0.10/0.12 % Problem : Vampire---4.8_23344 : TPTP v0.0.0. Released v0.0.0. 0.10/0.14 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s 0.14/0.35 % Computer : n028.cluster.edu 0.14/0.35 % Model : x86_64 x86_64 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.35 % Memory : 8042.1875MB 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.35 % CPULimit : 1440 0.14/0.35 % WCLimit : 180 0.14/0.35 % DateTime : Mon Jul 3 13:13:29 EDT 2023 0.14/0.35 % CPUTime : 0.14/0.35 This is a THF_ problem 0.14/0.36 Running vampire_rel_static_ahmed-new-hol_6848 --cores 8 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox2/tmp/tmp.tiVUk2IRLU/Vampire---4.8_23344 -m 12000 -t 180 0.14/0.38 % (23455)lrs+10_1:2_cnfonf=off:hud=1:inj=on:i=36:si=on:rtra=on_0 on Vampire---4 for (1799ds/36Mi) 0.14/0.38 % (23457)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) 0.14/0.38 % (23458)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on Vampire---4 for (1799ds/17Mi) 0.14/0.38 % (23459)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) 0.14/0.38 % (23456)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) 0.14/0.38 % (23460)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) 0.14/0.38 % (23460)Instruction limit reached! 0.14/0.38 % (23460)------------------------------ 0.14/0.38 % (23460)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.14/0.38 % (23460)Termination reason: Unknown 0.14/0.38 % (23460)Termination phase: Property scanning 0.14/0.38 0.14/0.38 % (23460)Memory used [KB]: 1023 0.14/0.38 % (23460)Time elapsed: 0.004 s 0.14/0.38 % (23460)Instructions burned: 5 (million) 0.14/0.38 % (23460)------------------------------ 0.14/0.38 % (23460)------------------------------ 0.14/0.38 % (23454)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on Vampire---4 for (1799ds/96Mi) 0.14/0.38 % (23455)Refutation not found, incomplete strategy 0.14/0.38 % (23455)------------------------------ 0.14/0.38 % (23455)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.14/0.38 % (23455)Termination reason: Refutation not found, incomplete strategy 0.14/0.38 0.14/0.38 0.14/0.38 % (23455)Memory used [KB]: 5628 0.14/0.38 % (23455)Time elapsed: 0.008 s 0.14/0.38 % (23455)Instructions burned: 12 (million) 0.14/0.38 % (23455)------------------------------ 0.14/0.38 % (23455)------------------------------ 0.14/0.38 % (23458)Instruction limit reached! 0.14/0.38 % (23458)------------------------------ 0.14/0.38 % (23458)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.14/0.38 % (23458)Termination reason: Unknown 0.14/0.38 % (23458)Termination phase: Saturation 0.14/0.38 0.14/0.39 % (23458)Memory used [KB]: 5756 0.14/0.39 % (23458)Time elapsed: 0.011 s 0.14/0.39 % (23458)Instructions burned: 18 (million) 0.14/0.39 % (23458)------------------------------ 0.14/0.39 % (23458)------------------------------ 0.14/0.39 % (23461)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) 0.14/0.39 % (23461)Refutation not found, incomplete strategy 0.14/0.39 % (23461)------------------------------ 0.14/0.39 % (23461)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.14/0.39 % (23461)Termination reason: Refutation not found, incomplete strategy 0.14/0.39 0.14/0.39 0.14/0.39 % (23461)Memory used [KB]: 5628 0.14/0.39 % (23461)Time elapsed: 0.006 s 0.14/0.39 % (23461)Instructions burned: 8 (million) 0.14/0.39 % (23461)------------------------------ 0.14/0.39 % (23461)------------------------------ 0.14/0.39 % (23462)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) 0.14/0.40 % (23463)lrs-3_1:1024_cbe=off:chr=on:tnu=1:i=7:si=on:rtra=on_0 on Vampire---4 for (1799ds/7Mi) 0.20/0.40 % (23456)Instruction limit reached! 0.20/0.40 % (23456)------------------------------ 0.20/0.40 % (23456)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.20/0.40 % (23456)Termination reason: Unknown 0.20/0.40 % (23456)Termination phase: Saturation 0.20/0.40 0.20/0.40 % (23456)Memory used [KB]: 5756 0.20/0.40 % (23456)Time elapsed: 0.019 s 0.20/0.40 % (23456)Instructions burned: 34 (million) 0.20/0.40 % (23456)------------------------------ 0.20/0.40 % (23456)------------------------------ 0.20/0.41 % (23463)Instruction limit reached! 0.20/0.41 % (23463)------------------------------ 0.20/0.41 % (23463)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.20/0.41 % (23463)Termination reason: Unknown 0.20/0.41 % (23463)Termination phase: Property scanning 0.20/0.41 0.20/0.41 % (23463)Memory used [KB]: 1023 0.20/0.41 % (23463)Time elapsed: 0.005 s 0.20/0.41 % (23463)Instructions burned: 7 (million) 0.20/0.41 % (23463)------------------------------ 0.20/0.41 % (23463)------------------------------ 0.20/0.41 % (23462)Instruction limit reached! 0.20/0.41 % (23462)------------------------------ 0.20/0.41 % (23462)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.20/0.41 % (23462)Termination reason: Unknown 0.20/0.41 % (23462)Termination phase: Saturation 0.20/0.41 0.20/0.41 % (23462)Memory used [KB]: 5756 0.20/0.41 % (23462)Time elapsed: 0.014 s 0.20/0.41 % (23462)Instructions burned: 22 (million) 0.20/0.41 % (23462)------------------------------ 0.20/0.41 % (23462)------------------------------ 0.20/0.41 % (23465)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) 0.20/0.41 % (23464)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) 0.20/0.42 % (23459)Instruction limit reached! 