0.00/0.06 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.07 % Command : run_vampire %s %d 0.06/0.25 % Computer : n004.cluster.edu 0.06/0.25 % Model : x86_64 x86_64 0.06/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.06/0.25 % Memory : 8042.1875MB 0.06/0.25 % OS : Linux 3.10.0-693.el7.x86_64 0.06/0.25 % CPULimit : 1200 0.06/0.25 % WCLimit : 120 0.06/0.25 % DateTime : Tue Jul 13 15:36:24 EDT 2021 0.06/0.25 % CPUTime : 0.06/0.25 This is a THF_ problem 0.06/0.25 Running vampire --ignore_missing on --mode casc_hol --cores 0 -t 120 /export/starexec/sandbox2/benchmark/theBenchmark.p 0.06/0.25 Running in auto input_syntax mode. Trying TPTP 0.06/0.28 % (6038)ott+1002_8:1_add=off:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:afr=on:afp=100000:afq=1.1:amm=off:anc=none:bd=off:bs=unit_only:fsr=off:gs=on:gsem=off:nm=32:nwc=10:sp=occurrence:urr=on:updr=off:thsq=on_14 on theBenchmark 0.06/0.28 % (6042)dis+1_2:3_acc=on:add=large:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:afp=40000:afq=2.0:amm=sco:anc=none:er=filter:fsr=off:gsp=input_only:gs=on:gsem=off:nm=64:newcnf=on:nwc=1:thsq=on_3 on theBenchmark 0.06/0.28 % (6043)dis+10_128_acc=on:add=off:add=off:afp=4000:afq=1.4:amm=off:bd=preordered:cond=on:fsr=off:fde=unused:gs=on:gsem=on:irw=on:lma=on:nm=64:nwc=1.2:nicw=on:sos=on:sp=occurrence:updr=off:uhcvi=on:thsq=on_40 on theBenchmark 0.06/0.28 % (6041)dis+1010_3:2_av=off:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:gsp=input_only:nm=2:nwc=1:sp=reverse_arity:urr=ec_only:thsq=on_29 on theBenchmark 0.06/0.28 % (6044)dis-11_3_add=off:afp=40000:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:afq=1.0:amm=sco:anc=none:gs=on:irw=on:lcm=reverse:nm=6:nwc=1:sd=4:ss=axioms:st=3.0:sos=on:sac=on:thsq=on_2 on theBenchmark 0.06/0.29 % (6039)lrs+1011_5:1_acc=on:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:amm=off:anc=all_dependent:bd=off:ccuc=small_ones:fde=unused:gs=on:gsaa=full_model:gsem=off:lcm=predicate:lwlo=on:nm=6:newcnf=on:nwc=2.5:stl=30:sp=occurrence:updr=off:thsq=on_3 on theBenchmark 0.06/0.29 % (6037)lrs+1010_8_add=off:afp=100000:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:afq=1.0:amm=off:anc=none:irw=on:nm=16:newcnf=on:nwc=1.1:nicw=on:stl=30:sp=reverse_arity:urr=on:thsq=on_13 on theBenchmark 0.06/0.29 % (6036)dis+10_128_acc=on:add=off:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:afp=4000:afq=1.4:amm=off:bd=preordered:cond=on:fsr=off:fde=unused:gs=on:gsem=on:irw=on:lma=on:nm=64:nwc=1.2:nicw=on:sos=on:sp=occurrence:updr=off:uhcvi=on:thsq=on_2 on theBenchmark 0.06/0.29 % (6065)dis-11_3_add=off:afp=40000:csup=on:inj=on:chr=on:e2e=on:prag=on:cases=on:cnfonf=eager:afq=1.0:fde=all:amm=sco:anc=none:gs=on:irw=on:lcm=reverse:nm=6:nwc=1:sd=4:ss=axioms:st=3.0:sos=on:sac=on:thsq=on_50 on theBenchmark 0.06/0.30 % (6059)lrs+1002_1_add=large:csup=on:inj=on:fe=off:chr=on:cases=on:cnfonf=eager:afr=on:afp=1000:afq=1.1:amm=sco:anc=none:er=known:fsr=off:gs=on:gsem=off:lma=on:nm=2:newcnf=on:nwc=2:stl=30:sd=1:ss=axioms:st=5.0:sp=reverse_arity:updr=off:thsq=on_50 on theBenchmark 0.06/0.30 % (6033)ott+1002_2_av=off:bd=preordered:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:irw=on:lma=on:nm=64:nwc=10:sp=reverse_arity:updr=off:thsq=on_2 on theBenchmark 0.06/0.30 % (6064)dis+1002_4_add=large:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:afp=40000:afq=1.0:anc=none:cond=fast:fde=none:gs=on:gsaa=full_model:lma=on:lwlo=on:nm=0:nwc=1.5:sp=reverse_arity:tha=off_300 on theBenchmark 0.06/0.30 % (6062)lrs+1_4_afp=100000:afq=1.2:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:anc=none:bd=off:cond=on:gs=on:gsem=off:nm=64:nwc=1:sd=2:ss=axioms:st=2.0:sos=all:updr=off:thsq=on_300 on theBenchmark 0.06/0.30 % (6035)lrs+1011_8_add=large:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:afp=100000:afq=1.1:er=filter:gsp=input_only:gs=on:gsem=on:lma=on:nm=6:nwc=1:stl=30:sd=2:ss=axioms:st=1.5:sos=on:thsq=on_3 on theBenchmark 0.06/0.30 % (6034)lrs-11_4:1_afp=4000:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:afq=2.0:anc=none:br=off:gs=on:lwlo=on:nm=64:nwc=3:stl=30:urr=on:thsq=on_2 on theBenchmark 0.06/0.30 % (6063)lrs-11_4:1_afp=4000:csup=on:inj=on:mXXn=1:cases=on:e2e=on:cnfonf=eager:afq=2.0:anc=none:br=off:gs=on:lwlo=on:nm=64:nwc=3:stl=30:urr=on:thsq=on_186 on theBenchmark 0.06/0.30 % (6048)ott+2_2_afp=10000:afq=1.4:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:amm=off:anc=none:gsp=input_only:gs=on:gsem=off:irw=on:lcm=predicate:nm=32:nwc=1.5:sos=on:sp=reverse_arity:thsq=on_7 on theBenchmark 0.06/0.31 % (6053)lrs+10_12_add=off:afp=100000:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:afq=1.4:amm=sco:anc=none:cond=on:lma=on:nm=64:nwc=1.3:stl=30:sac=on:urr=on:thsq=on_41 on theBenchmark 0.06/0.31 % (6051)ott+11_20_afr=on:afp=100000:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:afq=1.0:amm=sco:anc=all:bsr=on:irw=on:lma=on:nm=4:nwc=1.2:sac=on:sp=occurrence:thsq=on_6 on theBenchmark 0.06/0.31 % (6052)dis+1002_3:1_acc=model:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:afr=on:afp=40000:afq=1.1:anc=none:ccuc=first:fsr=off:gsp=input_only:irw=on:nm=16:nwc=1:sos=all:thsq=on_8 on theBenchmark 0.06/0.31 % (6061)lrs+1010_8_add=off:afp=100000:csup=on:inj=off:cases=on:chr=off:e2e=on:cnfonf=eager:afq=1.0:amm=off:anc=none:irw=on:nm=16:newcnf=on:nwc=1.1:nicw=on:stl=30:sp=reverse_arity:urr=on:thsq=on_13 on theBenchmark 0.06/0.31 % (6060)lrs+1011_5_add=large:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:afp=1000:afq=1.2:anc=none:fsr=off:irw=on:lma=on:nm=64:newcnf=on:nwc=1:stl=30:sd=3:ss=axioms:st=2.0:sos=on:sac=on:sp=reverse_arity:urr=on:updr=off:thsq=on_130 on theBenchmark 0.06/0.31 % (6049)lrs+1010_3:2_afr=on:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:afp=100000:afq=1.1:anc=none:gsp=input_only:irw=on:lwlo=on:nm=2:newcnf=on:nwc=1.7:sac=on:sp=occurrence:thsq=on_300 on theBenchmark 0.06/0.31 % (6058)dis+10_4_av=off:bsr=on:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:cond=fast:er=filter:fde=none:gsp=input_only:lcm=reverse:lma=on:nwc=4:sp=occurrence:urr=on:thsq=on_8 on theBenchmark 0.06/0.32 % (6040)lrs+4_3_av=off:br=off:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:nm=0:newcnf=on:nwc=1:stl=30:sp=occurrence:urr=on:thsq=on_32 on theBenchmark 0.10/0.32 % (6056)lrs-11_4:1_afp=4000:csup=on:inj=on:chr=on:cases=on:cnfonf=lazy_gen:afq=2.0:anc=none:br=off:gs=on:lwlo=on:nm=64:nwc=3:stl=30:urr=on:thsq=on_30 on theBenchmark 0.10/0.32 % (6047)lrs+1002_1_av=off:er=filter:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:fsr=off:gs=on:gsem=off:irw=on:lma=on:nm=4:nwc=1:stl=30:sd=3:ss=axioms:st=1.5:sos=on:thsq=on_1 on theBenchmark 0.10/0.32 % (6045)dis+1002_6_add=large:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:afp=40000:afq=2.0:bsr=on:cond=on:irw=on:lma=on:nm=2:nwc=2.5:nicw=on:sp=reverse_arity:updr=off:thsq=on_2 on theBenchmark 0.10/0.32 % (6050)lrs+1011_5:1_acc=on:csup=on:inj=on:e2e=on:prag=on:cases=on:cnfonf=eager:amm=off:anc=all_dependent:bd=off:ccuc=small_ones:fde=unused:gs=on:gsaa=full_model:gsem=off:lcm=predicate:lwlo=on:nm=6:newcnf=on:nwc=2.5:stl=30:sp=occurrence:updr=off:thsq=on_30 on theBenchmark 0.10/0.32 % (6046)lrs+1010_3_av=off:fsr=off:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:gs=on:gsem=off:nm=2:newcnf=on:nwc=2:stl=30:sp=reverse_arity:urr=on:updr=off:thsq=on_9 on theBenchmark 0.10/0.37 % (6061)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs. 0.10/0.38 % (6050)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs. 2.35/0.66 % (6049)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs. 3.09/0.68 % (6042)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs. 3.09/0.68 % (6037)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs. 3.09/0.69 % (6046)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs. 3.09/0.69 % (6039)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs. 3.36/0.72 % (6040)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs. 4.20/0.83 % (6058)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs. 4.20/0.84 % (6041)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs. 4.20/0.87 % (6049)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs. 4.72/0.88 % (6042)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs. 4.72/0.90 % (6048)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs. 4.72/0.91 % (6052)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs. 4.72/0.92 % (6059)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs. 5.52/0.98 % (6035)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs. 5.69/1.02 % (6036)Time limit reached! 5.69/1.02 % (6036)------------------------------ 5.69/1.02 % (6036)Version: Vampire 4.6.0 (commit 0afb7ed4a on 2021-06-23 15:27:21 +0100) 5.69/1.02 % (6036)Termination reason: Time limit 5.69/1.02 5.69/1.02 % (6036)Memory used [KB]: 28272 5.69/1.02 % (6036)Time elapsed: 0.729 s 5.69/1.02 % (6036)------------------------------ 5.69/1.02 % (6036)------------------------------ 5.69/1.02 % (6060)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs. 5.95/1.06 % (6066)dis+1011_10_add=large:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:afr=on:afp=4000:afq=1.0:amm=off:anc=none:lma=on:nm=64:nwc=4:sac=on:sp=occurrence:thsq=on_75 on theBenchmark 6.07/1.13 % (6044)Time limit reached! 6.07/1.13 % (6044)------------------------------ 6.07/1.13 % (6044)Version: Vampire 4.6.0 (commit 0afb7ed4a on 2021-06-23 15:27:21 +0100) 6.07/1.13 % (6044)Termination reason: Time limit 6.07/1.13 6.07/1.13 % (6044)Memory used [KB]: 14456 6.07/1.13 % (6044)Time elapsed: 0.861 s 6.07/1.13 % (6044)------------------------------ 6.07/1.13 % (6044)------------------------------ 6.95/1.18 % (6067)dis+1010_3:2_av=off:csup=on:prag=on:chr=on:cases=on:bet=on:cnfonf=lazy_not_be_gen:gsp=input_only:nm=2:nwc=1:sp=reverse_arity:urr=ec_only:thsq=on_29 on theBenchmark 9.22/1.46 % (6045)Time limit reached! 9.22/1.46 % (6045)------------------------------ 9.22/1.46 % (6045)Version: Vampire 4.6.0 (commit 0afb7ed4a on 2021-06-23 15:27:21 +0100) 9.22/1.46 % (6045)Termination reason: Time limit 9.22/1.46 9.22/1.46 % (6045)Memory used [KB]: 9466 9.22/1.46 % (6045)Time elapsed: 1.192 s 9.22/1.46 % (6045)------------------------------ 9.22/1.46 % (6045)------------------------------ 9.22/1.47 % (6033)Time limit reached! 9.22/1.47 % (6033)------------------------------ 9.22/1.47 % (6033)Version: Vampire 4.6.0 (commit 0afb7ed4a on 2021-06-23 15:27:21 +0100) 9.22/1.47 % (6033)Termination reason: Time limit 9.22/1.47 9.22/1.47 % (6033)Memory used [KB]: 5500 9.22/1.47 % (6033)Time elapsed: 1.202 s 9.22/1.47 % (6033)------------------------------ 9.22/1.47 % (6033)------------------------------ 9.22/1.51 % (6068)lrs+1011_8_add=large:csup=on:inj=on:prag=on:cases=on:cnfonf=eager:afp=100000:afq=1.1:er=filter:gsp=input_only:gs=on:gsem=on:lma=on:nm=6:nwc=1:stl=30:sd=2:ss=axioms:st=1.5:sos=on:thsq=on_26 on theBenchmark 9.22/1.52 % (6069)lrs+1011_8_add=large:csup=on:fe=off:cases=on:cnfonf=eager:afp=100000:afq=1.1:er=filter:gsp=input_only:gs=on:gsem=on:lma=on:nm=6:nwc=1:stl=30:sd=2:ss=axioms:st=1.5:sos=on:thsq=on_30 on theBenchmark 9.22/1.52 % (6042)Time limit reached! 9.22/1.52 % (6042)------------------------------ 9.22/1.52 % (6042)Version: Vampire 4.6.0 (commit 0afb7ed4a on 2021-06-23 15:27:21 +0100) 9.22/1.52 % (6042)Termination reason: Time limit 9.22/1.52 9.22/1.52 % (6042)Memory used [KB]: 14328 9.22/1.52 % (6042)Time elapsed: 1.252 s 9.22/1.52 % (6042)------------------------------ 9.22/1.52 % (6042)------------------------------ 9.74/1.56 % (6034)Time limit reached! 9.74/1.56 % (6034)------------------------------ 9.74/1.56 % (6034)Version: Vampire 4.6.0 (commit 0afb7ed4a on 2021-06-23 15:27:21 +0100) 9.74/1.56 % (6034)Termination reason: Time limit 9.74/1.56 9.74/1.56 % (6034)Memory used [KB]: 14839 9.74/1.56 % (6034)Time elapsed: 1.290 s 9.74/1.56 % (6034)------------------------------ 9.74/1.56 % (6034)------------------------------ 9.98/1.57 % (6070)dis+1002_4_add=large:csup=on:narr=off:inj=on:prag=on:cbe=off:cases=on:cnfonf=eager:afp=40000:afq=1.0:anc=none:cond=fast:fde=none:gs=on:gsaa=full_model:lma=on:lwlo=on:nm=0:nwc=1.5:sp=reverse_arity:thsq=on_27 on theBenchmark 9.98/1.62 % (6047)Time limit reached! 9.98/1.62 % (6047)------------------------------ 9.98/1.62 % (6047)Version: Vampire 4.6.0 (commit 0afb7ed4a on 2021-06-23 15:27:21 +0100) 9.98/1.63 % (6047)Termination reason: Time limit 9.98/1.63 9.98/1.63 % (6047)Memory used [KB]: 10490 9.98/1.63 % (6047)Time elapsed: 1.354 s 9.98/1.63 % (6047)------------------------------ 9.98/1.63 % (6047)------------------------------ 9.98/1.63 % (6071)dis+1_3_add=large:afp=4000:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:afq=1.0:anc=none:gs=on:gsem=off:inw=on:lcm=reverse:lwlo=on:nm=64:nwc=1:sos=all:sac=on:updr=off:uhcvi=on:thsq=on_125 on theBenchmark 10.51/1.65 % (6067)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs. 10.51/1.68 % (6072)dis+1010_3:1_av=off:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:irw=on:nm=32:nwc=1:sos=all:urr=ec_only:updr=off:thsq=on_77 on theBenchmark 11.10/1.78 % (6051)Time limit reached! 11.10/1.78 % (6051)------------------------------ 11.10/1.78 % (6051)Version: Vampire 4.6.0 (commit 0afb7ed4a on 2021-06-23 15:27:21 +0100) 11.10/1.78 % (6051)Termination reason: Time limit 11.10/1.78 11.10/1.78 % (6051)Memory used [KB]: 10874 11.10/1.78 % (6051)Time elapsed: 1.503 s 11.10/1.78 % (6051)------------------------------ 11.10/1.78 % (6051)------------------------------ 12.13/1.82 % (6035)Time limit reached! 