0.07/0.16 % Problem : Vampire---4.8_11085 : TPTP v0.0.0. Released v0.0.0. 0.07/0.18 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s 0.17/0.39 % Computer : n018.cluster.edu 0.17/0.39 % Model : x86_64 x86_64 0.17/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.17/0.39 % Memory : 8042.1875MB 0.17/0.39 % OS : Linux 3.10.0-693.el7.x86_64 0.17/0.39 % CPULimit : 1440 0.17/0.39 % WCLimit : 180 0.17/0.39 % DateTime : Mon Jul 3 13:14:16 EDT 2023 0.17/0.39 % CPUTime : 0.17/0.39 This is a THF_ problem 0.17/0.39 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.2N6dEsweBi/Vampire---4.8_11085 -m 12000 -t 180 0.24/0.42 % (11351)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) 0.24/0.43 % (11348)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on Vampire---4 for (1799ds/96Mi) 0.24/0.43 % (11350)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) 0.24/0.43 % (11349)lrs+10_1:2_cnfonf=off:hud=1:inj=on:i=36:si=on:rtra=on_0 on Vampire---4 for (1799ds/36Mi) 0.24/0.43 % (11352)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on Vampire---4 for (1799ds/17Mi) 0.24/0.43 % (11353)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) 0.24/0.43 % (11355)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) 0.24/0.43 % (11354)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) 0.24/0.43 % (11354)Instruction limit reached! 0.24/0.43 % (11354)------------------------------ 0.24/0.43 % (11354)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.24/0.43 % (11354)Termination reason: Unknown 0.24/0.43 % (11354)Termination phase: shuffling 0.24/0.43 0.24/0.43 % (11354)Memory used [KB]: 1407 0.24/0.43 % (11354)Time elapsed: 0.004 s 0.24/0.43 % (11354)Instructions burned: 4 (million) 0.24/0.43 % (11354)------------------------------ 0.24/0.43 % (11354)------------------------------ 0.24/0.43 % (11352)Instruction limit reached! 0.24/0.43 % (11352)------------------------------ 0.24/0.43 % (11352)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.24/0.43 % (11352)Termination reason: Unknown 0.24/0.43 % (11352)Termination phase: shuffling 0.24/0.43 0.24/0.43 % (11352)Memory used [KB]: 1663 0.24/0.43 % (11352)Time elapsed: 0.011 s 0.24/0.43 % (11352)Instructions burned: 17 (million) 0.24/0.43 % (11352)------------------------------ 0.24/0.43 % (11352)------------------------------ 0.24/0.44 % (11350)Instruction limit reached! 0.24/0.44 % (11350)------------------------------ 0.24/0.44 % (11350)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.24/0.44 % (11350)Termination reason: Unknown 0.24/0.44 % (11350)Termination phase: shuffling 0.24/0.44 0.24/0.44 % (11350)Memory used [KB]: 2174 0.24/0.44 % (11350)Time elapsed: 0.020 s 0.24/0.44 % (11350)Instructions burned: 35 (million) 0.24/0.44 % (11350)------------------------------ 0.24/0.44 % (11350)------------------------------ 0.24/0.44 % (11356)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 % (11349)Instruction limit reached! 0.24/0.44 % (11349)------------------------------ 0.24/0.44 % (11349)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.24/0.44 % (11349)Termination reason: Unknown 0.24/0.44 % (11349)Termination phase: Property scanning 0.24/0.44 0.24/0.44 % (11349)Memory used [KB]: 2046 0.24/0.44 % (11349)Time elapsed: 0.020 s 0.24/0.44 % (11349)Instructions burned: 37 (million) 0.24/0.44 % (11349)------------------------------ 0.24/0.44 % (11349)------------------------------ 0.24/0.45 % (11357)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 % (11357)Instruction limit reached! 0.24/0.45 % (11357)------------------------------ 0.24/0.45 % (11357)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.24/0.45 % (11357)Termination reason: Unknown 0.24/0.45 % (11357)Termination phase: shuffling 0.24/0.45 0.24/0.45 % (11357)Memory used [KB]: 1535 0.24/0.45 % (11357)Time elapsed: 0.006 s 0.24/0.45 % (11357)Instructions burned: 7 (million) 0.24/0.45 % (11357)------------------------------ 0.24/0.45 % (11357)------------------------------ 0.24/0.45 % (11356)Instruction limit reached! 0.24/0.45 % (11356)------------------------------ 0.24/0.45 % (11356)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.24/0.45 % (11356)Termination reason: Unknown 0.24/0.45 % (11356)Termination phase: shuffling 0.24/0.45 0.24/0.45 % (11356)Memory used [KB]: 1791 0.24/0.45 % (11356)Time elapsed: 0.013 s 0.24/0.45 % (11356)Instructions burned: 21 (million) 0.24/0.45 % (11356)------------------------------ 0.24/0.45 % (11356)------------------------------ 0.24/0.46 % (11358)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) 0.24/0.46 % (11359)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) 0.24/0.46 % (11353)Instruction limit reached! 0.24/0.46 % (11353)------------------------------ 0.24/0.46 % (11353)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.24/0.46 % (11353)Termination reason: Unknown 0.24/0.46 % (11353)Termination phase: Property scanning 0.24/0.46 0.24/0.46 % (11353)Memory used [KB]: 2174 0.24/0.46 % (11353)Time elapsed: 0.037 s 0.24/0.46 % (11353)Instructions burned: 76 (million) 0.24/0.46 % (11353)------------------------------ 0.24/0.46 % (11353)------------------------------ 0.24/0.47 % (11362)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) 0.24/0.47 % (11364)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 % (11348)Instruction limit reached! 0.24/0.47 % (11348)------------------------------ 0.24/0.47 % (11348)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.24/0.47 % (11348)Termination reason: Unknown 0.24/0.47 % (11348)Termination phase: Property scanning 0.24/0.47 0.24/0.47 % (11348)Memory used [KB]: 2430 0.24/0.47 % (11348)Time elapsed: 0.047 s 0.24/0.47 % (11348)Instructions burned: 97 (million) 0.24/0.47 % (11348)------------------------------ 0.24/0.47 % (11348)------------------------------ 0.24/0.47 % (11362)Instruction limit reached! 0.24/0.47 % (11362)------------------------------ 0.24/0.47 % (11362)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.24/0.47 % (11362)Termination reason: Unknown 0.24/0.47 % (11362)Termination phase: shuffling 0.24/0.47 0.24/0.47 % (11362)Memory used [KB]: 1535 0.24/0.47 % (11362)Time elapsed: 0.007 s 0.24/0.47 % (11362)Instructions burned: 10 (million) 0.24/0.47 % (11362)------------------------------ 0.24/0.47 % (11362)------------------------------ 0.24/0.48 % (11368)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) 0.24/0.49 % (11371)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 % (11372)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=14:si=on:rtra=on_0 on Vampire---4 for (1799ds/14Mi) 0.24/0.49 % (11359)Instruction limit reached! 0.24/0.49 % (11359)------------------------------ 0.24/0.49 % (11359)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.24/0.49 % (11359)Termination reason: Unknown 0.24/0.49 % (11359)Termination phase: Property scanning 0.24/0.49 0.24/0.49 % (11359)Memory used [KB]: 2174 0.24/0.49 % (11359)Time elapsed: 0.036 s 0.24/0.49 % (11359)Instructions burned: 71 (million) 0.24/0.49 % (11359)------------------------------ 0.24/0.49 % (11359)------------------------------ 0.24/0.50 % (11372)Instruction limit reached! 