0.20/0.42 % (23459)------------------------------ 0.20/0.42 % (23459)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.20/0.42 % (23459)Termination reason: Unknown 0.20/0.42 % (23459)Termination phase: Saturation 0.20/0.42 0.20/0.42 % (23459)Memory used [KB]: 6012 0.20/0.42 % (23459)Time elapsed: 0.045 s 0.20/0.42 % (23459)Instructions burned: 75 (million) 0.20/0.42 % (23466)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) 0.20/0.42 % (23459)------------------------------ 0.20/0.42 % (23459)------------------------------ 0.20/0.42 % (23467)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) 0.20/0.42 % (23468)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) 0.20/0.42 % (23466)Instruction limit reached! 0.20/0.42 % (23466)------------------------------ 0.20/0.42 % (23466)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.20/0.42 % (23466)Termination reason: Unknown 0.20/0.42 % (23466)Termination phase: Function definition elimination 0.20/0.42 0.20/0.42 % (23466)Memory used [KB]: 1023 0.20/0.42 % (23466)Time elapsed: 0.006 s 0.20/0.42 % (23466)Instructions burned: 9 (million) 0.20/0.42 % (23466)------------------------------ 0.20/0.42 % (23466)------------------------------ 0.20/0.43 % (23454)Instruction limit reached! 0.20/0.43 % (23454)------------------------------ 0.20/0.43 % (23454)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.20/0.43 % (23454)Termination reason: Unknown 0.20/0.43 % (23454)Termination phase: Saturation 0.20/0.43 0.20/0.43 % (23454)Memory used [KB]: 6140 0.20/0.43 % (23454)Time elapsed: 0.051 s 0.20/0.43 % (23454)Instructions burned: 96 (million) 0.20/0.43 % (23454)------------------------------ 0.20/0.43 % (23454)------------------------------ 0.20/0.43 % (23469)lrs+21_1:1_cond=on:e2e=on:i=61:si=on:rtra=on_0 on Vampire---4 for (1799ds/61Mi) 0.20/0.44 % (23470)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=14:si=on:rtra=on_0 on Vampire---4 for (1799ds/14Mi) 0.20/0.44 % (23471)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) 0.20/0.44 % (23471)Instruction limit reached! 0.20/0.44 % (23471)------------------------------ 0.20/0.44 % (23471)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.20/0.44 % (23471)Termination reason: Unknown 0.20/0.44 % (23471)Termination phase: shuffling 0.20/0.44 0.20/0.44 % (23471)Memory used [KB]: 1023 0.20/0.44 % (23471)Time elapsed: 0.003 s 0.20/0.44 % (23471)Instructions burned: 2 (million) 0.20/0.44 % (23471)------------------------------ 0.20/0.44 % (23471)------------------------------ 0.20/0.44 % (23470)Instruction limit reached! 0.20/0.44 % (23470)------------------------------ 0.20/0.44 % (23470)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.20/0.45 % (23470)Termination reason: Unknown 0.20/0.45 % (23470)Termination phase: Saturation 0.20/0.45 0.20/0.45 % (23470)Memory used [KB]: 5628 0.20/0.45 % (23470)Time elapsed: 0.009 s 0.20/0.45 % (23470)Instructions burned: 14 (million) 0.20/0.45 % (23470)------------------------------ 0.20/0.45 % (23470)------------------------------ 0.20/0.45 % (23465)Instruction limit reached! 0.20/0.45 % (23465)------------------------------ 0.20/0.45 % (23465)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.20/0.45 % (23465)Termination reason: Unknown 0.20/0.45 % (23465)Termination phase: Saturation 0.20/0.45 0.20/0.45 % (23465)Memory used [KB]: 5756 0.20/0.45 % (23465)Time elapsed: 0.046 s 0.20/0.45 % (23465)Instructions burned: 71 (million) 0.20/0.45 % (23465)------------------------------ 0.20/0.45 % (23465)------------------------------ 0.20/0.46 % (23472)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on Vampire---4 for (1799ds/1041Mi) 0.20/0.46 % (23473)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on Vampire---4 for (1799ds/11Mi) 0.20/0.46 % (23469)Instruction limit reached! 0.20/0.46 % (23469)------------------------------ 0.20/0.46 % (23469)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.20/0.46 % (23469)Termination reason: Unknown 0.20/0.46 % (23469)Termination phase: Saturation 0.20/0.46 0.20/0.46 % (23469)Memory used [KB]: 5884 0.20/0.46 % (23469)Time elapsed: 0.032 s 0.20/0.46 % (23469)Instructions burned: 62 (million) 0.20/0.46 % (23469)------------------------------ 0.20/0.46 % (23469)------------------------------ 0.20/0.46 % (23473)Instruction limit reached! 0.20/0.46 % (23473)------------------------------ 0.20/0.46 % (23473)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.20/0.46 % (23473)Termination reason: Unknown 0.20/0.46 % (23473)Termination phase: Saturation 0.20/0.46 0.20/0.46 % (23473)Memory used [KB]: 5628 0.20/0.46 % (23473)Time elapsed: 0.007 s 0.20/0.46 % (23473)Instructions burned: 11 (million) 0.20/0.46 % (23473)------------------------------ 0.20/0.46 % (23473)------------------------------ 0.20/0.47 % (23474)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 (1799ds/140Mi) 0.20/0.47 % (23468)Instruction limit reached! 