12.13/1.82 % (6035)------------------------------ 12.13/1.82 % (6035)Version: Vampire 4.6.0 (commit 0afb7ed4a on 2021-06-23 15:27:21 +0100) 12.13/1.82 % (6035)Termination reason: Time limit 12.13/1.82 12.13/1.82 % (6035)Memory used [KB]: 15223 12.13/1.82 % (6035)Time elapsed: 1.531 s 12.13/1.82 % (6035)------------------------------ 12.13/1.82 % (6035)------------------------------ 12.13/1.82 % (6073)lrs+1011_5:4_acc=on:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:add=large:afr=on:afp=10000:afq=2.0:amm=sco:anc=none:bsr=on:ccuc=first:cond=on:fde=unused:gs=on:gsaa=from_current:gsem=off:irw=on:nm=2:newcnf=on:nwc=1.2:stl=30:sos=on:sac=on:sp=reverse_arity:updr=off:thsq=on_126 on theBenchmark 12.20/1.84 % (6074)lrs+1002_1_add=large:csup=on:narr=off:inj=on:fe=off:chr=on:cases=on:cnfonf=eager:afr=on:afp=1000:afq=1.1:amm=sco:anc=none:er=known:fsr=off:gs=on:gsem=off:lma=on:nm=2:newcnf=on:nwc=2:stl=30:sd=1:ss=axioms:st=5.0:sp=reverse_arity:updr=off:thsq=on_50 on theBenchmark 13.35/2.04 % (6048)Time limit reached! 13.35/2.04 % (6048)------------------------------ 13.35/2.04 % (6048)Version: Vampire 4.6.0 (commit 0afb7ed4a on 2021-06-23 15:27:21 +0100) 13.35/2.04 % (6048)Termination reason: Time limit 13.35/2.04 % (6048)Termination phase: Saturation 13.35/2.04 13.35/2.04 % (6048)Memory used [KB]: 17270 13.35/2.04 % (6048)Time elapsed: 1.700 s 13.35/2.04 % (6048)------------------------------ 13.35/2.04 % (6048)------------------------------ 13.35/2.07 % (6068)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs. 14.15/2.09 % (6117)lrs-3_4:1_afp=1000:afq=1.4:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:amm=sco:fde=none:gs=on:lcm=reverse:lma=on:nwc=1.5:stl=30:sd=1:ss=axioms:sp=reverse_arity:urr=on:updr=off:uhcvi=on:thsq=on_11 on theBenchmark 14.40/2.19 % (6069)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs. 14.98/2.21 % (6073)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs. 14.98/2.29 % (6074)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs. 14.98/2.29 % (6040)First to succeed. 14.98/2.29 % (6052)Time limit reached! 14.98/2.29 % (6052)------------------------------ 14.98/2.29 % (6052)Version: Vampire 4.6.0 (commit 0afb7ed4a on 2021-06-23 15:27:21 +0100) 14.98/2.30 % (6040)Refutation found. Thanks to Tanya! 14.98/2.30 % SZS status Theorem for theBenchmark 14.98/2.30 % SZS output start Proof for theBenchmark 14.98/2.30 thf(type_def_6, type, >: ($tType * $tType) > $tType). 14.98/2.30 thf(func_def_7, type, in: $i > $i > $o). 14.98/2.30 thf(func_def_8, type, exu: ($i > $o) > $o). 14.98/2.30 thf(func_def_13, type, setadjoin: $i > $i > $i). 14.98/2.30 thf(func_def_15, type, powerset: $i > $i). 14.98/2.30 thf(func_def_17, type, setunion: $i > $i). 14.98/2.30 thf(func_def_26, type, descr: ($i > $o) > $i). 14.98/2.30 thf(func_def_28, type, dsetconstr: $i > ($i > $o) > $i). 14.98/2.30 thf(func_def_33, type, prop2set: $o > $i). 14.98/2.30 thf(func_def_43, type, nonempty: $i > $o). 14.98/2.30 thf(func_def_76, type, set2prop: $i > $o). 14.98/2.30 thf(func_def_95, type, subset: $i > $i > $o). 14.98/2.30 thf(func_def_96, type, disjoint: $i > $i > $o). 14.98/2.30 thf(func_def_97, type, setsmeet: $i > $i > $o). 14.98/2.30 thf(func_def_121, type, binunion: $i > $i > $i). 14.98/2.30 thf(func_def_129, type, binintersect: $i > $i > $i). 14.98/2.30 thf(func_def_142, type, regular: $i > $o). 14.98/2.30 thf(func_def_143, type, setminus: $i > $i > $i). 14.98/2.30 thf(func_def_154, type, symdiff: $i > $i > $i). 14.98/2.30 thf(func_def_160, type, iskpair: $i > $o). 14.98/2.30 thf(func_def_165, type, kpair: $i > $i > $i). 14.98/2.30 thf(func_def_167, type, cartprod: $i > $i > $i). 14.98/2.30 thf(func_def_184, type, singleton: $i > $o). 14.98/2.30 thf(func_def_186, type, ex1: $i > ($i > $o) > $o). 14.98/2.30 thf(func_def_191, type, atmost1p: $i > $o). 14.98/2.30 thf(func_def_192, type, atleast2p: $i > $o). 14.98/2.30 thf(func_def_193, type, atmost2p: $i > $o). 14.98/2.30 thf(func_def_194, type, upairsetp: $i > $o). 14.98/2.30 thf(func_def_198, type, kfst: $i > $i). 14.98/2.30 thf(func_def_210, type, ksnd: $i > $i). 14.98/2.30 thf(func_def_220, type, breln: $i > $i > $i > $o). 14.98/2.30 thf(func_def_221, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i). 14.98/2.30 thf(func_def_229, type, func: $i > $i > $i > $o). 14.98/2.30 thf(func_def_230, type, funcSet: $i > $i > $i). 14.98/2.30 thf(func_def_233, type, ap: $i > $i > $i > $i > $i). 14.98/2.30 thf(func_def_239, type, lam: $i > $i > ($i > $i) > $i). 14.98/2.30 thf(func_def_266, type, if: $i > $o > $i > $i > $i). 14.98/2.30 thf(func_def_275, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)). 14.98/2.30 thf(func_def_278, type, vEQ: !>[X0: $tType]:(X0 > X0 > $o)). 14.98/2.30 thf(func_def_279, type, vPI: !>[X0: $tType]:((X0 > $o) > $o)). 14.98/2.30 thf(func_def_280, type, cCOMB: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > X1 > X0 > X2)). 14.98/2.30 thf(func_def_281, type, bCOMB: !>[X0: $tType, X1: $tType, X2: $tType]:((X1 > X2) > (X0 > X1) > X0 > X2)). 14.98/2.30 thf(func_def_282, type, iCOMB: !>[X0: $tType]:(X0 > X0)). 14.98/2.30 thf(func_def_283, type, sCOMB: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > (X0 > X1) > X0 > X2)). 14.98/2.30 thf(func_def_284, type, kCOMB: !>[X0: $tType, X1: $tType]:(X0 > X1 > X0)). 14.98/2.30 thf(func_def_285, type, vIMP: $o > $o > $o). 14.98/2.30 thf(func_def_286, type, vAND: $o > $o > $o). 14.98/2.30 thf(func_def_287, type, vNOT: $o > $o). 14.98/2.30 thf(func_def_288, type, vSIGMA: !>[X0: $tType]:((X0 > $o) > $o)). 14.98/2.30 thf(func_def_289, type, vIFF: $o > $o > $o). 14.98/2.30 thf(func_def_290, type, vOR: $o > $o > $o). 14.98/2.30 thf(func_def_294, type, sK3: $i > $i > $i > $i). 14.98/2.30 thf(func_def_295, type, sK4: $i > $i > $i > $i). 14.98/2.30 thf(func_def_296, type, sK5: $i > $i > $i > $i > $i). 14.98/2.30 thf(func_def_297, type, sK6: $i > $i > $i > $i > $i). 14.98/2.30 thf(func_def_298, type, sK7: $i > $i > $i > $i > $i). 14.98/2.30 thf(func_def_299, type, sK8: $i > $i > $i > $i > $i). 14.98/2.30 thf(func_def_300, type, sK9: $i > $i > $i > $i > $i). 14.98/2.30 thf(func_def_301, type, sK10: $i > $i > $i > $i > $i). 14.98/2.30 thf(func_def_302, type, sK11: $i > $i > $i > $i > $i). 14.98/2.30 thf(func_def_303, type, sK12: $i > $i > $i > $i > $i). 14.98/2.30 thf(func_def_304, type, sK13: $i > $i > $i > $i > $i). 14.98/2.30 thf(func_def_305, type, sK14: $i > $i > $i > $i > $i). 14.98/2.30 thf(func_def_306, type, sK15: $i > $i > $i > $i > $i). 