 10.70/1.77 % (24006)Memory used [KB]: 8443 10.70/1.77 % (24006)Time elapsed: 0.332 s 10.70/1.77 % (24006)Instructions burned: 962 (million) 10.70/1.77 % (24006)------------------------------ 10.70/1.77 % (24006)------------------------------ 10.70/1.77 % (24011)Instruction limit reached! 10.70/1.77 % (24011)------------------------------ 10.70/1.77 % (24011)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 10.70/1.77 % (24011)Termination reason: Unknown 10.70/1.77 % (24011)Termination phase: Saturation 10.70/1.77 10.70/1.77 % (24011)Memory used [KB]: 7547 10.70/1.77 % (24011)Time elapsed: 0.132 s 10.70/1.77 % (24011)Instructions burned: 348 (million) 10.70/1.77 % (24011)------------------------------ 10.70/1.77 % (24011)------------------------------ 10.70/1.78 % (24014)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on Vampire---4 for (1786ds/6454Mi) 10.70/1.78 % (24015)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on Vampire---4 for (1786ds/1539Mi) 10.70/1.79 % (24012)Instruction limit reached! 10.70/1.79 % (24012)------------------------------ 10.70/1.79 % (24012)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 10.70/1.79 % (24012)Termination reason: Unknown 10.70/1.79 % (24012)Termination phase: Saturation 10.70/1.79 10.70/1.79 % (24012)Memory used [KB]: 7931 10.70/1.79 % (24012)Time elapsed: 0.103 s 10.70/1.79 % (24012)Instructions burned: 345 (million) 10.70/1.79 % (24012)------------------------------ 10.70/1.79 % (24012)------------------------------ 10.70/1.80 % (24016)ott+1002_1:1_bd=off:cnfonf=off:e2e=on:fd=off:fe=axiom:hud=5:prag=on:sos=on:i=501:si=on:rtra=on_0 on Vampire---4 for (1786ds/501Mi) 11.35/1.88 % (24007)Instruction limit reached! 11.35/1.88 % (24007)------------------------------ 11.35/1.88 % (24007)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 11.35/1.88 % (24007)Termination reason: Unknown 11.35/1.88 % (24007)Termination phase: Saturation 11.35/1.88 11.35/1.88 % (24007)Memory used [KB]: 9083 11.35/1.88 % (24007)Time elapsed: 0.345 s 11.35/1.88 % (24007)Instructions burned: 1085 (million) 11.35/1.88 % (24007)------------------------------ 11.35/1.88 % (24007)------------------------------ 11.35/1.89 % (24017)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=277:si=on:rtra=on_0 on Vampire---4 for (1785ds/277Mi) 11.59/1.95 % (24017)Instruction limit reached! 11.59/1.95 % (24017)------------------------------ 11.59/1.95 % (24017)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 11.59/1.95 % (24017)Termination reason: Unknown 11.59/1.95 % (24017)Termination phase: Saturation 11.59/1.95 11.59/1.95 % (24017)Memory used [KB]: 9083 11.59/1.95 % (24017)Time elapsed: 0.065 s 11.59/1.95 % (24017)Instructions burned: 277 (million) 11.59/1.95 % (24017)------------------------------ 11.59/1.95 % (24017)------------------------------ 11.59/1.95 % (24016)Instruction limit reached! 11.59/1.95 % (24016)------------------------------ 11.59/1.95 % (24016)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 11.59/1.95 % (24016)Termination reason: Unknown 11.59/1.95 % (24016)Termination phase: Saturation 11.59/1.95 11.59/1.95 % (24016)Memory used [KB]: 8955 11.59/1.95 % (24016)Time elapsed: 0.179 s 11.59/1.95 % (24016)Instructions burned: 503 (million) 11.59/1.95 % (24016)------------------------------ 11.59/1.95 % (24016)------------------------------ 11.59/1.96 % (24018)lrs+21_1:1_cha=on:cnfonf=off:hud=10:kws=inv_frequency:lcm=predicate:sgt=32:sos=on:sp=occurrence:ss=axioms:i=136:si=on:rtra=on_0 on Vampire---4 for (1784ds/136Mi) 11.59/1.96 % (24019)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=401:si=on:rtra=on_0 on Vampire---4 for (1784ds/401Mi) 11.91/1.98 % (24008)Instruction limit reached! 11.91/1.98 % (24008)------------------------------ 11.91/1.98 % (24008)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 11.91/1.98 % (24008)Termination reason: Unknown 11.91/1.98 % (24008)Termination phase: Saturation 11.91/1.98 11.91/1.98 % (24008)Memory used [KB]: 10490 11.91/1.98 % (24008)Time elapsed: 0.443 s 11.91/1.98 % (24008)Instructions burned: 1400 (million) 11.91/1.98 % (24008)------------------------------ 11.91/1.98 % (24008)------------------------------ 11.91/1.99 % (24020)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=4810:si=on:rtra=on_0 on Vampire---4 for (1784ds/4810Mi) 11.91/2.00 % (24018)Instruction limit reached! 11.91/2.00 % (24018)------------------------------ 11.91/2.00 % (24018)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 11.91/2.00 % (24018)Termination reason: Unknown 11.91/2.00 % (24018)Termination phase: Saturation 11.91/2.00 11.91/2.00 % (24018)Memory used [KB]: 6780 11.91/2.00 % (24018)Time elapsed: 0.038 s 11.91/2.00 % (24018)Instructions burned: 137 (million) 11.91/2.00 % (24018)------------------------------ 11.91/2.00 % (24018)------------------------------ 11.91/2.01 % (24021)lrs+1002_1:128_atotf=0.1:au=on:cbe=off:ntd=on:sp=const_frequency:i=2020:si=on:rtra=on_0 on Vampire---4 for (1783ds/2020Mi) 11.91/2.02 % (24010)Instruction limit reached! 11.91/2.02 % (24010)------------------------------ 11.91/2.02 % (24010)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 11.91/2.02 % (24010)Termination reason: Unknown 11.91/2.02 % (24010)Termination phase: Saturation 11.91/2.02 11.91/2.02 % (24010)Memory used [KB]: 10874 11.91/2.02 % (24010)Time elapsed: 0.391 s 11.91/2.02 % (24010)Instructions burned: 1210 (million) 11.91/2.02 % (24010)------------------------------ 11.91/2.02 % (24010)------------------------------ 12.08/2.03 % (24022)dis+10_1:1_atotf=0.1:cbe=off:sd=3:ss=axioms:st=2.0:i=375:si=on:rtra=on_0 on Vampire---4 for (1783ds/375Mi) 12.11/2.05 % (24019)Instruction limit reached! 12.11/2.05 % (24019)------------------------------ 12.11/2.05 % (24019)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 12.11/2.05 % (24019)Termination reason: Unknown 12.11/2.05 % (24019)Termination phase: Saturation 12.11/2.05 12.11/2.05 % (24019)Memory used [KB]: 6652 12.11/2.05 % (24019)Time elapsed: 0.088 s 12.11/2.05 % (24019)Instructions burned: 406 (million) 12.11/2.05 % (24019)------------------------------ 12.11/2.05 % (24019)------------------------------ 12.11/2.06 % (24023)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=8250:si=on:rtra=on_0 on Vampire---4 for (1783ds/8250Mi) 12.28/2.14 % (24022)Instruction limit reached! 12.28/2.14 % (24022)------------------------------ 12.28/2.14 % (24022)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 12.28/2.14 % (24022)Termination reason: Unknown 12.28/2.14 % (24022)Termination phase: Saturation 12.28/2.14 12.28/2.14 % (24022)Memory used [KB]: 7803 12.28/2.14 % (24022)Time elapsed: 0.113 s 12.28/2.14 % (24022)Instructions burned: 376 (million) 12.28/2.14 % (24022)------------------------------ 12.28/2.14 % (24022)------------------------------ 12.28/2.15 % (24024)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:plsq=on:plsqr=32,1:prag=on:i=187:si=on:rtra=on_0 on Vampire---4 for (1782ds/187Mi) 14.21/2.20 % (24024)Instruction limit reached! 14.21/2.20 % (24024)------------------------------ 14.21/2.20 % (24024)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 14.21/2.20 % (24024)Termination reason: Unknown 14.21/2.20 % (24024)Termination phase: Saturation 14.21/2.20 14.21/2.20 % (24024)Memory used [KB]: 7419 14.21/2.20 % (24024)Time elapsed: 0.053 s 14.21/2.20 % (24024)Instructions burned: 187 (million) 14.21/2.20 % (24024)------------------------------ 14.21/2.20 % (24024)------------------------------ 14.21/2.21 % (24025)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on Vampire---4 for (1781ds/393Mi) 14.77/2.26 % (24013)Instruction limit reached! 14.77/2.26 % (24013)------------------------------ 14.77/2.26 % (24013)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 14.77/2.26 % (24013)Termination reason: Unknown 14.77/2.26 % (24013)Termination phase: Saturation 14.77/2.26 14.77/2.26 % (24013)Memory used [KB]: 11257 14.77/2.26 % (24013)Time elapsed: 0.540 s 14.77/2.26 % (24013)Instructions burned: 1657 (million) 14.77/2.26 % (24013)------------------------------ 14.77/2.26 % (24013)------------------------------ 14.77/2.27 % (24015)Instruction limit reached! 14.77/2.27 % (24015)------------------------------ 14.77/2.27 % (24015)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 14.77/2.27 % (24015)Termination reason: Unknown 14.77/2.27 % (24015)Termination phase: Saturation 14.77/2.27 14.77/2.27 % (24015)Memory used [KB]: 7803 14.77/2.27 % (24015)Time elapsed: 0.506 s 14.77/2.27 % (24015)Instructions burned: 1541 (million) 14.77/2.27 % (24015)------------------------------ 14.77/2.27 % (24015)------------------------------ 14.77/2.27 % (24026)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on Vampire---4 for (1781ds/371Mi) 14.93/2.28 % (24027)lrs+1002_1:16_bd=off:e2e=on:fde=unused:kws=precedence:sac=on:sos=on:ss=axioms:i=434:si=on:rtra=on_0 on Vampire---4 for (1781ds/434Mi) 14.93/2.28 % (23997)Instruction limit reached! 14.93/2.28 % (23997)------------------------------ 14.93/2.28 % (23997)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 14.93/2.28 % (23997)Termination reason: Unknown 14.93/2.28 % (23997)Termination phase: Saturation 14.93/2.28 14.93/2.28 % (23997)Memory used [KB]: 7675 14.93/2.28 % (23997)Time elapsed: 1.057 s 14.93/2.28 % (23997)Instructions burned: 4760 (million) 14.93/2.28 % (23997)------------------------------ 14.93/2.28 % (23997)------------------------------ 14.93/2.29 % (24028)lrs+10_1:8_av=off:fe=off:hud=5:piset=or:prag=on:i=452:si=on:rtra=on_0 on Vampire---4 for (1781ds/452Mi) 15.14/2.33 % (24025)Instruction limit reached! 15.14/2.33 % (24025)------------------------------ 15.14/2.33 % (24025)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 15.14/2.33 % (24025)Termination reason: Unknown 15.14/2.33 % (24025)Termination phase: Saturation 15.14/2.33 15.14/2.33 % (24025)Memory used [KB]: 8443 15.14/2.33 % (24025)Time elapsed: 0.122 s 15.14/2.33 % (24025)Instructions burned: 393 (million) 15.14/2.33 % (24025)------------------------------ 15.14/2.33 % (24025)------------------------------ 15.14/2.34 % (24029)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=5411:si=on:rtra=on_0 on Vampire---4 for (1780ds/5411Mi) 15.31/2.38 % (24026)Instruction limit reached! 15.31/2.38 % (24026)------------------------------ 15.31/2.38 % (24026)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 15.31/2.38 % (24026)Termination reason: Unknown 15.31/2.38 % (24026)Termination phase: Saturation 15.31/2.38 15.31/2.38 % (24026)Memory used [KB]: 7803 15.31/2.38 % (24026)Time elapsed: 0.111 s 15.31/2.38 % (24026)Instructions burned: 373 (million) 15.31/2.38 % (24026)------------------------------ 15.31/2.38 % (24026)------------------------------ 15.31/2.39 % (24030)dis+1010_1:1_cnfonf=conj_eager:e2e=on:fe=axiom:fsr=off:ntd=on:nwc=10.0:s2a=on:sgt=5:sp=occurrence:ss=axioms:i=1110:si=on:rtra=on_0 on Vampire---4 for (1780ds/1110Mi) 15.73/2.43 % (24028)Instruction limit reached! 15.73/2.43 % (24028)------------------------------ 15.73/2.43 % (24028)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 15.73/2.43 % (24028)Termination reason: Unknown 15.73/2.43 % (24028)Termination phase: Saturation 15.73/2.43 15.73/2.43 % (24028)Memory used [KB]: 3582 15.73/2.43 % (24028)Time elapsed: 0.139 s 15.73/2.43 % (24028)Instructions burned: 454 (million) 15.73/2.43 % (24028)------------------------------ 15.73/2.43 % (24028)------------------------------ 15.73/2.44 % (24031)dis+1010_1:1_amm=off:cs=on:kws=precedence:nwc=10.0:piset=all:s2a=on:sac=on:sp=unary_frequency:spb=goal:ss=axioms:st=3.0:i=590:si=on:rtra=on_0 on Vampire---4 for (1779ds/590Mi) 16.10/2.49 % (24027)Instruction limit reached! 16.10/2.49 % (24027)------------------------------ 16.10/2.49 % (24027)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 16.10/2.49 % (24027)Termination reason: Unknown 16.10/2.49 % (24027)Termination phase: Saturation 16.10/2.49 16.10/2.49 % (24027)Memory used [KB]: 9083 16.10/2.49 % (24027)Time elapsed: 0.214 s 16.10/2.49 % (24027)Instructions burned: 434 (million) 16.10/2.49 % (24027)------------------------------ 16.10/2.49 % (24027)------------------------------ 16.10/2.51 % (24032)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=432:si=on:rtra=on_0 on Vampire---4 for (1779ds/432Mi) 16.76/2.61 % (24031)Instruction limit reached! 16.76/2.61 % (24031)------------------------------ 16.76/2.61 % (24031)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 16.76/2.61 % (24031)Termination reason: Unknown 16.76/2.61 % (24031)Termination phase: Saturation 16.76/2.61 16.76/2.61 % (24031)Memory used [KB]: 8187 16.76/2.61 % (24031)Time elapsed: 0.177 s 16.76/2.61 % (24031)Instructions burned: 590 (million) 16.76/2.61 % (24031)------------------------------ 16.76/2.61 % (24031)------------------------------ 16.76/2.62 % (24021)Instruction limit reached! 16.76/2.62 % (24021)------------------------------ 16.76/2.62 % (24021)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 16.76/2.62 % (24021)Termination reason: Unknown 16.76/2.62 % (24021)Termination phase: Saturation 16.76/2.62 16.76/2.62 % (24021)Memory used [KB]: 8443 16.76/2.62 % (24021)Time elapsed: 0.614 s 16.76/2.62 % (24021)Instructions burned: 2021 (million) 16.76/2.62 % (24021)------------------------------ 16.76/2.62 % (24021)------------------------------ 17.14/2.62 % (24033)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=2517:si=on:rtra=on_0 on Vampire---4 for (1777ds/2517Mi) 17.14/2.63 % (24034)dis+10_8:1_apa=on:cnfonf=off:e2e=on:plsq=on:plsqc=1:plsqr=32,1:ss=axioms:i=783:si=on:rtra=on_0 on Vampire---4 for (1777ds/783Mi) 17.19/2.69 % (24030)Instruction limit reached! 17.19/2.69 % (24030)------------------------------ 17.19/2.69 % (24030)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 17.19/2.69 % (24030)Termination reason: Unknown 17.19/2.69 % (24030)Termination phase: Saturation 17.19/2.69 17.19/2.69 % (24030)Memory used [KB]: 8443 17.19/2.69 % (24030)Time elapsed: 0.306 s 17.19/2.69 % (24030)Instructions burned: 1110 (million) 17.19/2.69 % (24030)------------------------------ 17.19/2.69 % (24030)------------------------------ 17.19/2.70 % (24035)dis+1002_1:1_amm=off:au=on:bsd=on:cbe=off:cnfonf=lazy_gen:sp=unary_frequency:i=481:si=on:rtra=on_0 on Vampire---4 for (1777ds/481Mi) 17.19/2.72 % (24032)Instruction limit reached! 17.19/2.72 % (24032)------------------------------ 17.19/2.72 % (24032)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 17.19/2.72 % (24032)Termination reason: Unknown 17.19/2.72 % (24032)Termination phase: Saturation 17.19/2.72 17.19/2.72 % (24032)Memory used [KB]: 7931 17.19/2.72 % (24032)Time elapsed: 0.210 s 17.19/2.72 % (24032)Instructions burned: 432 (million) 17.19/2.72 % (24032)------------------------------ 17.19/2.72 % (24032)------------------------------ 18.55/2.74 % (24036)lrs+1010_1:64_aac=none:acc=on:au=on:c=on:cbe=off:ccuc=small_ones:chr=on:cnfonf=lazy_not_gen:fde=unused:hud=10:kws=precedence:nicw=on:piset=all_but_not_eq:sd=2:sp=reverse_arity:ss=axioms:i=536:si=on:rtra=on_0 on Vampire---4 for (1776ds/536Mi) 18.93/2.82 % (24035)Instruction limit reached! 18.93/2.82 % (24035)------------------------------ 18.93/2.82 % (24035)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 18.93/2.82 % (24035)Termination reason: Unknown 18.93/2.82 % (24035)Termination phase: Saturation 18.93/2.82 18.93/2.82 % (24035)Memory used [KB]: 9466 18.93/2.82 % (24035)Time elapsed: 0.114 s 18.93/2.82 % (24035)Instructions burned: 482 (million) 18.93/2.82 % (24035)------------------------------ 18.93/2.82 % (24035)------------------------------ 18.93/2.82 % (24037)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on Vampire---4 for (1775ds/157Mi) 18.93/2.86 % (24037)Instruction limit reached! 18.93/2.86 % (24037)------------------------------ 18.93/2.86 % (24037)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 18.93/2.86 % (24037)Termination reason: Unknown 18.93/2.86 % (24037)Termination phase: Saturation 18.93/2.86 18.93/2.86 % (24037)Memory used [KB]: 6524 18.93/2.86 % (24037)Time elapsed: 0.039 s 18.93/2.86 % (24037)Instructions burned: 159 (million) 18.93/2.86 % (24037)------------------------------ 18.93/2.86 % (24037)------------------------------ 19.51/2.87 % (24038)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4350:si=on:rtra=on_0 on Vampire---4 for (1775ds/4350Mi) 19.51/2.88 % (24034)Instruction limit reached! 19.51/2.88 % (24034)------------------------------ 19.51/2.88 % (24034)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 19.51/2.88 % (24034)Termination reason: Unknown 19.51/2.88 % (24034)Termination phase: Saturation 19.51/2.88 19.51/2.88 % (24034)Memory used [KB]: 10234 19.51/2.88 % (24034)Time elapsed: 0.254 s 19.51/2.88 % (24034)Instructions burned: 785 (million) 19.51/2.88 % (24034)------------------------------ 19.51/2.88 % (24034)------------------------------ 19.61/2.89 % (24039)dis+10_1:1_au=on:nwc=5.0:s2a=on:s2at=2.0:sac=on:sd=7:ss=axioms:st=2.0:i=358:si=on:rtra=on_0 on Vampire---4 for (1775ds/358Mi) 19.78/2.92 % (24036)Instruction limit reached! 19.78/2.92 % (24036)------------------------------ 19.78/2.92 % (24036)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 19.78/2.92 % (24036)Termination reason: Unknown 19.78/2.92 % (24036)Termination phase: Saturation 19.78/2.92 19.78/2.92 % (24036)Memory used [KB]: 9722 19.78/2.92 % (24036)Time elapsed: 0.139 s 19.78/2.92 % (24036)Instructions burned: 537 (million) 19.78/2.92 % (24036)------------------------------ 19.78/2.92 % (24036)------------------------------ 19.78/2.93 % (24040)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=700:si=on:rtra=on_0 on Vampire---4 for (1774ds/700Mi) 19.99/2.99 % (24039)Instruction limit reached! 19.99/2.99 % (24039)------------------------------ 19.99/2.99 % (24039)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 19.99/2.99 % (24039)Termination reason: Unknown 19.99/2.99 % (24039)Termination phase: Saturation 19.99/2.99 19.99/2.99 % (24039)Memory used [KB]: 7675 19.99/2.99 % (24039)Time elapsed: 0.107 s 19.99/2.99 % (24039)Instructions burned: 358 (million) 19.99/2.99 % (24039)------------------------------ 19.99/2.99 % (24039)------------------------------ 19.99/3.00 % (24041)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on Vampire---4 for (1774ds/406Mi) 20.86/3.11 % (24020)Instruction limit reached! 20.86/3.11 % (24020)------------------------------ 20.86/3.11 % (24020)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 20.86/3.11 % (24020)Termination reason: Unknown 20.86/3.11 % (24020)Termination phase: Saturation 20.86/3.11 20.86/3.11 % (24020)Memory used [KB]: 9850 20.86/3.11 % (24020)Time elapsed: 1.122 s 20.86/3.11 % (24020)Instructions burned: 4812 (million) 20.86/3.11 % (24020)------------------------------ 20.86/3.11 % (24020)------------------------------ 20.86/3.12 % (24042)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:kws=arity:prag=on:i=283:si=on:rtra=on_0 on Vampire---4 for (1773ds/283Mi) 20.86/3.12 % (24041)Instruction limit reached! 20.86/3.12 % (24041)------------------------------ 20.86/3.12 % (24041)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 20.86/3.12 % (24041)Termination reason: Unknown 20.86/3.12 % (24041)Termination phase: Saturation 20.86/3.12 20.86/3.12 % (24041)Memory used [KB]: 7164 20.86/3.12 % (24041)Time elapsed: 0.116 s 20.86/3.12 % (24041)Instructions burned: 406 (million) 20.86/3.12 % (24041)------------------------------ 20.86/3.12 % (24041)------------------------------ 20.86/3.12 % (24043)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=641:si=on:rtra=on_0 on Vampire---4 for (1772ds/641Mi) 20.86/3.14 % (24040)Instruction limit reached! 20.86/3.14 % (24040)------------------------------ 20.86/3.14 % (24040)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 20.86/3.14 % (24040)Termination reason: Unknown 20.86/3.14 % (24040)Termination phase: Saturation 20.86/3.14 20.86/3.14 % (24040)Memory used [KB]: 7675 20.86/3.14 % (24040)Time elapsed: 0.216 s 20.86/3.14 % (24040)Instructions burned: 700 (million) 20.86/3.14 % (24040)------------------------------ 20.86/3.14 % (24040)------------------------------ 20.86/3.15 % (24044)lrs+1010_1:1_cbe=off:chr=on:er=known:hud=4:i=147:si=on:rtra=on_0 on Vampire---4 for (1772ds/147Mi) 21.66/3.19 % (24044)Instruction limit reached! 21.66/3.19 % (24044)------------------------------ 21.66/3.19 % (24044)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 21.66/3.19 % (24044)Termination reason: Unknown 21.66/3.19 % (24044)Termination phase: Saturation 21.66/3.19 21.66/3.19 % (24044)Memory used [KB]: 7164 21.66/3.19 % (24044)Time elapsed: 0.040 s 21.66/3.19 % (24044)Instructions burned: 148 (million) 21.66/3.19 % (24044)------------------------------ 21.66/3.19 % (24044)------------------------------ 21.66/3.20 % (24045)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=932:si=on:rtra=on_0 on Vampire---4 for (1772ds/932Mi) 21.66/3.20 % (24042)Instruction limit reached! 21.66/3.20 % (24042)------------------------------ 21.66/3.20 % (24042)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 21.66/3.20 % (24042)Termination reason: Unknown 21.66/3.20 % (24042)Termination phase: Saturation 21.66/3.20 21.66/3.20 % (24042)Memory used [KB]: 7675 21.66/3.20 % (24042)Time elapsed: 0.083 s 21.66/3.20 % (24042)Instructions burned: 284 (million) 21.66/3.20 % (24042)------------------------------ 21.66/3.20 % (24042)------------------------------ 21.66/3.21 % (24046)lrs+1002_1:8_av=off:fd=off:hud=5:tnu=1:i=2401:si=on:rtra=on_0 on Vampire---4 for (1772ds/2401Mi) 22.55/3.32 % (24043)Instruction limit reached! 22.55/3.32 % (24043)------------------------------ 22.55/3.32 % (24043)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 22.55/3.32 % (24043)Termination reason: Unknown 22.55/3.32 % (24043)Termination phase: Saturation 22.55/3.32 22.55/3.32 % (24043)Memory used [KB]: 7931 22.55/3.32 % (24043)Time elapsed: 0.194 s 22.55/3.32 % (24043)Instructions burned: 641 (million) 22.55/3.32 % (24043)------------------------------ 22.55/3.32 % (24043)------------------------------ 23.23/3.33 % (24047)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=576:si=on:rtra=on_0 on Vampire---4 for (1770ds/576Mi) 23.70/3.39 % (24033)Instruction limit reached! 23.70/3.39 % (24033)------------------------------ 23.70/3.39 % (24033)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 23.70/3.39 % (24033)Termination reason: Unknown 23.70/3.39 % (24033)Termination phase: Saturation 23.70/3.39 23.70/3.39 % (24033)Memory used [KB]: 11257 23.70/3.39 % (24033)Time elapsed: 0.772 s 23.70/3.39 % (24033)Instructions burned: 2519 (million) 23.70/3.39 % (24033)------------------------------ 23.70/3.39 % (24033)------------------------------ 23.70/3.40 % (24048)dis+10_1:1_av=off:bsd=on:bsr=unit_only:fd=off:hud=8:nm=16:prag=on:i=715:si=on:rtra=on_0 on Vampire---4 for (1770ds/715Mi) 23.70/3.42 % (24045)Instruction limit reached! 23.70/3.42 % (24045)------------------------------ 23.70/3.42 % (24045)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 23.70/3.42 % (24045)Termination reason: Unknown 23.70/3.42 % (24045)Termination phase: Saturation 23.70/3.42 23.70/3.42 % (24045)Memory used [KB]: 10618 23.70/3.42 % (24045)Time elapsed: 0.225 s 23.70/3.42 % (24045)Instructions burned: 934 (million) 23.70/3.42 % (24045)------------------------------ 23.70/3.42 % (24045)------------------------------ 23.70/3.43 % (24049)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=1762:si=on:rtra=on_0 on Vampire---4 for (1769ds/1762Mi) 24.13/3.46 % (24047)Instruction limit reached! 24.13/3.46 % (24047)------------------------------ 24.13/3.46 % (24047)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 24.13/3.46 % (24047)Termination reason: Unknown 24.13/3.46 % (24047)Termination phase: Saturation 24.13/3.46 24.13/3.46 % (24047)Memory used [KB]: 10362 24.13/3.46 % (24047)Time elapsed: 0.139 s 24.13/3.46 % (24047)Instructions burned: 576 (million) 24.13/3.46 % (24047)------------------------------ 24.13/3.46 % (24047)------------------------------ 24.31/3.47 % (24050)lrs+21_1:1_hud=5:kws=inv_frequency:nm=16:nwc=2.0:prag=on:sos=on:ss=axioms:i=503:si=on:rtra=on_0 on Vampire---4 for (1769ds/503Mi) 24.59/3.62 % (24048)Instruction limit reached! 24.59/3.62 % (24048)------------------------------ 24.59/3.62 % (24048)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 24.59/3.62 % (24048)Termination reason: Unknown 24.59/3.62 % (24048)Termination phase: Saturation 24.59/3.62 24.59/3.62 % (24048)Memory used [KB]: 3837 24.59/3.62 % (24048)Time elapsed: 0.220 s 25.07/3.62 % (24048)Instructions burned: 718 (million) 25.07/3.62 % (24048)------------------------------ 25.07/3.62 % (24048)------------------------------ 25.07/3.63 % (24050)Instruction limit reached! 