0.20/0.47 % (23468)------------------------------ 0.20/0.47 % (23468)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.20/0.47 % (23468)Termination reason: Unknown 0.20/0.47 % (23468)Termination phase: Saturation 0.20/0.47 0.20/0.47 % (23468)Memory used [KB]: 6652 0.20/0.47 % (23468)Time elapsed: 0.051 s 0.20/0.47 % (23468)Instructions burned: 128 (million) 0.20/0.47 % (23468)------------------------------ 0.20/0.47 % (23468)------------------------------ 0.20/0.47 % (23474)Refutation not found, incomplete strategy 0.20/0.47 % (23474)------------------------------ 0.20/0.47 % (23474)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.20/0.47 % (23474)Termination reason: Refutation not found, incomplete strategy 0.20/0.47 0.20/0.47 0.20/0.47 % (23474)Memory used [KB]: 5628 0.20/0.47 % (23474)Time elapsed: 0.007 s 0.20/0.47 % (23474)Instructions burned: 8 (million) 0.20/0.47 % (23474)------------------------------ 0.20/0.47 % (23474)------------------------------ 0.20/0.48 % (23475)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 (1799ds/26Mi) 0.20/0.48 % (23477)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on Vampire---4 for (1798ds/275Mi) 0.20/0.48 % (23476)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 (1799ds/56Mi) 0.20/0.48 % (23477)Refutation not found, incomplete strategy 0.20/0.48 % (23477)------------------------------ 0.20/0.48 % (23477)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.20/0.48 % (23477)Termination reason: Refutation not found, incomplete strategy 0.20/0.48 0.20/0.48 0.20/0.48 % (23477)Memory used [KB]: 5628 0.20/0.48 % (23477)Time elapsed: 0.003 s 0.20/0.48 % (23477)Instructions burned: 7 (million) 0.20/0.48 % (23477)------------------------------ 0.20/0.48 % (23477)------------------------------ 0.20/0.48 % (23478)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) 0.20/0.48 % (23475)Instruction limit reached! 0.20/0.48 % (23475)------------------------------ 0.20/0.48 % (23475)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.20/0.48 % (23475)Termination reason: Unknown 0.20/0.48 % (23475)Termination phase: Saturation 0.20/0.48 0.20/0.48 % (23475)Memory used [KB]: 5756 0.20/0.48 % (23475)Time elapsed: 0.010 s 0.20/0.48 % (23475)Instructions burned: 28 (million) 0.20/0.48 % (23475)------------------------------ 0.20/0.48 % (23475)------------------------------ 0.20/0.48 % (23478)Instruction limit reached! 0.20/0.48 % (23478)------------------------------ 0.20/0.48 % (23478)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.20/0.48 % (23478)Termination reason: Unknown 0.20/0.48 % (23478)Termination phase: shuffling 0.20/0.48 0.20/0.48 % (23478)Memory used [KB]: 1023 0.20/0.48 % (23478)Time elapsed: 0.002 s 0.20/0.48 % (23478)Instructions burned: 4 (million) 0.20/0.48 % (23478)------------------------------ 0.20/0.48 % (23478)------------------------------ 0.20/0.49 % (23479)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) 0.20/0.49 % (23479)Refutation not found, incomplete strategy 0.20/0.49 % (23479)------------------------------ 0.20/0.49 % (23479)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.20/0.49 % (23479)Termination reason: Refutation not found, incomplete strategy 0.20/0.49 0.20/0.49 0.20/0.49 % (23479)Memory used [KB]: 5628 0.20/0.49 % (23479)Time elapsed: 0.004 s 0.20/0.49 % (23479)Instructions burned: 9 (million) 0.20/0.49 % (23479)------------------------------ 0.20/0.49 % (23479)------------------------------ 0.20/0.49 % (23480)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) 0.20/0.49 % (23481)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) 0.20/0.49 % (23472)First to succeed. 0.20/0.50 % (23476)Instruction limit reached! 0.20/0.50 % (23476)------------------------------ 0.20/0.50 % (23476)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.20/0.50 % (23476)Termination reason: Unknown 0.20/0.50 % (23476)Termination phase: Saturation 0.20/0.50 0.20/0.50 % (23476)Memory used [KB]: 1407 0.20/0.50 % (23476)Time elapsed: 0.018 s 0.20/0.50 % (23476)Instructions burned: 59 (million) 0.20/0.50 % (23476)------------------------------ 0.20/0.50 % (23476)------------------------------ 0.20/0.50 % (23472)Refutation found. Thanks to Tanya! 0.20/0.50 % SZS status Theorem for Vampire---4 0.20/0.50 % SZS output start Proof for Vampire---4 0.20/0.50 thf(func_def_0, type, subrel: ($i > $i > $o) > ($i > $i > $o) > $o). 0.20/0.50 thf(func_def_2, type, inv: ($i > $i > $o) > $i > $i > $o). 0.20/0.50 thf(func_def_3, type, idem: (($i > $i > $o) > $i > $i > $o) > $o). 0.20/0.50 thf(func_def_4, type, infl: (($i > $i > $o) > $i > $i > $o) > $o). 0.20/0.50 thf(func_def_5, type, mono: (($i > $i > $o) > $i > $i > $o) > $o). 0.20/0.50 thf(func_def_6, type, refl: ($i > $i > $o) > $o). 0.20/0.50 thf(func_def_7, type, irrefl: ($i > $i > $o) > $o). 0.20/0.50 thf(func_def_8, type, rc: ($i > $i > $o) > $i > $i > $o). 0.20/0.50 thf(func_def_9, type, symm: ($i > $i > $o) > $o). 0.20/0.50 thf(func_def_10, type, antisymm: ($i > $i > $o) > $o). 0.20/0.50 thf(func_def_11, type, asymm: ($i > $i > $o) > $o). 0.20/0.50 thf(func_def_12, type, sc: ($i > $i > $o) > $i > $i > $o). 0.20/0.50 thf(func_def_13, type, trans: ($i > $i > $o) > $o). 0.20/0.50 thf(func_def_14, type, tc: ($i > $i > $o) > $i > $i > $o). 0.20/0.50 thf(func_def_15, type, trc: ($i > $i > $o) > $i > $i > $o). 0.20/0.50 thf(func_def_16, type, trsc: ($i > $i > $o) > $i > $i > $o). 0.20/0.50 thf(func_def_17, type, po: ($i > $i > $o) > $o). 