14.98/2.30 thf(func_def_307, type, sK16: $i > $i > $i > $i > $i). 14.98/2.30 thf(func_def_308, type, sK17: $i > $i > $i > $i > $i). 14.98/2.30 thf(func_def_309, type, sK18: $i > $i > $i > $i > $i). 14.98/2.30 thf(func_def_310, type, sK19: $i > $i > $i > $i > $i). 14.98/2.30 thf(func_def_311, type, sK20: ($i > $o) > $i > $i > $i > $i). 14.98/2.30 thf(func_def_312, type, sK21: ($i > $o) > $i > $i > $i > $i). 14.98/2.30 thf(func_def_313, type, sK22: ($i > $o) > $i > $i > $i > $i). 14.98/2.30 thf(func_def_314, type, sK23: ($i > $o) > $i > $i > $i > $i). 14.98/2.30 thf(func_def_315, type, sK24: $i > ($i > $o) > $i > $i). 14.98/2.30 thf(func_def_316, type, sK25: $i > $i > ($i > $i) > $i). 14.98/2.30 thf(func_def_317, type, sK26: $i > $i > ($i > $i) > $i). 14.98/2.30 thf(func_def_318, type, sK27: $i > $i > ($i > $i) > $i). 14.98/2.30 thf(func_def_319, type, sK28: $i > $i > ($i > $i) > $i). 14.98/2.30 thf(func_def_320, type, sK29: $i > $i > ($i > $i) > $i). 14.98/2.30 thf(func_def_321, type, sK30: $i > ($i > $o) > $i). 14.98/2.30 thf(func_def_322, type, sK31: $i > $i > $i). 14.98/2.30 thf(func_def_323, type, sK32: $o > $i > $i > $i). 14.98/2.30 thf(func_def_324, type, sK33: $i > ($i > $o) > $i). 14.98/2.30 thf(func_def_325, type, sK34: ($i > $o) > ($i > $o) > $i). 14.98/2.30 thf(func_def_326, type, sK35: ($i > $o) > ($i > $o) > $i). 14.98/2.30 thf(func_def_327, type, sK36: ($i > $o) > ($i > $o) > $i). 14.98/2.30 thf(func_def_328, type, sK37: ($i > $o) > ($i > $o) > $i). 14.98/2.30 thf(func_def_329, type, sK38: $i > ($i > $o) > $i). 14.98/2.30 thf(func_def_330, type, sK39: $i > ($i > $o) > $i). 14.98/2.30 thf(func_def_331, type, sK40: $i > ($i > $o) > $i). 14.98/2.30 thf(func_def_332, type, sK41: $i > ($i > $o) > $i). 14.98/2.30 thf(func_def_333, type, sK42: $i > ($i > $o) > $i). 14.98/2.30 thf(func_def_334, type, sK43: $i > ($i > $o) > $i). 14.98/2.30 thf(func_def_335, type, sK44: $i > $i > $i). 14.98/2.30 thf(func_def_336, type, sK45: ($i > $i > $o) > $i > $i). 14.98/2.30 thf(func_def_337, type, sK46: ($i > $i > $o) > $i > $i). 14.98/2.30 thf(func_def_338, type, sK47: $i > ($i > $i > $o) > $i > $i). 14.98/2.30 thf(func_def_339, type, sK48: ($i > $i > $o) > $i > $i). 14.98/2.30 thf(func_def_340, type, sK49: ($i > $i > $o) > $i > $i). 14.98/2.30 thf(func_def_341, type, sK50: $i > $i > $i). 14.98/2.30 thf(func_def_342, type, sK51: $i > $i > $i). 14.98/2.30 thf(func_def_343, type, sK52: $i > $i > $i). 14.98/2.30 thf(func_def_344, type, sK53: $i > $i > $i). 14.98/2.30 thf(func_def_345, type, sK54: $i > $i > $i). 14.98/2.30 thf(func_def_346, type, sK55: $i > $i > $i). 14.98/2.30 thf(func_def_347, type, sK56: $i > ($i > $o) > $i). 14.98/2.30 thf(func_def_348, type, sK57: $i > ($i > $o) > $i). 14.98/2.30 thf(func_def_349, type, sK58: $i > ($i > $o) > $i). 14.98/2.30 thf(func_def_350, type, sK59: $i > ($i > $o) > $i). 14.98/2.30 thf(func_def_351, type, sK60: $i > ($i > $o) > $i). 14.98/2.30 thf(func_def_352, type, sK61: $i > $i > $i). 14.98/2.30 thf(func_def_353, type, sK62: $i > ($i > $o) > $i). 14.98/2.30 thf(func_def_354, type, sK63: $i > ($i > $o) > $i). 14.98/2.30 thf(func_def_355, type, sK64: $i > ($i > $o) > $i). 14.98/2.30 thf(func_def_356, type, sK65: $i > ($i > $o) > $i). 14.98/2.30 thf(func_def_357, type, sK66: ($i > $o) > ($i > $o) > $i > $i > $i). 14.98/2.30 thf(func_def_358, type, sK67: ($i > $o) > ($i > $o) > $i > $i > $i). 14.98/2.30 thf(func_def_359, type, sK68: $i > $i). 14.98/2.30 thf(func_def_360, type, sK69: $i > $i > $i > $i). 14.98/2.30 thf(func_def_361, type, sK70: $i > $i > $i). 14.98/2.30 thf(func_def_362, type, sK71: $i > $i > $i). 14.98/2.30 thf(func_def_363, type, sK72: $i > $i > $i). 14.98/2.30 thf(func_def_364, type, sK73: $i > $i > $i). 14.98/2.30 thf(func_def_365, type, sK74: $i > $i > $i). 14.98/2.30 thf(func_def_366, type, sK75: $i > $i > $i). 14.98/2.30 thf(func_def_367, type, sK76: $i > ($i > $o) > $i). 14.98/2.30 thf(func_def_368, type, sK77: $i > ($i > $o) > $i). 14.98/2.30 thf(func_def_369, type, sK78: ($i > $o) > $i). 14.98/2.30 thf(func_def_370, type, sK79: ($i > $o) > $i). 14.98/2.30 thf(func_def_371, type, sK80: $i > ($i > $o) > $i). 14.98/2.30 thf(func_def_372, type, sK81: ($i > $o) > $i). 14.98/2.30 thf(func_def_373, type, sK82: ($i > $o) > $i). 14.98/2.30 thf(func_def_374, type, sK83: $i > ($i > $o) > $i). 14.98/2.30 thf(func_def_375, type, sK84: $i > ($i > $o) > $i). 14.98/2.30 thf(func_def_376, type, sK85: $i > $i). 14.98/2.30 thf(func_def_377, type, sK86: $i > $i). 14.98/2.30 thf(func_def_378, type, sK87: $i > $i). 14.98/2.30 thf(func_def_379, type, sK88: ($i > $o) > $i). 14.98/2.30 thf(func_def_380, type, sK89: ($i > $o) > $i). 14.98/2.30 thf(func_def_381, type, sK90: ($i > $o) > $i). 14.98/2.30 thf(func_def_382, type, sK91: ($i > $o) > $i). 14.98/2.30 thf(func_def_383, type, sK92: ($i > $o) > $i). 14.98/2.30 thf(func_def_384, type, sK93: $i > ($i > $o) > $i). 14.98/2.30 thf(func_def_385, type, sK94: ($i > $o) > $i). 14.98/2.30 thf(func_def_386, type, sK95: $i > $i). 14.98/2.30 thf(func_def_387, type, sK96: $i > $i). 14.98/2.30 thf(func_def_388, type, sK97: $i > $i). 14.98/2.30 thf(func_def_393, type, sK99: $o > $i). 14.98/2.30 thf(func_def_395, type, sK101: $o > $i). 14.98/2.30 thf(func_def_397, type, sK103: $o > $i). 14.98/2.30 thf(func_def_399, type, sK105: $o > $i). 14.98/2.30 thf(func_def_401, type, sK107: $o > $i). 14.98/2.30 thf(func_def_403, type, sK109: $o > $i). 14.98/2.30 thf(func_def_405, type, sK111: $o > $i). 14.98/2.30 thf(f11877,plain,( 14.98/2.30 $false), 14.98/2.30 inference(trivial_inequality_removal,[],[f11866])). 14.98/2.30 thf(f11866,plain,( 14.98/2.30 ($true = $false)), 14.98/2.30 inference(superposition,[],[f5548,f11660])). 14.98/2.30 thf(f11660,plain,( 14.98/2.30 ( ! [X2 : $i] : (($true = ((subset @ ((setminus @ sK1) @ X2)) @ sK0))) )), 14.98/2.30 inference(trivial_inequality_removal,[],[f11609])). 14.98/2.30 thf(f11609,plain,( 14.98/2.30 ( ! [X2 : $i] : (($true = $false) | ($true = ((subset @ ((setminus @ sK1) @ X2)) @ sK0))) )), 14.98/2.30 inference(superposition,[],[f7644,f2707])). 14.98/2.30 thf(f2707,plain,( 14.98/2.30 ( ! [X2 : $i,X1 : $i] : (($true = ((subset @ ((setminus @ X2) @ X1)) @ X2))) )), 14.98/2.30 inference(combinator_demodulation,[],[f2706])). 14.98/2.30 thf(f2706,plain,( 14.98/2.30 ( ! [X2 : $i,X1 : $i] : (($true = (((sCOMB @ ((bCOMB @ subset) @ ((cCOMB @ setminus) @ X1))) @ iCOMB) @ X2))) )), 14.98/2.30 inference(pi_clausification,[],[f2705])). 14.98/2.30 thf(f2705,plain,( 14.98/2.30 ( ! [X1 : $i] : (($true = (vPI($i) @ ((sCOMB @ ((bCOMB @ subset) @ ((cCOMB @ setminus) @ X1))) @ iCOMB)))) )), 14.98/2.30 inference(combinator_demodulation,[],[f2704])). 