25.07/3.63 % (24050)------------------------------ 25.07/3.63 % (24050)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 25.07/3.63 % (24050)Termination reason: Unknown 25.07/3.63 % (24050)Termination phase: Saturation 25.07/3.63 25.07/3.63 % (24050)Memory used [KB]: 7931 25.07/3.63 % (24050)Time elapsed: 0.177 s 25.07/3.63 % (24050)Instructions burned: 503 (million) 25.07/3.63 % (24050)------------------------------ 25.07/3.63 % (24050)------------------------------ 25.07/3.63 % (24051)dis+1010_3039923:1048576_bsr=unit_only:cbe=off:cha=on:cnfonf=off:e2e=on:fsr=off:hud=1:ixr=off:kws=precedence:lma=on:nm=4:piset=or:s2a=on:sp=frequency:spb=goal_then_units:i=5104:si=on:rtra=on_0 on Vampire---4 for (1767ds/5104Mi) 25.07/3.63 % (24052)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=312:si=on:rtra=on_0 on Vampire---4 for (1767ds/312Mi) 25.79/3.73 % (24052)Instruction limit reached! 25.79/3.73 % (24052)------------------------------ 25.79/3.73 % (24052)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 25.79/3.73 % (24052)Termination reason: Unknown 25.79/3.73 % (24052)Termination phase: Saturation 25.79/3.73 25.79/3.73 % (24052)Memory used [KB]: 7803 25.79/3.73 % (24052)Time elapsed: 0.116 s 25.79/3.73 % (24052)Instructions burned: 314 (million) 25.79/3.73 % (24052)------------------------------ 25.79/3.73 % (24052)------------------------------ 25.79/3.73 % (24053)ott+10_1:1_au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:sp=unary_first:i=153:si=on:rtra=on_0 on Vampire---4 for (1766ds/153Mi) 26.29/3.77 % (24053)Instruction limit reached! 26.29/3.77 % (24053)------------------------------ 26.29/3.77 % (24053)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 26.29/3.77 % (24053)Termination reason: Unknown 26.29/3.77 % (24053)Termination phase: Saturation 26.29/3.77 26.29/3.77 % (24053)Memory used [KB]: 6524 26.29/3.77 % (24053)Time elapsed: 0.037 s 26.29/3.77 % (24053)Instructions burned: 153 (million) 26.29/3.77 % (24053)------------------------------ 26.29/3.77 % (24053)------------------------------ 26.29/3.78 % (24054)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on Vampire---4 for (1766ds/258Mi) 27.13/3.82 % (24049)Instruction limit reached! 27.13/3.82 % (24049)------------------------------ 27.13/3.82 % (24049)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 27.13/3.82 % (24049)Termination reason: Unknown 27.13/3.82 % (24049)Termination phase: Saturation 27.13/3.82 27.13/3.82 % (24049)Memory used [KB]: 12665 27.13/3.82 % (24049)Time elapsed: 0.399 s 27.13/3.82 % (24049)Instructions burned: 1762 (million) 27.13/3.82 % (24049)------------------------------ 27.13/3.82 % (24049)------------------------------ 27.13/3.83 % (24055)lrs+1002_1:1_apa=on:cnfonf=off:fd=off:flr=on:hud=1:lcm=reverse:prag=on:sd=1:sos=on:ss=axioms:i=770:si=on:rtra=on_0 on Vampire---4 for (1765ds/770Mi) 27.34/3.85 % (24054)Instruction limit reached! 27.34/3.85 % (24054)------------------------------ 27.34/3.85 % (24054)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 27.34/3.85 % (24054)Termination reason: Unknown 27.34/3.85 % (24054)Termination phase: Saturation 27.34/3.85 27.34/3.85 % (24054)Memory used [KB]: 7803 27.34/3.85 % (24054)Time elapsed: 0.072 s 27.34/3.85 % (24054)Instructions burned: 261 (million) 27.34/3.85 % (24054)------------------------------ 27.34/3.85 % (24054)------------------------------ 27.34/3.86 % (24056)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=1001:si=on:rtra=on_0 on Vampire---4 for (1765ds/1001Mi) 27.92/3.96 % (24046)Instruction limit reached! 27.92/3.96 % (24046)------------------------------ 27.92/3.96 % (24046)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 27.92/3.96 % (24046)Termination reason: Unknown 27.92/3.96 % (24046)Termination phase: Saturation 27.92/3.96 27.92/3.96 % (24046)Memory used [KB]: 8443 27.92/3.96 % (24046)Time elapsed: 0.753 s 27.92/3.96 % (24046)Instructions burned: 2402 (million) 27.92/3.96 % (24046)------------------------------ 27.92/3.96 % (24046)------------------------------ 27.92/3.97 % (24057)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=4436:si=on:rtra=on_0 on Vampire---4 for (1764ds/4436Mi) 27.92/3.97 % (24014)Instruction limit reached! 27.92/3.97 % (24014)------------------------------ 27.92/3.97 % (24014)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 27.92/3.97 % (24014)Termination reason: Unknown 27.92/3.97 % (24014)Termination phase: Saturation 27.92/3.97 27.92/3.97 % (24014)Memory used [KB]: 14583 27.92/3.97 % (24014)Time elapsed: 2.203 s 27.92/3.97 % (24014)Instructions burned: 6454 (million) 27.92/3.97 % (24014)------------------------------ 27.92/3.97 % (24014)------------------------------ 27.92/3.98 % (24058)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on Vampire---4 for (1764ds/90Mi) 28.24/4.00 % (24058)Instruction limit reached! 28.24/4.00 % (24058)------------------------------ 28.24/4.00 % (24058)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 28.24/4.00 % (24058)Termination reason: Unknown 28.24/4.00 % (24058)Termination phase: Saturation 28.24/4.00 28.24/4.00 % (24058)Memory used [KB]: 6908 28.24/4.00 % (24058)Time elapsed: 0.026 s 28.24/4.00 % (24058)Instructions burned: 92 (million) 28.24/4.00 % (24058)------------------------------ 28.24/4.00 % (24058)------------------------------ 28.24/4.01 % (24059)lrs+2_1:1_au=on:bd=off:bsr=unit_only:sd=2:sgt=32:sos=all:ss=axioms:i=454:si=on:rtra=on_0 on Vampire---4 for (1764ds/454Mi) 28.56/4.07 % (24055)Instruction limit reached! 28.56/4.07 % (24055)------------------------------ 28.56/4.07 % (24055)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 28.56/4.07 % (24055)Termination reason: Unknown 28.56/4.07 % (24055)Termination phase: Saturation 28.56/4.07 28.56/4.07 % (24055)Memory used [KB]: 6908 28.56/4.07 % (24055)Time elapsed: 0.257 s 28.56/4.07 % (24055)Instructions burned: 770 (million) 28.56/4.07 % (24055)------------------------------ 28.56/4.07 % (24055)------------------------------ 28.56/4.07 % (24029)Instruction limit reached! 28.56/4.07 % (24029)------------------------------ 28.56/4.07 % (24029)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 28.56/4.07 % (24029)Termination reason: Unknown 28.56/4.07 % (24029)Termination phase: Saturation 28.56/4.07 28.56/4.07 % (24029)Memory used [KB]: 15991 28.56/4.07 % (24029)Time elapsed: 1.736 s 28.56/4.07 % (24029)Instructions burned: 5411 (million) 28.56/4.07 % (24029)------------------------------ 28.56/4.07 % (24029)------------------------------ 28.56/4.07 % (24060)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on Vampire---4 for (1763ds/346Mi) 28.56/4.08 % (24061)lrs+1666_1:1_au=on:s2a=on:sd=2:ss=axioms:st=5.0:i=1400:si=on:rtra=on_0 on Vampire---4 for (1763ds/1400Mi) 29.05/4.14 % (24059)Refutation not found, non-redundant clauses discarded% (24059)------------------------------ 29.05/4.14 % (24059)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 29.05/4.14 % (24059)Termination reason: Refutation not found, non-redundant clauses discarded 29.05/4.14 29.05/4.14 % (24059)Memory used [KB]: 8059 29.05/4.14 % (24059)Time elapsed: 0.160 s 29.05/4.14 % (24059)Instructions burned: 433 (million) 29.05/4.14 % (24059)------------------------------ 29.05/4.14 % (24059)------------------------------ 29.05/4.15 % (24062)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=1229:si=on:rtra=on_0 on Vampire---4 for (1762ds/1229Mi) 29.05/4.15 % (24060)Instruction limit reached! 29.05/4.15 % (24060)------------------------------ 29.05/4.15 % (24060)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 29.05/4.15 % (24060)Termination reason: Unknown 29.05/4.15 % (24060)Termination phase: Saturation 29.05/4.15 29.05/4.15 % (24060)Memory used [KB]: 9210 29.05/4.15 % (24060)Time elapsed: 0.080 s 29.05/4.15 % (24060)Instructions burned: 347 (million) 29.05/4.15 % (24060)------------------------------ 29.05/4.15 % (24060)------------------------------ 29.05/4.16 % (24063)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=466:si=on:rtra=on_0 on Vampire---4 for (1762ds/466Mi) 29.05/4.17 % (24056)Instruction limit reached! 29.05/4.17 % (24056)------------------------------ 29.05/4.17 % (24056)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 29.05/4.17 % (24056)Termination reason: Unknown 29.05/4.17 % (24056)Termination phase: Saturation 29.05/4.17 29.05/4.17 % (24056)Memory used [KB]: 9978 29.05/4.17 % (24056)Time elapsed: 0.341 s 29.05/4.17 % (24056)Instructions burned: 1003 (million) 29.05/4.17 % (24056)------------------------------ 29.05/4.17 % (24056)------------------------------ 29.05/4.18 % (24064)lrs+1010_1:6_au=on:cnfonf=conj_eager:nwc=10.0:pe=on:prag=on:s2a=on:ss=axioms:st=1.5:i=1335:si=on:rtra=on_0 on Vampire---4 for (1762ds/1335Mi) 29.05/4.23 % (24038)Instruction limit reached! 29.05/4.23 % (24038)------------------------------ 29.05/4.23 % (24038)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 29.05/4.23 % (24038)Termination reason: Unknown 29.05/4.23 % (24038)Termination phase: Saturation 29.05/4.23 29.05/4.23 % (24038)Memory used [KB]: 11129 29.05/4.23 % (24038)Time elapsed: 1.362 s 29.05/4.23 % (24038)Instructions burned: 4353 (million) 29.05/4.23 % (24038)------------------------------ 29.05/4.23 % (24038)------------------------------ 29.05/4.24 % (24065)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=1213:si=on:rtra=on_0 on Vampire---4 for (1761ds/1213Mi) 30.53/4.30 % (24063)Instruction limit reached! 30.53/4.30 % (24063)------------------------------ 30.53/4.30 % (24063)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 30.53/4.30 % (24063)Termination reason: Unknown 30.53/4.30 % (24063)Termination phase: Saturation 30.53/4.30 30.53/4.30 % (24063)Memory used [KB]: 8059 30.53/4.30 % (24063)Time elapsed: 0.143 s 30.53/4.30 % (24063)Instructions burned: 468 (million) 30.53/4.30 % (24063)------------------------------ 30.53/4.30 % (24063)------------------------------ 30.53/4.31 % (24066)lrs+1002_3:4_au=on:av=off:cnfonf=off:fd=off:fsr=off:ins=2:sd=1:sos=on:ss=axioms:i=4528:si=on:rtra=on_0 on Vampire---4 for (1760ds/4528Mi) 32.13/4.37 % (24066)Refutation not found, incomplete strategy 32.13/4.37 % (24066)------------------------------ 32.13/4.37 % (24066)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 32.13/4.37 % (24066)Termination reason: Refutation not found, incomplete strategy 32.13/4.37 32.13/4.37 32.13/4.37 % (24066)Memory used [KB]: 2046 32.13/4.37 % (24066)Time elapsed: 0.059 s 32.13/4.37 % (24066)Instructions burned: 214 (million) 32.13/4.37 % (24066)------------------------------ 32.13/4.37 % (24066)------------------------------ 32.13/4.38 % (24067)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on Vampire---4 for (1760ds/443Mi) 32.67/4.47 % (24062)Instruction limit reached! 32.67/4.47 % (24062)------------------------------ 32.67/4.47 % (24062)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 32.67/4.47 % (24062)Termination reason: Unknown 32.67/4.47 % (24062)Termination phase: Saturation 32.67/4.47 32.67/4.47 % (24062)Memory used [KB]: 3454 32.67/4.47 % (24062)Time elapsed: 0.309 s 32.67/4.47 % (24062)Instructions burned: 1230 (million) 32.67/4.47 % (24062)------------------------------ 32.67/4.47 % (24062)------------------------------ 32.67/4.48 % (24068)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on Vampire---4 for (1759ds/360Mi) 32.67/4.52 % (24067)Instruction limit reached! 32.67/4.52 % (24067)------------------------------ 32.67/4.52 % (24067)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 32.67/4.52 % (24067)Termination reason: Unknown 32.67/4.52 % (24067)Termination phase: Saturation 32.67/4.52 32.67/4.52 % (24067)Memory used [KB]: 8059 32.67/4.52 % (24067)Time elapsed: 0.138 s 32.67/4.52 % (24067)Instructions burned: 445 (million) 32.67/4.52 % (24067)------------------------------ 32.67/4.52 % (24067)------------------------------ 32.67/4.52 % (24061)Instruction limit reached! 32.67/4.52 % (24061)------------------------------ 32.67/4.52 % (24061)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 32.67/4.52 % (24061)Termination reason: Unknown 32.67/4.52 % (24061)Termination phase: Saturation 32.67/4.52 32.67/4.52 % (24061)Memory used [KB]: 9210 32.67/4.52 % (24061)Time elapsed: 0.443 s 32.67/4.52 % (24061)Instructions burned: 1402 (million) 32.67/4.52 % (24061)------------------------------ 32.67/4.52 % (24061)------------------------------ 32.67/4.52 % (24069)lrs+1002_1:1_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:cond=fast:fsr=off:piset=or:sp=const_frequency:uhcvi=on:updr=off:i=314:si=on:rtra=on_0 on Vampire---4 for (1758ds/314Mi) 32.67/4.53 % (24070)ott+10_1:1_aac=none:apa=on:au=on:cnfonf=off:ntd=on:nwc=12.0:sos=on:i=865:si=on:rtra=on_0 on Vampire---4 for (1758ds/865Mi) 33.34/4.55 % (24068)Instruction limit reached! 33.34/4.55 % (24068)------------------------------ 33.34/4.55 % (24068)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 33.34/4.55 % (24068)Termination reason: Unknown 33.34/4.55 % (24068)Termination phase: Saturation 33.34/4.55 33.34/4.55 % (24068)Memory used [KB]: 6652 33.34/4.55 % (24068)Time elapsed: 0.080 s 33.34/4.55 % (24068)Instructions burned: 362 (million) 33.34/4.55 % (24068)------------------------------ 33.34/4.55 % (24068)------------------------------ 33.34/4.56 % (24071)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=668:si=on:rtra=on_0 on Vampire---4 for (1758ds/668Mi) 33.66/4.59 % (24064)Refutation not found, non-redundant clauses discarded% (24064)------------------------------ 33.66/4.59 % (24064)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 33.66/4.59 % (24064)Termination reason: Refutation not found, non-redundant clauses discarded 33.66/4.59 33.66/4.59 % (24064)Memory used [KB]: 8443 33.66/4.59 % (24064)Time elapsed: 0.408 s 33.66/4.59 % (24064)Instructions burned: 1300 (million) 33.66/4.59 % (24064)------------------------------ 33.66/4.59 % (24064)------------------------------ 33.66/4.59 % (24069)Instruction limit reached! 33.66/4.59 % (24069)------------------------------ 33.66/4.59 % (24069)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 33.66/4.59 % (24069)Termination reason: Unknown 33.66/4.59 % (24069)Termination phase: Saturation 33.66/4.59 33.66/4.59 % (24069)Memory used [KB]: 6652 33.66/4.59 % (24069)Time elapsed: 0.070 s 33.66/4.59 % (24069)Instructions burned: 315 (million) 33.66/4.59 % (24069)------------------------------ 33.66/4.59 % (24069)------------------------------ 33.66/4.60 % (24072)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=517:si=on:rtra=on_0 on Vampire---4 for (1758ds/517Mi) 33.66/4.60 % (24073)dis+1010_1:1_aac=none:bd=preordered:e2e=on:fde=none:fe=axiom:nm=16:nwc=10.0:prag=on:i=1871:si=on:rtra=on_0 on Vampire---4 for (1758ds/1871Mi) 33.66/4.62 % (24065)Instruction limit reached! 33.66/4.62 % (24065)------------------------------ 33.66/4.62 % (24065)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 33.66/4.62 % (24065)Termination reason: Unknown 33.66/4.62 % (24065)Termination phase: Saturation 33.66/4.62 33.66/4.62 % (24065)Memory used [KB]: 11641 33.66/4.62 % (24065)Time elapsed: 0.381 s 33.66/4.62 % (24065)Instructions burned: 1215 (million) 33.66/4.62 % (24065)------------------------------ 33.66/4.62 % (24065)------------------------------ 33.66/4.63 % (24074)lrs+1010_1:1024_add=large:c=on:cbe=off:cnfonf=lazy_gen:fde=none:nm=30:piset=and:sac=on:uhcvi=on:i=578:si=on:rtra=on_0 on Vampire---4 for (1757ds/578Mi) 34.06/4.71 % (24072)Instruction limit reached! 34.06/4.71 % (24072)------------------------------ 34.06/4.71 % (24072)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 34.06/4.71 % (24072)Termination reason: Unknown 34.06/4.71 % (24072)Termination phase: Saturation 34.06/4.71 34.06/4.71 % (24072)Memory used [KB]: 9210 34.06/4.71 % (24072)Time elapsed: 0.116 s 34.06/4.71 % (24072)Instructions burned: 517 (million) 34.06/4.71 % (24072)------------------------------ 34.06/4.71 % (24072)------------------------------ 34.33/4.72 % (24071)Instruction limit reached! 34.33/4.72 % (24071)------------------------------ 34.33/4.72 % (24071)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 34.33/4.72 % (24071)Termination reason: Unknown 34.33/4.72 % (24071)Termination phase: Saturation 34.33/4.72 34.33/4.72 % (24071)Memory used [KB]: 13688 34.33/4.72 % (24071)Time elapsed: 0.156 s 34.33/4.72 % (24071)Instructions burned: 671 (million) 34.33/4.72 % (24071)------------------------------ 34.33/4.72 % (24071)------------------------------ 34.33/4.72 % (24075)lrs+10_1:1_fde=unused:prag=on:sd=2:sgt=32:ss=axioms:i=3174:si=on:rtra=on_0 on Vampire---4 for (1756ds/3174Mi) 34.33/4.73 % (24076)lrs+1010_1:7_bd=off:cnfonf=lazy_not_be_gen:fe=off:hud=10:tnu=1:i=348:si=on:rtra=on_0 on Vampire---4 for (1756ds/348Mi) 34.59/4.79 % (24070)Instruction limit reached! 34.59/4.79 % (24070)------------------------------ 34.59/4.79 % (24070)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 34.59/4.79 % (24070)Termination reason: Unknown 34.59/4.79 % (24070)Termination phase: Saturation 34.59/4.79 34.59/4.79 % (24070)Memory used [KB]: 7931 34.59/4.79 % (24070)Time elapsed: 0.256 s 34.59/4.79 % (24070)Instructions burned: 866 (million) 34.59/4.79 % (24070)------------------------------ 34.59/4.79 % (24070)------------------------------ 34.59/4.79 % (24074)Instruction limit reached! 34.59/4.79 % (24074)------------------------------ 34.59/4.79 % (24074)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 34.59/4.79 % (24074)Termination reason: Unknown 34.59/4.79 % (24074)Termination phase: Saturation 34.59/4.79 34.59/4.79 % (24074)Memory used [KB]: 8187 34.59/4.79 % (24074)Time elapsed: 0.160 s 34.59/4.79 % (24074)Instructions burned: 580 (million) 34.59/4.79 % (24074)------------------------------ 34.59/4.79 % (24074)------------------------------ 34.59/4.79 % (24077)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=5045:si=on:rtra=on_0 on Vampire---4 for (1756ds/5045Mi) 34.59/4.79 % (24078)dis+1002_1:1_acc=model:au=on:nwc=5.0:sd=5:ss=axioms:st=2.5:i=3672:si=on:rtra=on_0 on Vampire---4 for (1756ds/3672Mi) 34.59/4.82 % (24076)Instruction limit reached! 34.59/4.82 % (24076)------------------------------ 34.59/4.82 % (24076)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 34.59/4.82 % (24076)Termination reason: Unknown 34.59/4.82 % (24076)Termination phase: Saturation 34.59/4.82 34.59/4.82 % (24076)Memory used [KB]: 7547 34.59/4.82 % (24076)Time elapsed: 0.094 s 34.59/4.82 % (24076)Instructions burned: 350 (million) 34.59/4.82 % (24076)------------------------------ 34.59/4.82 % (24076)------------------------------ 35.38/4.83 % (24079)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=1201:si=on:rtra=on_0 on Vampire---4 for (1755ds/1201Mi) 38.48/5.19 % (24073)Instruction limit reached! 38.48/5.19 % (24073)------------------------------ 38.48/5.19 % (24073)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 38.48/5.19 % (24073)Termination reason: Unknown 38.48/5.19 % (24073)Termination phase: Saturation 38.48/5.19 38.48/5.19 % (24073)Memory used [KB]: 15223 38.48/5.19 % (24073)Time elapsed: 0.595 s 38.48/5.19 % (24073)Instructions burned: 1871 (million) 38.48/5.19 % (24073)------------------------------ 38.48/5.19 % (24073)------------------------------ 38.48/5.20 % (24080)dis+1010_1:1_anc=all:c=on:cnfonf=off:fsr=off:kws=inv_frequency:nwc=5.0:sos=on:sp=occurrence:i=344:si=on:rtra=on_0 on Vampire---4 for (1752ds/344Mi) 39.06/5.24 % (24079)Instruction limit reached! 39.06/5.24 % (24079)------------------------------ 39.06/5.24 % (24079)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 39.06/5.24 % (24079)Termination reason: Unknown 39.06/5.24 % (24079)Termination phase: Saturation 39.06/5.24 39.06/5.24 % (24079)Memory used [KB]: 9594 39.06/5.24 % (24079)Time elapsed: 0.427 s 39.06/5.24 % (24079)Instructions burned: 1202 (million) 39.06/5.24 % (24079)------------------------------ 39.06/5.24 % (24079)------------------------------ 39.06/5.25 % (24081)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on Vampire---4 for (1751ds/643Mi) 39.06/5.26 % (24051)Instruction limit reached! 39.06/5.26 % (24051)------------------------------ 39.06/5.26 % (24051)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 39.06/5.26 % (24051)Termination reason: Unknown 39.06/5.26 % (24051)Termination phase: Saturation 39.06/5.26 39.06/5.26 % (24051)Memory used [KB]: 18038 39.06/5.26 % (24051)Time elapsed: 1.653 s 39.06/5.26 % (24051)Instructions burned: 5105 (million) 39.06/5.26 % (24051)------------------------------ 39.06/5.26 % (24051)------------------------------ 39.06/5.27 % (24082)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=149:si=on:rtra=on_0 on Vampire---4 for (1751ds/149Mi) 39.23/5.31 % (24080)Instruction limit reached! 39.23/5.31 % (24080)------------------------------ 39.23/5.31 % (24080)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 39.23/5.31 % (24080)Termination reason: Unknown 39.23/5.31 % (24080)Termination phase: Saturation 39.23/5.31 39.23/5.31 % (24080)Memory used [KB]: 7036 39.23/5.31 % (24080)Time elapsed: 0.125 s 39.23/5.31 % (24080)Instructions burned: 344 (million) 39.23/5.31 % (24080)------------------------------ 39.23/5.31 % (24080)------------------------------ 39.23/5.31 % (24082)Instruction limit reached! 39.23/5.31 % (24082)------------------------------ 39.23/5.31 % (24082)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 39.23/5.31 % (24082)Termination reason: Unknown 39.23/5.31 % (24082)Termination phase: Saturation 39.23/5.31 39.23/5.31 % (24082)Memory used [KB]: 9338 39.23/5.31 % (24082)Time elapsed: 0.069 s 39.23/5.31 % (24082)Instructions burned: 150 (million) 39.23/5.31 % (24082)------------------------------ 39.23/5.31 % (24082)------------------------------ 39.23/5.31 % (24083)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=326:si=on:rtra=on_0 on Vampire---4 for (1751ds/326Mi) 39.23/5.32 % (24084)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on Vampire---4 for (1750ds/157Mi) 39.65/5.34 % (24075)Refutation not found, non-redundant clauses discarded% (24075)------------------------------ 39.65/5.34 % (24075)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 39.65/5.34 % (24075)Termination reason: Refutation not found, non-redundant clauses discarded 39.65/5.34 39.65/5.34 % (24075)Memory used [KB]: 16502 39.65/5.34 % (24075)Time elapsed: 0.622 s 39.65/5.34 % (24075)Instructions burned: 2035 (million) 39.65/5.34 % (24075)------------------------------ 39.65/5.34 % (24075)------------------------------ 39.77/5.35 % (24085)lrs+2_1:1024_anc=all:cnfonf=off:cs=on:e2e=on:nm=20:s2at=1.5:slsq=on:slsqr=1,2:spb=goal:i=340:si=on:rtra=on_0 on Vampire---4 for (1750ds/340Mi) 39.77/5.36 % (24084)Instruction limit reached! 39.77/5.36 % (24084)------------------------------ 39.77/5.36 % (24084)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 39.77/5.36 % (24084)Termination reason: Unknown 39.77/5.36 % (24084)Termination phase: Saturation 39.77/5.36 39.77/5.36 % (24084)Memory used [KB]: 6524 39.77/5.36 % (24084)Time elapsed: 0.039 s 39.77/5.36 % (24084)Instructions burned: 159 (million) 39.77/5.36 % (24084)------------------------------ 39.77/5.36 % (24084)------------------------------ 39.77/5.37 % (24086)dis+10_16:1_hud=1:plsq=on:plsqc=1:plsqr=32,1:prag=on:sd=1:sgt=64:ss=axioms:i=8062:si=on:rtra=on_0 on Vampire---4 for (1750ds/8062Mi) 39.77/5.39 % (24057)Instruction limit reached! 39.77/5.39 % (24057)------------------------------ 39.77/5.39 % (24057)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 39.77/5.39 % (24057)Termination reason: Unknown 39.77/5.39 % (24057)Termination phase: Saturation 39.77/5.39 39.77/5.39 % (24057)Memory used [KB]: 17398 39.77/5.39 % (24057)Time elapsed: 1.451 s 39.77/5.39 % (24057)Instructions burned: 4437 (million) 39.77/5.39 % (24057)------------------------------ 39.77/5.39 % (24057)------------------------------ 39.77/5.40 % (24081)Instruction limit reached! 39.77/5.40 % (24081)------------------------------ 39.77/5.40 % (24081)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 39.77/5.40 % (24081)Termination reason: Unknown 39.77/5.40 % (24081)Termination phase: Saturation 39.77/5.40 39.77/5.40 % (24081)Memory used [KB]: 9210 39.77/5.40 % (24081)Time elapsed: 0.145 s 39.77/5.40 % (24081)Instructions burned: 646 (million) 39.77/5.40 % (24081)------------------------------ 39.77/5.40 % (24081)------------------------------ 39.77/5.40 % (24087)lrs+1002_1:1_av=off:bd=off:bet=on:e2e=on:fde=unused:fe=off:plsq=on:prag=on:sos=on:i=1321:si=on:rtra=on_0 on Vampire---4 for (1750ds/1321Mi) 39.77/5.41 % (24088)dis+1010_1:1_au=on:bd=off:bsd=on:ixr=off:sp=const_max:i=2812:si=on:rtra=on_0 on Vampire---4 for (1749ds/2812Mi) 39.77/5.41 % (24083)Instruction limit reached! 