0.20/0.50 thf(func_def_18, type, so: ($i > $i > $o) > $o). 0.20/0.50 thf(func_def_19, type, total: ($i > $i > $o) > $o). 0.20/0.50 thf(func_def_20, type, term: ($i > $i > $o) > $o). 0.20/0.50 thf(func_def_21, type, ind: ($i > $i > $o) > $o). 0.20/0.50 thf(func_def_22, type, innf: ($i > $i > $o) > $i > $o). 0.20/0.50 thf(func_def_23, type, nfof: ($i > $i > $o) > $i > $i > $o). 0.20/0.50 thf(func_def_24, type, norm: ($i > $i > $o) > $o). 0.20/0.50 thf(func_def_25, type, join: ($i > $i > $o) > $i > $i > $o). 0.20/0.50 thf(func_def_26, type, lconfl: ($i > $i > $o) > $o). 0.20/0.50 thf(func_def_27, type, sconfl: ($i > $i > $o) > $o). 0.20/0.50 thf(func_def_28, type, confl: ($i > $i > $o) > $o). 0.20/0.50 thf(func_def_29, type, cr: ($i > $i > $o) > $o). 0.20/0.50 thf(func_def_50, type, ph1: !>[X0: $tType]:(X0)). 0.20/0.50 thf(func_def_51, type, sK2: $i > $i > $o). 0.20/0.50 thf(func_def_54, type, sK5: $i > $i > $o). 0.20/0.50 thf(func_def_57, type, sK8: $i > $i > $o). 0.20/0.50 thf(f431,plain,( 0.20/0.50 $false), 0.20/0.50 inference(avatar_sat_refutation,[],[f156,f163,f279,f282,f430])). 0.20/0.50 thf(f430,plain,( 0.20/0.50 ~spl0_4), 0.20/0.50 inference(avatar_contradiction_clause,[],[f429])). 0.20/0.50 thf(f429,plain,( 0.20/0.50 $false | ~spl0_4), 0.20/0.50 inference(trivial_inequality_removal,[],[f428])). 0.20/0.50 thf(f428,plain,( 0.20/0.50 ($true = $false) | ~spl0_4), 0.20/0.50 inference(forward_demodulation,[],[f427,f371])). 0.20/0.50 thf(f371,plain,( 0.20/0.50 ((sK8 @ sK10 @ sK9) = $false) | ~spl0_4), 0.20/0.50 inference(boolean_simplification,[],[f370])). 0.20/0.50 thf(f370,plain,( 0.20/0.50 (($true => (sK8 @ sK10 @ sK9)) = $false) | ~spl0_4), 0.20/0.50 inference(backward_demodulation,[],[f367,f369])). 0.20/0.50 thf(f369,plain,( 0.20/0.50 ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK10 @ sK9)))) = $true) | ~spl0_4), 0.20/0.50 inference(binary_proxy_clausification,[],[f367])). 0.20/0.50 thf(f367,plain,( 0.20/0.50 ($false = ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK10 @ sK9)))) => (sK8 @ sK10 @ sK9))) | ~spl0_4), 0.20/0.50 inference(beta_eta_normalization,[],[f366])). 0.20/0.50 thf(f366,plain,( 0.20/0.50 (((^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((sK2 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2)))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y4))))))))) => (Y1 @ Y0 @ sK9)))) => (sK8 @ Y0 @ sK9))) @ sK10) = $false) | ~spl0_4), 0.20/0.50 inference(sigma_clausification,[],[f356])). 0.20/0.50 thf(f356,plain,( 0.20/0.50 ((!! @ $i @ (^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((sK2 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2)))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y4))))))))) => (Y1 @ Y0 @ sK9)))) => (sK8 @ Y0 @ sK9)))) = $false) | ~spl0_4), 0.20/0.50 inference(beta_eta_normalization,[],[f354])). 0.20/0.50 thf(f354,plain,( 0.20/0.50 (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y5))))))))) => (Y2 @ Y1 @ Y0)))) => (sK8 @ Y1 @ Y0))))) @ sK9) = $false) | ~spl0_4), 0.20/0.50 inference(sigma_clausification,[],[f342])). 0.20/0.50 thf(f342,plain,( 0.20/0.50 ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y5))))))))) => (Y2 @ Y1 @ Y0)))) => (sK8 @ Y1 @ Y0))))))) | ~spl0_4), 0.20/0.50 inference(not_proxy_clausification,[],[f307])). 0.20/0.50 thf(f307,plain,( 0.20/0.50 ($true = (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y5))))))))) => (Y2 @ Y1 @ Y0)))) => (sK8 @ Y1 @ Y0)))))))) | ~spl0_4), 0.20/0.50 inference(boolean_simplification,[],[f305])). 0.20/0.50 thf(f305,plain,( 0.20/0.50 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y5))))))))) => (Y2 @ Y1 @ Y0)))) => (sK8 @ Y1 @ Y0)))))) & $true))) | ~spl0_4), 0.20/0.50 inference(backward_demodulation,[],[f302,f303])). 0.20/0.50 thf(f303,plain,( 0.20/0.50 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK8 @ Y0 @ Y2) & (sK8 @ Y1 @ Y0)) => (sK8 @ Y1 @ Y2))))))))) | ~spl0_4), 0.20/0.50 inference(binary_proxy_clausification,[],[f293])). 0.20/0.50 thf(f293,plain,( 0.20/0.50 ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1 @ Y0) => (sK8 @ Y1 @ Y0)))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK8 @ Y0 @ Y2) & (sK8 @ Y1 @ Y0)) => (sK8 @ Y1 @ Y2)))))))))) | ~spl0_4), 0.20/0.50 inference(binary_proxy_clausification,[],[f290])). 0.20/0.50 thf(f290,plain,( 0.20/0.50 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1 @ Y0) => (sK8 @ Y1 @ Y0)))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK8 @ Y0 @ Y2) & (sK8 @ Y1 @ Y0)) => (sK8 @ Y1 @ Y2))))))))) => (sK8 @ sK3 @ sK4))) | ~spl0_4), 0.20/0.50 inference(beta_eta_normalization,[],[f289])). 0.20/0.50 thf(f289,plain,( 0.20/0.50 (((^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK3 @ sK4))) @ sK8) = $false) | ~spl0_4), 0.20/0.50 inference(sigma_clausification,[],[f162])). 0.20/0.50 thf(f162,plain,( 0.20/0.50 ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK3 @ sK4)))) = $false) | ~spl0_4), 0.20/0.50 inference(avatar_component_clause,[],[f161])). 0.20/0.50 thf(f161,plain,( 0.20/0.50 spl0_4 <=> ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK3 @ sK4)))) = $false)), 0.20/0.50 introduced(avatar_definition,[new_symbols(naming,[spl0_4])])). 