14.98/2.30 thf(f2704,plain,( 14.98/2.30 ( ! [X1 : $i] : (($true = (((bCOMB @ vPI($i)) @ ((cCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ subset)) @ (cCOMB @ setminus)))) @ iCOMB)) @ X1))) )), 14.98/2.30 inference(pi_clausification,[],[f1278])). 14.98/2.30 thf(f1278,plain,( 14.98/2.30 ($true = (vPI($i) @ ((bCOMB @ vPI($i)) @ ((cCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ subset)) @ (cCOMB @ setminus)))) @ iCOMB))))), 14.98/2.30 inference(definition_unfolding,[],[f1045,f829])). 14.98/2.30 thf(f829,plain,( 14.98/2.30 (setminusLsub = $true)), 14.98/2.30 inference(cnf_transformation,[],[f703])). 14.98/2.30 thf(f703,plain,( 14.98/2.30 ((($true != ((in @ ((setminus @ sK1) @ sK2)) @ (powerset @ sK0))) & ($true = ((in @ sK2) @ (powerset @ sK0)))) & ($true = ((in @ sK1) @ (powerset @ sK0)))) & (powersetT_lem = $true) & (binunionT_lem = $true) & (binintersectT_lem = $true) & (iftrueorfalse = $true) & (iffalse = $true) & (iftrue = $true) & (theeq = $true) & (ifp = $true) & (ifSingleton = $true) & (iftrueProp2 = $true) & (iftrueProp1 = $true) & (iffalseProp2 = $true) & (iffalseProp1 = $true) & (eta2 = $true) & (beta2 = $true) & (lam2lamEq = $true) & (eta1 = $true) & (beta1 = $true) & (ap2apEq2 = $true) & (ap2apEq1 = $true) & (funcext2 = $true) & (funcext = $true) & (eqbreln = $true) & (subbreln = $true) & (funcGraphProp4 = $true) & (funcextLem = $true) & (funcGraphProp2 = $true) & (funcGraphProp3 = $true) & (funcGraphProp1 = $true) & (ex1E2 = $true) & (brelnall2 = $true) & (brelnall1 = $true) & (lam2p = $true) & (lamp = $true) & (lamProp = $true) & (funcinfuncset = $true) & (ap2p = $true) & (infuncsetfunc = $true) & (app = $true) & (apProp = $true) & (funcImageSingleton = $true) & (dpsetconstrER = $true) & (dpsetconstrEL2 = $true) & (dpsetconstrEL1 = $true) & (dpsetconstrERa = $true) & (setOfPairsIsBReln = $true) & (dpsetconstrSub = $true) & (dpsetconstrI = $true) & (cartprodpairsurjEq = $true) & (cartprodsndpairEq = $true) & (cartprodfstpairEq = $true) & (cartprodmempaircEq = $true) & (cartprodpairmemER = $true) & (cartprodpairmemEL = $true) & (cartprodsndin = $true) & (kpairsurjEq = $true) & (ksndpairEq = $true) & (ksndsingleton = $true) & (setukpairinjR = $true) & (setukpairinjR2 = $true) & (upairequniteq = $true) & (setukpairinjR1 = $true) & (setukpairinjR12 = $true) & (setukpairinjR11 = $true) & (setukpairinjL = $true) & (setukpairinjL2 = $true) & (cartprodfstin = $true) & (kfstpairEq = $true) & (theprop = $true) & (kfstsingleton = $true) & (setukpairinjL1 = $true) & (singletonsuniq = $true) & (ex1I2 = $true) & (ex1I = $true) & (ex1E1 = $true) & (singletonprop = $true) & (setunionsingleton = $true) & (setunionsingleton2 = $true) & (setunionsingleton1 = $true) & (setunionE2 = $true) & (cartprodmempair = $true) & (cartprodmempair1 = $true) & (cartprodpairin = $true) & (ubforcartprodlem3 = $true) & (ubforcartprodlem2 = $true) & (ubforcartprodlem1 = $true) & (upairinpowunion = $true) & (upairsubunion = $true) & (upairset2E = $true) & (singletoninpowunion = $true) & (singletoninpowerset = $true) & (singletonsubset = $true) & (kpairp = $true) & (kpairiskpair = $true) & (setukpairIR = $true) & (setukpairIL = $true) & (secondinupair = $true) & (symdiffIneg2 = $true) & (symdiffIneg1 = $true) & (symdiffI2 = $true) & (symdiffI1 = $true) & (symdiffE = $true) & (setminusSubset1 = $true) & (setminusLsub = $true) & (setminusIRneg = $true) & (setminusILneg = $true) & (setminusELneg = $true) & (setminusERneg = $true) & (setminusSubset2 = $true) & (setminusER = $true) & (setminusEL = $true) & (setminusI = $true) & (bs114d = $true) & (binintersectSubset1 = $true) & (binintersectSubset4 = $true) & (binintersectRsub = $true) & (disjointsetsI1 = $true) & (binintersectER = $true) & (binintersectSubset3 = $true) & (binintersectSubset2 = $true) & (binintersectLsub = $true) & (binintersectEL = $true) & (binintersectSubset5 = $true) & (binintersectI = $true) & (binunionRsub = $true) & (binunionLsub = $true) & (binunionE = $true) & (binunionEcases = $true) & (binunionIR = $true) & (upairset2IR = $true) & (binunionIL = $true) & (sepSubset = $true) & (sepInPowerset = $true) & (powersetsubset = $true) & (inPowerset = $true) & (powersetE1 = $true) & (powersetI1 = $true) & (subsetemptysetimpeq = $true) & (setextsub = $true) & (subset2powerset = $true) & (setadjoinSub2 = $true) & (setadjoinSub = $true) & (subsetTrans = $true) & (subsetRefl = $true) & (notequalI2 = $true) & (notequalI1 = $true) & (notsubsetI = $true) & (subsetE2 = $true) & (subsetE = $true) & (emptysetsubset = $true) & (subsetI2 = $true) & (eqimpsubset1 = $true) & (eqimpsubset2 = $true) & (subsetI1 = $true) & (dsetconstr__Cong = $true) & (descr__Cong = $true) & (exuEu = $true) & (omega__Cong = $true) & (setunion__Cong = $true) & (powerset__Cong = $true) & (setadjoin__Cong = $true) & (emptyset__Cong = $true) & (exu__Cong = $true) & (exuE3u = $true) & (in__Cong = $true) & (inCongP = $true) & (exuI2 = $true) & (exuI3 = $true) & (exuI1 = $true) & (notdallE = $true) & (notdexE = $true) & (prop2set2propI = $true) & (prop2setI = $true) & (quantDeMorgan4 = $true) & (quantDeMorgan3 = $true) & (quantDeMorgan2 = $true) & (quantDeMorgan1 = $true) & (vacuousDall = $true) & (emptyE1 = $true) & (upairsetIR = $true) & (upairsetIL = $true) & (upairsetE = $true) & (singletonsswitch = $true) & (eqinunit = $true) & (notinsingleton = $true) & (uniqinunit = $true) & (nonemptyImpWitness = $true) & (exuE2 = $true) & (subPowSU = $true) & (setunionE = $true) & (setunionI = $true) & (powersetE = $true) & (emptyInPowerset = $true) & (emptyinPowerset = $true) & (powersetI = $true) & (setoftrueEq = $true) & (setadjoinOr = $true) & (setadjoinE = $true) & (setadjoinIR = $true) & (emptyinunitempty = $true) & (setadjoinIL = $true) & (nonemptyI1 = $true) & (nonemptyI = $true) & (nonemptyE1 = $true) & (setbeta = $true) & (noeltsimpempty = $true) & (emptyI = $true) & (setext = $true) & (exuE3e = $true) & (notinemptyset = $true) & (emptysetimpfalse = $true) & (emptysetE = $true) & (prop2setE = $true) & (exuE1 = $true) & (dsetconstrER = $true) & (dsetconstrEL = $true) & (dsetconstrI = $true) & (descrp = $true) & (wellorderingAx = $true) & (foundationAx = $true) & (replAx = $true) & (omegaIndAx = $true) & (omegaSAx = $true) & (omega0Ax = $true) & (setunionAx = $true) & (powersetAx = $true) & (setadjoinAx = $true) & (emptysetAx = $true) & (setextAx = $true)), 14.98/2.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f700,f702,f701])). 14.98/2.30 thf(f701,plain,( 14.98/2.30 ? [X0,X1] : (? [X2] : (($true != ((in @ ((setminus @ X1) @ X2)) @ (powerset @ X0))) & ($true = ((in @ X2) @ (powerset @ X0)))) & ($true = ((in @ X1) @ (powerset @ X0)))) => (? [X2] : (($true != ((in @ ((setminus @ sK1) @ X2)) @ (powerset @ sK0))) & ($true = ((in @ X2) @ (powerset @ sK0)))) & ($true = ((in @ sK1) @ (powerset @ sK0))))), 14.98/2.30 introduced(choice_axiom,[])). 