39.77/5.41 % (24083)------------------------------ 39.77/5.41 % (24083)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 39.77/5.41 % (24083)Termination reason: Unknown 39.77/5.41 % (24083)Termination phase: Saturation 39.77/5.41 39.77/5.41 % (24083)Memory used [KB]: 7675 39.77/5.41 % (24083)Time elapsed: 0.122 s 39.77/5.41 % (24083)Instructions burned: 328 (million) 39.77/5.41 % (24083)------------------------------ 39.77/5.41 % (24083)------------------------------ 40.36/5.42 % (24089)ott+1004_1:24_anc=none:cbe=off:cnfonf=lazy_not_gen:fe=off:piset=not:prag=on:rp=on:i=5061:si=on:rtra=on_0 on Vampire---4 for (1749ds/5061Mi) 40.36/5.46 % (24085)Instruction limit reached! 40.36/5.46 % (24085)------------------------------ 40.36/5.46 % (24085)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 40.36/5.46 % (24085)Termination reason: Unknown 40.36/5.46 % (24085)Termination phase: Saturation 40.36/5.46 40.36/5.46 % (24085)Memory used [KB]: 8955 40.36/5.46 % (24085)Time elapsed: 0.109 s 40.36/5.46 % (24085)Instructions burned: 343 (million) 40.36/5.46 % (24085)------------------------------ 40.36/5.46 % (24085)------------------------------ 40.36/5.47 % (24090)lrs+1010_1:16_apa=on:bsd=on:cnfonf=off:hud=10:sac=on:sos=on:ss=axioms:i=7257:si=on:rtra=on_0 on Vampire---4 for (1749ds/7257Mi) 43.28/5.80 % (24087)Instruction limit reached! 43.28/5.80 % (24087)------------------------------ 43.28/5.80 % (24087)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 43.28/5.80 % (24087)Termination reason: Unknown 43.28/5.80 % (24087)Termination phase: Saturation 43.28/5.80 43.28/5.80 % (24087)Memory used [KB]: 6268 43.28/5.80 % (24087)Time elapsed: 0.405 s 43.28/5.80 % (24087)Instructions burned: 1322 (million) 43.28/5.80 % (24087)------------------------------ 43.28/5.80 % (24087)------------------------------ 43.28/5.81 % (24091)dis+1002_8:1_bd=off:sd=1:sgt=16:ss=axioms:i=4604:si=on:rtra=on_0 on Vampire---4 for (1745ds/4604Mi) 43.28/5.84 % (24023)Instruction limit reached! 43.28/5.84 % (24023)------------------------------ 43.28/5.84 % (24023)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 43.28/5.84 % (24023)Termination reason: Unknown 43.28/5.84 % (24023)Termination phase: Saturation 43.28/5.84 43.28/5.84 % (24023)Memory used [KB]: 22899 43.28/5.84 % (24023)Time elapsed: 3.790 s 43.28/5.84 % (24023)Instructions burned: 8250 (million) 43.28/5.84 % (24023)------------------------------ 43.28/5.84 % (24023)------------------------------ 43.91/5.86 % (24092)dis+1010_1:1_au=on:cnfonf=lazy_gen:ins=3:plsq=on:plsqc=1:plsqr=15142123,262144:sp=reverse_arity:i=3665:si=on:rtra=on_0 on Vampire---4 for (1745ds/3665Mi) 44.42/5.97 % (24078)Instruction limit reached! 44.42/5.97 % (24078)------------------------------ 44.42/5.97 % (24078)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 44.42/5.97 % (24078)Termination reason: Unknown 44.42/5.97 % (24078)Termination phase: Saturation 44.42/5.97 44.42/5.97 % (24078)Memory used [KB]: 11641 44.42/5.97 % (24078)Time elapsed: 1.177 s 44.42/5.97 % (24078)Instructions burned: 3673 (million) 44.42/5.97 % (24078)------------------------------ 44.42/5.97 % (24078)------------------------------ 44.42/5.98 % (24097)lrs+1010_1:1_cbe=off:chr=on:er=known:hud=4:i=147:si=on:rtra=on_0 on Vampire---4 for (1744ds/147Mi) 44.42/6.02 % (24097)Instruction limit reached! 44.42/6.02 % (24097)------------------------------ 44.42/6.02 % (24097)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 44.42/6.02 % (24097)Termination reason: Unknown 44.42/6.02 % (24097)Termination phase: Saturation 44.42/6.02 44.42/6.02 % (24097)Memory used [KB]: 7036 44.42/6.02 % (24097)Time elapsed: 0.040 s 44.42/6.02 % (24097)Instructions burned: 150 (million) 44.42/6.02 % (24097)------------------------------ 44.42/6.02 % (24097)------------------------------ 45.29/6.03 % (24102)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=3710:si=on:rtra=on_0 on Vampire---4 for (1743ds/3710Mi) 47.30/6.34 % (24088)Instruction limit reached! 47.30/6.34 % (24088)------------------------------ 47.30/6.34 % (24088)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 47.30/6.34 % (24088)Termination reason: Unknown 47.30/6.34 % (24088)Termination phase: Saturation 47.30/6.34 47.30/6.34 % (24088)Memory used [KB]: 11257 47.30/6.34 % (24088)Time elapsed: 0.940 s 47.30/6.34 % (24088)Instructions burned: 2814 (million) 47.30/6.34 % (24088)------------------------------ 47.30/6.34 % (24088)------------------------------ 47.30/6.35 % (24233)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=9872:si=on:rtra=on_0 on Vampire---4 for (1740ds/9872Mi) 47.77/6.41 % (24077)Instruction limit reached! 47.77/6.41 % (24077)------------------------------ 47.77/6.41 % (24077)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 47.77/6.41 % (24077)Termination reason: Unknown 47.77/6.41 % (24077)Termination phase: Saturation 47.77/6.41 47.77/6.41 % (24077)Memory used [KB]: 15991 47.77/6.41 % (24077)Time elapsed: 1.614 s 47.77/6.41 % (24077)Instructions burned: 5047 (million) 47.77/6.41 % (24077)------------------------------ 47.77/6.41 % (24077)------------------------------ 47.77/6.42 % (24262)ott+1010_1:32_apa=on:atotf=0.3:au=on:c=on:cnfonf=off:fe=off:fsr=off:nm=6:piset=or:sac=on:sos=on:i=644:si=on:rtra=on_0 on Vampire---4 for (1739ds/644Mi) 49.38/6.61 % (24262)Instruction limit reached! 49.38/6.61 % (24262)------------------------------ 49.38/6.61 % (24262)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 49.38/6.61 % (24262)Termination reason: Unknown 49.38/6.61 % (24262)Termination phase: Saturation 49.38/6.61 49.38/6.61 % (24262)Memory used [KB]: 7291 49.38/6.61 % (24262)Time elapsed: 0.201 s 49.38/6.61 % (24262)Instructions burned: 645 (million) 49.38/6.61 % (24262)------------------------------ 49.38/6.61 % (24262)------------------------------ 50.06/6.62 % (24289)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on Vampire---4 for (1737ds/307Mi) 50.55/6.69 % (24289)Instruction limit reached! 50.55/6.69 % (24289)------------------------------ 50.55/6.69 % (24289)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 50.55/6.69 % (24289)Termination reason: Unknown 50.55/6.69 % (24289)Termination phase: Saturation 50.55/6.69 50.55/6.69 % (24289)Memory used [KB]: 6652 50.55/6.69 % (24289)Time elapsed: 0.071 s 50.55/6.69 % (24289)Instructions burned: 308 (million) 50.55/6.69 % (24289)------------------------------ 50.55/6.69 % (24289)------------------------------ 50.55/6.70 % (24332)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=831:si=on:rtra=on_0 on Vampire---4 for (1737ds/831Mi) 50.55/6.71 % (24092)Instruction limit reached! 50.55/6.71 % (24092)------------------------------ 50.55/6.71 % (24092)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 50.55/6.71 % (24092)Termination reason: Unknown 50.55/6.71 % (24092)Termination phase: Saturation 50.55/6.71 50.55/6.71 % (24092)Memory used [KB]: 9594 50.55/6.71 % (24092)Time elapsed: 0.853 s 50.55/6.71 % (24092)Instructions burned: 3668 (million) 50.55/6.71 % (24092)------------------------------ 50.55/6.71 % (24092)------------------------------ 50.55/6.71 % (24089)Instruction limit reached! 50.55/6.71 % (24089)------------------------------ 50.55/6.71 % (24089)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 50.55/6.71 % (24089)Termination reason: Unknown 50.55/6.71 % (24089)Termination phase: Saturation 50.55/6.71 50.55/6.71 % (24089)Memory used [KB]: 8827 50.55/6.71 % (24089)Time elapsed: 1.295 s 50.55/6.71 % (24089)Instructions burned: 5063 (million) 50.55/6.71 % (24089)------------------------------ 50.55/6.71 % (24089)------------------------------ 50.55/6.72 % (24337)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on Vampire---4 for (1736ds/474Mi) 50.55/6.72 % (24339)lrs+10_1:1_au=on:erd=off:s2a=on:s2at=3.0:sos=all:i=1174:si=on:rtra=on_0 on Vampire---4 for (1736ds/1174Mi) 51.26/6.82 % (24337)Instruction limit reached! 51.26/6.82 % (24337)------------------------------ 51.26/6.82 % (24337)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 51.26/6.82 % (24337)Termination reason: Unknown 51.26/6.82 % (24337)Termination phase: Saturation 51.26/6.82 51.26/6.82 % (24337)Memory used [KB]: 9466 51.26/6.82 % (24337)Time elapsed: 0.110 s 51.26/6.82 % (24337)Instructions burned: 475 (million) 51.26/6.82 % (24337)------------------------------ 51.26/6.82 % (24337)------------------------------ 51.50/6.83 % (24340)lrs+1010_1:4_amm=sco:awrs=converge:bd=off:nwc=5.0:sd=3:sgt=15:ss=axioms:st=2.0:i=2077:si=on:rtra=on_0 on Vampire---4 for (1735ds/2077Mi) 51.97/6.93 % (24102)Instruction limit reached! 51.97/6.93 % (24102)------------------------------ 51.97/6.93 % (24102)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 51.97/6.93 % (24102)Termination reason: Unknown 51.97/6.93 % (24102)Termination phase: Saturation 51.97/6.93 51.97/6.93 % (24102)Memory used [KB]: 10490 51.97/6.93 % (24102)Time elapsed: 0.903 s 51.97/6.93 % (24102)Instructions burned: 3711 (million) 51.97/6.93 % (24102)------------------------------ 51.97/6.93 % (24102)------------------------------ 51.97/6.94 % (24341)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=5271:si=on:rtra=on_0 on Vampire---4 for (1734ds/5271Mi) 51.97/6.96 % (24332)Instruction limit reached! 51.97/6.96 % (24332)------------------------------ 51.97/6.96 % (24332)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 51.97/6.96 % (24332)Termination reason: Unknown 51.97/6.96 % (24332)Termination phase: Saturation 51.97/6.96 51.97/6.96 % (24332)Memory used [KB]: 8443 51.97/6.96 % (24332)Time elapsed: 0.264 s 51.97/6.96 % (24332)Instructions burned: 831 (million) 51.97/6.96 % (24332)------------------------------ 51.97/6.96 % (24332)------------------------------ 51.97/6.97 % (24342)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on Vampire---4 for (1734ds/346Mi) 52.53/7.05 % (24342)Instruction limit reached! 52.53/7.05 % (24342)------------------------------ 52.53/7.05 % (24342)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 52.53/7.05 % (24342)Termination reason: Unknown 52.53/7.05 % (24342)Termination phase: Saturation 52.53/7.05 52.53/7.05 % (24342)Memory used [KB]: 9210 52.53/7.05 % (24342)Time elapsed: 0.082 s 52.53/7.05 % (24342)Instructions burned: 350 (million) 52.53/7.05 % (24342)------------------------------ 52.53/7.05 % (24342)------------------------------ 52.53/7.06 % (24343)lrs+1666_1:1_au=on:s2a=on:sd=2:ss=axioms:st=5.0:i=1400:si=on:rtra=on_0 on Vampire---4 for (1733ds/1400Mi) 52.94/7.09 % (24339)Instruction limit reached! 52.94/7.09 % (24339)------------------------------ 52.94/7.09 % (24339)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 52.94/7.09 % (24339)Termination reason: Unknown 52.94/7.09 % (24339)Termination phase: Saturation 52.94/7.09 52.94/7.09 % (24339)Memory used [KB]: 8827 52.94/7.09 % (24339)Time elapsed: 0.372 s 52.94/7.09 % (24339)Instructions burned: 1174 (million) 52.94/7.09 % (24339)------------------------------ 52.94/7.09 % (24339)------------------------------ 52.94/7.10 % (24344)lrs+1002_1:1_au=on:cbe=off:fde=none:ins=1:sp=const_max:i=2325:si=on:rtra=on_0 on Vampire---4 for (1733ds/2325Mi) 54.96/7.25 % (24091)Instruction limit reached! 54.96/7.25 % (24091)------------------------------ 54.96/7.25 % (24091)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 54.96/7.25 % (24091)Termination reason: Unknown 54.96/7.25 % (24091)Termination phase: Saturation 54.96/7.25 54.96/7.25 % (24091)Memory used [KB]: 13432 54.96/7.25 % (24091)Time elapsed: 1.441 s 54.96/7.25 % (24091)Instructions burned: 4606 (million) 54.96/7.25 % (24091)------------------------------ 54.96/7.25 % (24091)------------------------------ 54.96/7.26 % (24345)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=2573:si=on:rtra=on_0 on Vampire---4 for (1731ds/2573Mi) 56.41/7.49 % (24340)Instruction limit reached! 56.41/7.49 % (24340)------------------------------ 56.41/7.49 % (24340)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 56.41/7.49 % (24340)Termination reason: Unknown 56.41/7.49 % (24340)Termination phase: Saturation 56.41/7.49 56.41/7.49 % (24340)Memory used [KB]: 9083 56.41/7.49 % (24340)Time elapsed: 0.664 s 56.41/7.49 % (24340)Instructions burned: 2079 (million) 56.41/7.49 % (24340)------------------------------ 56.41/7.49 % (24340)------------------------------ 56.41/7.50 % (24343)Instruction limit reached! 56.41/7.50 % (24343)------------------------------ 56.41/7.50 % (24343)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 56.41/7.50 % (24343)Termination reason: Unknown 56.41/7.50 % (24343)Termination phase: Saturation 56.41/7.50 56.41/7.50 % (24343)Memory used [KB]: 9083 56.41/7.50 % (24343)Time elapsed: 0.445 s 56.41/7.50 % (24343)Instructions burned: 1402 (million) 56.41/7.50 % (24343)------------------------------ 56.41/7.50 % (24343)------------------------------ 56.41/7.50 % (24346)lrs+1666_1:64_cnfonf=lazy_simp:hud=5:plsq=on:plsql=on:plsqr=152565,524288:tnu=2:i=1046:si=on:rtra=on_0 on Vampire---4 for (1729ds/1046Mi) 56.41/7.51 % (24347)dis-1002_3:1_acc=model:bd=off:bsd=on:bsdmm=1:cnfonf=lazy_not_be_gen:fd=off:fe=off:ntd=on:nwc=10.0:piset=equals:plsq=on:plsqc=1:plsqr=32,1:sp=const_max:uhcvi=on:i=1535:si=on:rtra=on_0 on Vampire---4 for (1729ds/1535Mi) 58.77/7.73 % (24346)Instruction limit reached! 58.77/7.73 % (24346)------------------------------ 58.77/7.73 % (24346)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 58.77/7.73 % (24346)Termination reason: Unknown 58.77/7.73 % (24346)Termination phase: Saturation 58.77/7.73 58.77/7.73 % (24346)Memory used [KB]: 6780 58.77/7.73 % (24346)Time elapsed: 0.223 s 58.77/7.73 % (24346)Instructions burned: 1047 (million) 58.77/7.73 % (24346)------------------------------ 58.77/7.73 % (24346)------------------------------ 58.77/7.73 % (24090)Instruction limit reached! 58.77/7.73 % (24090)------------------------------ 58.77/7.73 % (24090)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 58.77/7.73 % (24090)Termination reason: Unknown 58.77/7.73 % (24090)Termination phase: Saturation 58.77/7.73 58.77/7.73 % (24090)Memory used [KB]: 9338 58.77/7.73 % (24090)Time elapsed: 2.262 s 58.77/7.73 % (24090)Instructions burned: 7257 (million) 58.77/7.73 % (24090)------------------------------ 58.77/7.73 % (24090)------------------------------ 58.77/7.73 % (24348)lrs+1010_1:1_cnfonf=off:ntd=on:nwc=3.0:s2a=on:sp=const_frequency:i=865:si=on:rtra=on_0 on Vampire---4 for (1726ds/865Mi) 58.77/7.74 % (24349)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on Vampire---4 for (1726ds/360Mi) 59.03/7.81 % (24349)Instruction limit reached! 59.03/7.81 % (24349)------------------------------ 59.03/7.81 % (24349)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 59.03/7.81 % (24349)Termination reason: Unknown 59.03/7.81 % (24349)Termination phase: Saturation 59.03/7.81 59.03/7.81 % (24349)Memory used [KB]: 6652 59.03/7.81 % (24349)Time elapsed: 0.081 s 59.03/7.81 % (24349)Instructions burned: 362 (million) 59.03/7.81 % (24349)------------------------------ 59.03/7.81 % (24349)------------------------------ 59.03/7.82 % (24350)lrs+1010_1:1_anc=all_dependent:apa=on:au=on:bd=off:c=on:cnfonf=off:ntd=on:i=2561:si=on:rtra=on_0 on Vampire---4 for (1725ds/2561Mi) 59.03/7.82 % (24344)Refutation not found, non-redundant clauses discarded% (24344)------------------------------ 59.03/7.82 % (24344)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 59.03/7.82 % (24344)Termination reason: Refutation not found, non-redundant clauses discarded 59.03/7.82 59.03/7.82 % (24344)Memory used [KB]: 15863 59.03/7.82 % (24344)Time elapsed: 0.722 s 59.03/7.82 % (24344)Instructions burned: 2310 (million) 59.03/7.82 % (24344)------------------------------ 59.03/7.82 % (24344)------------------------------ 59.61/7.83 % (24351)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:i=1312:si=on:rtra=on_0 on Vampire---4 for (1725ds/1312Mi) 59.61/7.87 % (24347)Instruction limit reached! 59.61/7.87 % (24347)------------------------------ 59.61/7.87 % (24347)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 59.61/7.87 % (24347)Termination reason: Unknown 59.61/7.87 % (24347)Termination phase: Saturation 59.61/7.87 59.61/7.87 % (24347)Memory used [KB]: 11513 59.61/7.87 % (24347)Time elapsed: 0.360 s 59.61/7.87 % (24347)Instructions burned: 1535 (million) 59.61/7.87 % (24347)------------------------------ 59.61/7.87 % (24347)------------------------------ 59.61/7.88 % (24345)Instruction limit reached! 59.61/7.88 % (24345)------------------------------ 59.61/7.88 % (24345)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 59.61/7.88 % (24345)Termination reason: Unknown 59.61/7.88 % (24345)Termination phase: Saturation 59.61/7.88 59.61/7.88 % (24345)Memory used [KB]: 10490 59.61/7.88 % (24345)Time elapsed: 0.616 s 59.61/7.88 % (24345)Instructions burned: 2574 (million) 59.61/7.88 % (24345)------------------------------ 59.61/7.88 % (24345)------------------------------ 59.61/7.88 % (24352)dis+10_1:4_atotf=0.1:avsq=on:bsr=unit_only:e2e=on:sd=1:sp=const_max:ss=axioms:i=1516:si=on:rtra=on_0 on Vampire---4 for (1725ds/1516Mi) 59.88/7.89 % (24353)dis+21_1:1024_au=on:cnfonf=lazy_pi_sigma_gen:nm=32:ss=axioms:i=1307:si=on:rtra=on_0 on Vampire---4 for (1725ds/1307Mi) 59.88/7.94 % (24086)Instruction limit reached! 59.88/7.94 % (24086)------------------------------ 59.88/7.94 % (24086)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 59.88/7.94 % (24086)Termination reason: Unknown 59.88/7.94 % (24086)Termination phase: Saturation 59.88/7.94 59.88/7.94 % (24086)Memory used [KB]: 12665 59.88/7.94 % (24086)Time elapsed: 2.568 s 59.88/7.94 % (24086)Instructions burned: 8063 (million) 59.88/7.94 % (24086)------------------------------ 59.88/7.94 % (24086)------------------------------ 59.88/7.95 % (24354)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=2537:si=on:rtra=on_0 on Vampire---4 for (1724ds/2537Mi) 60.10/7.99 % (24348)Instruction limit reached! 60.10/7.99 % (24348)------------------------------ 60.10/7.99 % (24348)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 60.10/7.99 % (24348)Termination reason: Unknown 60.10/7.99 % (24348)Termination phase: Saturation 60.10/7.99 60.10/7.99 % (24348)Memory used [KB]: 7036 60.10/7.99 % (24348)Time elapsed: 0.261 s 60.10/7.99 % (24348)Instructions burned: 865 (million) 60.10/7.99 % (24348)------------------------------ 60.10/7.99 % (24348)------------------------------ 60.10/8.00 % (24355)lrs+32_1:1_au=on:bet=on:cbe=off:cs=on:ins=3:i=6102:si=on:rtra=on_0 on Vampire---4 for (1724ds/6102Mi) 60.70/8.15 % (24353)Instruction limit reached! 60.70/8.15 % (24353)------------------------------ 60.70/8.15 % (24353)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 60.70/8.15 % (24353)Termination reason: Unknown 60.70/8.15 % (24353)Termination phase: Saturation 60.70/8.15 60.70/8.15 % (24353)Memory used [KB]: 6652 60.70/8.15 % (24353)Time elapsed: 0.265 s 60.70/8.15 % (24353)Instructions burned: 1307 (million) 60.70/8.15 % (24353)------------------------------ 60.70/8.15 % (24353)------------------------------ 60.70/8.15 % (24341)Instruction limit reached! 60.70/8.15 % (24341)------------------------------ 60.70/8.15 % (24341)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 60.70/8.15 % (24341)Termination reason: Unknown 60.70/8.15 % (24341)Termination phase: Saturation 60.70/8.15 60.70/8.15 % (24341)Memory used [KB]: 10746 60.70/8.15 % (24341)Time elapsed: 1.202 s 60.70/8.15 % (24341)Instructions burned: 5272 (million) 60.70/8.15 % (24341)------------------------------ 60.70/8.15 % (24341)------------------------------ 60.70/8.16 % (24356)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=454:si=on:rtra=on_0 on Vampire---4 for (1722ds/454Mi) 60.70/8.16 % (24357)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=430:si=on:rtra=on_0 on Vampire---4 for (1722ds/430Mi) 61.06/8.19 % (24351)Instruction limit reached! 61.06/8.19 % (24351)------------------------------ 61.06/8.19 % (24351)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 61.06/8.19 % (24351)Termination reason: Unknown 61.06/8.19 % (24351)Termination phase: Saturation 61.06/8.19 61.06/8.19 % (24351)Memory used [KB]: 10106 61.06/8.19 % (24351)Time elapsed: 0.363 s 61.06/8.19 % (24351)Instructions burned: 1313 (million) 61.06/8.19 % (24351)------------------------------ 61.06/8.19 % (24351)------------------------------ 61.06/8.20 % (24358)lrs+1010_1:1_au=on:bd=off:e2e=on:fde=unused:nm=4:s2a=on:sos=all:sp=const_frequency:i=18808:si=on:rtra=on_0 on Vampire---4 for (1722ds/18808Mi) 63.09/8.26 % (24356)Instruction limit reached! 63.09/8.26 % (24356)------------------------------ 63.09/8.26 % (24356)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 63.09/8.26 % (24356)Termination reason: Unknown 63.09/8.26 % (24356)Termination phase: Saturation 63.09/8.26 63.09/8.26 % (24356)Memory used [KB]: 13816 63.09/8.26 % (24356)Time elapsed: 0.105 s 63.09/8.26 % (24356)Instructions burned: 456 (million) 63.09/8.26 % (24356)------------------------------ 63.09/8.26 % (24356)------------------------------ 63.09/8.26 % (24357)Instruction limit reached! 63.09/8.26 % (24357)------------------------------ 63.09/8.26 % (24357)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 63.09/8.26 % (24357)Termination reason: Unknown 63.09/8.26 % (24357)Termination phase: Saturation 63.09/8.26 63.09/8.26 % (24357)Memory used [KB]: 10234 63.09/8.26 % (24357)Time elapsed: 0.105 s 63.09/8.26 % (24357)Instructions burned: 431 (million) 63.09/8.26 % (24357)------------------------------ 63.09/8.26 % (24357)------------------------------ 63.09/8.27 % (24359)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=951:si=on:rtra=on_0 on Vampire---4 for (1721ds/951Mi) 63.25/8.27 % (24360)lrs+1002_1:28_bd=off:cnfonf=lazy_simp:plsq=on:plsqr=1,1:prag=on:i=1003:si=on:rtra=on_0 on Vampire---4 for (1721ds/1003Mi) 63.55/8.33 % (24352)Instruction limit reached! 63.55/8.33 % (24352)------------------------------ 63.55/8.33 % (24352)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 63.55/8.33 % (24352)Termination reason: Unknown 63.55/8.33 % (24352)Termination phase: Saturation 63.55/8.33 63.55/8.33 % (24352)Memory used [KB]: 11001 63.55/8.33 % (24352)Time elapsed: 0.455 s 63.55/8.33 % (24352)Instructions burned: 1516 (million) 63.55/8.33 % (24352)------------------------------ 63.55/8.33 % (24352)------------------------------ 63.55/8.34 % (24361)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=14651:si=on:rtra=on_0 on Vampire---4 for (1720ds/14651Mi) 64.07/8.47 % (24354)First to succeed. 64.32/8.48 % (24359)Instruction limit reached! 64.32/8.48 % (24359)------------------------------ 64.32/8.48 % (24359)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 64.32/8.48 % (24359)Termination reason: Unknown 64.32/8.48 % (24359)Termination phase: Saturation 64.32/8.48 64.32/8.48 % (24359)Memory used [KB]: 9338 64.32/8.48 % (24359)Time elapsed: 0.215 s 64.32/8.48 % (24359)Instructions burned: 954 (million) 64.32/8.48 % (24359)------------------------------ 64.32/8.48 % (24359)------------------------------ 64.32/8.49 % (24360)Instruction limit reached! 64.32/8.49 % (24360)------------------------------ 64.32/8.49 % (24360)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 64.32/8.49 % (24360)Termination reason: Unknown 64.32/8.49 % (24360)Termination phase: Saturation 64.32/8.49 64.32/8.49 % (24360)Memory used [KB]: 6780 64.32/8.49 % (24360)Time elapsed: 0.217 s 64.32/8.49 % (24360)Instructions burned: 1003 (million) 64.32/8.49 % (24360)------------------------------ 64.32/8.49 % (24360)------------------------------ 64.32/8.49 % (24362)dis+1010_1:1_aac=none:bd=preordered:e2e=on:fde=none:fe=axiom:nm=16:nwc=10.0:prag=on:i=1658:si=on:rtra=on_0 on Vampire---4 for (1719ds/1658Mi) 64.32/8.50 % (24363)dis+10_1:1_avsq=on:avsqr=9,8:cnfonf=lazy_gen:fe=off:ntd=on:i=3186:si=on:rtra=on_0 on Vampire---4 for (1719ds/3186Mi) 65.51/8.64 % (24350)Instruction limit reached! 65.51/8.64 % (24350)------------------------------ 65.51/8.64 % (24350)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 65.51/8.64 % (24350)Termination reason: Unknown 65.51/8.64 % (24350)Termination phase: Saturation 65.51/8.64 65.51/8.64 % (24350)Memory used [KB]: 10618 65.51/8.64 % (24350)Time elapsed: 0.831 s 65.51/8.64 % (24350)Instructions burned: 2563 (million) 65.51/8.64 % (24350)------------------------------ 65.51/8.64 % (24350)------------------------------ 65.63/8.65 % (24364)dis+21_1:1_aac=none:bsr=on:nwc=3.0:s2a=on:i=3201:si=on:rtra=on_0 on Vampire---4 for (1717ds/3201Mi) 67.27/8.83 % (24354)Refutation found. Thanks to Tanya! 67.27/8.83 % SZS status Theorem for Vampire---4 67.27/8.83 % SZS output start Proof for Vampire---4 67.27/8.83 thf(func_def_0, type, in: $i > $i > $o). 67.27/8.83 thf(func_def_1, type, exu: ($i > $o) > $o). 67.27/8.83 thf(func_def_6, type, setadjoin: $i > $i > $i). 67.27/8.83 thf(func_def_8, type, powerset: $i > $i). 