0.24/0.50 % (11372)------------------------------ 0.24/0.50 % (11372)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.24/0.50 % (11372)Termination reason: Unknown 0.24/0.50 % (11372)Termination phase: shuffling 0.24/0.50 0.24/0.50 % (11372)Memory used [KB]: 1663 0.24/0.50 % (11372)Time elapsed: 0.011 s 0.24/0.50 % (11372)Instructions burned: 14 (million) 0.24/0.50 % (11372)------------------------------ 0.24/0.50 % (11372)------------------------------ 0.24/0.51 % (11378)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) 0.24/0.51 % (11378)Instruction limit reached! 0.24/0.51 % (11378)------------------------------ 0.24/0.51 % (11378)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.24/0.51 % (11378)Termination reason: Unknown 0.24/0.51 % (11378)Termination phase: shuffling 0.24/0.51 0.24/0.51 % (11378)Memory used [KB]: 1407 0.24/0.51 % (11378)Time elapsed: 0.003 s 0.24/0.51 % (11378)Instructions burned: 2 (million) 0.24/0.51 % (11378)------------------------------ 0.24/0.51 % (11378)------------------------------ 0.24/0.51 % (11380)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) 0.24/0.52 % (11371)Instruction limit reached! 0.24/0.52 % (11371)------------------------------ 0.24/0.52 % (11371)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.24/0.52 % (11371)Termination reason: Unknown 0.24/0.52 % (11371)Termination phase: Preprocessing 3 0.24/0.52 0.24/0.52 % (11371)Memory used [KB]: 2942 0.24/0.52 % (11371)Time elapsed: 0.037 s 0.24/0.52 % (11371)Instructions burned: 62 (million) 0.24/0.52 % (11371)------------------------------ 0.24/0.52 % (11371)------------------------------ 0.24/0.52 % (11384)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on Vampire---4 for (1798ds/11Mi) 0.24/0.53 % (11384)Instruction limit reached! 0.24/0.53 % (11384)------------------------------ 0.24/0.53 % (11384)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.24/0.53 % (11384)Termination reason: Unknown 0.24/0.53 % (11384)Termination phase: shuffling 0.24/0.53 0.24/0.53 % (11384)Memory used [KB]: 1535 0.24/0.53 % (11384)Time elapsed: 0.008 s 0.24/0.53 % (11384)Instructions burned: 13 (million) 0.24/0.53 % (11384)------------------------------ 0.24/0.53 % (11384)------------------------------ 0.24/0.53 % (11368)Instruction limit reached! 0.24/0.53 % (11368)------------------------------ 0.24/0.53 % (11368)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.24/0.53 % (11368)Termination reason: Unknown 0.24/0.53 % (11368)Termination phase: Saturation 0.24/0.53 0.24/0.53 % (11368)Memory used [KB]: 6908 0.24/0.53 % (11368)Time elapsed: 0.059 s 0.24/0.53 % (11368)Instructions burned: 129 (million) 0.24/0.53 % (11368)------------------------------ 0.24/0.53 % (11368)------------------------------ 0.24/0.53 % (11388)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on Vampire---4 for (1798ds/140Mi) 0.24/0.54 % (11391)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=26:si=on:rtra=on_0 on Vampire---4 for (1798ds/26Mi) 0.24/0.54 % (11351)Instruction limit reached! 0.24/0.54 % (11351)------------------------------ 0.24/0.54 % (11351)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.24/0.54 % (11351)Termination reason: Unknown 0.24/0.54 % (11351)Termination phase: Saturation 0.24/0.54 0.24/0.54 % (11351)Memory used [KB]: 8571 0.24/0.54 % (11351)Time elapsed: 0.123 s 0.24/0.54 % (11351)Instructions burned: 388 (million) 0.24/0.54 % (11351)------------------------------ 0.24/0.54 % (11351)------------------------------ 0.24/0.54 % (11394)lrs+1002_1:4_au=on:av=off:bsr=on:cbe=off:nm=2:i=56:si=on:rtra=on_0 on Vampire---4 for (1798ds/56Mi) 0.24/0.55 % (11355)First to succeed. 0.24/0.55 % (11391)Instruction limit reached! 0.24/0.55 % (11391)------------------------------ 0.24/0.55 % (11391)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.24/0.55 % (11391)Termination reason: Unknown 0.24/0.55 % (11391)Termination phase: shuffling 0.24/0.55 0.24/0.55 % (11391)Memory used [KB]: 1918 0.24/0.55 % (11391)Time elapsed: 0.009 s 0.24/0.55 % (11391)Instructions burned: 29 (million) 0.24/0.55 % (11391)------------------------------ 0.24/0.55 % (11391)------------------------------ 0.24/0.55 % (11399)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) 0.24/0.55 % (11355)Refutation found. Thanks to Tanya! 0.24/0.55 % SZS status Theorem for Vampire---4 0.24/0.55 % SZS output start Proof for Vampire---4 0.24/0.55 thf(func_def_0, type, in: $i > $i > $o). 0.24/0.55 thf(func_def_1, type, exu: ($i > $o) > $o). 0.24/0.55 thf(func_def_6, type, setadjoin: $i > $i > $i). 0.24/0.55 thf(func_def_8, type, powerset: $i > $i). 0.24/0.55 thf(func_def_10, type, setunion: $i > $i). 0.24/0.55 thf(func_def_19, type, descr: ($i > $o) > $i). 0.24/0.55 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i). 0.24/0.55 thf(func_def_26, type, prop2set: $o > $i). 0.24/0.55 thf(func_def_36, type, nonempty: $i > $o). 0.24/0.55 thf(func_def_69, type, set2prop: $i > $o). 0.24/0.55 thf(func_def_88, type, subset: $i > $i > $o). 0.24/0.55 thf(func_def_89, type, disjoint: $i > $i > $o). 0.24/0.55 thf(func_def_90, type, setsmeet: $i > $i > $o). 0.24/0.55 thf(func_def_114, type, binunion: $i > $i > $i). 0.24/0.55 thf(func_def_122, type, binintersect: $i > $i > $i). 0.24/0.55 thf(func_def_135, type, regular: $i > $o). 0.24/0.55 thf(func_def_136, type, setminus: $i > $i > $i). 0.24/0.55 thf(func_def_147, type, symdiff: $i > $i > $i). 0.24/0.55 thf(func_def_153, type, iskpair: $i > $o). 0.24/0.55 thf(func_def_158, type, kpair: $i > $i > $i). 0.24/0.55 thf(func_def_160, type, cartprod: $i > $i > $i). 0.24/0.55 thf(func_def_177, type, singleton: $i > $o). 0.24/0.55 thf(func_def_179, type, ex1: $i > ($i > $o) > $o). 0.24/0.55 thf(func_def_184, type, atmost1p: $i > $o). 0.24/0.55 thf(func_def_185, type, atleast2p: $i > $o). 0.24/0.55 thf(func_def_186, type, atmost2p: $i > $o). 0.24/0.55 thf(func_def_187, type, upairsetp: $i > $o). 0.24/0.55 thf(func_def_191, type, kfst: $i > $i). 0.24/0.55 thf(func_def_203, type, ksnd: $i > $i). 0.24/0.55 thf(func_def_213, type, breln: $i > $i > $i > $o). 0.24/0.55 thf(func_def_214, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i). 0.24/0.55 thf(func_def_222, type, func: $i > $i > $i > $o). 0.24/0.55 thf(func_def_223, type, funcSet: $i > $i > $i). 0.24/0.55 thf(func_def_226, type, ap: $i > $i > $i > $i > $i). 0.24/0.55 thf(func_def_232, type, lam: $i > $i > ($i > $i) > $i). 0.24/0.55 thf(func_def_257, type, sP2: $i > $o > $i > $i > $o). 0.24/0.55 thf(func_def_260, type, sP5: $i > $i > $o). 0.24/0.55 thf(func_def_261, type, sP6: $i > $o). 0.24/0.55 thf(func_def_262, type, sP7: $i > $i > $o). 0.24/0.55 thf(func_def_263, type, sP8: $i > $i > $o). 0.24/0.55 thf(func_def_264, type, sK9: $i > $o). 0.24/0.55 thf(func_def_267, type, sK12: $i > ($i > $o) > $i). 0.24/0.55 thf(func_def_268, type, sK13: $i > $o). 0.24/0.55 thf(func_def_270, type, sK15: $i > ($i > $o) > $i). 0.24/0.55 thf(func_def_284, type, sK29: ($i > $o) > $i > $i > $i). 