14.98/2.30 thf(f702,plain,( 14.98/2.30 ? [X2] : (($true != ((in @ ((setminus @ sK1) @ X2)) @ (powerset @ sK0))) & ($true = ((in @ X2) @ (powerset @ sK0)))) => (($true != ((in @ ((setminus @ sK1) @ sK2)) @ (powerset @ sK0))) & ($true = ((in @ sK2) @ (powerset @ sK0))))), 14.98/2.30 introduced(choice_axiom,[])). 14.98/2.30 thf(f700,plain,( 14.98/2.30 ? [X0,X1] : (? [X2] : (($true != ((in @ ((setminus @ X1) @ X2)) @ (powerset @ X0))) & ($true = ((in @ X2) @ (powerset @ X0)))) & ($true = ((in @ X1) @ (powerset @ X0)))) & (powersetT_lem = $true) & (binunionT_lem = $true) & (binintersectT_lem = $true) & (iftrueorfalse = $true) & (iffalse = $true) & (iftrue = $true) & (theeq = $true) & (ifp = $true) & (ifSingleton = $true) & (iftrueProp2 = $true) & (iftrueProp1 = $true) & (iffalseProp2 = $true) & (iffalseProp1 = $true) & (eta2 = $true) & (beta2 = $true) & (lam2lamEq = $true) & (eta1 = $true) & (beta1 = $true) & (ap2apEq2 = $true) & (ap2apEq1 = $true) & (funcext2 = $true) & (funcext = $true) & (eqbreln = $true) & (subbreln = $true) & (funcGraphProp4 = $true) & (funcextLem = $true) & (funcGraphProp2 = $true) & (funcGraphProp3 = $true) & (funcGraphProp1 = $true) & (ex1E2 = $true) & (brelnall2 = $true) & (brelnall1 = $true) & (lam2p = $true) & (lamp = $true) & (lamProp = $true) & (funcinfuncset = $true) & (ap2p = $true) & (infuncsetfunc = $true) & (app = $true) & (apProp = $true) & (funcImageSingleton = $true) & (dpsetconstrER = $true) & (dpsetconstrEL2 = $true) & (dpsetconstrEL1 = $true) & (dpsetconstrERa = $true) & (setOfPairsIsBReln = $true) & (dpsetconstrSub = $true) & (dpsetconstrI = $true) & (cartprodpairsurjEq = $true) & (cartprodsndpairEq = $true) & (cartprodfstpairEq = $true) & (cartprodmempaircEq = $true) & (cartprodpairmemER = $true) & (cartprodpairmemEL = $true) & (cartprodsndin = $true) & (kpairsurjEq = $true) & (ksndpairEq = $true) & (ksndsingleton = $true) & (setukpairinjR = $true) & (setukpairinjR2 = $true) & (upairequniteq = $true) & (setukpairinjR1 = $true) & (setukpairinjR12 = $true) & (setukpairinjR11 = $true) & (setukpairinjL = $true) & (setukpairinjL2 = $true) & (cartprodfstin = $true) & (kfstpairEq = $true) & (theprop = $true) & (kfstsingleton = $true) & (setukpairinjL1 = $true) & (singletonsuniq = $true) & (ex1I2 = $true) & (ex1I = $true) & (ex1E1 = $true) & (singletonprop = $true) & (setunionsingleton = $true) & (setunionsingleton2 = $true) & (setunionsingleton1 = $true) & (setunionE2 = $true) & (cartprodmempair = $true) & (cartprodmempair1 = $true) & (cartprodpairin = $true) & (ubforcartprodlem3 = $true) & (ubforcartprodlem2 = $true) & (ubforcartprodlem1 = $true) & (upairinpowunion = $true) & (upairsubunion = $true) & (upairset2E = $true) & (singletoninpowunion = $true) & (singletoninpowerset = $true) & (singletonsubset = $true) & (kpairp = $true) & (kpairiskpair = $true) & (setukpairIR = $true) & (setukpairIL = $true) & (secondinupair = $true) & (symdiffIneg2 = $true) & (symdiffIneg1 = $true) & (symdiffI2 = $true) & (symdiffI1 = $true) & (symdiffE = $true) & (setminusSubset1 = $true) & (setminusLsub = $true) & (setminusIRneg = $true) & (setminusILneg = $true) & (setminusELneg = $true) & (setminusERneg = $true) & (setminusSubset2 = $true) & (setminusER = $true) & (setminusEL = $true) & (setminusI = $true) & (bs114d = $true) & (binintersectSubset1 = $true) & (binintersectSubset4 = $true) & (binintersectRsub = $true) & (disjointsetsI1 = $true) & (binintersectER = $true) & (binintersectSubset3 = $true) & (binintersectSubset2 = $true) & (binintersectLsub = $true) & (binintersectEL = $true) & (binintersectSubset5 = $true) & (binintersectI = $true) & (binunionRsub = $true) & (binunionLsub = $true) & (binunionE = $true) & (binunionEcases = $true) & (binunionIR = $true) & (upairset2IR = $true) & (binunionIL = $true) & (sepSubset = $true) & (sepInPowerset = $true) & (powersetsubset = $true) & (inPowerset = $true) & (powersetE1 = $true) & (powersetI1 = $true) & (subsetemptysetimpeq = $true) & (setextsub = $true) & (subset2powerset = $true) & (setadjoinSub2 = $true) & (setadjoinSub = $true) & (subsetTrans = $true) & (subsetRefl = $true) & (notequalI2 = $true) & (notequalI1 = $true) & (notsubsetI = $true) & (subsetE2 = $true) & (subsetE = $true) & (emptysetsubset = $true) & (subsetI2 = $true) & (eqimpsubset1 = $true) & (eqimpsubset2 = $true) & (subsetI1 = $true) & (dsetconstr__Cong = $true) & (descr__Cong = $true) & (exuEu = $true) & (omega__Cong = $true) & (setunion__Cong = $true) & (powerset__Cong = $true) & (setadjoin__Cong = $true) & (emptyset__Cong = $true) & (exu__Cong = $true) & (exuE3u = $true) & (in__Cong = $true) & (inCongP = $true) & (exuI2 = $true) & (exuI3 = $true) & (exuI1 = $true) & (notdallE = $true) & (notdexE = $true) & (prop2set2propI = $true) & (prop2setI = $true) & (quantDeMorgan4 = $true) & (quantDeMorgan3 = $true) & (quantDeMorgan2 = $true) & (quantDeMorgan1 = $true) & (vacuousDall = $true) & (emptyE1 = $true) & (upairsetIR = $true) & (upairsetIL = $true) & (upairsetE = $true) & (singletonsswitch = $true) & (eqinunit = $true) & (notinsingleton = $true) & (uniqinunit = $true) & (nonemptyImpWitness = $true) & (exuE2 = $true) & (subPowSU = $true) & (setunionE = $true) & (setunionI = $true) & (powersetE = $true) & (emptyInPowerset = $true) & (emptyinPowerset = $true) & (powersetI = $true) & (setoftrueEq = $true) & (setadjoinOr = $true) & (setadjoinE = $true) & (setadjoinIR = $true) & (emptyinunitempty = $true) & (setadjoinIL = $true) & (nonemptyI1 = $true) & (nonemptyI = $true) & (nonemptyE1 = $true) & (setbeta = $true) & (noeltsimpempty = $true) & (emptyI = $true) & (setext = $true) & (exuE3e = $true) & (notinemptyset = $true) & (emptysetimpfalse = $true) & (emptysetE = $true) & (prop2setE = $true) & (exuE1 = $true) & (dsetconstrER = $true) & (dsetconstrEL = $true) & (dsetconstrI = $true) & (descrp = $true) & (wellorderingAx = $true) & (foundationAx = $true) & (replAx = $true) & (omegaIndAx = $true) & (omegaSAx = $true) & (omega0Ax = $true) & (setunionAx = $true) & (powersetAx = $true) & (setadjoinAx = $true) & (emptysetAx = $true) & (setextAx = $true)), 14.98/2.30 inference(flattening,[],[f699])). 