67.27/8.83 thf(func_def_10, type, setunion: $i > $i). 67.27/8.83 thf(func_def_19, type, descr: ($i > $o) > $i). 67.27/8.83 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i). 67.27/8.83 thf(func_def_26, type, prop2set: $o > $i). 67.27/8.83 thf(func_def_36, type, nonempty: $i > $o). 67.27/8.83 thf(func_def_69, type, set2prop: $i > $o). 67.27/8.83 thf(func_def_88, type, subset: $i > $i > $o). 67.27/8.83 thf(func_def_89, type, disjoint: $i > $i > $o). 67.27/8.83 thf(func_def_90, type, setsmeet: $i > $i > $o). 67.27/8.83 thf(func_def_114, type, binunion: $i > $i > $i). 67.27/8.83 thf(func_def_122, type, binintersect: $i > $i > $i). 67.27/8.83 thf(func_def_135, type, regular: $i > $o). 67.27/8.83 thf(func_def_136, type, setminus: $i > $i > $i). 67.27/8.83 thf(func_def_147, type, symdiff: $i > $i > $i). 67.27/8.83 thf(func_def_153, type, iskpair: $i > $o). 67.27/8.83 thf(func_def_158, type, kpair: $i > $i > $i). 67.27/8.83 thf(func_def_160, type, cartprod: $i > $i > $i). 67.27/8.83 thf(func_def_177, type, singleton: $i > $o). 67.27/8.83 thf(func_def_179, type, ex1: $i > ($i > $o) > $o). 67.27/8.83 thf(f996,plain,( 67.27/8.83 $false), 67.27/8.83 inference(trivial_inequality_removal,[],[f995])). 67.27/8.83 thf(f995,plain,( 67.27/8.83 ($true = $false)), 67.27/8.83 inference(forward_demodulation,[],[f990,f993])). 67.27/8.83 thf(f993,plain,( 67.27/8.83 ($false = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))), 67.27/8.83 inference(binary_proxy_clausification,[],[f991])). 67.27/8.83 thf(f991,plain,( 67.27/8.83 (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y3 @ (dsetconstr @ Y1 @ Y0)))))))))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))) = $false)), 67.27/8.83 inference(binary_proxy_clausification,[],[f989])). 67.27/8.83 thf(f989,plain,( 67.27/8.83 (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))) => (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y3 @ (dsetconstr @ Y1 @ Y0)))))))))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))) = $false)), 67.27/8.83 inference(binary_proxy_clausification,[],[f987])). 67.27/8.83 thf(f987,plain,( 67.27/8.83 ($false = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))) => (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y3 @ (dsetconstr @ Y1 @ Y0)))))))))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))), 67.27/8.83 inference(binary_proxy_clausification,[],[f985])). 67.27/8.83 thf(f985,plain,( 67.27/8.83 ($false = ((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))) => (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y3 @ (dsetconstr @ Y1 @ Y0)))))))))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))), 67.27/8.83 inference(binary_proxy_clausification,[],[f983])). 67.27/8.83 thf(f983,plain,( 67.27/8.83 (((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))) => ((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))) => (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y3 @ (dsetconstr @ Y1 @ Y0)))))))))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))) = $false)), 67.27/8.83 inference(binary_proxy_clausification,[],[f981])). 67.27/8.83 thf(f981,plain,( 67.27/8.83 (((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))) => ((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))) => (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y3 @ (dsetconstr @ Y1 @ Y0)))))))))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))) = $false)), 67.27/8.83 inference(binary_proxy_clausification,[],[f979])). 67.27/8.83 thf(f979,plain,( 67.27/8.83 ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))) => ((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))) => (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y3 @ (dsetconstr @ Y1 @ Y0)))))))))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))), 67.27/8.83 inference(binary_proxy_clausification,[],[f977])). 67.27/8.83 thf(f977,plain,( 67.27/8.83 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y2 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ Y1)) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (setunion @ Y1)) & ((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y4 @ emptyset)) @ emptyset)) = Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))) => ((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))) => (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y3 @ (dsetconstr @ Y1 @ Y0)))))))))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))) = $false)), 67.27/8.83 inference(binary_proxy_clausification,[],[f975])). 67.27/8.83 thf(f975,plain,( 67.27/8.83 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y4 @ emptyset)) @ emptyset)) = Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y2 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ Y1)) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (setunion @ Y1)) & ((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y4 @ emptyset)) @ emptyset)) = Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))) => ((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))) => (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y3 @ (dsetconstr @ Y1 @ Y0)))))))))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))) = $false)), 67.27/8.83 inference(binary_proxy_clausification,[],[f973])). 67.27/8.83 thf(f973,plain,( 67.27/8.83 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (cartprod @ Y1 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y4 @ emptyset)) @ emptyset)) = Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y2 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ Y1)) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (setunion @ Y1)) & ((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y4 @ emptyset)) @ emptyset)) = Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))) => ((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))) => (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y3 @ (dsetconstr @ Y1 @ Y0)))))))))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))) = $false)), 67.27/8.83 inference(binary_proxy_clausification,[],[f971])). 67.27/8.83 thf(f971,plain,( 67.27/8.83 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y2 @ Y0)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (cartprod @ Y1 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y4 @ emptyset)) @ emptyset)) = Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y2 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ Y1)) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (setunion @ Y1)) & ((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y4 @ emptyset)) @ emptyset)) = Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))) => ((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))) => (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y3 @ (dsetconstr @ Y1 @ Y0)))))))))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))) = $false)), 67.27/8.83 inference(binary_proxy_clausification,[],[f969])). 67.27/8.83 thf(f969,plain,( 67.27/8.83 ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y2 @ Y0)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (cartprod @ Y1 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y4 @ emptyset)) @ emptyset)) = Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y2 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ Y1)) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (setunion @ Y1)) & ((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y4 @ emptyset)) @ emptyset)) = Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))) => ((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))) => (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y3 @ (dsetconstr @ Y1 @ Y0)))))))))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))), 67.27/8.83 inference(binary_proxy_clausification,[],[f967])). 67.27/8.83 thf(f967,plain,( 67.27/8.83 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ Y1 @ Y2))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y2 @ Y0)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (cartprod @ Y1 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y4 @ emptyset)) @ emptyset)) = Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y2 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ Y1)) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (setunion @ Y1)) & ((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y4 @ emptyset)) @ emptyset)) = Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))) => ((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))) => (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y3 @ (dsetconstr @ Y1 @ Y0)))))))))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))) = $false)), 67.27/8.83 inference(binary_proxy_clausification,[],[f965])). 67.27/8.83 thf(f965,plain,( 67.27/8.83 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y1))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ Y1 @ Y2))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y2 @ Y0)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (cartprod @ Y1 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y4 @ emptyset)) @ emptyset)) = Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y2 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ Y1)) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (setunion @ Y1)) & ((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y4 @ emptyset)) @ emptyset)) = Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))) => ((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))) => (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y3 @ (dsetconstr @ Y1 @ Y0)))))))))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))) = $false)), 67.27/8.83 inference(binary_proxy_clausification,[],[f963])). 67.27/8.83 thf(f963,plain,( 67.27/8.83 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (subset @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y0 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y1))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ Y1 @ Y2))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y2 @ Y0)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (cartprod @ Y1 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y4 @ emptyset)) @ emptyset)) = Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y2 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ Y1)) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (setunion @ Y1)) & ((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y4 @ emptyset)) @ emptyset)) = Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))) => ((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))) => (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))) => ((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))) => (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y3 @ (dsetconstr @ Y1 @ Y0)))))))))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))) = $false)), 67.27/8.83 inference(binary_proxy_clausification,[],[f959])). 67.27/8.83 thf(f959,plain,( 67.27/8.83 ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y0 @ Y2)))))))))) => ((!! 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@ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y2 @ Y0)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (cartprod @ Y1 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y4 @ emptyset)) @ emptyset)) = Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y2 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ Y1)) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (setunion @ Y1)) & ((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y4 @ emptyset)) @ emptyset)) = Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))) => ((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))) => (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y3 @ (dsetconstr @ Y1 @ Y0)))))))))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))), 67.27/8.83 inference(binary_proxy_clausification,[],[f957])). 67.27/8.83 thf(f957,plain,( 67.27/8.83 ($false = ((!! 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@ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ Y1 @ Y2))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y2 @ Y0)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (cartprod @ Y1 @ Y0)))))))))))) => ((!! 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@ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))) => (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y3 @ (dsetconstr @ Y1 @ Y0)))))))))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))), 67.27/8.83 inference(binary_proxy_clausification,[],[f955])). 67.27/8.83 thf(f955,plain,( 67.27/8.83 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ (setadjoin @ Y1 @ emptyset) @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ (setadjoin @ Y0 @ emptyset) @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (subset @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y0 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y1))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ Y1 @ Y2))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y2 @ Y0)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (cartprod @ Y1 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y4 @ emptyset)) @ emptyset)) = Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y2 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ Y1)) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (setunion @ Y1)) & ((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y4 @ emptyset)) @ emptyset)) = Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))) => ((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))) => (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y3 @ (dsetconstr @ Y1 @ Y0)))))))))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))) = $false)), 67.27/8.83 inference(binary_proxy_clausification,[],[f953])). 67.27/8.83 thf(f953,plain,( 67.27/8.83 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))) & (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))) & ((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ (setadjoin @ Y1 @ emptyset) @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ (setadjoin @ Y0 @ emptyset) @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (subset @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y0 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y1))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ Y1 @ Y2))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y2 @ Y0)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (cartprod @ Y1 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y4 @ emptyset)) @ emptyset)) = Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y2 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ Y1)) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (setunion @ Y1)) & ((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y4 @ emptyset)) @ emptyset)) = Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))) => ((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))) => (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y3 @ (dsetconstr @ Y1 @ Y0)))))))))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))) = $false)), 67.27/8.83 inference(binary_proxy_clausification,[],[f951])). 67.27/8.83 thf(f951,plain,( 67.27/8.83 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))) & (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))) & ((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))) & (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))) & ((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ (setadjoin @ Y1 @ emptyset) @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ (setadjoin @ Y0 @ emptyset) @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (subset @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y0 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y1))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ Y1 @ Y2))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y2 @ Y0)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (cartprod @ Y1 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y4 @ emptyset)) @ emptyset)) = Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y2 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ Y1)) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (setunion @ Y1)) & ((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y4 @ emptyset)) @ emptyset)) = Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))) => ((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))) => (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y3 @ (dsetconstr @ Y1 @ Y0)))))))))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))) = $false)), 67.27/8.83 inference(binary_proxy_clausification,[],[f949])). 67.27/8.83 thf(f949,plain,( 67.27/8.83 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))) & (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))) & ((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))) & (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))) & ((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ (setadjoin @ Y1 @ emptyset) @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ (setadjoin @ Y0 @ emptyset) @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (subset @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y0 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y1))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ Y1 @ Y2))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y2 @ Y0)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (cartprod @ Y1 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y4 @ emptyset)) @ emptyset)) = Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y2 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ Y1)) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (setunion @ Y1)) & ((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y4 @ emptyset)) @ emptyset)) = Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))) => ((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))) => (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y3 @ (dsetconstr @ Y1 @ Y0)))))))))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))) = $false)), 67.27/8.83 inference(binary_proxy_clausification,[],[f947])). 67.27/8.83 thf(f947,plain,( 67.27/8.83 ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))) & (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))) & ((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))) & (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))) & ((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ (setadjoin @ Y1 @ emptyset) @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ (setadjoin @ Y0 @ emptyset) @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (subset @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y0 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y1))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ Y1 @ Y2))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y2 @ Y0)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! 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@ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))) => (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y3 @ (dsetconstr @ Y1 @ Y0)))))))))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))) = $false)), 67.27/8.83 inference(binary_proxy_clausification,[],[f941])). 67.27/8.83 thf(f941,plain,( 67.27/8.83 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ (symdiff @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((in @ Y1 @ Y0) => (~ (in @ Y1 @ (symdiff @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))) & (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))) & ((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))) & (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))) & ((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ (setadjoin @ Y1 @ emptyset) @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ (setadjoin @ Y0 @ emptyset) @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (subset @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y0 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y1))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ Y1 @ Y2))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y2 @ Y0)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (cartprod @ Y1 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y4 @ emptyset)) @ emptyset)) = Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y2 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ Y1)) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (setunion @ Y1)) & ((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y4 @ emptyset)) @ emptyset)) = Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))) => ((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))) => (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y3 @ (dsetconstr @ Y1 @ Y0)))))))))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))) = $false)), 67.27/8.83 inference(binary_proxy_clausification,[],[f939])). 67.27/8.83 thf(f939,plain,( 67.27/8.83 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (in @ Y0 @ (symdiff @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ (symdiff @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((in @ Y1 @ Y0) => (~ (in @ Y1 @ (symdiff @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))) & (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))) & ((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))) & (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))) & ((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ (setadjoin @ Y1 @ emptyset) @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ (setadjoin @ Y0 @ emptyset) @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (subset @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y0 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y1))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ Y1 @ Y2))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y2 @ Y0)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (cartprod @ Y1 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y4 @ emptyset)) @ emptyset)) = Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y2 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ Y1)) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (setunion @ Y1)) & ((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y4 @ emptyset)) @ emptyset)) = Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))) => ((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))) => (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y3 @ (dsetconstr @ Y1 @ Y0)))))))))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))) = $false)), 67.27/8.83 inference(binary_proxy_clausification,[],[f937])). 67.27/8.83 thf(f937,plain,( 67.27/8.83 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (symdiff @ Y2 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => Y3)) => (((~ (in @ Y1 @ Y2)) => ((in @ Y1 @ Y0) => Y3)) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (in @ Y0 @ (symdiff @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ (symdiff @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((in @ Y1 @ Y0) => (~ (in @ Y1 @ (symdiff @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))) & (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))) & ((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))) & (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))) & ((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ (setadjoin @ Y1 @ emptyset) @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ (setadjoin @ Y0 @ emptyset) @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (subset @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y0 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y1))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ Y1 @ Y2))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y2 @ Y0)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (cartprod @ Y1 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y4 @ emptyset)) @ emptyset)) = Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y2 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ Y1)) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (setunion @ Y1)) & ((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y4 @ emptyset)) @ emptyset)) = Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))) => ((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))) => (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y3 @ (dsetconstr @ Y1 @ Y0)))))))))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))) = $false)), 67.27/8.83 inference(binary_proxy_clausification,[],[f935])). 