0.24/0.55 thf(func_def_287, type, sK32: $i > $o). 0.24/0.55 thf(func_def_292, type, sK37: ($i > $o) > $i > $i > $i > $i). 0.24/0.55 thf(func_def_293, type, sK38: ($i > $o) > $i > $i > $i > $i). 0.24/0.55 thf(func_def_297, type, sK42: $i > $o). 0.24/0.55 thf(func_def_299, type, sK44: ($i > $o) > $i > $i). 0.24/0.55 thf(func_def_301, type, sK46: $i > $o). 0.24/0.55 thf(func_def_303, type, sK48: $i > $i > $i). 0.24/0.55 thf(func_def_306, type, sK51: $i > $i > $o). 0.24/0.55 thf(func_def_308, type, sK53: $i > $i). 0.24/0.55 thf(func_def_309, type, sK54: $i > $i). 0.24/0.55 thf(func_def_310, type, sK55: $i > ($i > $i > $o) > $i). 0.24/0.55 thf(func_def_311, type, sK56: $i > ($i > $i > $o) > $i). 0.24/0.55 thf(func_def_312, type, sK57: $i > $i > ($i > $i > $o) > $i). 0.24/0.55 thf(func_def_327, type, sK72: ($i > $o) > $i > $i). 0.24/0.55 thf(func_def_329, type, sK74: $i > $o). 0.24/0.55 thf(func_def_334, type, sK79: $i > $o). 0.24/0.55 thf(func_def_335, type, sK80: ($i > $o) > $i). 0.24/0.55 thf(func_def_338, type, sK83: $i > $i > $o). 0.24/0.55 thf(func_def_345, type, sK90: $i > $o). 0.24/0.55 thf(func_def_346, type, sK91: $i > $i). 0.24/0.55 thf(func_def_355, type, sK100: $i > $i). 0.24/0.55 thf(func_def_357, type, sK102: $i > $i). 0.24/0.55 thf(func_def_363, type, sK108: ($i > $o) > $i). 0.24/0.55 thf(func_def_364, type, sK109: $i > $o). 0.24/0.55 thf(func_def_365, type, sK110: $i > $i). 0.24/0.55 thf(func_def_367, type, sK112: $i > $i). 0.24/0.55 thf(func_def_384, type, sK129: $i > $o). 0.24/0.55 thf(func_def_387, type, sK132: $i > $o). 0.24/0.55 thf(func_def_392, type, sK137: $i > $i > $o). 0.24/0.55 thf(func_def_396, type, sK141: $i > $i > $i). 0.24/0.55 thf(func_def_397, type, sK142: $i > $o). 0.24/0.55 thf(func_def_398, type, sK143: $i > $o). 0.24/0.55 thf(func_def_399, type, sK144: ($i > $o) > ($i > $o) > $i). 0.24/0.55 thf(func_def_400, type, sK145: ($i > $o) > ($i > $o) > $i). 0.24/0.55 thf(func_def_412, type, sK157: $i > ($i > $o) > $i). 0.24/0.55 thf(func_def_413, type, sK158: $i > $o). 0.24/0.55 thf(func_def_417, type, sK162: $i > $o). 0.24/0.55 thf(func_def_419, type, sK164: ($i > $o) > $i > $i). 0.24/0.55 thf(func_def_420, type, sK165: ($i > $o) > $i > $i). 0.24/0.55 thf(func_def_423, type, sK168: $i > ($i > $o) > $i). 0.24/0.55 thf(func_def_424, type, sK169: $i > $o). 0.24/0.55 thf(func_def_427, type, sK172: $i > $o). 0.24/0.55 thf(func_def_432, type, sK177: $i > $i). 0.24/0.55 thf(func_def_439, type, sK184: $i > $o). 0.24/0.55 thf(func_def_444, type, sK189: $i > $i > $i > $i). 0.24/0.55 thf(func_def_445, type, sK190: $i > $i > $i > $i). 0.24/0.55 thf(func_def_456, type, sK201: ($i > $o) > $i > $i). 0.24/0.55 thf(func_def_458, type, sK203: $i > $o). 0.24/0.55 thf(func_def_467, type, sK212: $i > $i). 0.24/0.55 thf(func_def_469, type, sK214: $i > ($i > $i) > $i > $i). 0.24/0.55 thf(func_def_484, type, sK229: $i > $i > $o). 0.24/0.55 thf(func_def_500, type, sK245: $i > $i). 0.24/0.55 thf(func_def_502, type, sK247: $i > ($i > $i) > $i > $i). 0.24/0.55 thf(func_def_503, type, sK248: $i > $i > ($i > $i) > $i). 0.24/0.55 thf(func_def_504, type, sK249: $i > $i). 0.24/0.55 thf(func_def_516, type, sK261: $i > $o). 0.24/0.55 thf(func_def_532, type, sK277: $i > $o). 0.24/0.55 thf(func_def_534, type, sK279: $i > $o). 0.24/0.55 thf(func_def_540, type, sK285: $i > $i > $i). 0.24/0.55 thf(func_def_550, type, sK295: $i > $i). 0.24/0.55 thf(func_def_570, type, sK315: $i > $i > $i). 0.24/0.55 thf(func_def_574, type, sK319: $i > $i). 0.24/0.55 thf(func_def_589, type, sK334: $i > $i > $i > $i > $i). 0.24/0.55 thf(func_def_592, type, sK337: $i > $o). 0.24/0.55 thf(func_def_594, type, sK339: ($i > $o) > $i). 0.24/0.55 thf(func_def_595, type, sK340: ($i > $o) > $i). 0.24/0.55 thf(func_def_598, type, sK343: $i > $i > $i). 0.24/0.55 thf(func_def_629, type, sK374: $i > $i > $o). 0.24/0.55 thf(func_def_669, type, sK414: $i > $o). 0.24/0.55 thf(func_def_674, type, sK419: $i > $i > $i). 0.24/0.55 thf(func_def_678, type, sK423: $i > $o). 0.24/0.55 thf(func_def_680, type, sK425: $i > ($i > $o) > $i). 0.24/0.55 thf(func_def_684, type, sK429: $i > $o). 0.24/0.55 thf(func_def_691, type, sK436: $o > $i > $i > $i). 0.24/0.55 thf(func_def_703, type, sK448: $i > $i > $i). 0.24/0.55 thf(func_def_709, type, sK454: $i > $o). 0.24/0.55 thf(func_def_711, type, sK456: ($i > $o) > $i > $i > $i > $i). 0.24/0.55 thf(func_def_712, type, sK457: ($i > $o) > $i > $i > $i > $i). 0.24/0.55 thf(func_def_720, type, sK465: $i > ($i > $o) > $i). 0.24/0.55 thf(func_def_721, type, sK466: $i > $o). 0.24/0.55 thf(func_def_727, type, sK472: $i > $i > $o). 0.24/0.55 thf(func_def_734, type, sK479: $i > $i > $i). 0.24/0.55 thf(func_def_744, type, sK489: ($i > $o) > $i). 0.24/0.55 thf(func_def_745, type, sK490: $i > $o). 0.24/0.55 thf(func_def_746, type, sK491: $i > $i). 0.24/0.55 thf(func_def_749, type, sK494: $i > $o). 0.24/0.55 thf(func_def_752, type, sK497: $i > $i > $o). 0.24/0.55 thf(func_def_763, type, sK508: $i > $o). 0.24/0.55 thf(func_def_764, type, sK509: $i > $o). 0.24/0.55 thf(func_def_765, type, sK510: ($i > $o) > ($i > $o) > $i > $i > $i). 0.24/0.55 thf(func_def_766, type, sK511: ($i > $o) > ($i > $o) > $i > $i > $i). 0.24/0.55 thf(func_def_795, type, sK540: $i > $o). 0.24/0.55 thf(func_def_827, type, sK572: $i > $o). 0.24/0.55 thf(func_def_833, type, sK578: $i > $i > $o). 0.24/0.55 thf(func_def_839, type, sK584: $i > $i > $i). 0.24/0.55 thf(func_def_840, type, sK585: $i > $i > $i). 0.24/0.55 thf(func_def_846, type, sK591: $i > $o). 0.24/0.55 thf(func_def_848, type, sK593: ($i > $o) > $i > $i). 0.24/0.55 thf(func_def_849, type, sK594: ($i > $o) > $i > $i). 0.24/0.55 thf(func_def_850, type, sK595: $i > $i > $i). 0.24/0.55 thf(func_def_851, type, sK596: $i > $i > $i). 0.24/0.55 thf(func_def_852, type, sK597: $i > $i > $i). 0.24/0.55 thf(func_def_853, type, sK598: $i > $i > $i). 0.24/0.55 thf(func_def_854, type, sK599: $i > $i > $i). 0.24/0.55 thf(func_def_855, type, sK600: $i > $i > $i > $i). 0.24/0.55 thf(func_def_856, type, sK601: $i > $i). 0.24/0.55 thf(func_def_857, type, sK602: $i > $i). 0.24/0.55 thf(func_def_858, type, sK603: $i > $i). 0.24/0.55 thf(func_def_859, type, sK604: $i > $i). 0.24/0.55 thf(func_def_860, type, sK605: $i > $i > $i). 0.24/0.55 thf(func_def_861, type, sK606: $i > $i > $i > $i). 0.24/0.55 thf(func_def_862, type, sK607: $i > $i > $i > $i). 0.24/0.55 thf(func_def_863, type, sK608: $i > $i > $i). 0.24/0.55 thf(func_def_864, type, sK609: $i > $i > $i). 0.24/0.55 thf(func_def_866, type, sK611: $i > $i). 0.24/0.55 thf(func_def_867, type, sK612: $i > $i). 0.24/0.55 thf(func_def_868, type, sK613: $i > $i). 0.24/0.55 thf(func_def_869, type, sK614: ($i > $o) > ($i > $o) > $i). 0.24/0.55 thf(func_def_870, type, sK615: ($i > $o) > ($i > $o) > $i). 0.24/0.55 thf(func_def_871, type, sK616: $i > $o). 0.24/0.55 thf(func_def_872, type, sK617: $i > $o). 0.24/0.55 thf(func_def_874, type, ph619: !>[X0: $tType]:(X0)). 0.24/0.55 thf(f3041,plain,( 0.24/0.55 $false), 0.24/0.55 inference(subsumption_resolution,[],[f3037,f2215])). 