0.20/0.50 thf(f302,plain,( 0.20/0.50 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y5))))))))) => (Y2 @ Y1 @ Y0)))) => (sK8 @ Y1 @ Y0)))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK8 @ Y0 @ Y2) & (sK8 @ Y1 @ Y0)) => (sK8 @ Y1 @ Y2))))))))))) | ~spl0_4), 0.20/0.50 inference(boolean_simplification,[],[f301])). 0.20/0.50 thf(f301,plain,( 0.20/0.50 ($true = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y5))))))))) => (Y2 @ Y1 @ Y0)))) => (sK8 @ Y1 @ Y0)))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK8 @ Y0 @ Y2) & (sK8 @ Y1 @ Y0)) => (sK8 @ Y1 @ Y2))))))))) => $false)) | ~spl0_4), 0.20/0.50 inference(superposition,[],[f288,f292])). 0.20/0.50 thf(f292,plain,( 0.20/0.50 ((sK8 @ sK3 @ sK4) = $false) | ~spl0_4), 0.20/0.50 inference(binary_proxy_clausification,[],[f290])). 0.20/0.50 thf(f288,plain,( 0.20/0.50 ( ! [X1 : $i > $i > $o] : (($true = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y5))))))))) => (Y2 @ Y1 @ Y0)))) => (X1 @ Y1 @ Y0)))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((X1 @ Y0 @ Y2) & (X1 @ Y1 @ Y0)) => (X1 @ Y1 @ Y2))))))))) => (X1 @ sK3 @ sK4)))) ) | ~spl0_4), 0.20/0.50 inference(beta_eta_normalization,[],[f287])). 0.20/0.50 thf(f287,plain,( 0.20/0.50 ( ! [X1 : $i > $i > $o] : (($true = ((^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((sK2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4)))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y6))))))))) => (Y3 @ Y2 @ Y1)))) => (Y0 @ Y2 @ Y1)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK3 @ sK4))) @ X1))) ) | ~spl0_4), 0.20/0.50 inference(pi_clausification,[],[f283])). 0.20/0.50 thf(f283,plain,( 0.20/0.50 ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((sK2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4)))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y6))))))))) => (Y3 @ Y2 @ Y1)))) => (Y0 @ Y2 @ Y1)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK3 @ sK4)))) != $false) | ~spl0_4), 0.20/0.50 inference(forward_demodulation,[],[f147,f162])). 0.20/0.50 thf(f147,plain,( 0.20/0.50 ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((sK2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4)))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y6))))))))) => (Y3 @ Y2 @ Y1)))) => (Y0 @ Y2 @ Y1)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK3 @ sK4)))) != (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK3 @ sK4)))))), 0.20/0.50 inference(beta_eta_normalization,[],[f146])). 0.20/0.50 thf(f146,plain,( 0.20/0.50 (((^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((sK2 @ Y6 @ Y5) => (Y4 @ Y6 @ Y5)))))) & (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y5 @ Y7) & (Y4 @ Y6 @ Y5)) => (Y4 @ Y6 @ Y7))))))))) => (Y4 @ Y3 @ Y2)))) => (Y1 @ Y3 @ Y2)))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y4))))))))) => (Y1 @ sK3 @ Y0))))) @ sK4) != ((^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((sK2 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2)))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y4))))))))) => (Y1 @ sK3 @ Y0))))) @ sK4))), 0.20/0.50 inference(negative_extensionality,[],[f145])). 0.20/0.50 thf(f145,plain,( 0.20/0.50 ((^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((sK2 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2)))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y4))))))))) => (Y1 @ sK3 @ Y0))))) != (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((sK2 @ Y6 @ Y5) => (Y4 @ Y6 @ Y5)))))) & (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y5 @ Y7) & (Y4 @ Y6 @ Y5)) => (Y4 @ Y6 @ Y7))))))))) => (Y4 @ Y3 @ Y2)))) => (Y1 @ Y3 @ Y2)))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y4))))))))) => (Y1 @ sK3 @ Y0))))))), 0.20/0.50 inference(beta_eta_normalization,[],[f144])). 0.20/0.50 thf(f144,plain,( 0.20/0.50 (((^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((sK2 @ Y7 @ Y6) => (Y5 @ Y7 @ Y6)))))) & (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y6 @ Y8) & (Y5 @ Y7 @ Y6)) => (Y5 @ Y7 @ Y8))))))))) => (Y5 @ Y4 @ Y3)))) => (Y2 @ Y4 @ Y3)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y5))))))))) => (Y2 @ Y0 @ Y1))))))) @ sK3) != ((^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y5))))))))) => (Y2 @ Y0 @ Y1))))))) @ sK3))), 0.20/0.50 inference(negative_extensionality,[],[f143])). 0.20/0.50 thf(f143,plain,( 0.20/0.50 ((^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((sK2 @ Y7 @ Y6) => (Y5 @ Y7 @ Y6)))))) & (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y6 @ Y8) & (Y5 @ Y7 @ Y6)) => (Y5 @ Y7 @ Y8))))))))) => (Y5 @ Y4 @ Y3)))) => (Y2 @ Y4 @ Y3)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y5))))))))) => (Y2 @ Y0 @ Y1))))))) != (^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y5))))))))) => (Y2 @ Y0 @ Y1))))))))), 0.20/0.50 inference(equality_proxy_clausification,[],[f142])). 0.20/0.50 thf(f142,plain,( 0.20/0.50 ($false = ((^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((sK2 @ Y7 @ Y6) => (Y5 @ Y7 @ Y6)))))) & (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y6 @ Y8) & (Y5 @ Y7 @ Y6)) => (Y5 @ Y7 @ Y8))))))))) => (Y5 @ Y4 @ Y3)))) => (Y2 @ Y4 @ Y3)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y5))))))))) => (Y2 @ Y0 @ Y1))))))) = (^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y5))))))))) => (Y2 @ Y0 @ Y1)))))))))), 0.20/0.50 inference(beta_eta_normalization,[],[f141])). 