67.27/8.83 thf(f935,plain,( 67.27/8.83 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (symdiff @ Y2 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => Y3)) => (((~ (in @ Y1 @ Y2)) => ((in @ Y1 @ Y0) => Y3)) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (in @ Y0 @ (symdiff @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ (symdiff @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((in @ Y1 @ Y0) => (~ (in @ Y1 @ (symdiff @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))) & (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))) & ((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))) & (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))) & ((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ (setadjoin @ Y1 @ emptyset) @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ (setadjoin @ Y0 @ emptyset) @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (subset @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y0 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y1))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ Y1 @ Y2))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y2 @ Y0)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (cartprod @ Y1 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y4 @ emptyset)) @ emptyset)) = Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y2 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ Y1)) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (setunion @ Y1)) & ((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y4 @ emptyset)) @ emptyset)) = Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))) => ((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))) => (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y3 @ (dsetconstr @ Y1 @ Y0)))))))))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))) = $false)), 67.27/8.83 inference(binary_proxy_clausification,[],[f933])). 67.27/8.83 thf(f933,plain,( 67.27/8.83 ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (symdiff @ Y2 @ Y0)) => (!! 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@ $o @ (^[Y3 : $o]: (((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => Y3)) => (((~ (in @ Y1 @ Y2)) => ((in @ Y1 @ Y0) => Y3)) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (in @ Y0 @ (symdiff @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ (symdiff @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((in @ Y1 @ Y0) => (~ (in @ Y1 @ (symdiff @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))) & (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))) & ((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))) & (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))) & ((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ (setadjoin @ Y1 @ emptyset) @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ (setadjoin @ Y0 @ emptyset) @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (subset @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y0 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y1))))))))))))) => ((!! 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@ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (cartprod @ Y1 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y4 @ emptyset)) @ emptyset)) = Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y2 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ Y1)) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (setunion @ Y1)) & ((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y4 @ emptyset)) @ emptyset)) = Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))) => ((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))) => (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y3 @ (dsetconstr @ Y1 @ Y0)))))))))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))), 67.27/8.83 inference(binary_proxy_clausification,[],[f917])). 67.27/8.83 thf(f917,plain,( 67.27/8.83 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setminus @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setminus @ Y0 @ Y2)) => (~ (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (emptyset = (setminus @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y0 @ Y2))) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y2 @ Y0))) => ((~ (in @ Y1 @ Y0)) => (~ (in @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ Y2)) => (~ (in @ Y1 @ (setminus @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (~ (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))) & (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))) & ((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))) & (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))) & ((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ (setadjoin @ Y1 @ emptyset) @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ (setadjoin @ Y0 @ emptyset) @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (subset @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y0 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y1))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ Y1 @ Y2))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y2 @ Y0)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (cartprod @ Y1 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y4 @ emptyset)) @ emptyset)) = Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y2 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ Y1)) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (setunion @ Y1)) & ((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y4 @ emptyset)) @ emptyset)) = Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))) => ((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))) => (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y3 @ (dsetconstr @ Y1 @ Y0)))))))))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 67.27/8.83 inference(binary_proxy_clausification,[],[f915])). 67.27/8.83 thf(f915,plain,( 67.27/8.83 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binunion @ (binintersect @ Y2 @ Y1) @ (binintersect @ Y2 @ Y0)) = (binintersect @ Y2 @ (binunion @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setminus @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setminus @ Y0 @ Y2)) => (~ (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (emptyset = (setminus @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y0 @ Y2))) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y2 @ Y0))) => ((~ (in @ Y1 @ Y0)) => (~ (in @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ Y2)) => (~ (in @ Y1 @ (setminus @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (~ (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (symdiff @ Y2 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => Y3)) => (((~ (in @ Y1 @ Y2)) => ((in @ Y1 @ Y0) => Y3)) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (in @ Y0 @ (symdiff @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ (symdiff @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((in @ Y1 @ Y0) => (~ (in @ Y1 @ (symdiff @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))) & (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))) & ((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))) & (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))) & ((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ (setadjoin @ Y1 @ emptyset) @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ (setadjoin @ Y0 @ emptyset) @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (subset @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y0 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y1))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ Y1 @ Y2))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y2 @ Y0)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (cartprod @ Y1 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y4 @ emptyset)) @ emptyset)) = Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y2 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ Y1)) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (setunion @ Y1)) & ((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y4 @ emptyset)) @ emptyset)) = Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))) => ((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))) => (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y3 @ (dsetconstr @ Y1 @ Y0)))))))))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 67.27/8.83 inference(binary_proxy_clausification,[],[f913])). 67.27/8.83 thf(f913,plain,( 67.27/8.83 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binunion @ (binintersect @ Y2 @ Y1) @ (binintersect @ Y2 @ Y0)) = (binintersect @ Y2 @ (binunion @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setminus @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setminus @ Y0 @ Y2)) => (~ (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (emptyset = (setminus @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y0 @ Y2))) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! 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@ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y3 @ (dsetconstr @ Y1 @ Y0)))))))))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))), 67.27/8.83 inference(binary_proxy_clausification,[],[f909])). 67.27/8.83 thf(f909,plain,( 67.27/8.83 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y0 @ Y1) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y2 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ Y1)) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (setunion @ Y1)) & ((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y4 @ emptyset)) @ emptyset)) = Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))) => ((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))) => (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y3 @ (dsetconstr @ Y1 @ Y0)))))))))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 67.27/8.83 inference(binary_proxy_clausification,[],[f897])). 67.27/8.83 thf(f897,plain,( 67.27/8.83 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y0 @ Y1) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y0 @ Y2)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))) => (emptyset = (binintersect @ Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y0 @ Y1) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binunion @ (binintersect @ Y2 @ Y1) @ (binintersect @ Y2 @ Y0)) = (binintersect @ Y2 @ (binunion @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setminus @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setminus @ Y0 @ Y2)) => (~ (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (emptyset = (setminus @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y0 @ Y2))) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y2 @ Y0))) => ((~ (in @ Y1 @ Y0)) => (~ (in @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ Y2)) => (~ (in @ Y1 @ (setminus @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (~ (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (symdiff @ Y2 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => Y3)) => (((~ (in @ Y1 @ Y2)) => ((in @ Y1 @ Y0) => Y3)) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (in @ Y0 @ (symdiff @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ (symdiff @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((in @ Y1 @ Y0) => (~ (in @ Y1 @ (symdiff @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))) & (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))) & ((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))) & (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))) & ((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ (setadjoin @ Y1 @ emptyset) @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ (setadjoin @ Y0 @ emptyset) @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (subset @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y0 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y1))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ Y1 @ Y2))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y2 @ Y0)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (cartprod @ Y1 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y4 @ emptyset)) @ emptyset)) = Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y2 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ Y1)) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (setunion @ Y1)) & ((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y4 @ emptyset)) @ emptyset)) = Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))) => ((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))) => (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y3 @ (dsetconstr @ Y1 @ Y0)))))))))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 67.27/8.83 inference(binary_proxy_clausification,[],[f895])). 67.27/8.83 thf(f895,plain,( 67.27/8.83 ($false = ((!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (subset @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y0 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y1))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ Y1 @ Y2))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y2 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ Y1)) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (setunion @ Y1)) & ((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y4 @ emptyset)) @ emptyset)) = Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))) => ((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))) => (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y3 @ (dsetconstr @ Y1 @ Y0)))))))))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 67.27/8.83 inference(boolean_simplification,[],[f883])). 67.27/8.83 thf(f883,plain,( 67.27/8.83 ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ (binunion @ Y0 @ Y3)) => (((in @ Y1 @ Y0) => Y2) => (((in @ Y1 @ Y3) => Y2) => Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binunion @ Y2 @ Y1)) => ((in @ Y0 @ Y2) | (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ (binintersect @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y0) => ((subset @ Y2 @ Y1) => (subset @ Y2 @ (binintersect @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y0 @ Y1) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y0 @ Y2)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))) => (emptyset = (binintersect @ Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y0 @ Y1) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binunion @ (binintersect @ Y2 @ Y1) @ (binintersect @ Y2 @ Y0)) = (binintersect @ Y2 @ (binunion @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setminus @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setminus @ Y0 @ Y2)) => (~ (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (emptyset = (setminus @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y0 @ Y2))) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y2 @ Y0))) => ((~ (in @ Y1 @ Y0)) => (~ (in @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ Y2)) => (~ (in @ Y1 @ (setminus @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (~ (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (symdiff @ Y2 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => Y3)) => (((~ (in @ Y1 @ Y2)) => ((in @ Y1 @ Y0) => Y3)) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (in @ Y0 @ (symdiff @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ (symdiff @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((in @ Y1 @ Y0) => (~ (in @ Y1 @ (symdiff @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ($true => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))) & (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))) & ((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))) & (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))) & ((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ (setadjoin @ Y1 @ emptyset) @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ (setadjoin @ Y0 @ emptyset) @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (subset @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y0 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y1))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ Y1 @ Y2))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y2 @ Y0)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (cartprod @ Y1 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y4 @ emptyset)) @ emptyset)) = Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y2 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ Y1)) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (setunion @ Y1)) & ((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y4 @ emptyset)) @ emptyset)) = Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))) => ((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))) => (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y3 @ (dsetconstr @ Y1 @ Y0)))))))))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 67.27/8.83 inference(forward_demodulation,[],[f881,f882])). 67.27/8.83 thf(f882,plain,( 67.27/8.83 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))))), 67.27/8.83 inference(binary_proxy_clausification,[],[f879])). 67.27/8.83 thf(f879,plain,( 67.27/8.83 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ (binunion @ Y0 @ Y3)) => (((in @ Y1 @ Y0) => Y2) => (((in @ Y1 @ Y3) => Y2) => Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binunion @ Y2 @ Y1)) => ((in @ Y0 @ Y2) | (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ (binintersect @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y0) => ((subset @ Y2 @ Y1) => (subset @ Y2 @ (binintersect @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y0 @ Y1) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y0 @ Y2)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))) => (emptyset = (binintersect @ Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y0 @ Y1) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binunion @ (binintersect @ Y2 @ Y1) @ (binintersect @ Y2 @ Y0)) = (binintersect @ Y2 @ (binunion @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setminus @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setminus @ Y0 @ Y2)) => (~ (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (emptyset = (setminus @ Y1 @ Y0))))))) => ((!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (in @ Y0 @ (symdiff @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ (symdiff @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((in @ Y1 @ Y0) => (~ (in @ Y1 @ (symdiff @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))) & (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))) & ((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))) & (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))) & ((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ (setadjoin @ Y1 @ emptyset) @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ (setadjoin @ Y0 @ emptyset) @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (subset @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y0 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y1))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ Y1 @ Y2))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y2 @ Y0)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (cartprod @ Y1 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y4 @ emptyset)) @ emptyset)) = Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y2 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ Y1)) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (setunion @ Y1)) & ((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y4 @ emptyset)) @ emptyset)) = Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))) => ((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))) => (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y3 @ (dsetconstr @ Y1 @ Y0)))))))))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 67.27/8.83 inference(binary_proxy_clausification,[],[f877])). 67.27/8.83 thf(f877,plain,( 67.27/8.83 ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ (binunion @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ (binunion @ Y0 @ Y3)) => (((in @ Y1 @ Y0) => Y2) => (((in @ Y1 @ Y3) => Y2) => Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binunion @ Y2 @ Y1)) => ((in @ Y0 @ Y2) | (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ (binintersect @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y0) => ((subset @ Y2 @ Y1) => (subset @ Y2 @ (binintersect @ Y0 @ Y1)))))))))) => ((!! 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@ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))) => ((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))) => (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y3 @ (dsetconstr @ Y1 @ Y0)))))))))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 67.27/8.83 inference(binary_proxy_clausification,[],[f849])). 67.27/8.83 thf(f849,plain,( 67.27/8.83 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => ((~ (in @ Y1 @ Y2)) => (~ (Y2 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! 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@ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))) => (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y3 @ (dsetconstr @ Y1 @ Y0)))))))))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 67.27/8.83 inference(binary_proxy_clausification,[],[f827])). 67.27/8.83 thf(f827,plain,( 67.27/8.83 (((!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ (binunion @ Y0 @ Y3)) => (((in @ Y1 @ Y0) => Y2) => (((in @ Y1 @ Y3) => Y2) => Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binunion @ Y2 @ Y1)) => ((in @ Y0 @ Y2) | (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ (binintersect @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y0) => ((subset @ Y2 @ Y1) => (subset @ Y2 @ (binintersect @ Y0 @ Y1)))))))))) => ((!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binunion @ (binintersect @ Y2 @ Y1) @ (binintersect @ Y2 @ Y0)) = (binintersect @ Y2 @ (binunion @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setminus @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setminus @ Y0 @ Y2)) => (~ (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (emptyset = (setminus @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y0 @ Y2))) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y2 @ Y0))) => ((~ (in @ Y1 @ Y0)) => (~ (in @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ Y2)) => (~ (in @ Y1 @ (setminus @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (~ (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (symdiff @ Y2 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => Y3)) => (((~ (in @ Y1 @ Y2)) => ((in @ Y1 @ Y0) => Y3)) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (in @ Y0 @ (symdiff @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ (symdiff @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((in @ Y1 @ Y0) => (~ (in @ Y1 @ (symdiff @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))) & (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))) & ((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))) & (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))) & ((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ (setadjoin @ Y1 @ emptyset) @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ (setadjoin @ Y0 @ emptyset) @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (subset @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y0 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y1))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ Y1 @ Y2))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y2 @ Y0)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (cartprod @ Y1 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y4 @ emptyset)) @ emptyset)) = Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y2 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ Y1)) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (setunion @ Y1)) & ((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y4 @ emptyset)) @ emptyset)) = Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))) => ((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))) => (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y3 @ (dsetconstr @ Y1 @ Y0)))))))))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 67.27/8.83 inference(boolean_simplification,[],[f819])). 67.27/8.83 thf(f819,plain,( 67.27/8.83 (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) = (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ($true => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) => ((?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))) => ((descr @ Y1) = (descr @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y3 @ Y4) = (Y2 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y2) = (dsetconstr @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1))))))))) => ((!! 