0.24/0.55 thf(f2215,plain,( 0.24/0.55 ((in @ sK156 @ sK152) = $true)), 0.24/0.55 inference(cnf_transformation,[],[f1123])). 0.24/0.55 thf(f1123,plain,( 0.24/0.55 (setunionI = $true) & (dsetconstr__Cong = $true) & (cartprodsndpairEq = $true) & (funcGraphProp2 = $true) & (setadjoinSub = $true) & (setminusSubset2 = $true) & (setunionAx = $true) & (subsetemptysetimpeq = $true) & (binintersectEL = $true) & (notdallE = $true) & (replAx = $true) & (dpsetconstrEL1 = $true) & (ex1I = $true) & (singletonsuniq = $true) & (sepSubset = $true) & (emptysetE = $true) & (setminusIRneg = $true) & (emptyinPowerset = $true) & (setoftrueEq = $true) & (vacuousDall = $true) & (subsetI2 = $true) & (subsetE = $true) & (binintersectRsub = $true) & (emptysetAx = $true) & (cartprodpairmemEL = $true) & (cartprodmempair1 = $true) & (kpairp = $true) & (singletonsswitch = $true) & (dsetconstrEL = $true) & (powersetsubset = $true) & (powersetE = $true) & (((((in @ sK156 @ sK152) = $true) & (sK156 != (ap @ sK154 @ sK152 @ sK153 @ sK155)) & ((in @ (kpair @ sK155 @ sK156) @ sK153) = $true)) & ((in @ sK155 @ sK154) = $true)) & ((in @ sK153 @ (funcSet @ sK154 @ sK152)) = $true)) & (nonemptyE1 = $true) & (setunionsingleton1 = $true) & (funcImageSingleton = $true) & (lam2p = $true) & (setunionsingleton = $true) & (binunionE = $true) & (funcGraphProp3 = $true) & (binunionEcases = $true) & (lamp = $true) & (setunionE2 = $true) & (binintersectI = $true) & (cartprodsndin = $true) & (subPowSU = $true) & (binunionLsub = $true) & (lamProp = $true) & (setukpairinjR1 = $true) & (noeltsimpempty = $true) & (dpsetconstrEL2 = $true) & (exuE1 = $true) & (cartprodfstin = $true) & (setadjoinE = $true) & (subsetTrans = $true) & (kpairiskpair = $true) & (notsubsetI = $true) & (prop2setE = $true) & (ubforcartprodlem3 = $true) & (binunionIL = $true) & (setukpairinjR2 = $true) & (upairsetIL = $true) & (upairsetIR = $true) & (omegaSAx = $true) & (binintersectSubset4 = $true) & (symdiffIneg1 = $true) & (upairsubunion = $true) & (setextsub = $true) & (setminusELneg = $true) & (setadjoinOr = $true) & (ex1E1 = $true) & (setukpairinjL = $true) & (dsetconstrER = $true) & (singletonsubset = $true) & (omega__Cong = $true) & (setadjoin__Cong = $true) & (setadjoinAx = $true) & (dsetconstrI = $true) & (wellorderingAx = $true) & (nonemptyImpWitness = $true) & (powersetI1 = $true) & (kfstpairEq = $true) & (subsetI1 = $true) & (emptyinunitempty = $true) & (quantDeMorgan3 = $true) & (subsetRefl = $true) & (foundationAx = $true) & (powerset__Cong = $true) & (setadjoinSub2 = $true) & (symdiffI2 = $true) & (subsetE2 = $true) & (inPowerset = $true) & (theprop = $true) & (notdexE = $true) & (setext = $true) & (funcGraphProp1 = $true) & (omega0Ax = $true) & (singletonprop = $true) & (emptyset__Cong = $true) & (setbeta = $true) & (funcinfuncset = $true) & (dpsetconstrER = $true) & (upairinpowunion = $true) & (setukpairinjL1 = $true) & (inCongP = $true) & (setminusEL = $true) & (ubforcartprodlem1 = $true) & (binunionRsub = $true) & (notinemptyset = $true) & (cartprodfstpairEq = $true) & (binintersectSubset5 = $true) & (infuncsetfunc = $true) & (exuE3u = $true) & (emptysetsubset = $true) & (ksndpairEq = $true) & (prop2set2propI = $true) & (eqinunit = $true) & (symdiffIneg2 = $true) & (ex1I2 = $true) & (exuE2 = $true) & (in__Cong = $true) & (emptysetimpfalse = $true) & (binintersectSubset2 = $true) & (upairequniteq = $true) & (powersetE1 = $true) & (ubforcartprodlem2 = $true) & (setadjoinIR = $true) & (binunionIR = $true) & (setunion__Cong = $true) & (disjointsetsI1 = $true) & (ksndsingleton = $true) & (singletoninpowerset = $true) & (secondinupair = $true) & (setextAx = $true) & (exuI3 = $true) & (cartprodpairin = $true) & (brelnall1 = $true) & (cartprodmempaircEq = $true) & (symdiffE = $true) & (omegaIndAx = $true) & (emptyI = $true) & (symdiffI1 = $true) & (setukpairinjL2 = $true) & (exuE3e = $true) & (quantDeMorgan2 = $true) & (subset2powerset = $true) & (eqimpsubset1 = $true) & (dpsetconstrSub = $true) & (cartprodpairmemER = $true) & (upairset2IR = $true) & (dpsetconstrERa = $true) & (setOfPairsIsBReln = $true) & (uniqinunit = $true) & (singletoninpowunion = $true) & (setukpairinjR = $true) & (setminusER = $true) & (emptyInPowerset = $true) & (exuI2 = $true) & (binintersectSubset3 = $true) & (setunionsingleton2 = $true) & (descr__Cong = $true) & (nonemptyI1 = $true) & (upairset2E = $true) & (notequalI2 = $true) & (kpairsurjEq = $true) & (cartprodpairsurjEq = $true) & (nonemptyI = $true) & (setminusI = $true) & (emptyE1 = $true) & (binintersectSubset1 = $true) & (exuI1 = $true) & (quantDeMorgan4 = $true) & (brelnall2 = $true) & (ex1E2 = $true) & (eqimpsubset2 = $true) & (setadjoinIL = $true) & (sepInPowerset = $true) & (powersetI = $true) & (cartprodmempair = $true) & (funcextLem = $true) & (upairsetE = $true) & (quantDeMorgan1 = $true) & (setunionE = $true) & (setukpairinjR12 = $true) & (setukpairinjR11 = $true) & (prop2setI = $true) & (dpsetconstrI = $true) & (ap2p = $true) & (descrp = $true) & (powersetAx = $true) & (kfstsingleton = $true) & (setminusLsub = $true) & (setminusSubset1 = $true) & (setminusERneg = $true) & (setukpairIR = $true) & (setminusILneg = $true) & (exu__Cong = $true) & (binintersectLsub = $true) & (bs114d = $true) & (exuEu = $true) & (apProp = $true) & (notequalI1 = $true) & (binintersectER = $true) & (setukpairIL = $true) & (notinsingleton = $true) & (app = $true)), 0.24/0.55 inference(skolemisation,[status(esa),new_symbols(skolem,[sK152,sK153,sK154,sK155,sK156])],[f801,f1122,f1121,f1120])). 0.24/0.55 thf(f1120,plain,( 0.24/0.55 ? [X0,X1,X2] : (? [X3] : (? [X4] : (((in @ X4 @ X0) = $true) & ((ap @ X2 @ X0 @ X1 @ X3) != X4) & ((in @ (kpair @ X3 @ X4) @ X1) = $true)) & ((in @ X3 @ X2) = $true)) & ((in @ X1 @ (funcSet @ X2 @ X0)) = $true)) => (? [X3] : (? [X4] : (($true = (in @ X4 @ sK152)) & ((ap @ sK154 @ sK152 @ sK153 @ X3) != X4) & ((in @ (kpair @ X3 @ X4) @ sK153) = $true)) & ((in @ X3 @ sK154) = $true)) & ((in @ sK153 @ (funcSet @ sK154 @ sK152)) = $true))), 0.24/0.55 introduced(choice_axiom,[])). 0.24/0.55 thf(f1121,plain,( 0.24/0.55 ? [X3] : (? [X4] : (($true = (in @ X4 @ sK152)) & ((ap @ sK154 @ sK152 @ sK153 @ X3) != X4) & ((in @ (kpair @ X3 @ X4) @ sK153) = $true)) & ((in @ X3 @ sK154) = $true)) => (? [X4] : (($true = (in @ X4 @ sK152)) & ((ap @ sK154 @ sK152 @ sK153 @ sK155) != X4) & ((in @ (kpair @ sK155 @ X4) @ sK153) = $true)) & ((in @ sK155 @ sK154) = $true))), 0.24/0.55 introduced(choice_axiom,[])). 0.24/0.55 thf(f1122,plain,( 0.24/0.55 ? [X4] : (($true = (in @ X4 @ sK152)) & ((ap @ sK154 @ sK152 @ sK153 @ sK155) != X4) & ((in @ (kpair @ sK155 @ X4) @ sK153) = $true)) => (((in @ sK156 @ sK152) = $true) & (sK156 != (ap @ sK154 @ sK152 @ sK153 @ sK155)) & ((in @ (kpair @ sK155 @ sK156) @ sK153) = $true))), 0.24/0.55 introduced(choice_axiom,[])). 