0.20/0.50 thf(f141,plain,( 0.20/0.50 (((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y0 @ Y8 @ Y7) => (Y6 @ Y8 @ Y7)))))) & (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y7 @ Y9) & (Y6 @ Y8 @ Y7)) => (Y6 @ Y8 @ Y9))))))))) => (Y6 @ Y5 @ Y4)))) => (Y3 @ Y5 @ Y4)))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y6))))))))) => (Y3 @ Y1 @ Y2))))))) = (^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y0 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4)))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y6))))))))) => (Y3 @ Y1 @ Y2))))))))) @ sK2) = $false)), 0.20/0.50 inference(sigma_clausification,[],[f138])). 0.20/0.50 thf(f138,plain,( 0.20/0.50 ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y0 @ Y8 @ Y7) => (Y6 @ Y8 @ Y7)))))) & (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y7 @ Y9) & (Y6 @ Y8 @ Y7)) => (Y6 @ Y8 @ Y9))))))))) => (Y6 @ Y5 @ Y4)))) => (Y3 @ Y5 @ Y4)))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y6))))))))) => (Y3 @ Y1 @ Y2))))))) = (^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y0 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4)))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y6))))))))) => (Y3 @ Y1 @ Y2)))))))))) = $false)), 0.20/0.50 inference(not_proxy_clausification,[],[f137])). 0.20/0.50 thf(f137,plain,( 0.20/0.50 ($true = (~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y0 @ Y8 @ Y7) => (Y6 @ Y8 @ Y7)))))) & (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y7 @ Y9) & (Y6 @ Y8 @ Y7)) => (Y6 @ Y8 @ Y9))))))))) => (Y6 @ Y5 @ Y4)))) => (Y3 @ Y5 @ Y4)))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y6))))))))) => (Y3 @ Y1 @ Y2))))))) = (^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y0 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4)))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y6))))))))) => (Y3 @ Y1 @ Y2))))))))))))), 0.20/0.50 inference(beta_eta_normalization,[],[f136])). 0.20/0.50 thf(f136,plain,( 0.20/0.50 ((~ ((^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ (Y0 @ Y1)) = (Y0 @ Y1))))) @ (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: ((((^[Y4 : $i > $i > $o]: ((^[Y5 : $i > $i > $o]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y4 @ Y7 @ Y6) => (Y5 @ Y7 @ Y6))))))))) @ Y0 @ Y3) & ((^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y5 @ Y7) & (Y4 @ Y6 @ Y5)) => (Y4 @ Y6 @ Y7))))))))) @ Y3)) => (Y3 @ Y1 @ Y2))))))))))) = $true)), 0.20/0.50 inference(definition_unfolding,[],[f106,f100,f123])). 0.20/0.50 thf(f123,plain,( 0.20/0.50 (tc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: ((((^[Y4 : $i > $i > $o]: ((^[Y5 : $i > $i > $o]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y4 @ Y7 @ Y6) => (Y5 @ Y7 @ Y6))))))))) @ Y0 @ Y3) & ((^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y5 @ Y7) & (Y4 @ Y6 @ Y5)) => (Y4 @ Y6 @ Y7))))))))) @ Y3)) => (Y3 @ Y1 @ Y2))))))))))), 0.20/0.50 inference(definition_unfolding,[],[f101,f92,f93])). 0.20/0.50 thf(f93,plain,( 0.20/0.50 (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))))), 0.20/0.50 inference(cnf_transformation,[],[f45])). 0.20/0.50 thf(f45,plain,( 0.20/0.50 (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))))), 0.20/0.50 inference(fool_elimination,[],[f44])). 0.20/0.50 thf(f44,plain,( 0.20/0.50 (trans = (^[X0 : $i > $i > $o] : (! [X1,X2,X3] : (((X0 @ X2 @ X3) & (X0 @ X3 @ X1)) => (X0 @ X2 @ X1)))))), 0.20/0.50 inference(rectify,[],[f13])). 0.20/0.50 thf(f13,axiom,( 0.20/0.50 (trans = (^[X0 : $i > $i > $o] : (! [X5,X2,X3] : (((X0 @ X2 @ X3) & (X0 @ X3 @ X5)) => (X0 @ X2 @ X5)))))), 0.20/0.50 file('/export/starexec/sandbox2/tmp/tmp.tiVUk2IRLU/Vampire---4.8_23344',transitive)). 0.20/0.50 thf(f92,plain,( 0.20/0.50 (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))))))), 0.20/0.50 inference(cnf_transformation,[],[f47])). 0.20/0.50 thf(f47,plain,( 0.20/0.50 (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))))))), 0.20/0.50 inference(fool_elimination,[],[f46])). 0.20/0.50 thf(f46,plain,( 0.20/0.50 ((^[X0 : $i > $i > $o, X1 : $i > $i > $o] : (! [X2,X3] : ((X0 @ X2 @ X3) => (X1 @ X2 @ X3)))) = subrel)), 0.20/0.50 inference(rectify,[],[f1])). 0.20/0.50 thf(f1,axiom,( 0.20/0.50 ((^[X0 : $i > $i > $o, X1 : $i > $i > $o] : (! [X2,X3] : ((X0 @ X2 @ X3) => (X1 @ X2 @ X3)))) = subrel)), 0.20/0.50 file('/export/starexec/sandbox2/tmp/tmp.tiVUk2IRLU/Vampire---4.8_23344',subrel)). 0.20/0.50 thf(f101,plain,( 0.20/0.50 (tc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((subrel @ Y0 @ Y3) & (trans @ Y3)) => (Y3 @ Y1 @ Y2))))))))))), 0.20/0.50 inference(cnf_transformation,[],[f88])). 0.20/0.50 thf(f88,plain,( 0.20/0.50 (tc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((subrel @ Y0 @ Y3) & (trans @ Y3)) => (Y3 @ Y1 @ Y2))))))))))), 0.20/0.50 inference(fool_elimination,[],[f87])). 0.20/0.50 thf(f87,plain,( 0.20/0.50 (tc = (^[X0 : $i > $i > $o, X1 : $i, X2 : $i] : (! [X3 : $i > $i > $o] : (((trans @ X3) & (subrel @ X0 @ X3)) => (X3 @ X1 @ X2)))))), 0.20/0.50 inference(rectify,[],[f14])). 0.20/0.50 thf(f14,axiom,( 0.20/0.50 (tc = (^[X0 : $i > $i > $o, X2 : $i, X3 : $i] : (! [X1 : $i > $i > $o] : (((trans @ X1) & (subrel @ X0 @ X1)) => (X1 @ X2 @ X3)))))), 0.20/0.50 file('/export/starexec/sandbox2/tmp/tmp.tiVUk2IRLU/Vampire---4.8_23344',transitive_closure)). 