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@ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y2 @ Y0)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (cartprod @ Y1 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y4 @ emptyset)) @ emptyset)) = Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y2 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ Y1)) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (setunion @ Y1)) & ((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y4 @ emptyset)) @ emptyset)) = Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))) => ((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))) => (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y3 @ (dsetconstr @ Y1 @ Y0)))))))))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 67.27/8.83 inference(forward_demodulation,[],[f817,f818])). 67.27/8.83 thf(f818,plain,( 67.27/8.83 ($true = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))))), 67.27/8.83 inference(binary_proxy_clausification,[],[f815])). 67.27/8.83 thf(f815,plain,( 67.27/8.83 ($false = ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) = (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) => ((?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))) => ((descr @ Y1) = (descr @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((in @ Y1 @ Y0) => (~ (in @ Y1 @ (symdiff @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))) & (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))) & ((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))) & (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))) & ((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ (setadjoin @ Y1 @ emptyset) @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ (setadjoin @ Y0 @ emptyset) @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (subset @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y0 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y1))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ Y1 @ Y2))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y2 @ Y0)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (cartprod @ Y1 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y4 @ emptyset)) @ emptyset)) = Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y2 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ Y1)) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (setunion @ Y1)) & ((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y4 @ emptyset)) @ emptyset)) = Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))) => ((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))) => (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y3 @ (dsetconstr @ Y1 @ Y0)))))))))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 67.27/8.84 inference(forward_demodulation,[],[f733,f734])). 67.27/8.84 thf(f734,plain,( 67.27/8.84 ($true = (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))))), 67.27/8.84 inference(binary_proxy_clausification,[],[f731])). 67.27/8.84 thf(f731,plain,( 67.27/8.84 (((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) = (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y1 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ Y0)) => ((Y2 = Y1) | (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (powerset @ Y2)) => ((in @ Y0 @ Y1) => (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! 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@ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y3 @ (dsetconstr @ Y1 @ Y0)))))))))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 67.27/8.84 inference(binary_proxy_clausification,[],[f729])). 67.27/8.84 thf(f729,plain,( 67.27/8.84 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (subset @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y0 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y1))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ Y1 @ Y2))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y2 @ Y0)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (cartprod @ Y1 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y4 @ emptyset)) @ emptyset)) = Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y2 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ Y1)) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (setunion @ Y1)) & ((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y4 @ emptyset)) @ emptyset)) = Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))) => ((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))) => (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y3 @ (dsetconstr @ Y1 @ Y0)))))))))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 67.27/8.84 inference(forward_demodulation,[],[f721,f722])). 67.27/8.84 thf(f722,plain,( 67.27/8.84 ($true = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ($true))))), 67.27/8.84 inference(binary_proxy_clausification,[],[f719])). 67.27/8.84 thf(f719,plain,( 67.27/8.84 (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ($true))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) = (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y1 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ Y0)) => ((Y2 = Y1) | (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (powerset @ Y2)) => ((in @ Y0 @ Y1) => (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y1 @ Y0) => (in @ Y2 @ (setunion @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (~ (emptyset = (dsetconstr @ Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((~ (Y1 @ Y2)) & (in @ Y2 @ Y0)))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 @ Y2)) & (in @ Y2 @ Y0))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ($true))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y1) = (in @ Y3 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) = (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! 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@ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))) => (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y3 @ (dsetconstr @ Y1 @ Y0)))))))))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 67.27/8.84 inference(binary_proxy_clausification,[],[f705])). 67.27/8.84 thf(f705,plain,( 67.27/8.84 (((!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))) & (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))) & ((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))) & (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))) & ((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ (setadjoin @ Y1 @ emptyset) @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ (setadjoin @ Y0 @ emptyset) @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (subset @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y0 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y1))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ Y1 @ Y2))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y2 @ Y0)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (cartprod @ Y1 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y4 @ emptyset)) @ emptyset)) = Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y2 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ Y1)) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (setunion @ Y1)) & ((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y4 @ emptyset)) @ emptyset)) = Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))) => ((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))) => (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y3 @ (dsetconstr @ Y1 @ Y0)))))))))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 67.27/8.84 inference(boolean_simplification,[],[f693])). 67.27/8.84 thf(f693,plain,( 67.27/8.84 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ Y0)) = ((in @ Y2 @ Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))) & (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))) & ((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))) & (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))) & ((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ (setadjoin @ Y1 @ emptyset) @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ (setadjoin @ Y0 @ emptyset) @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (subset @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y0 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y1))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ Y1 @ Y2))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y2 @ Y0)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (cartprod @ Y1 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y4 @ emptyset)) @ emptyset)) = Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y2 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ Y1)) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (setunion @ Y1)) & ((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y4 @ emptyset)) @ emptyset)) = Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))) => ((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))) => (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y3 @ (dsetconstr @ Y1 @ Y0)))))))))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 67.27/8.84 inference(boolean_simplification,[],[f692])). 67.27/8.84 thf(f692,plain,( 67.27/8.84 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ Y0)) = ((in @ Y2 @ Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ (binintersect @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y0) => ((subset @ Y2 @ Y1) => (subset @ Y2 @ (binintersect @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y0 @ Y1) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y0 @ Y2)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))) => (emptyset = (binintersect @ Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y0 @ Y1) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binunion @ (binintersect @ Y2 @ Y1) @ (binintersect @ Y2 @ Y0)) = (binintersect @ Y2 @ (binunion @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setminus @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setminus @ Y0 @ Y2)) => (~ (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (emptyset = (setminus @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y0 @ Y2))) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y2 @ Y0))) => ((~ (in @ Y1 @ Y0)) => (~ (in @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ Y2)) => (~ (in @ Y1 @ (setminus @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (~ (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (symdiff @ Y2 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => Y3)) => (((~ (in @ Y1 @ Y2)) => ((in @ Y1 @ Y0) => Y3)) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (in @ Y0 @ (symdiff @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ (symdiff @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((in @ Y1 @ Y0) => (~ (in @ Y1 @ (symdiff @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))) & (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))) & ((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))) & (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))) & ((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ (setadjoin @ Y1 @ emptyset) @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ (setadjoin @ Y0 @ emptyset) @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (subset @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y0 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y1))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ Y1 @ Y2))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y2 @ Y0)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (cartprod @ Y1 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y4 @ emptyset)) @ emptyset)) = Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y2 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ Y1)) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (setunion @ Y1)) & ((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y4 @ emptyset)) @ emptyset)) = Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))) => ((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))) => (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y3 @ (dsetconstr @ Y1 @ Y0)))))))))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 67.27/8.84 inference(forward_demodulation,[],[f690,f691])). 67.27/8.84 thf(f691,plain,( 67.27/8.84 ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) = $true)), 67.27/8.84 inference(binary_proxy_clausification,[],[f688])). 67.27/8.84 thf(f688,plain,( 67.27/8.84 ($false = ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ Y0)) = ((in @ Y2 @ Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y0 @ Y2)))) = (in @ Y0 @ (setunion @ Y1))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y0 @ Y2 @ Y3))))))) => (?? @ $i @ (^[Y2 : $i]: (!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))) & (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))) & ((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))) & (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))) & ((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ (setadjoin @ Y1 @ emptyset) @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ (setadjoin @ Y0 @ emptyset) @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (subset @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y0 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y1))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ Y1 @ Y2))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y2 @ Y0)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (cartprod @ Y1 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y4 @ emptyset)) @ emptyset)) = Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y2 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ Y1)) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (setunion @ Y1)) & ((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y4 @ emptyset)) @ emptyset)) = Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))) => ((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))) => (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y3 @ (dsetconstr @ Y1 @ Y0)))))))))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 67.27/8.84 inference(boolean_simplification,[],[f681])). 67.27/8.84 thf(f681,plain,( 67.27/8.84 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((in @ Y1 @ Y0) => (~ (in @ Y1 @ (symdiff @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))) & (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))) & ((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))) & (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))) & ((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ (setadjoin @ Y1 @ emptyset) @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ (setadjoin @ Y0 @ emptyset) @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (subset @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y0 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y1))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ Y1 @ Y2))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y2 @ Y0)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (cartprod @ Y1 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y4 @ emptyset)) @ emptyset)) = Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y2 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ Y1)) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (setunion @ Y1)) & ((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y4 @ emptyset)) @ emptyset)) = Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))) => ((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))) => (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y3 @ (dsetconstr @ Y1 @ Y0)))))))))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 67.27/8.84 inference(boolean_simplification,[],[f680])). 67.27/8.84 thf(f680,plain,( 67.27/8.84 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ Y0)) = ((in @ Y2 @ Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y0 @ Y2)))) = (in @ Y0 @ (setunion @ Y1))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! 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@ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))) => ((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))) => (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y3 @ (dsetconstr @ Y1 @ Y0)))))))))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 67.27/8.84 inference(boolean_simplification,[],[f679])). 67.27/8.84 thf(f679,plain,( 67.27/8.84 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! 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@ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y2 @ Y0)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (cartprod @ Y1 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y4 @ emptyset)) @ emptyset)) = Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y2 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ Y1)) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (setunion @ Y1)) & ((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y4 @ emptyset)) @ emptyset)) = Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))) => ((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))) => (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y3 @ (dsetconstr @ Y1 @ Y0)))))))))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 67.27/8.84 inference(boolean_simplification,[],[f678])). 67.27/8.84 thf(f678,plain,( 67.27/8.84 ($true = (~ ((!! 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@ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y3 @ (dsetconstr @ Y1 @ Y0)))))))))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 67.27/8.84 inference(beta_eta_normalization,[],[f677])). 67.27/8.84 thf(f677,plain,( 67.27/8.84 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! 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@ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (((^[Y2 : $i]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (?? @ $i @ (^[Y5 : $i]: (((setadjoin @ Y5 @ emptyset) = Y4) & (in @ Y5 @ Y4))))) @ (dsetconstr @ Y2 @ (^[Y4 : $i]: (Y3 @ Y4))))))) @ Y1 @ (^[Y2 : $i]: (Y0 @ Y2))) => (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => ((^[Y3 : $i]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (?? @ $i @ (^[Y6 : $i]: (((setadjoin @ Y6 @ emptyset) = Y5) & (in @ Y6 @ Y5))))) @ (dsetconstr @ Y3 @ (^[Y5 : $i]: (Y4 @ Y5))))))) @ Y1 @ (^[Y3 : $i]: (Y0 @ Y3)))))))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => ((^[Y2 : $i]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (?? @ $i @ (^[Y5 : $i]: (((setadjoin @ Y5 @ emptyset) = Y4) & (in @ Y5 @ Y4))))) @ (dsetconstr @ Y2 @ (^[Y4 : $i]: (Y3 @ Y4))))))) @ Y1 @ (^[Y2 : $i]: (Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 67.27/8.84 inference(definition_unfolding,[],[f578,f508,f599,f533,f504,f638,f502,f506,f488,f651,f602,f514,f652,f612,f493,f617,f653,f645,f534,f618,f492,f654,f606,f522,f572,f499,f655,f656,f657,f644,f589,f635,f500,f649,f632,f616,f600,f619,f585,f535,f601,f556,f658,f659,f520,f631,f569,f524,f562,f610,f489,f633,f516,f622,f512,f503,f568,f626,f530,f571,f561,f660,f661,f662,f642,f586,f663,f664,f559,f593,f539,f545,f628,f665,f666,f611,f555,f579,f603,f490,f550,f615,f531,f540,f630,f590,f532,f544,f648,f596,f491,f501,f625,f595,f543,f551,f564,f563,f588,f496,f553,f582,f495,f505,f518,f620,f621,f608,f552,f529,f548,f538,f509,f536,f637,f597,f646,f594,f587,f570,f641,f498,f497,f609,f567,f549,f584,f541,f523,f557,f598,f510,f528,f605,f513,f527,f667,f668,f614,f629,f604,f554,f494,f558,f547,f650,f669,f670,f671,f672,f542,f592,f507,f566,f673,f675,f676,f674])). 67.27/8.84 thf(f674,plain,( 67.27/8.84 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = Y2) & (in @ Y3 @ Y2))))) @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))), 67.27/8.84 inference(definition_unfolding,[],[f613,f639])). 67.27/8.84 thf(f639,plain,( 67.27/8.84 (singleton = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = Y0) & (in @ Y1 @ Y0))))))), 67.27/8.84 inference(cnf_transformation,[],[f237])). 67.27/8.84 thf(f237,plain,( 67.27/8.84 (singleton = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ Y1 @ emptyset) = Y0) & (in @ Y1 @ Y0))))))), 67.27/8.84 inference(fool_elimination,[],[f236])). 67.27/8.84 thf(f236,plain,( 67.27/8.84 ((^[X0 : $i] : (? [X1] : ((in @ X1 @ X0) & ((setadjoin @ X1 @ emptyset) = X0)))) = singleton)), 67.27/8.84 inference(rectify,[],[f158])). 67.27/8.84 thf(f158,axiom,( 67.27/8.84 ((^[X3 : $i] : (? [X1] : ((in @ X1 @ X3) & ((setadjoin @ X1 @ emptyset) = X3)))) = singleton)), 67.27/8.84 file('/export/starexec/sandbox/tmp/tmp.PGvlXuhj1t/Vampire---4.8_23783',singleton)). 67.27/8.84 thf(f613,plain,( 67.27/8.84 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))), 67.27/8.84 inference(cnf_transformation,[],[f366])). 67.27/8.84 thf(f366,plain,( 67.27/8.84 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))), 67.27/8.84 inference(fool_elimination,[],[f365])). 67.27/8.84 thf(f365,plain,( 67.27/8.84 ((^[X0 : $i, X1 : $i > $o] : (singleton @ (dsetconstr @ X0 @ (^[X2 : $i] : (X1 @ X2))))) = ex1)), 67.27/8.84 inference(rectify,[],[f160])). 67.27/8.84 thf(f160,axiom,( 67.27/8.84 ((^[X3 : $i, X0 : $i > $o] : (singleton @ (dsetconstr @ X3 @ (^[X1 : $i] : (X0 @ X1))))) = ex1)), 67.27/8.84 file('/export/starexec/sandbox/tmp/tmp.PGvlXuhj1t/Vampire---4.8_23783',ex1)). 67.27/8.84 thf(f676,plain,( 67.27/8.84 (ex1I = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => ((^[Y3 : $i]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (?? @ $i @ (^[Y6 : $i]: (((setadjoin @ Y6 @ emptyset) = Y5) & (in @ Y6 @ Y5))))) @ (dsetconstr @ Y3 @ (^[Y5 : $i]: (Y4 @ Y5))))))) @ Y1 @ (^[Y3 : $i]: (Y0 @ Y3)))))))))))))), 67.27/8.84 inference(definition_unfolding,[],[f573,f674])). 67.27/8.84 thf(f573,plain,( 67.27/8.84 (ex1I = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (ex1 @ Y1 @ (^[Y3 : $i]: (Y0 @ Y3)))))))))))))), 67.27/8.84 inference(cnf_transformation,[],[f171])). 67.27/8.84 thf(f171,plain,( 67.27/8.84 (ex1I = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (ex1 @ Y1 @ (^[Y3 : $i]: (Y0 @ Y3)))))))))))))), 67.27/8.84 inference(fool_elimination,[],[f170])). 67.27/8.84 thf(f170,plain,( 67.27/8.84 (! 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[X2] : ((in @ X2 @ X3) => ((X0 @ X2) => (X1 = X2))) => (ex1 @ X3 @ (^[X2 : $i] : (X0 @ X2)))))) = ex1I)), 67.27/8.84 file('/export/starexec/sandbox/tmp/tmp.PGvlXuhj1t/Vampire---4.8_23783',ex1I)). 67.27/8.84 thf(f675,plain,( 67.27/8.84 (ex1E1 = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (((^[Y2 : $i]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (?? @ $i @ (^[Y5 : $i]: (((setadjoin @ Y5 @ emptyset) = Y4) & (in @ Y5 @ Y4))))) @ (dsetconstr @ Y2 @ (^[Y4 : $i]: (Y3 @ Y4))))))) @ Y1 @ (^[Y2 : $i]: (Y0 @ Y2))) => (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))))))))), 67.27/8.84 inference(definition_unfolding,[],[f537,f674])). 67.27/8.84 thf(f537,plain,( 67.27/8.84 (ex1E1 = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((ex1 @ Y1 @ (^[Y2 : $i]: (Y0 @ Y2))) => (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))))))))), 67.27/8.84 inference(cnf_transformation,[],[f362])). 67.27/8.84 thf(f362,plain,( 67.27/8.84 (ex1E1 = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((ex1 @ Y1 @ (^[Y2 : $i]: (Y0 @ Y2))) => (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))))))))), 67.27/8.84 inference(fool_elimination,[],[f361])). 67.27/8.84 thf(f361,plain,( 67.27/8.84 (ex1E1 = ! 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[X3] : (subset @ (setunion @ (setadjoin @ X3 @ emptyset)) @ X3) = setunionsingleton1)), 67.27/8.84 file('/export/starexec/sandbox/tmp/tmp.PGvlXuhj1t/Vampire---4.8_23783',setunionsingleton1)). 67.27/8.84 thf(f542,plain,( 67.27/8.84 (setunionE2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))))), 67.27/8.84 inference(cnf_transformation,[],[f463])). 67.27/8.84 thf(f463,plain,( 67.27/8.84 (setunionE2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))))), 67.27/8.84 inference(fool_elimination,[],[f462])). 67.27/8.84 thf(f462,plain,( 67.27/8.84 (setunionE2 = ! [X0,X1] : ((in @ X0 @ (setunion @ X1)) => ? [X2] : ((in @ X2 @ X1) & (in @ X0 @ X2))))), 67.27/8.84 inference(rectify,[],[f154])). 67.27/8.84 thf(f154,axiom,( 67.27/8.84 (setunionE2 = ! [X1,X3] : ((in @ X1 @ (setunion @ X3)) => ? [X11] : ((in @ X11 @ X3) & (in @ X1 @ X11))))), 67.27/8.84 file('/export/starexec/sandbox/tmp/tmp.PGvlXuhj1t/Vampire---4.8_23783',setunionE2)). 67.27/8.84 thf(f672,plain,( 67.27/8.84 (cartprodmempair = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y2 @ Y0)) => ((^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (setunion @ Y3)) & (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (setunion @ Y3)) & ((setadjoin @ (setadjoin @ Y4 @ emptyset) @ (setadjoin @ (setadjoin @ Y4 @ (setadjoin @ Y5 @ emptyset)) @ emptyset)) = Y3)))))))) @ Y1)))))))))), 67.27/8.84 inference(definition_unfolding,[],[f560,f583])). 