0.24/0.55 thf(f801,plain,( 0.24/0.55 (setunionI = $true) & (dsetconstr__Cong = $true) & (cartprodsndpairEq = $true) & (funcGraphProp2 = $true) & (setadjoinSub = $true) & (setminusSubset2 = $true) & (setunionAx = $true) & (subsetemptysetimpeq = $true) & (binintersectEL = $true) & (notdallE = $true) & (replAx = $true) & (dpsetconstrEL1 = $true) & (ex1I = $true) & (singletonsuniq = $true) & (sepSubset = $true) & (emptysetE = $true) & (setminusIRneg = $true) & (emptyinPowerset = $true) & (setoftrueEq = $true) & (vacuousDall = $true) & (subsetI2 = $true) & (subsetE = $true) & (binintersectRsub = $true) & (emptysetAx = $true) & (cartprodpairmemEL = $true) & (cartprodmempair1 = $true) & (kpairp = $true) & (singletonsswitch = $true) & (dsetconstrEL = $true) & (powersetsubset = $true) & (powersetE = $true) & ? [X0,X1,X2] : (? [X3] : (? [X4] : (((in @ X4 @ X0) = $true) & ((ap @ X2 @ X0 @ X1 @ X3) != X4) & ((in @ (kpair @ X3 @ X4) @ X1) = $true)) & ((in @ X3 @ X2) = $true)) & ((in @ X1 @ (funcSet @ X2 @ X0)) = $true)) & (nonemptyE1 = $true) & (setunionsingleton1 = $true) & (funcImageSingleton = $true) & (lam2p = $true) & (setunionsingleton = $true) & (binunionE = $true) & (funcGraphProp3 = $true) & (binunionEcases = $true) & (lamp = $true) & (setunionE2 = $true) & (binintersectI = $true) & (cartprodsndin = $true) & (subPowSU = $true) & (binunionLsub = $true) & (lamProp = $true) & (setukpairinjR1 = $true) & (noeltsimpempty = $true) & (dpsetconstrEL2 = $true) & (exuE1 = $true) & (cartprodfstin = $true) & (setadjoinE = $true) & (subsetTrans = $true) & (kpairiskpair = $true) & (notsubsetI = $true) & (prop2setE = $true) & (ubforcartprodlem3 = $true) & (binunionIL = $true) & (setukpairinjR2 = $true) & (upairsetIL = $true) & (upairsetIR = $true) & (omegaSAx = $true) & (binintersectSubset4 = $true) & (symdiffIneg1 = $true) & (upairsubunion = $true) & (setextsub = $true) & (setminusELneg = $true) & (setadjoinOr = $true) & (ex1E1 = $true) & (setukpairinjL = $true) & (dsetconstrER = $true) & (singletonsubset = $true) & (omega__Cong = $true) & (setadjoin__Cong = $true) & (setadjoinAx = $true) & (dsetconstrI = $true) & (wellorderingAx = $true) & (nonemptyImpWitness = $true) & (powersetI1 = $true) & (kfstpairEq = $true) & (subsetI1 = $true) & (emptyinunitempty = $true) & (quantDeMorgan3 = $true) & (subsetRefl = $true) & (foundationAx = $true) & (powerset__Cong = $true) & (setadjoinSub2 = $true) & (symdiffI2 = $true) & (subsetE2 = $true) & (inPowerset = $true) & (theprop = $true) & (notdexE = $true) & (setext = $true) & (funcGraphProp1 = $true) & (omega0Ax = $true) & (singletonprop = $true) & (emptyset__Cong = $true) & (setbeta = $true) & (funcinfuncset = $true) & (dpsetconstrER = $true) & (upairinpowunion = $true) & (setukpairinjL1 = $true) & (inCongP = $true) & (setminusEL = $true) & (ubforcartprodlem1 = $true) & (binunionRsub = $true) & (notinemptyset = $true) & (cartprodfstpairEq = $true) & (binintersectSubset5 = $true) & (infuncsetfunc = $true) & (exuE3u = $true) & (emptysetsubset = $true) & (ksndpairEq = $true) & (prop2set2propI = $true) & (eqinunit = $true) & (symdiffIneg2 = $true) & (ex1I2 = $true) & (exuE2 = $true) & (in__Cong = $true) & (emptysetimpfalse = $true) & (binintersectSubset2 = $true) & (upairequniteq = $true) & (powersetE1 = $true) & (ubforcartprodlem2 = $true) & (setadjoinIR = $true) & (binunionIR = $true) & (setunion__Cong = $true) & (disjointsetsI1 = $true) & (ksndsingleton = $true) & (singletoninpowerset = $true) & (secondinupair = $true) & (setextAx = $true) & (exuI3 = $true) & (cartprodpairin = $true) & (brelnall1 = $true) & (cartprodmempaircEq = $true) & (symdiffE = $true) & (omegaIndAx = $true) & (emptyI = $true) & (symdiffI1 = $true) & (setukpairinjL2 = $true) & (exuE3e = $true) & (quantDeMorgan2 = $true) & (subset2powerset = $true) & (eqimpsubset1 = $true) & (dpsetconstrSub = $true) & (cartprodpairmemER = $true) & (upairset2IR = $true) & (dpsetconstrERa = $true) & (setOfPairsIsBReln = $true) & (uniqinunit = $true) & (singletoninpowunion = $true) & (setukpairinjR = $true) & (setminusER = $true) & (emptyInPowerset = $true) & (exuI2 = $true) & (binintersectSubset3 = $true) & (setunionsingleton2 = $true) & (descr__Cong = $true) & (nonemptyI1 = $true) & (upairset2E = $true) & (notequalI2 = $true) & (kpairsurjEq = $true) & (cartprodpairsurjEq = $true) & (nonemptyI = $true) & (setminusI = $true) & (emptyE1 = $true) & (binintersectSubset1 = $true) & (exuI1 = $true) & (quantDeMorgan4 = $true) & (brelnall2 = $true) & (ex1E2 = $true) & (eqimpsubset2 = $true) & (setadjoinIL = $true) & (sepInPowerset = $true) & (powersetI = $true) & (cartprodmempair = $true) & (funcextLem = $true) & (upairsetE = $true) & (quantDeMorgan1 = $true) & (setunionE = $true) & (setukpairinjR12 = $true) & (setukpairinjR11 = $true) & (prop2setI = $true) & (dpsetconstrI = $true) & (ap2p = $true) & (descrp = $true) & (powersetAx = $true) & (kfstsingleton = $true) & (setminusLsub = $true) & (setminusSubset1 = $true) & (setminusERneg = $true) & (setukpairIR = $true) & (setminusILneg = $true) & (exu__Cong = $true) & (binintersectLsub = $true) & (bs114d = $true) & (exuEu = $true) & (apProp = $true) & (notequalI1 = $true) & (binintersectER = $true) & (setukpairIL = $true) & (notinsingleton = $true) & (app = $true)), 0.24/0.55 inference(flattening,[],[f800])). 0.24/0.55 thf(f800,plain,( 0.24/0.55 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0,X1,X2] : (? [X3] : (? [X4] : ((((ap @ X2 @ X0 @ X1 @ X3) != X4) & ((in @ (kpair @ X3 @ X4) @ X1) = $true)) & ((in @ X4 @ X0) = $true)) & ((in @ X3 @ X2) = $true)) & ((in @ X1 @ (funcSet @ X2 @ X0)) = $true)) & (funcextLem = $true)) & (funcGraphProp2 = $true)) & (funcGraphProp3 = $true)) & (funcGraphProp1 = $true)) & (ex1E2 = $true)) & (brelnall2 = $true)) & (brelnall1 = $true)) & (lam2p = $true)) & (lamp = $true)) & (lamProp = $true)) & (funcinfuncset = $true)) & (ap2p = $true)) & (infuncsetfunc = $true)) & (app = $true)) & (apProp = $true)) & (funcImageSingleton = $true)) & (dpsetconstrER = $true)) & (dpsetconstrEL2 = $true)) & (dpsetconstrEL1 = $true)) & (dpsetconstrERa = $true)) & (setOfPairsIsBReln = $true)) & (dpsetconstrSub = $true)) & (dpsetconstrI = $true)) & (cartprodpairsurjEq = $true)) & (cartprodsndpairEq = $true)) & (cartprodfstpairEq = $true)) & (cartprodmempaircEq = $true)) & (cartprodpairmemER = $true)) & (cartprodpairmemEL = $true)) & (cartprodsndin = $true)) & (kpairsurjEq = $true)) & (ksndpairEq = $true)) & (ksndsingleton = $true)) & (setukpairinjR = $true)) & (setukpairinjR2 = $true)) & (upairequniteq = $true)) & (setukpairinjR1 = $true)) & (setukpairinjR12 = $true)) & (setukpairinjR11 = $true)) & (setukpairinjL = $true)) & (setukpairinjL2 = $true)) & (cartprodfstin = $true)) & (kfstpairEq = $true)) & (theprop = $true)) & (kfstsingleton = $true)) & (setukpairinjL1 = $true)) & (singletonsuniq = $true)) & (ex1I2 = $true)) & (ex1I = $true)) & (ex1E1 = $true)) & (singletonprop = $true)) & (setunionsingleton = $true)) & (setunionsingleton2 = $true)) & (setunionsingleton1 = $true)) & (setunionE2 = $true)) & (cartprodmempair = $true)) & (cartprodmempair1 = $true)) & (cartprodpairin = $true)) & (ubforcartprodlem3 = $true)) & (ubforcartprodlem2 = $true)) & (ubforcartprodlem1 = $true)) & (upairinpowunion = $true)) & (upairsubunion = $true)) & (upairset2E = $true)) & (singletoninpowunion = $true)) & (singletoninpowerset = $true)) & (singletonsubset = $true)) & (kpairp = $true)) & (kpairiskpair = $true)) & (setukpairIR = $true)) & (setukpairIL = $true)) & (secondinupair = $true)) & (symdiffIneg2 = $true)) & (symdiffIneg1 = $true)) & (symdiffI2 = $true)) & (symdiffI1 = $true)) & (symdiffE = $true)) & (setminusSubset1 = $true)) & (setminusLsub = $true)) & (setminusIRneg = $true)) & (setminusILneg = $true)) & (setminusELneg = $true)) & (setminusERneg = $true)) & (setminusSubset2 = $true)) & (setminusER = $true)) & (setminusEL = $true)) & (setminusI = $true)) & (bs114d = $true)) & (binintersectSubset1 = $true)) & (binintersectSubset4 = $true)) & (binintersectRsub = $true)) & (disjointsetsI1 = $true)) & (binintersectER = $true)) & (binintersectSubset3 = $true)) & (binintersectSubset2 = $true)) & (binintersectLsub = $true)) & (binintersectEL = $true)) & (binintersectSubset5 = $true)) & (binintersectI = $true)) & (binunionRsub = $true)) & (binunionLsub = $true)) & (binunionE = $true)) & (binunionEcases = $true)) & (binunionIR = $true)) & (upairset2IR = $true)) & (binunionIL = $true)) & (sepSubset = $true)) & (sepInPowerset = $true)) & (powersetsubset = $true)) & (inPowerset = $true)) & (powersetE1 = $true)) & (powersetI1 = $true)) & (subsetemptysetimpeq = $true)) & (setextsub = $true)) & (subset2powerset = $true)) & (setadjoinSub2 = $true)) & (setadjoinSub = $true)) & (subsetTrans = $true)) & (subsetRefl = $true)) & (notequalI2 = $true)) & (notequalI1 = $true)) & (notsubsetI = $true)) & (subsetE2 = $true)) & (subsetE = $true)) & (emptysetsubset = $true)) & (subsetI2 = $true)) & (eqimpsubset1 = $true)) & (eqimpsubset2 = $true)) & (subsetI1 = $true)) & (dsetconstr__Cong = $true)) & (descr__Cong = $true)) & (exuEu = $true)) & (omega__Cong = $true)) & (setunion__Cong = $true)) & (powerset__Cong = $true)) & (setadjoin__Cong = $true)) & (emptyset__Cong = $true)) & (exu__Cong = $true)) & (exuE3u = $true)) & (in__Cong = $true)) & (inCongP = $true)) & (exuI2 = $true)) & (exuI3 = $true)) & (exuI1 = $true)) & (notdallE = $true)) & (notdexE = $true)) & (prop2set2propI = $true)) & (prop2setI = $true)) & (quantDeMorgan4 = $true)) & (quantDeMorgan3 = $true)) & (quantDeMorgan2 = $true)) & (quantDeMorgan1 = $true)) & (vacuousDall = $true)) & (emptyE1 = $true)) & (upairsetIR = $true)) & (upairsetIL = $true)) & (upairsetE = $true)) & (singletonsswitch = $true)) & (eqinunit = $true)) & (notinsingleton = $true)) & (uniqinunit = $true)) & (nonemptyImpWitness = $true)) & (exuE2 = $true)) & (subPowSU = $true)) & (setunionE = $true)) & (setunionI = $true)) & (powersetE = $true)) & (emptyInPowerset = $true)) & (emptyinPowerset = $true)) & (powersetI = $true)) & (setoftrueEq = $true)) & (setadjoinOr = $true)) & (setadjoinE = $true)) & (setadjoinIR = $true)) & (emptyinunitempty = $true)) & (setadjoinIL = $true)) & (nonemptyI1 = $true)) & (nonemptyI = $true)) & (nonemptyE1 = $true)) & (setbeta = $true)) & (noeltsimpempty = $true)) & (emptyI = $true)) & (setext = $true)) & (exuE3e = $true)) & (notinemptyset = $true)) & (emptysetimpfalse = $true)) & (emptysetE = $true)) & (prop2setE = $true)) & (exuE1 = $true)) & (dsetconstrER = $true)) & (dsetconstrEL = $true)) & (dsetconstrI = $true)) & (descrp = $true)) & (wellorderingAx = $true)) & (foundationAx = $true)) & (replAx = $true)) & (omegaIndAx = $true)) & (omegaSAx = $true)) & (omega0Ax = $true)) & (setunionAx = $true)) & (powersetAx = $true)) & (setadjoinAx = $true)) & (emptysetAx = $true)) & (setextAx = $true)), 0.24/0.55 inference(ennf_transformation,[],[f508])). 0.24/0.55 thf(f508,plain,( 0.24/0.55 ~((setextAx = $true) => ((emptysetAx = $true) => ((setadjoinAx = $true) => ((powersetAx = $true) => ((setunionAx = $true) => ((omega0Ax = $true) => ((omegaSAx = $true) => ((omegaIndAx = $true) => ((replAx = $true) => ((foundationAx = $true) => ((wellorderingAx = $true) => ((descrp = $true) => ((dsetconstrI = $true) => ((dsetconstrEL = $true) => ((dsetconstrER = $true) => ((exuE1 = $true) => ((prop2setE = $true) => ((emptysetE = $true) => ((emptysetimpfalse = $true) => ((notinemptyset = $true) => ((exuE3e = $true) => ((setext = $true) => ((emptyI = $true) => ((noeltsimpempty = $true) => ((setbeta = $true) => ((nonemptyE1 = $true) => ((nonemptyI = $true) => ((nonemptyI1 = $true) => ((setadjoinIL = $true) => ((emptyinunitempty = $true) => ((setadjoinIR = $true) => ((setadjoinE = $true) => ((setadjoinOr = $true) => ((setoftrueEq = $true) => ((powersetI = $true) => ((emptyinPowerset = $true) => ((emptyInPowerset = $true) => ((powersetE = $true) => ((setunionI = $true) => ((setunionE = $true) => ((subPowSU = $true) => ((exuE2 = $true) => ((nonemptyImpWitness = $true) => ((uniqinunit = $true) => ((notinsingleton = $true) => ((eqinunit = $true) => ((singletonsswitch = $true) => ((upairsetE = $true) => ((upairsetIL = $true) => ((upairsetIR = $true) => ((emptyE1 = $true) => ((vacuousDall = $true) => ((quantDeMorgan1 = $true) => ((quantDeMorgan2 = $true) => ((quantDeMorgan3 = $true) => ((quantDeMorgan4 = $true) => ((prop2setI = $true) => ((prop2set2propI = $true) => ((notdexE = $true) => ((notdallE = $true) => ((exuI1 = $true) => ((exuI3 = $true) => ((exuI2 = $true) => ((inCongP = $true) => ((in__Cong = $true) => ((exuE3u = $true) => ((exu__Cong = $true) => ((emptyset__Cong = $true) => ((setadjoin__Cong = $true) => ((powerset__Cong = $true) => ((setunion__Cong = $true) => ((omega__Cong = $true) => ((exuEu = $true) => ((descr__Cong = $true) => ((dsetconstr__Cong = $true) => ((subsetI1 = $true) => ((eqimpsubset2 = $true) => ((eqimpsubset1 = $true) => ((subsetI2 = $true) => ((emptysetsubset = $true) => ((subsetE = $true) => ((subsetE2 = $true) => ((notsubsetI = $true) => ((notequalI1 = $true) => ((notequalI2 = $true) => ((subsetRefl = $true) => ((subsetTrans = $true) => ((setadjoinSub = $true) => ((setadjoinSub2 = $true) => ((subset2powerset = $true) => ((setextsub = $true) => ((subsetemptysetimpeq = $true) => ((powersetI1 = $true) => ((powersetE1 = $true) => ((inPowerset = $true) => ((powersetsubset = $true) => ((sepInPowerset = $true) => ((sepSubset = $true) => ((binunionIL = $true) => ((upairset2IR = $true) => ((binunionIR = $true) => ((binunionEcases = $true) => ((binunionE = $true) => ((binunionLsub = $true) => ((binunionRsub = $true) => ((binintersectI = $true) => ((binintersectSubset5 = $true) => ((binintersectEL = $true) => ((binintersectLsub = $true) => ((binintersectSubset2 = $true) => ((binintersectSubset3 = $true) => ((binintersectER = $true) => ((disjointsetsI1 = $true) => ((binintersectRsub = $true) => ((binintersectSubset4 = $true) => ((binintersectSubset1 = $true) => ((bs114d = $true) => ((setminusI = $true) => ((setminusEL = $true) => ((setminusER = $true) => ((setminusSubset2 = $true) => ((setminusERneg = $true) => ((setminusELneg = $true) => ((setminusILneg = $true) => ((setminusIRneg = $true) => ((setminusLsub = $true) => ((setminusSubset1 = $true) => ((symdiffE = $true) => ((symdiffI1 = $true) => ((symdiffI2 = $true) => ((symdiffIneg1 = $true) => ((symdiffIneg2 = $true) => ((secondinupair = $true) => ((setukpairIL = $true) => ((setukpairIR = $true) => ((kpairiskpair = $true) => ((kpairp = $true) => ((singletonsubset = $true) => ((singletoninpowerset = $true) => ((singletoninpowunion = $true) => ((upairset2E = $true) => ((upairsubunion = $true) => ((upairinpowunion = $true) => ((ubforcartprodlem1 = $true) => ((ubforcartprodlem2 = $true) => ((ubforcartprodlem3 = $true) => ((cartprodpairin = $true) => ((cartprodmempair1 = $true) => ((cartprodmempair = $true) => ((setunionE2 = $true) => ((setunionsingleton1 = $true) => ((setunionsingleton2 = $true) => ((setunionsingleton = $true) => ((singletonprop = $true) => ((ex1E1 = $true) => ((ex1I = $true) => ((ex1I2 = $true) => ((singletonsuniq = $true) => ((setukpairinjL1 = $true) => ((kfstsingleton = $true) => ((theprop = $true) => ((kfstpairEq = $true) => ((cartprodfstin = $true) => ((setukpairinjL2 = $true) => ((setukpairinjL = $true) => ((setukpairinjR11 = $true) => ((setukpairinjR12 = $true) => ((setukpairinjR1 = $true) => ((upairequniteq = $true) => ((setukpairinjR2 = $true) => ((setukpairinjR = $true) => ((ksndsingleton = $true) => ((ksndpairEq = $true) => ((kpairsurjEq = $true) => ((cartprodsndin = $true) => ((cartprodpairmemEL = $true) => ((cartprodpairmemER = $true) => ((cartprodmempaircEq = $true) => ((cartprodfstpairEq = $true) => ((cartprodsndpairEq = $true) => ((cartprodpairsurjEq = $true) => ((dpsetconstrI = $true) => ((dpsetconstrSub = $true) => ((setOfPairsIsBReln = $true) => ((dpsetconstrERa = $true) => ((dpsetconstrEL1 = $true) => ((dpsetconstrEL2 = $true) => ((dpsetconstrER = $true) => ((funcImageSingleton = $true) => ((apProp = $true) => ((app = $true) => ((infuncsetfunc = $true) => ((ap2p = $true) => ((funcinfuncset = $true) => ((lamProp = $true) => ((lamp = $true) => ((lam2p = $true) => ((brelnall1 = $true) => ((brelnall2 = $true) => ((ex1E2 = $true) => ((funcGraphProp1 = $true) => ((funcGraphProp3 = $true) => ((funcGraphProp2 = $true) => ((funcextLem = $true) => ! [X0,X1,X2] : (((in @ X1 @ (funcSet @ X2 @ X0)) = $true) => ! [X3] : (((in @ X3 @ X2) = $true) => ! [X4] : (((in @ X4 @ X0) = $true) => (((in @ (kpair @ X3 @ X4) @ X1) = $true) => ((ap @ X2 @ X0 @ X1 @ X3) = X4)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 0.24/0.55 inference(fool_elimination,[],[f507])). 0.24/0.55 thf(f507,plain,( 0.24/0.55 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => ! [X0,X1,X2] : ((in @ X1 @ (funcSet @ X2 @ X0)) => ! [X3] : ((in @ X3 @ X2) => ! [X4] : ((in @ X4 @ X0) => ((in @ (kpair @ X3 @ X4) @ X1) => ((ap @ X2 @ X0 @ X1 @ X3) = X4)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 0.24/0.55 inference(rectify,[],[f213])). 0.24/0.55 thf(f213,negated_conjecture,( 0.24/0.55 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => ! [X4,X13,X3] : ((in @ X13 @ (funcSet @ X3 @ X4)) => ! [X1] : ((in @ X1 @ X3) => ! [X2] : ((in @ X2 @ X4) => ((in @ (kpair @ X1 @ X2) @ X13) => ((ap @ X3 @ X4 @ X13 @ X1) = X2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 0.24/0.55 inference(negated_conjecture,[],[f212])). 0.24/0.55 thf(f212,conjecture,( 0.24/0.55 setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => ! [X4,X13,X3] : ((in @ X13 @ (funcSet @ X3 @ X4)) => ! [X1] : ((in @ X1 @ X3) => ! [X2] : ((in @ X2 @ X4) => ((in @ (kpair @ X1 @ X2) @ X13) => ((ap @ X3 @ X4 @ X13 @ X1) = X2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 0.24/0.55 file('/export/starexec/sandbox/tmp/tmp.2N6dEsweBi/Vampire---4.8_11085',funcGraphProp4)). 0.24/0.55 thf(f3037,plain,( 0.24/0.55 ((in @ sK156 @ sK152) != $true)), 0.24/0.55 inference(trivial_inequality_removal,[],[f3026])). 0.24/0.55 thf(f3026,plain,( 0.24/0.55 ($true != $true) | ((in @ sK156 @ sK152) != $true) | (sK156 != sK156)), 0.24/0.55 inference(superposition,[],[f3025,f2213])). 0.24/0.55 thf(f2213,plain,( 0.24/0.55 ((in @ (kpair @ sK155 @ sK156) @ sK153) = $true)), 0.24/0.55 inference(cnf_transformation,[],[f1123])). 0.24/0.55 thf(f3025,plain,( 0.24/0.55 ( ! [X0 : $i] : (($true != (in @ (kpair @ sK155 @ X0) @ sK153)) | (sK156 != X0) | ((in @ X0 @ sK152) != $true)) )), 0.24/0.55 inference(subsumption_resolution,[],[f3024,f3018])). 0.24/0.55 thf(f3018,plain,( 0.24/0.55 ((func @ sK154 @ sK152 @ sK153) = $true)), 0.24/0.55 inference(subsumption_resolution,[],[f3015,f2132])). 0.24/0.55 thf(f2132,plain,( 0.24/0.55 (infuncsetfunc = $true)), 0.24/0.55 inference(cnf_transformation,[],[f1123])). 0.24/0.55 thf(f3015,plain,( 0.24/0.55 ((func @ sK154 @ sK152 @ sK153) = $true) | (infuncsetfunc != $true)), 0.24/0.55 inference(trivial_inequality_removal,[],[f3013])). 0.24/0.55 thf(f3013,plain,( 0.24/0.55 ($true != $true) | (infuncsetfunc != $true) | ((func @ sK154 @ sK152 @ sK153) = $true)), 0.24/0.55 inference(superposition,[],[f2705,f2211])). 0.24/0.55 thf(f2211,plain,( 0.24/0.55 ((in @ sK153 @ (funcSet @ sK154 @ sK152)) = $true)), 0.24/0.55 inference(cnf_transformation,[],[f1123])). 0.24/0.55 thf(f2705,plain,( 0.24/0.55 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ (funcSet @ X1 @ X0)) != $true) | (infuncsetfunc != $true) | ((func @ X1 @ X0 @ X2) = $true)) )), 0.24/0.55 inference(cnf_transformation,[],[f1678])). 0.24/0.55 thf(f1678,plain,( 0.24/0.55 (! [X0,X1,X2] : (((in @ X2 @ (funcSet @ X1 @ X0)) != $true) | ((func @ X1 @ X0 @ X2) = $true)) | (infuncsetfunc != $true)) & ((infuncsetfunc = $true) | (((in @ sK514 @ (funcSet @ sK513 @ sK512)) = $true) & ((func @ sK513 @ sK512 @ sK514) != $true)))), 0.24/0.55 inference(skolemisation,[status(esa),new_symbols(skolem,[sK512,sK513,sK514])],[f1676,f1677])). 0.24/0.55 thf(f1677,plain,( 0.24/0.55 ? [X3,X4,X5] : (($true = (in @ X5 @ (funcSet @ X4 @ X3))) & ((func @ X4 @ X3 @ X5) != $true)) => (((in @ sK514 @ (funcSet @ sK513 @ sK512)) = $true) & ((func @ sK513 @ sK512 @ sK514) != $true))), 0.24/0.55 introduced(choice_axiom,[])). 0.24/0.55 thf(f1676,plain,( 0.24/0.55 (! [X0,X1,X2] : (((in @ X2 @ (funcSet @ X1 @ X0)) != $true) | ((func @ X1 @ X0 @ X2) = $true)) | (infuncsetfunc != $true)) & ((infuncsetfunc = $true) | ? [X3,X4,X5] : (($true = (in @ X5 @ (funcSet @ X4 @ X3))) & ((func @ X4 @ X3 @ X5) != $true)))), 0.24/0.55 inference(rectify,[],[f1675])). 0.24/0.55 thf(f1675,plain,( 0.24/0.55 (! [X0,X1,X2] : (((in @ X2 @ (funcSet @ X1 @ X0)) != $true) | ((func @ X1 @ X0 @ X2) = $true)) | (infuncsetfunc != $true)) & ((infuncsetfunc = $true) | ? [X0,X1,X2] : (((in @ X2 @ (funcSet @ X1 @ X0)) = $true) & ((func @ X1 @ X0 @ X2) != $true)))), 0.24/0.55 inference(nnf_transformation,[],[f711])). 0.24/0.55 thf(f711,plain,( 0.24/0.55 ! [X0,X1,X2] : (((in @ X2 @ (funcSet @ X1 @ X0)) != $true) | ((func @ X1 @ X0 @ X2) = $true)) <=> (infuncsetfunc = $true)), 0.24/0.55 inference(ennf_transformation,[],[f540])). 0.24/0.55 thf(f540,plain,( 0.24/0.55 ! [X0,X1,X2] : (((in @ X2 @ (funcSet @ X1 @ X0)) = $true) => ((func @ X1 @ X0 @ X2) = $true)) <=> (infuncsetfunc = $true)), 0.24/0.55 inference(fool_elimination,[],[f539])). 0.24/0.55 thf(f539,plain,( 0.24/0.55 (infuncsetfunc = ! [X0,X1,X2] : ((in @ X2 @ (funcSet @ X1 @ X0)) => (func @ X1 @ X0 @ X2)))), 0.24/0.55 inference(rectify,[],[f198])). 