14.98/2.30 thf(f699,plain,( 14.98/2.30 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0,X1] : (? [X2] : (($true != ((in @ ((setminus @ X1) @ X2)) @ (powerset @ X0))) & ($true = ((in @ X2) @ (powerset @ X0)))) & ($true = ((in @ X1) @ (powerset @ X0)))) & (powersetT_lem = $true)) & (binunionT_lem = $true)) & (binintersectT_lem = $true)) & (iftrueorfalse = $true)) & (iffalse = $true)) & (iftrue = $true)) & (theeq = $true)) & (ifp = $true)) & (ifSingleton = $true)) & (iftrueProp2 = $true)) & (iftrueProp1 = $true)) & (iffalseProp2 = $true)) & (iffalseProp1 = $true)) & (eta2 = $true)) & (beta2 = $true)) & (lam2lamEq = $true)) & (eta1 = $true)) & (beta1 = $true)) & (ap2apEq2 = $true)) & (ap2apEq1 = $true)) & (funcext2 = $true)) & (funcext = $true)) & (eqbreln = $true)) & (subbreln = $true)) & (funcGraphProp4 = $true)) & (funcextLem = $true)) & (funcGraphProp2 = $true)) & (funcGraphProp3 = $true)) & (funcGraphProp1 = $true)) & (ex1E2 = $true)) & (brelnall2 = $true)) & (brelnall1 = $true)) & (lam2p = $true)) & (lamp = $true)) & (lamProp = $true)) & (funcinfuncset = $true)) & (ap2p = $true)) & (infuncsetfunc = $true)) & (app = $true)) & (apProp = $true)) & (funcImageSingleton = $true)) & (dpsetconstrER = $true)) & (dpsetconstrEL2 = $true)) & (dpsetconstrEL1 = $true)) & (dpsetconstrERa = $true)) & (setOfPairsIsBReln = $true)) & (dpsetconstrSub = $true)) & (dpsetconstrI = $true)) & (cartprodpairsurjEq = $true)) & (cartprodsndpairEq = $true)) & (cartprodfstpairEq = $true)) & (cartprodmempaircEq = $true)) & (cartprodpairmemER = $true)) & (cartprodpairmemEL = $true)) & (cartprodsndin = $true)) & (kpairsurjEq = $true)) & (ksndpairEq = $true)) & (ksndsingleton = $true)) & (setukpairinjR = $true)) & (setukpairinjR2 = $true)) & (upairequniteq = $true)) & (setukpairinjR1 = $true)) & (setukpairinjR12 = $true)) & (setukpairinjR11 = $true)) & (setukpairinjL = $true)) & (setukpairinjL2 = $true)) & (cartprodfstin = $true)) & (kfstpairEq = $true)) & (theprop = $true)) & (kfstsingleton = $true)) & (setukpairinjL1 = $true)) & (singletonsuniq = $true)) & (ex1I2 = $true)) & (ex1I = $true)) & (ex1E1 = $true)) & (singletonprop = $true)) & (setunionsingleton = $true)) & (setunionsingleton2 = $true)) & (setunionsingleton1 = $true)) & (setunionE2 = $true)) & (cartprodmempair = $true)) & (cartprodmempair1 = $true)) & (cartprodpairin = $true)) & (ubforcartprodlem3 = $true)) & (ubforcartprodlem2 = $true)) & (ubforcartprodlem1 = $true)) & (upairinpowunion = $true)) & (upairsubunion = $true)) & (upairset2E = $true)) & (singletoninpowunion = $true)) & (singletoninpowerset = $true)) & (singletonsubset = $true)) & (kpairp = $true)) & (kpairiskpair = $true)) & (setukpairIR = $true)) & (setukpairIL = $true)) & (secondinupair = $true)) & (symdiffIneg2 = $true)) & (symdiffIneg1 = $true)) & (symdiffI2 = $true)) & (symdiffI1 = $true)) & (symdiffE = $true)) & (setminusSubset1 = $true)) & (setminusLsub = $true)) & (setminusIRneg = $true)) & (setminusILneg = $true)) & (setminusELneg = $true)) & (setminusERneg = $true)) & (setminusSubset2 = $true)) & (setminusER = $true)) & (setminusEL = $true)) & (setminusI = $true)) & (bs114d = $true)) & (binintersectSubset1 = $true)) & (binintersectSubset4 = $true)) & (binintersectRsub = $true)) & (disjointsetsI1 = $true)) & (binintersectER = $true)) & (binintersectSubset3 = $true)) & (binintersectSubset2 = $true)) & (binintersectLsub = $true)) & (binintersectEL = $true)) & (binintersectSubset5 = $true)) & (binintersectI = $true)) & (binunionRsub = $true)) & (binunionLsub = $true)) & (binunionE = $true)) & (binunionEcases = $true)) & (binunionIR = $true)) & (upairset2IR = $true)) & (binunionIL = $true)) & (sepSubset = $true)) & (sepInPowerset = $true)) & (powersetsubset = $true)) & (inPowerset = $true)) & (powersetE1 = $true)) & (powersetI1 = $true)) & (subsetemptysetimpeq = $true)) & (setextsub = $true)) & (subset2powerset = $true)) & (setadjoinSub2 = $true)) & (setadjoinSub = $true)) & (subsetTrans = $true)) & (subsetRefl = $true)) & (notequalI2 = $true)) & (notequalI1 = $true)) & (notsubsetI = $true)) & (subsetE2 = $true)) & (subsetE = $true)) & (emptysetsubset = $true)) & (subsetI2 = $true)) & (eqimpsubset1 = $true)) & (eqimpsubset2 = $true)) & (subsetI1 = $true)) & (dsetconstr__Cong = $true)) & (descr__Cong = $true)) & (exuEu = $true)) & (omega__Cong = $true)) & (setunion__Cong = $true)) & (powerset__Cong = $true)) & (setadjoin__Cong = $true)) & (emptyset__Cong = $true)) & (exu__Cong = $true)) & (exuE3u = $true)) & (in__Cong = $true)) & (inCongP = $true)) & (exuI2 = $true)) & (exuI3 = $true)) & (exuI1 = $true)) & (notdallE = $true)) & (notdexE = $true)) & (prop2set2propI = $true)) & (prop2setI = $true)) & (quantDeMorgan4 = $true)) & (quantDeMorgan3 = $true)) & (quantDeMorgan2 = $true)) & (quantDeMorgan1 = $true)) & (vacuousDall = $true)) & (emptyE1 = $true)) & (upairsetIR = $true)) & (upairsetIL = $true)) & (upairsetE = $true)) & (singletonsswitch = $true)) & (eqinunit = $true)) & (notinsingleton = $true)) & (uniqinunit = $true)) & (nonemptyImpWitness = $true)) & (exuE2 = $true)) & (subPowSU = $true)) & (setunionE = $true)) & (setunionI = $true)) & (powersetE = $true)) & (emptyInPowerset = $true)) & (emptyinPowerset = $true)) & (powersetI = $true)) & (setoftrueEq = $true)) & (setadjoinOr = $true)) & (setadjoinE = $true)) & (setadjoinIR = $true)) & (emptyinunitempty = $true)) & (setadjoinIL = $true)) & (nonemptyI1 = $true)) & (nonemptyI = $true)) & (nonemptyE1 = $true)) & (setbeta = $true)) & (noeltsimpempty = $true)) & (emptyI = $true)) & (setext = $true)) & (exuE3e = $true)) & (notinemptyset = $true)) & (emptysetimpfalse = $true)) & (emptysetE = $true)) & (prop2setE = $true)) & (exuE1 = $true)) & (dsetconstrER = $true)) & (dsetconstrEL = $true)) & (dsetconstrI = $true)) & (descrp = $true)) & (wellorderingAx = $true)) & (foundationAx = $true)) & (replAx = $true)) & (omegaIndAx = $true)) & (omegaSAx = $true)) & (omega0Ax = $true)) & (setunionAx = $true)) & (powersetAx = $true)) & (setadjoinAx = $true)) & (emptysetAx = $true)) & (setextAx = $true)), 14.98/2.30 inference(ennf_transformation,[],[f238])). 