67.27/8.84 thf(f583,plain,( 67.27/8.84 (iskpair = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) & (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setunion @ Y0)) & ((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0)))))))))), 67.27/8.84 inference(cnf_transformation,[],[f282])). 67.27/8.84 thf(f282,plain,( 67.27/8.84 (iskpair = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) & (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setunion @ Y0)) & ((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0)))))))))), 67.27/8.84 inference(fool_elimination,[],[f281])). 67.27/8.84 thf(f281,plain,( 67.27/8.84 (iskpair = (^[X0 : $i] : (? [X1] : (? [X2] : (((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) = X0) & (in @ X2 @ (setunion @ X0))) & (in @ X1 @ (setunion @ X0))))))), 67.27/8.84 inference(rectify,[],[f135])). 67.27/8.84 thf(f135,axiom,( 67.27/8.84 (iskpair = (^[X3 : $i] : (? [X1] : (? [X2] : (((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) = X3) & (in @ X2 @ (setunion @ X3))) & (in @ X1 @ (setunion @ X3))))))), 67.27/8.84 file('/export/starexec/sandbox/tmp/tmp.PGvlXuhj1t/Vampire---4.8_23783',iskpair)). 67.27/8.84 thf(f560,plain,( 67.27/8.84 (cartprodmempair = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y2 @ Y0)) => (iskpair @ Y1)))))))))), 67.27/8.84 inference(cnf_transformation,[],[f245])). 67.27/8.84 thf(f245,plain,( 67.27/8.84 (cartprodmempair = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y2 @ Y0)) => (iskpair @ Y1)))))))))), 67.27/8.84 inference(fool_elimination,[],[f244])). 67.27/8.84 thf(f244,plain,( 67.27/8.84 (! [X0,X1,X2] : ((in @ X1 @ (cartprod @ X0 @ X2)) => (iskpair @ X1)) = cartprodmempair)), 67.27/8.84 inference(rectify,[],[f153])). 67.27/8.84 thf(f153,axiom,( 67.27/8.84 (! [X3,X10,X4] : ((in @ X10 @ (cartprod @ X3 @ X4)) => (iskpair @ X10)) = cartprodmempair)), 67.27/8.84 file('/export/starexec/sandbox/tmp/tmp.PGvlXuhj1t/Vampire---4.8_23783',cartprodmempair)). 67.27/8.84 thf(f671,plain,( 67.27/8.84 (cartprodmempair1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (((^[Y5 : $i]: ((^[Y6 : $i]: (setadjoin @ (setadjoin @ Y5 @ emptyset) @ (setadjoin @ (setadjoin @ Y5 @ (setadjoin @ Y6 @ emptyset)) @ emptyset))))) @ Y3 @ Y4) = Y2)))))))))))))))), 67.27/8.84 inference(definition_unfolding,[],[f517,f525])). 67.27/8.84 thf(f525,plain,( 67.27/8.84 (kpair = (^[Y0 : $i]: ((^[Y1 : $i]: (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))), 67.27/8.84 inference(cnf_transformation,[],[f402])). 67.27/8.84 thf(f402,plain,( 67.27/8.84 (kpair = (^[Y0 : $i]: ((^[Y1 : $i]: (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))), 67.27/8.84 inference(fool_elimination,[],[f401])). 67.27/8.84 thf(f401,plain,( 67.27/8.84 ((^[X0 : $i, X1 : $i] : (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) = kpair)), 67.27/8.84 inference(rectify,[],[f140])). 67.27/8.84 thf(f140,axiom,( 67.27/8.84 ((^[X1 : $i, X2 : $i] : (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset))) = kpair)), 67.27/8.84 file('/export/starexec/sandbox/tmp/tmp.PGvlXuhj1t/Vampire---4.8_23783',kpair)). 67.27/8.84 thf(f517,plain,( 67.27/8.84 (cartprodmempair1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((kpair @ Y3 @ Y4) = Y2)))))))))))))))), 67.27/8.84 inference(cnf_transformation,[],[f471])). 67.27/8.84 thf(f471,plain,( 67.27/8.84 (cartprodmempair1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((kpair @ Y3 @ Y4) = Y2)))))))))))))))), 67.27/8.84 inference(fool_elimination,[],[f470])). 67.27/8.84 thf(f470,plain,( 67.27/8.84 (cartprodmempair1 = ! [X0,X1,X2] : ((in @ X0 @ (cartprod @ X1 @ X2)) => ? [X3] : (? [X4] : (((kpair @ X3 @ X4) = X0) & (in @ X4 @ X2)) & (in @ X3 @ X1))))), 67.27/8.84 inference(rectify,[],[f152])). 67.27/8.84 thf(f152,axiom,( 67.27/8.84 (cartprodmempair1 = ! [X10,X3,X4] : ((in @ X10 @ (cartprod @ X3 @ X4)) => ? [X1] : (? [X2] : (((kpair @ X1 @ X2) = X10) & (in @ X2 @ X4)) & (in @ X1 @ X3))))), 67.27/8.84 file('/export/starexec/sandbox/tmp/tmp.PGvlXuhj1t/Vampire---4.8_23783',cartprodmempair1)). 67.27/8.84 thf(f670,plain,( 67.27/8.84 (cartprodpairin = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ ((^[Y4 : $i]: ((^[Y5 : $i]: (setadjoin @ (setadjoin @ Y4 @ emptyset) @ (setadjoin @ (setadjoin @ Y4 @ (setadjoin @ Y5 @ emptyset)) @ emptyset))))) @ Y2 @ Y3) @ (cartprod @ Y1 @ Y0)))))))))))))), 67.27/8.84 inference(definition_unfolding,[],[f623,f525])). 67.27/8.84 thf(f623,plain,( 67.27/8.84 (cartprodpairin = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (kpair @ Y2 @ Y3) @ (cartprod @ Y1 @ Y0)))))))))))))), 67.27/8.84 inference(cnf_transformation,[],[f340])). 67.27/8.84 thf(f340,plain,( 67.27/8.84 (cartprodpairin = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (kpair @ Y2 @ Y3) @ (cartprod @ Y1 @ Y0)))))))))))))), 67.27/8.84 inference(fool_elimination,[],[f339])). 67.27/8.84 thf(f339,plain,( 67.27/8.84 (cartprodpairin = ! [X0,X1,X2] : ((in @ X0 @ X1) => ! [X3] : ((in @ X3 @ X2) => (in @ (kpair @ X0 @ X3) @ (cartprod @ X1 @ X2)))))), 67.27/8.84 inference(rectify,[],[f151])). 67.27/8.84 thf(f151,axiom,( 67.27/8.84 (cartprodpairin = ! [X1,X3,X4] : ((in @ X1 @ X3) => ! [X2] : ((in @ X2 @ X4) => (in @ (kpair @ X1 @ X2) @ (cartprod @ X3 @ X4)))))), 67.27/8.84 file('/export/starexec/sandbox/tmp/tmp.PGvlXuhj1t/Vampire---4.8_23783',cartprodpairin)). 67.27/8.84 thf(f669,plain,( 67.27/8.84 (ubforcartprodlem3 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ ((^[Y4 : $i]: ((^[Y5 : $i]: (setadjoin @ (setadjoin @ Y4 @ emptyset) @ (setadjoin @ (setadjoin @ Y4 @ (setadjoin @ Y5 @ emptyset)) @ emptyset))))) @ Y1 @ Y3) @ (powerset @ (powerset @ (binunion @ Y2 @ Y0)))))))))))))))), 67.27/8.84 inference(definition_unfolding,[],[f521,f525])). 67.27/8.84 thf(f521,plain,( 67.27/8.84 (ubforcartprodlem3 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (kpair @ Y1 @ Y3) @ (powerset @ (powerset @ (binunion @ Y2 @ Y0)))))))))))))))), 67.27/8.84 inference(cnf_transformation,[],[f442])). 67.27/8.84 thf(f442,plain,( 67.27/8.84 (ubforcartprodlem3 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (kpair @ Y1 @ Y3) @ (powerset @ (powerset @ (binunion @ Y2 @ Y0)))))))))))))))), 67.27/8.84 inference(fool_elimination,[],[f441])). 67.27/8.84 thf(f441,plain,( 67.27/8.84 (! [X0,X1,X2] : ((in @ X1 @ X0) => ! [X3] : ((in @ X3 @ X2) => (in @ (kpair @ X1 @ X3) @ (powerset @ (powerset @ (binunion @ X0 @ X2)))))) = ubforcartprodlem3)), 67.27/8.84 inference(rectify,[],[f150])). 67.27/8.84 thf(f150,axiom,( 67.27/8.84 (! [X3,X1,X4] : ((in @ X1 @ X3) => ! [X2] : ((in @ X2 @ X4) => (in @ (kpair @ X1 @ X2) @ (powerset @ (powerset @ (binunion @ X3 @ X4)))))) = ubforcartprodlem3)), 67.27/8.84 file('/export/starexec/sandbox/tmp/tmp.PGvlXuhj1t/Vampire---4.8_23783',ubforcartprodlem3)). 67.27/8.84 thf(f650,plain,( 67.27/8.84 (ubforcartprodlem2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y2)))))))))))))))), 67.27/8.84 inference(cnf_transformation,[],[f188])). 67.27/8.84 thf(f188,plain,( 67.27/8.84 (ubforcartprodlem2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y2)))))))))))))))), 67.27/8.84 inference(fool_elimination,[],[f187])). 67.27/8.84 thf(f187,plain,( 67.27/8.84 (ubforcartprodlem2 = ! [X0,X1,X2] : ((in @ X1 @ X2) => ! [X3] : ((in @ X3 @ X0) => (in @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X2 @ X0)))))))), 67.27/8.84 inference(rectify,[],[f149])). 67.27/8.84 thf(f149,axiom,( 67.27/8.84 (ubforcartprodlem2 = ! [X4,X1,X3] : ((in @ X1 @ X3) => ! [X2] : ((in @ X2 @ X4) => (in @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X3 @ X4)))))))), 67.27/8.84 file('/export/starexec/sandbox/tmp/tmp.PGvlXuhj1t/Vampire---4.8_23783',ubforcartprodlem2)). 67.27/8.84 thf(f547,plain,( 67.27/8.84 (ubforcartprodlem1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ Y1 @ Y2))))))))))))))), 67.27/8.84 inference(cnf_transformation,[],[f336])). 67.27/8.84 thf(f336,plain,( 67.27/8.84 (ubforcartprodlem1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ Y1 @ Y2))))))))))))))), 67.27/8.84 inference(fool_elimination,[],[f335])). 67.27/8.84 thf(f335,plain,( 67.27/8.84 (! [X0,X1,X2] : ((in @ X2 @ X1) => ! [X3] : ((in @ X3 @ X0) => (subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X1 @ X0))))) = ubforcartprodlem1)), 67.27/8.84 inference(rectify,[],[f148])). 67.27/8.84 thf(f148,axiom,( 67.27/8.84 (! [X4,X3,X1] : ((in @ X1 @ X3) => ! [X2] : ((in @ X2 @ X4) => (subset @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X3 @ X4))))) = ubforcartprodlem1)), 67.27/8.84 file('/export/starexec/sandbox/tmp/tmp.PGvlXuhj1t/Vampire---4.8_23783',ubforcartprodlem1)). 67.27/8.84 thf(f558,plain,( 67.27/8.84 (upairinpowunion = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y1))))))))))))))), 67.27/8.84 inference(cnf_transformation,[],[f251])). 67.27/8.84 thf(f251,plain,( 67.27/8.84 (upairinpowunion = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y1))))))))))))))), 67.27/8.84 inference(fool_elimination,[],[f250])). 67.27/8.84 thf(f250,plain,( 67.27/8.84 (! [X0,X1,X2] : ((in @ X2 @ X0) => ! [X3] : ((in @ X3 @ X1) => (in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X0 @ X1))))) = upairinpowunion)), 67.27/8.84 inference(rectify,[],[f147])). 67.27/8.84 thf(f147,axiom,( 67.27/8.84 (! [X3,X4,X1] : ((in @ X1 @ X3) => ! [X2] : ((in @ X2 @ X4) => (in @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ (powerset @ (binunion @ X3 @ X4))))) = upairinpowunion)), 67.27/8.84 file('/export/starexec/sandbox/tmp/tmp.PGvlXuhj1t/Vampire---4.8_23783',upairinpowunion)). 67.27/8.84 thf(f494,plain,( 67.27/8.84 (upairsubunion = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (subset @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y0 @ Y1)))))))))))))), 67.27/8.84 inference(cnf_transformation,[],[f288])). 67.27/8.84 thf(f288,plain,( 67.27/8.84 (upairsubunion = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (subset @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y0 @ Y1)))))))))))))), 67.27/8.84 inference(fool_elimination,[],[f287])). 67.27/8.84 thf(f287,plain,( 67.27/8.84 (upairsubunion = ! [X0,X1,X2] : ((in @ X0 @ X2) => ! [X3] : ((in @ X3 @ X1) => (subset @ (setadjoin @ X0 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X2 @ X1)))))), 67.27/8.84 inference(rectify,[],[f146])). 67.27/8.84 thf(f146,axiom,( 67.27/8.84 (upairsubunion = ! [X1,X4,X3] : ((in @ X1 @ X3) => ! [X2] : ((in @ X2 @ X4) => (subset @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ (binunion @ X3 @ X4)))))), 67.27/8.84 file('/export/starexec/sandbox/tmp/tmp.PGvlXuhj1t/Vampire---4.8_23783',upairsubunion)). 67.27/8.84 thf(f554,plain,( 67.27/8.84 (upairset2E = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))))), 67.27/8.84 inference(cnf_transformation,[],[f428])). 67.27/8.84 thf(f428,plain,( 67.27/8.84 (upairset2E = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))))), 67.27/8.84 inference(fool_elimination,[],[f427])). 67.27/8.84 thf(f427,plain,( 67.27/8.84 (upairset2E = ! [X0,X1,X2] : ((in @ X1 @ (setadjoin @ X2 @ (setadjoin @ X0 @ emptyset))) => ((X1 = X2) | (X0 = X1))))), 67.27/8.84 inference(rectify,[],[f145])). 67.27/8.84 thf(f145,axiom,( 67.27/8.84 (upairset2E = ! 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[X1,X3] : ((in @ X1 @ X3) => (subset @ (setadjoin @ X1 @ emptyset) @ X3)) = singletonsubset)), 67.27/8.84 file('/export/starexec/sandbox/tmp/tmp.PGvlXuhj1t/Vampire---4.8_23783',singletonsubset)). 67.27/8.84 thf(f668,plain,( 67.27/8.84 (kpairp = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ Y2)) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (setunion @ Y2)) & ((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y4 @ emptyset)) @ emptyset)) = Y2)))))))) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))))) @ Y0 @ Y1)))))))), 67.27/8.84 inference(definition_unfolding,[],[f515,f583,f525])). 67.27/8.84 thf(f515,plain,( 67.27/8.84 (kpairp = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (kpair @ Y0 @ Y1)))))))), 67.27/8.84 inference(cnf_transformation,[],[f354])). 67.27/8.84 thf(f354,plain,( 67.27/8.84 (kpairp = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (kpair @ Y0 @ Y1)))))))), 67.27/8.84 inference(fool_elimination,[],[f353])). 67.27/8.84 thf(f353,plain,( 67.27/8.84 (! 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[X2,X1] : (iskpair @ (kpair @ X1 @ X2)) = kpairp)), 67.27/8.84 file('/export/starexec/sandbox/tmp/tmp.PGvlXuhj1t/Vampire---4.8_23783',kpairp)). 67.27/8.84 thf(f667,plain,( 67.27/8.84 (kpairiskpair = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ Y2)) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (setunion @ Y2)) & ((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y4 @ emptyset)) @ emptyset)) = Y2)))))))) @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))))))))), 67.27/8.84 inference(definition_unfolding,[],[f640,f583])). 67.27/8.84 thf(f640,plain,( 67.27/8.84 (kpairiskpair = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))))))))), 67.27/8.84 inference(cnf_transformation,[],[f206])). 67.27/8.84 thf(f206,plain,( 67.27/8.84 (kpairiskpair = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))))))))), 67.27/8.84 inference(fool_elimination,[],[f205])). 67.27/8.84 thf(f205,plain,( 67.27/8.84 (kpairiskpair = ! 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[X3 : $o] : (((in @ X1 @ X0) => (~(in @ X1 @ X2) => X3)) => ((~(in @ X1 @ X0) => ((in @ X1 @ X2) => X3)) => X3))) = symdiffE)), 67.27/8.84 inference(rectify,[],[f130])). 67.27/8.84 thf(f130,axiom,( 67.27/8.84 (! [X3,X1,X4] : ((in @ X1 @ (symdiff @ X3 @ X4)) => ! [X0 : $o] : (((in @ X1 @ X3) => (~(in @ X1 @ X4) => X0)) => ((~(in @ X1 @ X3) => ((in @ X1 @ X4) => X0)) => X0))) = symdiffE)), 67.27/8.84 file('/export/starexec/sandbox/tmp/tmp.PGvlXuhj1t/Vampire---4.8_23783',symdiffE)). 67.27/8.84 thf(f541,plain,( 67.27/8.84 (setminusSubset1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0)))))))), 67.27/8.84 inference(cnf_transformation,[],[f358])). 67.27/8.84 thf(f358,plain,( 67.27/8.84 (setminusSubset1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0)))))))), 67.27/8.84 inference(fool_elimination,[],[f357])). 67.27/8.84 thf(f357,plain,( 67.27/8.84 (! [X0,X1] : ((emptyset = (setminus @ X0 @ X1)) => (subset @ X0 @ X1)) = setminusSubset1)), 67.27/8.84 inference(rectify,[],[f129])). 67.27/8.84 thf(f129,axiom,( 67.27/8.84 (! [X3,X4] : ((emptyset = (setminus @ X3 @ X4)) => (subset @ X3 @ X4)) = setminusSubset1)), 67.27/8.84 file('/export/starexec/sandbox/tmp/tmp.PGvlXuhj1t/Vampire---4.8_23783',setminusSubset1)). 67.27/8.84 thf(f584,plain,( 67.27/8.84 (setminusLsub = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y0 @ Y1) @ Y0))))))), 67.27/8.84 inference(cnf_transformation,[],[f324])). 67.27/8.84 thf(f324,plain,( 67.27/8.84 (setminusLsub = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y0 @ Y1) @ Y0))))))), 67.27/8.84 inference(fool_elimination,[],[f323])). 67.27/8.84 thf(f323,plain,( 67.27/8.84 (setminusLsub = ! [X0,X1] : (subset @ (setminus @ X1 @ X0) @ X1))), 67.27/8.84 inference(rectify,[],[f128])). 67.27/8.84 thf(f128,axiom,( 67.27/8.84 (setminusLsub = ! [X4,X3] : (subset @ (setminus @ X3 @ X4) @ X3))), 67.27/8.84 file('/export/starexec/sandbox/tmp/tmp.PGvlXuhj1t/Vampire---4.8_23783',setminusLsub)). 67.27/8.84 thf(f549,plain,( 67.27/8.84 (setminusIRneg = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (~ (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))))), 67.27/8.84 inference(cnf_transformation,[],[f298])). 67.27/8.84 thf(f298,plain,( 67.27/8.84 (setminusIRneg = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (~ (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))))), 67.27/8.84 inference(fool_elimination,[],[f297])). 67.27/8.84 thf(f297,plain,( 67.27/8.84 (! [X0,X1,X2] : ((in @ X2 @ X0) => ~(in @ X2 @ (setminus @ X1 @ X0))) = setminusIRneg)), 67.27/8.84 inference(rectify,[],[f127])). 67.27/8.84 thf(f127,axiom,( 67.27/8.84 (! [X4,X3,X1] : ((in @ X1 @ X4) => ~(in @ X1 @ (setminus @ X3 @ X4))) = setminusIRneg)), 67.27/8.84 file('/export/starexec/sandbox/tmp/tmp.PGvlXuhj1t/Vampire---4.8_23783',setminusIRneg)). 67.27/8.84 thf(f567,plain,( 67.27/8.84 (setminusILneg = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ Y2)) => (~ (in @ Y1 @ (setminus @ Y2 @ Y0)))))))))))), 67.27/8.84 inference(cnf_transformation,[],[f398])). 67.27/8.84 thf(f398,plain,( 67.27/8.84 (setminusILneg = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ Y2)) => (~ (in @ Y1 @ (setminus @ Y2 @ Y0)))))))))))), 67.27/8.84 inference(fool_elimination,[],[f397])). 67.27/8.84 thf(f397,plain,( 67.27/8.84 (setminusILneg = ! [X0,X1,X2] : (~(in @ X1 @ X0) => ~(in @ X1 @ (setminus @ X0 @ X2))))), 67.27/8.84 inference(rectify,[],[f126])). 67.27/8.84 thf(f126,axiom,( 67.27/8.84 (setminusILneg = ! [X3,X1,X4] : (~(in @ X1 @ X3) => ~(in @ X1 @ (setminus @ X3 @ X4))))), 67.27/8.84 file('/export/starexec/sandbox/tmp/tmp.PGvlXuhj1t/Vampire---4.8_23783',setminusILneg)). 67.27/8.84 thf(f609,plain,( 67.27/8.84 (setminusELneg = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y2 @ Y0))) => ((~ (in @ Y1 @ Y0)) => (~ (in @ Y1 @ Y2)))))))))))), 67.27/8.84 inference(cnf_transformation,[],[f332])). 67.27/8.84 thf(f332,plain,( 67.27/8.84 (setminusELneg = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y2 @ Y0))) => ((~ (in @ Y1 @ Y0)) => (~ (in @ Y1 @ Y2)))))))))))), 67.27/8.84 inference(fool_elimination,[],[f331])). 67.27/8.84 thf(f331,plain,( 67.27/8.84 (! [X0,X1,X2] : (~(in @ X1 @ (setminus @ X0 @ X2)) => (~(in @ X1 @ X2) => ~(in @ X1 @ X0))) = setminusELneg)), 67.27/8.84 inference(rectify,[],[f125])). 67.27/8.84 thf(f125,axiom,( 67.27/8.84 (! [X3,X1,X4] : (~(in @ X1 @ (setminus @ X3 @ X4)) => (~(in @ X1 @ X4) => ~(in @ X1 @ X3))) = setminusELneg)), 67.27/8.84 file('/export/starexec/sandbox/tmp/tmp.PGvlXuhj1t/Vampire---4.8_23783',setminusELneg)). 67.27/8.84 thf(f497,plain,( 67.27/8.84 (setminusERneg = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y0 @ Y2))) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))))), 67.27/8.84 inference(cnf_transformation,[],[f424])). 67.27/8.84 thf(f424,plain,( 67.27/8.84 (setminusERneg = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y0 @ Y2))) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))))), 67.27/8.84 inference(fool_elimination,[],[f423])). 67.27/8.84 thf(f423,plain,( 67.27/8.84 (setminusERneg = ! [X0,X1,X2] : (~(in @ X1 @ (setminus @ X2 @ X0)) => ((in @ X1 @ X2) => (in @ X1 @ X0))))), 67.27/8.84 inference(rectify,[],[f124])). 67.27/8.84 thf(f124,axiom,( 67.27/8.84 (setminusERneg = ! [X4,X1,X3] : (~(in @ X1 @ (setminus @ X3 @ X4)) => ((in @ X1 @ X3) => (in @ X1 @ X4))))), 67.27/8.84 file('/export/starexec/sandbox/tmp/tmp.PGvlXuhj1t/Vampire---4.8_23783',setminusERneg)). 67.27/8.84 thf(f498,plain,( 67.27/8.84 (setminusSubset2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (emptyset = (setminus @ Y1 @ Y0))))))))), 67.27/8.84 inference(cnf_transformation,[],[f386])). 67.27/8.84 thf(f386,plain,( 67.27/8.84 (setminusSubset2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (emptyset = (setminus @ Y1 @ Y0))))))))), 67.27/8.84 inference(fool_elimination,[],[f385])). 67.27/8.84 thf(f385,plain,( 67.27/8.84 (! [X0,X1] : ((subset @ X0 @ X1) => (emptyset = (setminus @ X0 @ X1))) = setminusSubset2)), 67.27/8.84 inference(rectify,[],[f123])). 67.27/8.84 thf(f123,axiom,( 67.27/8.84 (! [X3,X4] : ((subset @ X3 @ X4) => (emptyset = (setminus @ X3 @ X4))) = setminusSubset2)), 67.27/8.84 file('/export/starexec/sandbox/tmp/tmp.PGvlXuhj1t/Vampire---4.8_23783',setminusSubset2)). 67.27/8.84 thf(f641,plain,( 67.27/8.84 (setminusER = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setminus @ Y0 @ Y2)) => (~ (in @ Y1 @ Y2))))))))))), 67.27/8.84 inference(cnf_transformation,[],[f390])). 67.27/8.84 thf(f390,plain,( 67.27/8.84 (setminusER = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setminus @ Y0 @ Y2)) => (~ (in @ Y1 @ Y2))))))))))), 67.27/8.84 inference(fool_elimination,[],[f389])). 67.27/8.84 thf(f389,plain,( 67.27/8.84 (! [X0,X1,X2] : ((in @ X1 @ (setminus @ X2 @ X0)) => ~(in @ X1 @ X0)) = setminusER)), 67.27/8.84 inference(rectify,[],[f122])). 67.27/8.84 thf(f122,axiom,( 67.27/8.84 (! [X4,X1,X3] : ((in @ X1 @ (setminus @ X3 @ X4)) => ~(in @ X1 @ X4)) = setminusER)), 67.27/8.84 file('/export/starexec/sandbox/tmp/tmp.PGvlXuhj1t/Vampire---4.8_23783',setminusER)). 67.27/8.84 thf(f570,plain,( 67.27/8.84 (setminusEL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setminus @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))))), 67.27/8.84 inference(cnf_transformation,[],[f173])). 67.27/8.84 thf(f173,plain,( 67.27/8.84 (setminusEL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setminus @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))))), 67.27/8.84 inference(fool_elimination,[],[f172])). 67.27/8.84 thf(f172,plain,( 67.27/8.84 (! [X0,X1,X2] : ((in @ X1 @ (setminus @ X0 @ X2)) => (in @ X1 @ X0)) = setminusEL)), 67.27/8.84 inference(rectify,[],[f121])). 67.27/8.84 thf(f121,axiom,( 67.27/8.84 (! [X3,X1,X4] : ((in @ X1 @ (setminus @ X3 @ X4)) => (in @ X1 @ X3)) = setminusEL)), 67.27/8.84 file('/export/starexec/sandbox/tmp/tmp.PGvlXuhj1t/Vampire---4.8_23783',setminusEL)). 67.27/8.84 thf(f587,plain,( 67.27/8.84 (setminusI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))))), 67.27/8.84 inference(cnf_transformation,[],[f344])). 67.27/8.84 thf(f344,plain,( 67.27/8.84 (setminusI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))))), 67.27/8.84 inference(fool_elimination,[],[f343])). 67.27/8.84 thf(f343,plain,( 67.27/8.84 (setminusI = ! [X0,X1,X2] : ((in @ X2 @ X0) => (~(in @ X2 @ X1) => (in @ X2 @ (setminus @ X0 @ X1)))))), 67.27/8.84 inference(rectify,[],[f120])). 67.27/8.84 thf(f120,axiom,( 67.27/8.84 (setminusI = ! [X3,X4,X1] : ((in @ X1 @ X3) => (~(in @ X1 @ X4) => (in @ X1 @ (setminus @ X3 @ X4)))))), 67.27/8.84 file('/export/starexec/sandbox/tmp/tmp.PGvlXuhj1t/Vampire---4.8_23783',setminusI)). 67.27/8.84 thf(f594,plain,( 67.27/8.84 (bs114d = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binunion @ (binintersect @ Y2 @ Y1) @ (binintersect @ Y2 @ Y0)) = (binintersect @ Y2 @ (binunion @ Y1 @ Y0))))))))))), 67.27/8.84 inference(cnf_transformation,[],[f235])). 67.27/8.84 thf(f235,plain,( 67.27/8.84 (bs114d = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binunion @ (binintersect @ Y2 @ Y1) @ (binintersect @ Y2 @ Y0)) = (binintersect @ Y2 @ (binunion @ Y1 @ Y0))))))))))), 67.27/8.84 inference(fool_elimination,[],[f234])). 67.27/8.84 thf(f234,plain,( 67.27/8.84 (bs114d = ! [X0,X1,X2] : ((binunion @ (binintersect @ X0 @ X1) @ (binintersect @ X0 @ X2)) = (binintersect @ X0 @ (binunion @ X1 @ X2))))), 67.27/8.84 inference(rectify,[],[f119])). 67.27/8.84 thf(f119,axiom,( 67.27/8.84 (bs114d = ! [X3,X4,X5] : ((binintersect @ X3 @ (binunion @ X4 @ X5)) = (binunion @ (binintersect @ X3 @ X4) @ (binintersect @ X3 @ X5))))), 67.27/8.84 file('/export/starexec/sandbox/tmp/tmp.PGvlXuhj1t/Vampire---4.8_23783',bs114d)). 67.27/8.84 thf(f646,plain,( 67.27/8.84 (binintersectSubset1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y1) => (subset @ Y1 @ Y0)))))))), 67.27/8.84 inference(cnf_transformation,[],[f342])). 67.27/8.84 thf(f342,plain,( 67.27/8.84 (binintersectSubset1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y1) => (subset @ Y1 @ Y0)))))))), 67.27/8.84 inference(fool_elimination,[],[f341])). 67.27/8.84 thf(f341,plain,( 67.27/8.84 (binintersectSubset1 = ! [X0,X1] : (((binintersect @ X0 @ X1) = X0) => (subset @ X0 @ X1)))), 67.27/8.84 inference(rectify,[],[f118])). 67.27/8.84 thf(f118,axiom,( 67.27/8.84 (binintersectSubset1 = ! [X3,X4] : (((binintersect @ X3 @ X4) = X3) => (subset @ X3 @ X4)))), 67.27/8.84 file('/export/starexec/sandbox/tmp/tmp.PGvlXuhj1t/Vampire---4.8_23783',binintersectSubset1)). 67.27/8.84 thf(f597,plain,( 67.27/8.84 (binintersectSubset4 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y0 @ Y1) = Y1)))))))), 67.27/8.84 inference(cnf_transformation,[],[f223])). 67.27/8.84 thf(f223,plain,( 67.27/8.84 (binintersectSubset4 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y0 @ Y1) = Y1)))))))), 67.27/8.84 inference(fool_elimination,[],[f222])). 67.27/8.84 thf(f222,plain,( 67.27/8.84 (! [X0,X1] : ((subset @ X0 @ X1) => ((binintersect @ X1 @ X0) = X0)) = binintersectSubset4)), 67.27/8.84 inference(rectify,[],[f117])). 67.27/8.84 thf(f117,axiom,( 67.27/8.84 (! [X4,X3] : ((subset @ X4 @ X3) => ((binintersect @ X3 @ X4) = X4)) = binintersectSubset4)), 67.27/8.84 file('/export/starexec/sandbox/tmp/tmp.PGvlXuhj1t/Vampire---4.8_23783',binintersectSubset4)). 67.27/8.84 thf(f637,plain,( 67.27/8.84 (binintersectRsub = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1))))))), 67.27/8.84 inference(cnf_transformation,[],[f290])). 