0.24/0.55 thf(f198,axiom,( 0.24/0.55 (infuncsetfunc = ! [X4,X3,X13] : ((in @ X13 @ (funcSet @ X3 @ X4)) => (func @ X3 @ X4 @ X13)))), 0.24/0.55 file('/export/starexec/sandbox/tmp/tmp.2N6dEsweBi/Vampire---4.8_11085',infuncsetfunc)). 0.24/0.55 thf(f3024,plain,( 0.24/0.55 ( ! [X0 : $i] : ((sK156 != X0) | ((in @ X0 @ sK152) != $true) | ((func @ sK154 @ sK152 @ sK153) != $true) | ($true != (in @ (kpair @ sK155 @ X0) @ sK153))) )), 0.24/0.55 inference(subsumption_resolution,[],[f3023,f2212])). 0.24/0.55 thf(f2212,plain,( 0.24/0.55 ((in @ sK155 @ sK154) = $true)), 0.24/0.55 inference(cnf_transformation,[],[f1123])). 0.24/0.55 thf(f3023,plain,( 0.24/0.55 ( ! [X0 : $i] : (((in @ sK155 @ sK154) != $true) | ($true != (in @ (kpair @ sK155 @ X0) @ sK153)) | ((in @ X0 @ sK152) != $true) | ((func @ sK154 @ sK152 @ sK153) != $true) | (sK156 != X0)) )), 0.24/0.55 inference(subsumption_resolution,[],[f3022,f2243])). 0.24/0.55 thf(f2243,plain,( 0.24/0.55 (funcGraphProp2 = $true)), 0.24/0.55 inference(cnf_transformation,[],[f1123])). 0.24/0.55 thf(f3022,plain,( 0.24/0.55 ( ! [X0 : $i] : ((sK156 != X0) | ((in @ X0 @ sK152) != $true) | (funcGraphProp2 != $true) | ((func @ sK154 @ sK152 @ sK153) != $true) | ((in @ sK155 @ sK154) != $true) | ($true != (in @ (kpair @ sK155 @ X0) @ sK153))) )), 0.24/0.55 inference(superposition,[],[f2214,f1994])). 0.24/0.55 thf(f1994,plain,( 0.24/0.55 ( ! [X8 : $i,X6 : $i,X9 : $i,X7 : $i,X5 : $i] : (((ap @ X7 @ X5 @ X6 @ X8) = X9) | ((in @ (kpair @ X8 @ X9) @ X6) != $true) | ($true != (in @ X9 @ X5)) | ((in @ X8 @ X7) != $true) | ((func @ X7 @ X5 @ X6) != $true) | (funcGraphProp2 != $true)) )), 0.24/0.55 inference(cnf_transformation,[],[f1073])). 0.24/0.55 thf(f1073,plain,( 0.24/0.55 ((funcGraphProp2 = $true) | (((func @ sK118 @ sK116 @ sK117) = $true) & (((in @ sK119 @ sK118) = $true) & (((in @ (kpair @ sK119 @ sK120) @ sK117) = $true) & ((ap @ sK118 @ sK116 @ sK117 @ sK119) != sK120) & ((in @ sK120 @ sK116) = $true))))) & (! [X5,X6,X7] : (((func @ X7 @ X5 @ X6) != $true) | ! [X8] : (((in @ X8 @ X7) != $true) | ! [X9] : (((in @ (kpair @ X8 @ X9) @ X6) != $true) | ((ap @ X7 @ X5 @ X6 @ X8) = X9) | ($true != (in @ X9 @ X5))))) | (funcGraphProp2 != $true))), 0.24/0.55 inference(skolemisation,[status(esa),new_symbols(skolem,[sK116,sK117,sK118,sK119,sK120])],[f1069,f1072,f1071,f1070])). 0.24/0.55 thf(f1070,plain,( 0.24/0.55 ? [X0,X1,X2] : (($true = (func @ X2 @ X0 @ X1)) & ? [X3] : (((in @ X3 @ X2) = $true) & ? [X4] : (((in @ (kpair @ X3 @ X4) @ X1) = $true) & ((ap @ X2 @ X0 @ X1 @ X3) != X4) & ((in @ X4 @ X0) = $true)))) => (((func @ sK118 @ sK116 @ sK117) = $true) & ? [X3] : (($true = (in @ X3 @ sK118)) & ? [X4] : (($true = (in @ (kpair @ X3 @ X4) @ sK117)) & ((ap @ sK118 @ sK116 @ sK117 @ X3) != X4) & ((in @ X4 @ sK116) = $true))))), 0.24/0.55 introduced(choice_axiom,[])). 0.24/0.55 thf(f1071,plain,( 0.24/0.55 ? [X3] : (($true = (in @ X3 @ sK118)) & ? [X4] : (($true = (in @ (kpair @ X3 @ X4) @ sK117)) & ((ap @ sK118 @ sK116 @ sK117 @ X3) != X4) & ((in @ X4 @ sK116) = $true))) => (((in @ sK119 @ sK118) = $true) & ? [X4] : (((in @ (kpair @ sK119 @ X4) @ sK117) = $true) & ((ap @ sK118 @ sK116 @ sK117 @ sK119) != X4) & ((in @ X4 @ sK116) = $true)))), 0.24/0.55 introduced(choice_axiom,[])). 0.24/0.55 thf(f1072,plain,( 0.24/0.55 ? [X4] : (((in @ (kpair @ sK119 @ X4) @ sK117) = $true) & ((ap @ sK118 @ sK116 @ sK117 @ sK119) != X4) & ((in @ X4 @ sK116) = $true)) => (((in @ (kpair @ sK119 @ sK120) @ sK117) = $true) & ((ap @ sK118 @ sK116 @ sK117 @ sK119) != sK120) & ((in @ sK120 @ sK116) = $true))), 0.24/0.55 introduced(choice_axiom,[])). 0.24/0.55 thf(f1069,plain,( 0.24/0.55 ((funcGraphProp2 = $true) | ? [X0,X1,X2] : (($true = (func @ X2 @ X0 @ X1)) & ? [X3] : (((in @ X3 @ X2) = $true) & ? [X4] : (((in @ (kpair @ X3 @ X4) @ X1) = $true) & ((ap @ X2 @ X0 @ X1 @ X3) != X4) & ((in @ X4 @ X0) = $true))))) & (! [X5,X6,X7] : (((func @ X7 @ X5 @ X6) != $true) | ! [X8] : (((in @ X8 @ X7) != $true) | ! [X9] : (((in @ (kpair @ X8 @ X9) @ X6) != $true) | ((ap @ X7 @ X5 @ X6 @ X8) = X9) | ($true != (in @ X9 @ X5))))) | (funcGraphProp2 != $true))), 0.24/0.55 inference(rectify,[],[f1068])). 0.24/0.55 thf(f1068,plain,( 0.24/0.55 ((funcGraphProp2 = $true) | ? [X0,X1,X2] : (($true = (func @ X2 @ X0 @ X1)) & ? [X3] : (((in @ X3 @ X2) = $true) & ? [X4] : (((in @ (kpair @ X3 @ X4) @ X1) = $true) & ((ap @ X2 @ X0 @ X1 @ X3) != X4) & ((in @ X4 @ X0) = $true))))) & (! [X0,X1,X2] : (($true != (func @ X2 @ X0 @ X1)) | ! [X3] : (((in @ X3 @ X2) != $true) | ! [X4] : (((in @ (kpair @ X3 @ X4) @ X1) != $true) | ((ap @ X2 @ X0 @ X1 @ X3) = X4) | ((in @ X4 @ X0) != $true)))) | (funcGraphProp2 != $true))), 0.24/0.55 inference(nnf_transformation,[],[f840])). 0.24/0.55 thf(f840,plain,( 0.24/0.55 (funcGraphProp2 = $true) <=> ! [X0,X1,X2] : (($true != (func @ X2 @ X0 @ X1)) | ! [X3] : (((in @ X3 @ X2) != $true) | ! [X4] : (((in @ (kpair @ X3 @ X4) @ X1) != $true) | ((ap @ X2 @ X0 @ X1 @ X3) = X4) | ((in @ X4 @ X0) != $true))))), 0.24/0.55 inference(flattening,[],[f839])). 0.24/0.55 thf(f839,plain,( 0.24/0.55 ! [X0,X1,X2] : (! [X3] : (! [X4] : ((((ap @ X2 @ X0 @ X1 @ X3) = X4) | ((in @ (kpair @ X3 @ X4) @ X1) != $true)) | ((in @ X4 @ X0) != $true)) | ((in @ X3 @ X2) != $true)) | ($true != (func @ X2 @ X0 @ X1))) <=> (funcGraphProp2 = $true)), 0.24/0.55 inference(ennf_transformation,[],[f420])). 0.24/0.55 thf(f420,plain,( 0.24/0.55 ! [X0,X1,X2] : (($true = (func @ X2 @ X0 @ X1)) => ! [X3] : (((in @ X3 @ X2) = $true) => ! [X4] : (((in @ X4 @ X0) = $true) => (((in @ (kpair @ X3 @ X4) @ X1) = $true) => ((ap @ X2 @ X0 @ X1 @ X3) = X4))))) <=> (funcGraphProp2 = $true)), 0.24/0.55 inference(fool_elimination,[],[f419])). 0.24/0.55 thf(f419,plain,( 0.24/0.55 (! [X0,X1,X2] : ((func @ X2 @ X0 @ X1) => ! [X3] : ((in @ X3 @ X2) => ! [X4] : ((in @ X4 @ X0) => ((in @ (kpair @ X3 @ X4) @ X1) => ((ap @ X2 @ X0 @ X1 @ X3) = X4))))) = funcGraphProp2)), 0.24/0.55 inference(rectify,[],[f210])). 0.24/0.55 thf(f210,axiom,( 0.24/0.55 (! [X4,X13,X3] : ((func @ X3 @ X4 @ X13) => ! [X1] : ((in @ X1 @ X3) => ! [X2] : ((in @ X2 @ X4) => ((in @ (kpair @ X1 @ X2) @ X13) => ((ap @ X3 @ X4 @ X13 @ X1) = X2))))) = funcGraphProp2)), 0.24/0.55 file('/export/starexec/sandbox/tmp/tmp.2N6dEsweBi/Vampire---4.8_11085',funcGraphProp2)). 0.24/0.55 thf(f2214,plain,( 0.24/0.55 (sK156 != (ap @ sK154 @ sK152 @ sK153 @ sK155))), 0.24/0.55 inference(cnf_transformation,[],[f1123])). 0.24/0.55 % SZS output end Proof for Vampire---4 0.24/0.55 % (11355)------------------------------ 0.24/0.55 % (11355)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.24/0.55 % (11355)Termination reason: Refutation 0.24/0.55 0.24/0.55 % (11355)Memory used [KB]: 9210 0.24/0.55 % (11355)Time elapsed: 0.125 s 0.24/0.55 % (11355)Instructions burned: 255 (million) 0.24/0.55 % (11355)------------------------------ 0.24/0.55 % (11355)------------------------------ 0.24/0.55 % (11338)Success in time 0.145 s 0.24/0.55 % Vampire---4.8 exiting 0.24/0.55 EOF