0.20/0.50 thf(f100,plain,( 0.20/0.50 (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ (Y0 @ Y1)) = (Y0 @ Y1))))))), 0.20/0.50 inference(cnf_transformation,[],[f73])). 0.20/0.50 thf(f73,plain,( 0.20/0.50 (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ (Y0 @ Y1)) = (Y0 @ Y1))))))), 0.20/0.50 inference(fool_elimination,[],[f72])). 0.20/0.50 thf(f72,plain,( 0.20/0.50 (idem = (^[X0 : ($i > $i > $o) > $i > $i > $o] : (! [X1 : $i > $i > $o] : ((X0 @ (X0 @ X1)) = (X0 @ X1)))))), 0.20/0.50 inference(rectify,[],[f3])). 0.20/0.50 thf(f3,axiom,( 0.20/0.50 (idem = (^[X4 : ($i > $i > $o) > $i > $i > $o] : (! [X0 : $i > $i > $o] : ((X4 @ X0) = (X4 @ (X4 @ X0))))))), 0.20/0.50 file('/export/starexec/sandbox2/tmp/tmp.tiVUk2IRLU/Vampire---4.8_23344',idempotent)). 0.20/0.50 thf(f106,plain,( 0.20/0.50 ($true = (~ (idem @ tc)))), 0.20/0.50 inference(cnf_transformation,[],[f69])). 0.20/0.50 thf(f69,plain,( 0.20/0.50 ($true = (~ (idem @ tc)))), 0.20/0.50 inference(fool_elimination,[],[f68])). 0.20/0.50 thf(f68,plain,( 0.20/0.50 ~(idem @ tc)), 0.20/0.50 inference(rectify,[],[f31])). 0.20/0.50 thf(f31,negated_conjecture,( 0.20/0.50 ~(idem @ tc)), 0.20/0.50 inference(negated_conjecture,[],[f30])). 0.20/0.50 thf(f30,conjecture,( 0.20/0.50 (idem @ tc)), 0.20/0.50 file('/export/starexec/sandbox2/tmp/tmp.tiVUk2IRLU/Vampire---4.8_23344',transitive_closure_op_is_idempotent)). 0.20/0.50 thf(f427,plain,( 0.20/0.50 ($true = (sK8 @ sK10 @ sK9)) | ~spl0_4), 0.20/0.50 inference(boolean_simplification,[],[f426])). 0.20/0.50 thf(f426,plain,( 0.20/0.50 ($true = ($true => (sK8 @ sK10 @ sK9))) | ~spl0_4), 0.20/0.50 inference(forward_demodulation,[],[f410,f303])). 0.20/0.50 thf(f410,plain,( 0.20/0.50 ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK8 @ Y0 @ Y2) & (sK8 @ Y1 @ Y0)) => (sK8 @ Y1 @ Y2)))))))) => (sK8 @ sK10 @ sK9))) | ~spl0_4), 0.20/0.50 inference(boolean_simplification,[],[f409])). 0.20/0.50 thf(f409,plain,( 0.20/0.50 ($true = (($true & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK8 @ Y0 @ Y2) & (sK8 @ Y1 @ Y0)) => (sK8 @ Y1 @ Y2))))))))) => (sK8 @ sK10 @ sK9))) | ~spl0_4), 0.20/0.50 inference(superposition,[],[f404,f308])). 0.20/0.50 thf(f308,plain,( 0.20/0.50 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1 @ Y0) => (sK8 @ Y1 @ Y0))))))) | ~spl0_4), 0.20/0.50 inference(boolean_simplification,[],[f306])). 0.20/0.50 thf(f306,plain,( 0.20/0.50 ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1 @ Y0) => (sK8 @ Y1 @ Y0)))))) & $true)) | ~spl0_4), 0.20/0.50 inference(backward_demodulation,[],[f293,f303])). 0.20/0.50 thf(f404,plain,( 0.20/0.50 ( ! [X1 : $i > $i > $o] : (($true = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1 @ Y0) => (X1 @ Y1 @ Y0)))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((X1 @ Y0 @ Y2) & (X1 @ Y1 @ Y0)) => (X1 @ Y1 @ Y2))))))))) => (X1 @ sK10 @ sK9)))) ) | ~spl0_4), 0.20/0.50 inference(beta_eta_normalization,[],[f403])). 0.20/0.50 thf(f403,plain,( 0.20/0.50 ( ! [X1 : $i > $i > $o] : (($true = ((^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK10 @ sK9))) @ X1))) ) | ~spl0_4), 0.20/0.50 inference(pi_clausification,[],[f369])). 0.20/0.50 thf(f282,plain,( 0.20/0.50 ~spl0_1 | ~spl0_3), 0.20/0.50 inference(avatar_contradiction_clause,[],[f281])). 0.20/0.50 thf(f281,plain,( 0.20/0.50 $false | (~spl0_1 | ~spl0_3)), 0.20/0.50 inference(trivial_inequality_removal,[],[f280])). 0.20/0.50 thf(f280,plain,( 0.20/0.50 ($true = $false) | (~spl0_1 | ~spl0_3)), 0.20/0.50 inference(forward_demodulation,[],[f152,f159])). 0.20/0.50 thf(f159,plain,( 0.20/0.50 ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((sK2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4)))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y6))))))))) => (Y3 @ Y2 @ Y1)))) => (Y0 @ Y2 @ Y1)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK3 @ sK4)))) = $false) | ~spl0_3), 0.20/0.50 inference(avatar_component_clause,[],[f158])). 0.20/0.50 thf(f158,plain,( 0.20/0.50 spl0_3 <=> ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((sK2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4)))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y6))))))))) => (Y3 @ Y2 @ Y1)))) => (Y0 @ Y2 @ Y1)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK3 @ sK4)))) = $false)), 0.20/0.50 introduced(avatar_definition,[new_symbols(naming,[spl0_3])])). 0.20/0.50 thf(f152,plain,( 0.20/0.50 ($true = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((sK2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4)))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y6))))))))) => (Y3 @ Y2 @ Y1)))) => (Y0 @ Y2 @ Y1)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK3 @ sK4))))) | ~spl0_1), 0.20/0.50 inference(avatar_component_clause,[],[f151])). 0.20/0.50 thf(f151,plain,( 0.20/0.50 spl0_1 <=> ($true = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((sK2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4)))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y6))))))))) => (Y3 @ Y2 @ Y1)))) => (Y0 @ Y2 @ Y1)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK3 @ sK4)))))), 0.20/0.50 introduced(avatar_definition,[new_symbols(naming,[spl0_1])])). 