67.27/8.84 thf(f290,plain,( 67.27/8.84 (binintersectRsub = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1))))))), 67.27/8.84 inference(fool_elimination,[],[f289])). 67.27/8.84 thf(f289,plain,( 67.27/8.84 (binintersectRsub = ! [X0,X1] : (subset @ (binintersect @ X1 @ X0) @ X0))), 67.27/8.84 inference(rectify,[],[f116])). 67.27/8.84 thf(f116,axiom,( 67.27/8.84 (binintersectRsub = ! [X4,X3] : (subset @ (binintersect @ X3 @ X4) @ X4))), 67.27/8.84 file('/export/starexec/sandbox/tmp/tmp.PGvlXuhj1t/Vampire---4.8_23783',binintersectRsub)). 67.27/8.84 thf(f536,plain,( 67.27/8.84 (disjointsetsI1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))) => (emptyset = (binintersect @ Y0 @ Y1))))))))), 67.27/8.84 inference(cnf_transformation,[],[f459])). 67.27/8.84 thf(f459,plain,( 67.27/8.84 (disjointsetsI1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))) => (emptyset = (binintersect @ Y0 @ Y1))))))))), 67.27/8.84 inference(fool_elimination,[],[f458])). 67.27/8.84 thf(f458,plain,( 67.27/8.84 (disjointsetsI1 = ! [X0,X1] : (~? [X2] : ((in @ X2 @ X1) & (in @ X2 @ X0)) => (emptyset = (binintersect @ X1 @ X0))))), 67.27/8.84 inference(rectify,[],[f115])). 67.27/8.84 thf(f115,axiom,( 67.27/8.84 (disjointsetsI1 = ! [X4,X3] : (~? [X1] : ((in @ X1 @ X3) & (in @ X1 @ X4)) => (emptyset = (binintersect @ X3 @ X4))))), 67.27/8.84 file('/export/starexec/sandbox/tmp/tmp.PGvlXuhj1t/Vampire---4.8_23783',disjointsetsI1)). 67.27/8.84 thf(f509,plain,( 67.27/8.84 (binintersectER = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y0 @ Y2)) => (in @ Y1 @ Y2)))))))))), 67.27/8.84 inference(cnf_transformation,[],[f184])). 67.27/8.84 thf(f184,plain,( 67.27/8.84 (binintersectER = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y0 @ Y2)) => (in @ Y1 @ Y2)))))))))), 67.27/8.84 inference(fool_elimination,[],[f183])). 67.27/8.84 thf(f183,plain,( 67.27/8.84 (! 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[X3,X4] : ((X3 = X4) => (subset @ X3 @ X4)) = eqimpsubset1)), 67.27/8.84 file('/export/starexec/sandbox/tmp/tmp.PGvlXuhj1t/Vampire---4.8_23783',eqimpsubset1)). 67.27/8.84 thf(f579,plain,( 67.27/8.84 (eqimpsubset2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))))), 67.27/8.84 inference(cnf_transformation,[],[f406])). 67.27/8.84 thf(f406,plain,( 67.27/8.84 (eqimpsubset2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))))), 67.27/8.84 inference(fool_elimination,[],[f405])). 67.27/8.84 thf(f405,plain,( 67.27/8.84 (eqimpsubset2 = ! [X0,X1] : ((X0 = X1) => (subset @ X1 @ X0)))), 67.27/8.84 inference(rectify,[],[f79])). 67.27/8.84 thf(f79,axiom,( 67.27/8.84 (eqimpsubset2 = ! [X3,X4] : ((X3 = X4) => (subset @ X4 @ X3)))), 67.27/8.84 file('/export/starexec/sandbox/tmp/tmp.PGvlXuhj1t/Vampire---4.8_23783',eqimpsubset2)). 67.27/8.84 thf(f555,plain,( 67.27/8.84 (subsetI1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))))), 67.27/8.84 inference(cnf_transformation,[],[f384])). 67.27/8.84 thf(f384,plain,( 67.27/8.84 (subsetI1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))))), 67.27/8.84 inference(fool_elimination,[],[f383])). 67.27/8.84 thf(f383,plain,( 67.27/8.84 (subsetI1 = ! [X0,X1] : (! [X2] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (subset @ X1 @ X0)))), 67.27/8.84 inference(rectify,[],[f78])). 67.27/8.84 thf(f78,axiom,( 67.27/8.84 (subsetI1 = ! [X4,X3] : (! [X1] : ((in @ X1 @ X3) => (in @ X1 @ X4)) => (subset @ X3 @ X4)))), 67.27/8.84 file('/export/starexec/sandbox/tmp/tmp.PGvlXuhj1t/Vampire---4.8_23783',subsetI1)). 67.27/8.84 thf(f611,plain,( 67.27/8.84 (dsetconstr__Cong = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y3 @ Y4) = (Y2 @ Y5))))))))) => ((dsetconstr @ Y0 @ (^[Y4 : $i]: (Y2 @ Y4))) = (dsetconstr @ Y1 @ (^[Y4 : $i]: (Y3 @ Y4)))))))))))))))), 67.27/8.84 inference(cnf_transformation,[],[f477])). 67.27/8.84 thf(f477,plain,( 67.27/8.84 (dsetconstr__Cong = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y3 @ Y4) = (Y2 @ Y5))))))))) => ((dsetconstr @ Y0 @ (^[Y4 : $i]: (Y2 @ Y4))) = (dsetconstr @ Y1 @ (^[Y4 : $i]: (Y3 @ Y4)))))))))))))))), 67.27/8.84 inference(fool_elimination,[],[f476])). 67.27/8.84 thf(f476,plain,( 67.27/8.84 (! [X0,X1] : ((X0 = X1) => ! [X2 : $i > $o,X3 : $i > $o] : (! [X4] : ((in @ X4 @ X0) => ! [X5] : ((in @ X5 @ X1) => ((X4 = X5) => ((X2 @ X4) <=> (X3 @ X5))))) => ((dsetconstr @ X1 @ (^[X6 : $i] : (X3 @ X6))) = (dsetconstr @ X0 @ (^[X7 : $i] : (X2 @ X7)))))) = dsetconstr__Cong)), 67.27/8.84 inference(rectify,[],[f77])). 67.27/8.84 thf(f77,axiom,( 67.27/8.84 (! [X3,X4] : ((X3 = X4) => ! [X0 : $i > $o,X9 : $i > $o] : (! [X1] : ((in @ X1 @ X3) => ! [X2] : ((in @ X2 @ X4) => ((X1 = X2) => ((X0 @ X1) <=> (X9 @ X2))))) => ((dsetconstr @ X4 @ (^[X1 : $i] : (X9 @ X1))) = (dsetconstr @ X3 @ (^[X1 : $i] : (X0 @ X1)))))) = dsetconstr__Cong)), 67.27/8.84 file('/export/starexec/sandbox/tmp/tmp.PGvlXuhj1t/Vampire---4.8_23783',dsetconstr__Cong)). 67.27/8.84 thf(f666,plain,( 67.27/8.84 (descr__Cong = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => (((^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) => (Y3 = Y4)))) & (Y2 @ Y3))))) @ (^[Y2 : $i]: (Y0 @ Y2))) => (((^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) => (Y3 = Y4)))) & (Y2 @ Y3))))) @ (^[Y2 : $i]: (Y1 @ Y2))) => ((descr @ (^[Y2 : $i]: (Y1 @ Y2))) = (descr @ (^[Y2 : $i]: (Y0 @ Y2))))))))))))), 67.27/8.84 inference(definition_unfolding,[],[f580,f581,f581])). 67.27/8.84 thf(f581,plain,( 67.27/8.84 (exu = (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))), 67.27/8.84 inference(cnf_transformation,[],[f434])). 67.27/8.84 thf(f434,plain,( 67.27/8.84 (exu = (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))), 67.27/8.84 inference(fool_elimination,[],[f433])). 67.27/8.84 thf(f433,plain,( 67.27/8.84 ((^[X0 : $i > $o] : (? [X1] : ((X0 @ X1) & ! [X2] : ((X0 @ X2) => (X1 = X2))))) = exu)), 67.27/8.84 inference(rectify,[],[f1])). 67.27/8.84 thf(f1,axiom,( 67.27/8.84 ((^[X0 : $i > $o] : (? [X1] : ((X0 @ X1) & ! [X2] : ((X0 @ X2) => (X1 = X2))))) = exu)), 67.27/8.84 file('/export/starexec/sandbox/tmp/tmp.PGvlXuhj1t/Vampire---4.8_23783',exu)). 67.27/8.84 thf(f580,plain,( 67.27/8.84 (descr__Cong = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((exu @ (^[Y2 : $i]: (Y0 @ Y2))) => ((exu @ (^[Y2 : $i]: (Y1 @ Y2))) => ((descr @ (^[Y2 : $i]: (Y1 @ Y2))) = (descr @ (^[Y2 : $i]: (Y0 @ Y2))))))))))))), 67.27/8.84 inference(cnf_transformation,[],[f479])). 67.27/8.84 thf(f479,plain,( 67.27/8.84 (descr__Cong = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((exu @ (^[Y2 : $i]: (Y0 @ Y2))) => ((exu @ (^[Y2 : $i]: (Y1 @ Y2))) => ((descr @ (^[Y2 : $i]: (Y1 @ Y2))) = (descr @ (^[Y2 : $i]: (Y0 @ Y2))))))))))))), 67.27/8.84 inference(fool_elimination,[],[f478])). 67.27/8.84 thf(f478,plain,( 67.27/8.84 (descr__Cong = ! [X0 : $i > $o,X1 : $i > $o] : (! [X2,X3] : ((X2 = X3) => ((X1 @ X2) <=> (X0 @ X3))) => ((exu @ (^[X4 : $i] : (X1 @ X4))) => ((exu @ (^[X5 : $i] : (X0 @ X5))) => ((descr @ (^[X6 : $i] : (X0 @ X6))) = (descr @ (^[X7 : $i] : (X1 @ X7))))))))), 67.27/8.84 inference(rectify,[],[f76])). 67.27/8.84 thf(f76,axiom,( 67.27/8.84 (descr__Cong = ! [X9 : $i > $o,X0 : $i > $o] : (! [X1,X2] : ((X1 = X2) => ((X0 @ X1) <=> (X9 @ X2))) => ((exu @ (^[X1 : $i] : (X0 @ X1))) => ((exu @ (^[X1 : $i] : (X9 @ X1))) => ((descr @ (^[X1 : $i] : (X9 @ X1))) = (descr @ (^[X1 : $i] : (X0 @ X1))))))))), 67.27/8.84 file('/export/starexec/sandbox/tmp/tmp.PGvlXuhj1t/Vampire---4.8_23783',descr__Cong)). 67.27/8.84 thf(f665,plain,( 67.27/8.84 (exuEu = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2))))) @ (^[Y1 : $i]: (Y0 @ Y1))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))))), 67.27/8.84 inference(definition_unfolding,[],[f634,f581])). 67.27/8.84 thf(f634,plain,( 67.27/8.84 (exuEu = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((exu @ (^[Y1 : $i]: (Y0 @ Y1))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))))), 67.27/8.84 inference(cnf_transformation,[],[f440])). 67.27/8.84 thf(f440,plain,( 67.27/8.84 (exuEu = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((exu @ (^[Y1 : $i]: (Y0 @ Y1))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))))), 67.27/8.84 inference(fool_elimination,[],[f439])). 67.27/8.84 thf(f439,plain,( 67.27/8.84 (! [X0 : $i > $o] : ((exu @ (^[X1 : $i] : (X0 @ X1))) => ! [X2,X3] : ((X0 @ X2) => ((X0 @ X3) => (X2 = X3)))) = exuEu)), 67.27/8.84 inference(rectify,[],[f75])). 67.27/8.84 thf(f75,axiom,( 67.27/8.84 (! [X0 : $i > $o] : ((exu @ (^[X1 : $i] : (X0 @ X1))) => ! [X1,X2] : ((X0 @ X1) => ((X0 @ X2) => (X1 = X2)))) = exuEu)), 67.27/8.84 file('/export/starexec/sandbox/tmp/tmp.PGvlXuhj1t/Vampire---4.8_23783',exuEu)). 67.27/8.84 thf(f628,plain,( 67.27/8.84 (omega__Cong = (omega = omega))), 67.27/8.84 inference(cnf_transformation,[],[f211])). 67.27/8.84 thf(f211,plain,( 67.27/8.84 (omega__Cong = (omega = omega))), 67.27/8.84 inference(fool_elimination,[],[f74])). 67.27/8.84 thf(f74,axiom,( 67.27/8.84 ((omega = omega) = omega__Cong)), 67.27/8.84 file('/export/starexec/sandbox/tmp/tmp.PGvlXuhj1t/Vampire---4.8_23783',omega__Cong)). 67.27/8.84 thf(f545,plain,( 67.27/8.84 (setunion__Cong = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))))), 67.27/8.84 inference(cnf_transformation,[],[f272])). 67.27/8.84 thf(f272,plain,( 67.27/8.84 (setunion__Cong = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))))), 67.27/8.84 inference(fool_elimination,[],[f271])). 67.27/8.84 thf(f271,plain,( 67.27/8.84 (setunion__Cong = ! [X0,X1] : ((X0 = X1) => ((setunion @ X1) = (setunion @ X0))))), 67.27/8.84 inference(rectify,[],[f73])). 67.27/8.84 thf(f73,axiom,( 67.27/8.84 (setunion__Cong = ! [X3,X4] : ((X3 = X4) => ((setunion @ X3) = (setunion @ X4))))), 67.27/8.84 file('/export/starexec/sandbox/tmp/tmp.PGvlXuhj1t/Vampire---4.8_23783',setunion__Cong)). 67.27/8.84 thf(f539,plain,( 67.27/8.84 (powerset__Cong = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))))), 67.27/8.84 inference(cnf_transformation,[],[f436])). 67.27/8.84 thf(f436,plain,( 67.27/8.84 (powerset__Cong = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))))), 67.27/8.84 inference(fool_elimination,[],[f435])). 67.27/8.84 thf(f435,plain,( 67.27/8.84 (! [X0,X1] : ((X0 = X1) => ((powerset @ X0) = (powerset @ X1))) = powerset__Cong)), 67.27/8.84 inference(rectify,[],[f72])). 67.27/8.84 thf(f72,axiom,( 67.27/8.84 (! [X4,X3] : ((X3 = X4) => ((powerset @ X3) = (powerset @ X4))) = powerset__Cong)), 67.27/8.84 file('/export/starexec/sandbox/tmp/tmp.PGvlXuhj1t/Vampire---4.8_23783',powerset__Cong)). 67.27/8.84 thf(f593,plain,( 67.27/8.84 (setadjoin__Cong = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))))), 67.27/8.84 inference(cnf_transformation,[],[f204])). 67.27/8.84 thf(f204,plain,( 67.27/8.84 (setadjoin__Cong = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))))), 67.27/8.84 inference(fool_elimination,[],[f203])). 67.27/8.84 thf(f203,plain,( 67.27/8.84 (! [X0,X1] : ((X0 = X1) => ! [X2,X3] : ((X2 = X3) => ((setadjoin @ X1 @ X2) = (setadjoin @ X0 @ X3)))) = setadjoin__Cong)), 67.27/8.84 inference(rectify,[],[f71])). 67.27/8.84 thf(f71,axiom,( 67.27/8.84 (! [X1,X2] : ((X1 = X2) => ! [X10,X8] : ((X8 = X10) => ((setadjoin @ X1 @ X8) = (setadjoin @ X2 @ X10)))) = setadjoin__Cong)), 67.27/8.84 file('/export/starexec/sandbox/tmp/tmp.PGvlXuhj1t/Vampire---4.8_23783',setadjoin__Cong)). 67.27/8.84 thf(f559,plain,( 67.27/8.84 (emptyset__Cong = (emptyset = emptyset))), 67.27/8.84 inference(cnf_transformation,[],[f182])). 67.27/8.84 thf(f182,plain,( 67.27/8.84 (emptyset__Cong = (emptyset = emptyset))), 67.27/8.84 inference(fool_elimination,[],[f70])). 67.27/8.84 thf(f70,axiom,( 67.27/8.84 (emptyset__Cong = (emptyset = emptyset))), 67.27/8.84 file('/export/starexec/sandbox/tmp/tmp.PGvlXuhj1t/Vampire---4.8_23783',emptyset__Cong)). 67.27/8.84 thf(f664,plain,( 67.27/8.84 (exu__Cong = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ Y3))))))) => (((^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) => (Y3 = Y4)))) & (Y2 @ Y3))))) @ (^[Y2 : $i]: (Y0 @ Y2))) = ((^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) => (Y3 = Y4)))) & (Y2 @ Y3))))) @ (^[Y2 : $i]: (Y1 @ Y2))))))))))), 67.27/8.84 inference(definition_unfolding,[],[f607,f581,f581])). 67.27/8.84 thf(f607,plain,( 67.27/8.84 (exu__Cong = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ Y3))))))) => ((exu @ (^[Y2 : $i]: (Y0 @ Y2))) = (exu @ (^[Y2 : $i]: (Y1 @ Y2))))))))))), 67.27/8.84 inference(cnf_transformation,[],[f310])). 67.27/8.84 thf(f310,plain,( 67.27/8.84 (exu__Cong = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ Y3))))))) => ((exu @ (^[Y2 : $i]: (Y0 @ Y2))) = (exu @ (^[Y2 : $i]: (Y1 @ Y2))))))))))), 67.27/8.84 inference(fool_elimination,[],[f309])). 67.27/8.84 thf(f309,plain,( 67.27/8.84 (exu__Cong = ! [X0 : $i > $o,X1 : $i > $o] : (! [X2,X3] : ((X2 = X3) => ((X1 @ X3) <=> (X0 @ X2))) => ((exu @ (^[X4 : $i] : (X1 @ X4))) <=> (exu @ (^[X5 : $i] : (X0 @ X5))))))), 67.27/8.84 inference(rectify,[],[f69])). 67.27/8.84 thf(f69,axiom,( 67.27/8.84 (exu__Cong = ! [X0 : $i > $o,X9 : $i > $o] : (! [X1,X2] : ((X1 = X2) => ((X9 @ X2) <=> (X0 @ X1))) => ((exu @ (^[X1 : $i] : (X9 @ X1))) <=> (exu @ (^[X1 : $i] : (X0 @ X1))))))), 67.27/8.84 file('/export/starexec/sandbox/tmp/tmp.PGvlXuhj1t/Vampire---4.8_23783',exu__Cong)). 67.27/8.84 thf(f663,plain,( 67.27/8.84 (exuE3u = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2))))) @ (^[Y1 : $i]: (Y0 @ Y1))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))))), 67.27/8.84 inference(definition_unfolding,[],[f577,f581])). 67.27/8.84 thf(f577,plain,( 67.27/8.84 (exuE3u = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((exu @ (^[Y1 : $i]: (Y0 @ Y1))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))))), 67.27/8.84 inference(cnf_transformation,[],[f370])). 67.27/8.84 thf(f370,plain,( 67.27/8.84 (exuE3u = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((exu @ (^[Y1 : $i]: (Y0 @ Y1))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))))), 67.27/8.84 inference(fool_elimination,[],[f369])). 67.27/8.84 thf(f369,plain,( 67.27/8.84 (! [X0 : $i > $o] : ((exu @ (^[X1 : $i] : (X0 @ X1))) => ! [X2,X3] : ((X0 @ X2) => ((X0 @ X3) => (X2 = X3)))) = exuE3u)), 67.27/8.84 inference(rectify,[],[f68])). 67.27/8.84 thf(f68,axiom,( 67.27/8.84 (! [X0 : $i > $o] : ((exu @ (^[X1 : $i] : (X0 @ X1))) => ! [X1,X2] : ((X0 @ X1) => ((X0 @ X2) => (X1 = X2)))) = exuE3u)), 67.27/8.84 file('/export/starexec/sandbox/tmp/tmp.PGvlXuhj1t/Vampire---4.8_23783',exuE3u)). 67.27/8.84 thf(f586,plain,( 67.27/8.84 (in__Cong = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y1) = (in @ Y3 @ Y0)))))))))))))), 67.27/8.84 inference(cnf_transformation,[],[f487])). 67.27/8.84 thf(f487,plain,( 67.27/8.84 (in__Cong = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y1) = (in @ Y3 @ Y0)))))))))))))), 67.27/8.84 inference(fool_elimination,[],[f486])). 67.27/8.84 thf(f486,plain,( 67.27/8.84 (! [X0,X1] : ((X0 = X1) => ! [X2,X3] : ((X2 = X3) => ((in @ X3 @ X0) <=> (in @ X2 @ X1)))) = in__Cong)), 67.27/8.84 inference(rectify,[],[f67])). 67.27/8.84 thf(f67,axiom,( 67.27/8.84 (! [X3,X4] : ((X3 = X4) => ! [X2,X1] : ((X1 = X2) => ((in @ X1 @ X3) <=> (in @ X2 @ X4)))) = in__Cong)), 67.27/8.84 file('/export/starexec/sandbox/tmp/tmp.PGvlXuhj1t/Vampire---4.8_23783',in__Cong)). 67.27/8.84 thf(f642,plain,( 67.27/8.84 (inCongP = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))))), 67.27/8.84 inference(cnf_transformation,[],[f430])). 67.27/8.84 thf(f430,plain,( 67.27/8.84 (inCongP = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))))), 67.27/8.84 inference(fool_elimination,[],[f429])). 67.27/8.84 thf(f429,plain,( 67.27/8.84 (! [X0,X1] : ((X0 = X1) => ! [X2,X3] : ((X2 = X3) => ((in @ X2 @ X0) => (in @ X3 @ X1)))) = inCongP)), 67.27/8.84 inference(rectify,[],[f66])). 67.27/8.84 thf(f66,axiom,( 67.27/8.84 (! [X3,X4] : ((X3 = X4) => ! [X1,X2] : ((X1 = X2) => ((in @ X1 @ X3) => (in @ X2 @ X4)))) = inCongP)), 67.27/8.84 file('/export/starexec/sandbox/tmp/tmp.PGvlXuhj1t/Vampire---4.8_23783',inCongP)). 67.27/8.84 thf(f662,plain,( 67.27/8.84 (exuI2 = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2))))) @ (^[Y1 : $i]: (Y0 @ Y1)))))))), 67.27/8.84 inference(definition_unfolding,[],[f526,f581])). 67.27/8.84 thf(f526,plain,( 67.27/8.84 (exuI2 = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (exu @ (^[Y1 : $i]: (Y0 @ Y1)))))))), 67.27/8.84 inference(cnf_transformation,[],[f254])). 67.27/8.84 thf(f254,plain,( 67.27/8.84 (exuI2 = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (exu @ (^[Y1 : $i]: (Y0 @ Y1)))))))), 67.27/8.84 inference(fool_elimination,[],[f253])). 67.27/8.84 thf(f253,plain,( 67.27/8.84 (exuI2 = ! [X0 : $i > $o] : (? [X1] : ! [X2] : ((X0 @ X2) <=> (X1 = X2)) => (exu @ (^[X3 : $i] : (X0 @ X3)))))), 67.27/8.84 inference(rectify,[],[f65])). 67.27/8.84 thf(f65,axiom,( 67.27/8.84 (exuI2 = ! [X0 : $i > $o] : (? [X1] : ! [X2] : ((X0 @ X2) <=> (X1 = X2)) => (exu @ (^[X1 : $i] : (X0 @ X1)))))), 67.27/8.84 file('/export/starexec/sandbox/tmp/tmp.PGvlXuhj1t/Vampire---4.8_23783',exuI2)). 67.27/8.84 thf(f661,plain,( 67.27/8.84 (exuI3 = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1))))))) => ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2))))) @ (^[Y1 : $i]: (Y0 @ Y1))))))))), 67.27/8.84 inference(definition_unfolding,[],[f575,f581])). 67.27/8.84 thf(f575,plain,( 67.27/8.84 (exuI3 = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1))))))) => (exu @ (^[Y1 : $i]: (Y0 @ Y1))))))))), 67.27/8.84 inference(cnf_transformation,[],[f270])). 67.27/8.84 thf(f270,plain,( 67.27/8.84 (exuI3 = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1))))))) => (exu @ (^[Y1 : $i]: (Y0 @ Y1))))))))), 67.27/8.84 inference(fool_elimination,[],[f269])). 67.27/8.84 thf(f269,plain,( 67.27/8.84 (exuI3 = ! [X0 : $i > $o] : (? [X1] : (X0 @ X1) => (! [X2,X3] : ((X0 @ X2) => ((X0 @ X3) => (X2 = X3))) => (exu @ (^[X4 : $i] : (X0 @ X4))))))), 67.27/8.84 inference(rectify,[],[f64])). 67.27/8.84 thf(f64,axiom,( 67.27/8.84 (exuI3 = ! [X0 : $i > $o] : (? [X1] : (X0 @ X1) => (! 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[X2] : ((in @ X2 @ X7) => (in @ X2 @ X6)) | (in @ X1 @ X7))) & (in @ X6 @ X4) & (in @ X1 @ X5) & ~? [X2] : ((in @ X2 @ X5) & (in @ X2 @ X6)))) & ! [X6,X5] : (((in @ X6 @ X4) & (in @ X5 @ X4)) => (! [X1] : ((in @ X1 @ X6) => (in @ X1 @ X5)) | ! [X1] : ((in @ X1 @ X5) => (in @ X1 @ X6)))) & ! [X5] : ((in @ X5 @ X4) => ! [X1] : ((in @ X1 @ X5) => (in @ X1 @ X3))) & ! [X1,X2] : (((in @ X1 @ X3) & (in @ X2 @ X3)) => (! 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@ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (ex1 @ Y1 @ (^[Y2 : $i]: (Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 67.27/8.84 inference(fool_elimination,[],[f283])). 67.27/8.84 thf(f283,plain,( 67.27/8.84 ~(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 => ! [X0,X1 : $i > $o] : (! [X2] : ((in @ X2 @ X0) => ! [X3] : ((in @ X3 @ X0) => ((X1 @ X2) => ((X1 @ X3) => (X2 = X3))))) => (? [X4] : ((X1 @ X4) & (in @ X4 @ X0)) => (ex1 @ X0 @ (^[X5 : $i] : (X1 @ X5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 67.27/8.84 inference(rectify,[],[f164])). 67.27/8.84 thf(f164,negated_conjecture,( 67.27/8.84 ~(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 => ! [X3,X0 : $i > $o] : (! [X1] : ((in @ X1 @ X3) => ! [X2] : ((in @ X2 @ X3) => ((X0 @ X1) => ((X0 @ X2) => (X1 = X2))))) => (? [X1] : ((X0 @ X1) & (in @ X1 @ X3)) => (ex1 @ X3 @ (^[X1 : $i] : (X0 @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 67.27/8.84 inference(negated_conjecture,[],[f163])). 67.27/8.84 thf(f163,conjecture,( 67.27/8.84 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 => ! [X3,X0 : $i > $o] : (! [X1] : ((in @ X1 @ X3) => ! [X2] : ((in @ X2 @ X3) => ((X0 @ X1) => ((X0 @ X2) => (X1 = X2))))) => (? [X1] : ((X0 @ X1) & (in @ X1 @ X3)) => (ex1 @ X3 @ (^[X1 : $i] : (X0 @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 67.27/8.84 file('/export/starexec/sandbox/tmp/tmp.PGvlXuhj1t/Vampire---4.8_23783',ex1I2)). 67.27/8.84 thf(f690,plain,( 67.27/8.84 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ Y0)) = ((in @ Y2 @ Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y0 @ Y2)))) = (in @ Y0 @ (setunion @ Y1))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y0 @ Y2 @ Y3))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y2 @ Y4) = (in @ Y3 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! 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@ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y3 @ (dsetconstr @ Y1 @ Y0)))))))))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 67.27/8.84 inference(binary_proxy_clausification,[],[f815])). 67.27/8.84 thf(f881,plain,( 67.27/8.84 ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ (binunion @ Y0 @ Y3)) => (((in @ Y1 @ Y0) => Y2) => (((in @ Y1 @ Y3) => Y2) => Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binunion @ Y2 @ Y1)) => ((in @ Y0 @ Y2) | (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ (binintersect @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y0) => ((subset @ Y2 @ Y1) => (subset @ Y2 @ (binintersect @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y0 @ Y1) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y0 @ Y2)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))) => (emptyset = (binintersect @ Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y0 @ Y1) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binunion @ (binintersect @ Y2 @ Y1) @ (binintersect @ Y2 @ Y0)) = (binintersect @ Y2 @ (binunion @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setminus @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setminus @ Y0 @ Y2)) => (~ (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (emptyset = (setminus @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y0 @ Y2))) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y2 @ Y0))) => ((~ (in @ Y1 @ Y0)) => (~ (in @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ Y2)) => (~ (in @ Y1 @ (setminus @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (~ (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (symdiff @ Y2 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => Y3)) => (((~ (in @ Y1 @ Y2)) => ((in @ Y1 @ Y0) => Y3)) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (in @ Y0 @ (symdiff @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ (symdiff @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((in @ Y1 @ Y0) => (~ (in @ Y1 @ (symdiff @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))) & (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))) & ((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))) & (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))) & ((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ (setadjoin @ Y1 @ emptyset) @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ (setadjoin @ Y0 @ emptyset) @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (subset @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y0 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y1))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ Y1 @ Y2))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y2 @ Y0)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (cartprod @ Y1 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y4 @ emptyset)) @ emptyset)) = Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y2 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (setunion @ Y1)) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (setunion @ Y1)) & ((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y4 @ emptyset)) @ emptyset)) = Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))) => ((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))) => (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: (((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y3 @ (dsetconstr @ Y1 @ Y0)))))))))))))) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 67.27/8.84 inference(binary_proxy_clausification,[],[f879])). 67.27/8.84 thf(f990,plain,( 67.27/8.84 ($true = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0)) & (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))))))), 67.27/8.84 inference(binary_proxy_clausification,[],[f987])). 67.27/8.84 % SZS output end Proof for Vampire---4 67.27/8.84 % (24354)------------------------------ 67.27/8.84 % (24354)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 67.27/8.84 % (24354)Termination reason: Refutation 67.27/8.84 67.27/8.84 % (24354)Memory used [KB]: 78932 67.27/8.84 % (24354)Time elapsed: 0.881 s 67.27/8.84 % (24354)Instructions burned: 2441 (million) 67.27/8.84 % (24354)------------------------------ 67.27/8.84 % (24354)------------------------------ 67.27/8.84 % (23890)Success in time 8.443 s 67.27/8.84 % Vampire---4.8 exiting 67.27/8.84 EOF