0.20/0.50 thf(f279,plain,( 0.20/0.50 ~spl0_2 | ~spl0_3), 0.20/0.50 inference(avatar_contradiction_clause,[],[f278])). 0.20/0.50 thf(f278,plain,( 0.20/0.50 $false | (~spl0_2 | ~spl0_3)), 0.20/0.50 inference(trivial_inequality_removal,[],[f277])). 0.20/0.50 thf(f277,plain,( 0.20/0.50 ($true = $false) | (~spl0_2 | ~spl0_3)), 0.20/0.50 inference(forward_demodulation,[],[f271,f173])). 0.20/0.50 thf(f173,plain,( 0.20/0.50 ((sK5 @ sK3 @ sK4) = $false) | ~spl0_3), 0.20/0.50 inference(binary_proxy_clausification,[],[f172])). 0.20/0.50 thf(f172,plain,( 0.20/0.50 ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y5))))))))) => (Y2 @ Y1 @ Y0)))) => (sK5 @ Y1 @ Y0)))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK5 @ Y0 @ Y2) & (sK5 @ Y1 @ Y0)) => (sK5 @ Y1 @ Y2))))))))) => (sK5 @ sK3 @ sK4)) = $false) | ~spl0_3), 0.20/0.50 inference(beta_eta_normalization,[],[f171])). 0.20/0.50 thf(f171,plain,( 0.20/0.50 (((^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((sK2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4)))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y6))))))))) => (Y3 @ Y2 @ Y1)))) => (Y0 @ Y2 @ Y1)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK3 @ sK4))) @ sK5) = $false) | ~spl0_3), 0.20/0.50 inference(sigma_clausification,[],[f159])). 0.20/0.50 thf(f271,plain,( 0.20/0.50 ($true = (sK5 @ sK3 @ sK4)) | (~spl0_2 | ~spl0_3)), 0.20/0.50 inference(boolean_simplification,[],[f269])). 0.20/0.50 thf(f269,plain,( 0.20/0.50 ($true = ($true => (sK5 @ sK3 @ sK4))) | (~spl0_2 | ~spl0_3)), 0.20/0.50 inference(superposition,[],[f265,f155])). 0.20/0.50 thf(f155,plain,( 0.20/0.50 ($true = (!! 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[X2 : $i,X1 : $i] : (($true = ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ X2 @ X1)))) => (sK5 @ X2 @ X1)))) ) | ~spl0_3), 0.20/0.50 inference(beta_eta_normalization,[],[f264])). 0.20/0.50 thf(f264,plain,( 0.20/0.50 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((sK2 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2)))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y4))))))))) => (Y1 @ Y0 @ X1)))) => (sK5 @ Y0 @ X1))) @ X2))) ) | ~spl0_3), 0.20/0.50 inference(pi_clausification,[],[f256])). 0.20/0.50 thf(f256,plain,( 0.20/0.50 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((sK2 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2)))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y2 @ Y4) & (Y1 @ Y3 @ Y2)) => (Y1 @ Y3 @ Y4))))))))) => (Y1 @ Y0 @ X1)))) => (sK5 @ Y0 @ X1)))))) ) | ~spl0_3), 0.20/0.50 inference(beta_eta_normalization,[],[f255])). 0.20/0.50 thf(f255,plain,( 0.20/0.50 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y5))))))))) => (Y2 @ Y1 @ Y0)))) => (sK5 @ Y1 @ Y0))))) @ X1))) ) | ~spl0_3), 0.20/0.50 inference(pi_clausification,[],[f182])). 0.20/0.50 thf(f182,plain,( 0.20/0.50 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y5))))))))) => (Y2 @ Y1 @ Y0)))) => (sK5 @ Y1 @ Y0))))))) | ~spl0_3), 0.20/0.50 inference(binary_proxy_clausification,[],[f174])). 0.20/0.50 thf(f174,plain,( 0.20/0.50 ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y3 @ Y5) & (Y2 @ Y4 @ Y3)) => (Y2 @ Y4 @ Y5))))))))) => (Y2 @ Y1 @ Y0)))) => (sK5 @ Y1 @ Y0)))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK5 @ Y0 @ Y2) & (sK5 @ Y1 @ Y0)) => (sK5 @ Y1 @ Y2)))))))))) | ~spl0_3), 0.20/0.50 inference(binary_proxy_clausification,[],[f172])). 0.20/0.50 thf(f163,plain,( 0.20/0.50 spl0_3 | spl0_4), 0.20/0.50 inference(avatar_split_clause,[],[f149,f161,f158])). 0.20/0.50 thf(f149,plain,( 0.20/0.50 ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((sK2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4)))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y6))))))))) => (Y3 @ Y2 @ Y1)))) => (Y0 @ Y2 @ Y1)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK3 @ sK4)))) = $false) | ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK3 @ sK4)))) = $false)), 0.20/0.50 inference(binary_proxy_clausification,[],[f147])). 0.20/0.50 thf(f156,plain,( 0.20/0.50 spl0_1 | spl0_2), 0.20/0.50 inference(avatar_split_clause,[],[f148,f154,f151])). 0.20/0.50 thf(f148,plain,( 0.20/0.50 ($true = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK3 @ sK4))))) | ($true = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((sK2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4)))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y6) & (Y3 @ Y5 @ Y4)) => (Y3 @ Y5 @ Y6))))))))) => (Y3 @ Y2 @ Y1)))) => (Y0 @ Y2 @ Y1)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y2 @ Y1)) => (Y0 @ Y2 @ Y3))))))))) => (Y0 @ sK3 @ sK4)))))), 0.20/0.50 inference(binary_proxy_clausification,[],[f147])). 0.20/0.50 % SZS output end Proof for Vampire---4 0.20/0.50 % (23472)------------------------------ 0.20/0.50 % (23472)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.20/0.50 % (23472)Termination reason: Refutation 0.20/0.50 0.20/0.50 % (23472)Memory used [KB]: 6140 0.20/0.50 % (23472)Time elapsed: 0.041 s 0.20/0.50 % (23472)Instructions burned: 75 (million) 0.20/0.50 % (23472)------------------------------ 0.20/0.50 % (23472)------------------------------ 0.20/0.50 % (23453)Success in time 0.127 s 0.20/0.50 % Vampire---4.8 exiting 0.20/0.50 EOF