14.98/2.30 thf(f238,plain,( 14.98/2.30 ~((setextAx = $true) => ((emptysetAx = $true) => ((setadjoinAx = $true) => ((powersetAx = $true) => ((setunionAx = $true) => ((omega0Ax = $true) => ((omegaSAx = $true) => ((omegaIndAx = $true) => ((replAx = $true) => ((foundationAx = $true) => ((wellorderingAx = $true) => ((descrp = $true) => ((dsetconstrI = $true) => ((dsetconstrEL = $true) => ((dsetconstrER = $true) => ((exuE1 = $true) => ((prop2setE = $true) => ((emptysetE = $true) => ((emptysetimpfalse = $true) => ((notinemptyset = $true) => ((exuE3e = $true) => ((setext = $true) => ((emptyI = $true) => ((noeltsimpempty = $true) => ((setbeta = $true) => ((nonemptyE1 = $true) => ((nonemptyI = $true) => ((nonemptyI1 = $true) => ((setadjoinIL = $true) => ((emptyinunitempty = $true) => ((setadjoinIR = $true) => ((setadjoinE = $true) => ((setadjoinOr = $true) => ((setoftrueEq = $true) => ((powersetI = $true) => ((emptyinPowerset = $true) => ((emptyInPowerset = $true) => ((powersetE = $true) => ((setunionI = $true) => ((setunionE = $true) => ((subPowSU = $true) => ((exuE2 = $true) => ((nonemptyImpWitness = $true) => ((uniqinunit = $true) => ((notinsingleton = $true) => ((eqinunit = $true) => ((singletonsswitch = $true) => ((upairsetE = $true) => ((upairsetIL = $true) => ((upairsetIR = $true) => ((emptyE1 = $true) => ((vacuousDall = $true) => ((quantDeMorgan1 = $true) => ((quantDeMorgan2 = $true) => ((quantDeMorgan3 = $true) => ((quantDeMorgan4 = $true) => ((prop2setI = $true) => ((prop2set2propI = $true) => ((notdexE = $true) => ((notdallE = $true) => ((exuI1 = $true) => ((exuI3 = $true) => ((exuI2 = $true) => ((inCongP = $true) => ((in__Cong = $true) => ((exuE3u = $true) => ((exu__Cong = $true) => ((emptyset__Cong = $true) => ((setadjoin__Cong = $true) => ((powerset__Cong = $true) => ((setunion__Cong = $true) => ((omega__Cong = $true) => ((exuEu = $true) => ((descr__Cong = $true) => ((dsetconstr__Cong = $true) => ((subsetI1 = $true) => ((eqimpsubset2 = $true) => ((eqimpsubset1 = $true) => ((subsetI2 = $true) => ((emptysetsubset = $true) => ((subsetE = $true) => ((subsetE2 = $true) => ((notsubsetI = $true) => ((notequalI1 = $true) => ((notequalI2 = $true) => ((subsetRefl = $true) => ((subsetTrans = $true) => ((setadjoinSub = $true) => ((setadjoinSub2 = $true) => ((subset2powerset = $true) => ((setextsub = $true) => ((subsetemptysetimpeq = $true) => ((powersetI1 = $true) => ((powersetE1 = $true) => ((inPowerset = $true) => ((powersetsubset = $true) => ((sepInPowerset = $true) => ((sepSubset = $true) => ((binunionIL = $true) => ((upairset2IR = $true) => ((binunionIR = $true) => ((binunionEcases = $true) => ((binunionE = $true) => ((binunionLsub = $true) => ((binunionRsub = $true) => ((binintersectI = $true) => ((binintersectSubset5 = $true) => ((binintersectEL = $true) => ((binintersectLsub = $true) => ((binintersectSubset2 = $true) => ((binintersectSubset3 = $true) => ((binintersectER = $true) => ((disjointsetsI1 = $true) => ((binintersectRsub = $true) => ((binintersectSubset4 = $true) => ((binintersectSubset1 = $true) => ((bs114d = $true) => ((setminusI = $true) => ((setminusEL = $true) => ((setminusER = $true) => ((setminusSubset2 = $true) => ((setminusERneg = $true) => ((setminusELneg = $true) => ((setminusILneg = $true) => ((setminusIRneg = $true) => ((setminusLsub = $true) => ((setminusSubset1 = $true) => ((symdiffE = $true) => ((symdiffI1 = $true) => ((symdiffI2 = $true) => ((symdiffIneg1 = $true) => ((symdiffIneg2 = $true) => ((secondinupair = $true) => ((setukpairIL = $true) => ((setukpairIR = $true) => ((kpairiskpair = $true) => ((kpairp = $true) => ((singletonsubset = $true) => ((singletoninpowerset = $true) => ((singletoninpowunion = $true) => ((upairset2E = $true) => ((upairsubunion = $true) => ((upairinpowunion = $true) => ((ubforcartprodlem1 = $true) => ((ubforcartprodlem2 = $true) => ((ubforcartprodlem3 = $true) => ((cartprodpairin = $true) => ((cartprodmempair1 = $true) => ((cartprodmempair = $true) => ((setunionE2 = $true) => ((setunionsingleton1 = $true) => ((setunionsingleton2 = $true) => ((setunionsingleton = $true) => ((singletonprop = $true) => ((ex1E1 = $true) => ((ex1I = $true) => ((ex1I2 = $true) => ((singletonsuniq = $true) => ((setukpairinjL1 = $true) => ((kfstsingleton = $true) => ((theprop = $true) => ((kfstpairEq = $true) => ((cartprodfstin = $true) => ((setukpairinjL2 = $true) => ((setukpairinjL = $true) => ((setukpairinjR11 = $true) => ((setukpairinjR12 = $true) => ((setukpairinjR1 = $true) => ((upairequniteq = $true) => ((setukpairinjR2 = $true) => ((setukpairinjR = $true) => ((ksndsingleton = $true) => ((ksndpairEq = $true) => ((kpairsurjEq = $true) => ((cartprodsndin = $true) => ((cartprodpairmemEL = $true) => ((cartprodpairmemER = $true) => ((cartprodmempaircEq = $true) => ((cartprodfstpairEq = $true) => ((cartprodsndpairEq = $true) => ((cartprodpairsurjEq = $true) => ((dpsetconstrI = $true) => ((dpsetconstrSub = $true) => ((setOfPairsIsBReln = $true) => ((dpsetconstrERa = $true) => ((dpsetconstrEL1 = $true) => ((dpsetconstrEL2 = $true) => ((dpsetconstrER = $true) => ((funcImageSingleton = $true) => ((apProp = $true) => ((app = $true) => ((infuncsetfunc = $true) => ((ap2p = $true) => ((funcinfuncset = $true) => ((lamProp = $true) => ((lamp = $true) => ((lam2p = $true) => ((brelnall1 = $true) => ((brelnall2 = $true) => ((ex1E2 = $true) => ((funcGraphProp1 = $true) => ((funcGraphProp3 = $true) => ((funcGraphProp2 = $true) => ((funcextLem = $true) => ((funcGraphProp4 = $true) => ((subbreln = $true) => ((eqbreln = $true) => ((funcext = $true) => ((funcext2 = $true) => ((ap2apEq1 = $true) => ((ap2apEq2 = $true) => ((beta1 = $true) => ((eta1 = $true) => ((lam2lamEq = $true) => ((beta2 = $true) => ((eta2 = $true) => ((iffalseProp1 = $true) => ((iffalseProp2 = $true) => ((iftrueProp1 = $true) => ((iftrueProp2 = $true) => ((ifSingleton = $true) => ((ifp = $true) => ((theeq = $true) => ((iftrue = $true) => ((iffalse = $true) => ((iftrueorfalse = $true) => ((binintersectT_lem = $true) => ((binunionT_lem = $true) => ((powersetT_lem = $true) => ! [X0,X1] : (($true = ((in @ X1) @ (powerset @ X0))) => ! [X2] : (($true = ((in @ X2) @ (powerset @ X0))) => ($true = ((in @ ((setminus @ X1) @ X2)) @ (powerset @ X0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 14.98/2.30 inference(fool_elimination,[],[f237])). 14.98/2.30 thf(f237,plain,( 14.98/2.30 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => ! [X0,X1] : (((in @ X1) @ (powerset @ X0)) => ! [X2] : (((in @ X2) @ (powerset @ X0)) => ((in @ ((setminus @ X1) @ X2)) @ (powerset @ X0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 14.98/2.30 inference(rectify,[],[f235])). 14.98/2.30 thf(f235,negated_conjecture,( 14.98/2.30 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => ! [X3,X11] : (((in @ X11) @ (powerset @ X3)) => ! [X16] : (((in @ X16) @ (powerset @ X3)) => ((in @ ((setminus @ X11) @ X16)) @ (powerset @ X3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 14.98/2.30 inference(negated_conjecture,[],[f234])). 14.98/2.30 thf(f234,conjecture,( 14.98/2.30 setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => ! [X3,X11] : (((in @ X11) @ (powerset @ X3)) => ! [X16] : (((in @ X16) @ (powerset @ X3)) => ((in @ ((setminus @ X11) @ X16)) @ (powerset @ X3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 14.98/2.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusT_lem)). 14.98/2.30 thf(f1045,plain,( 14.98/2.30 (setminusLsub = (vPI($i) @ ((bCOMB @ vPI($i)) @ ((cCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ subset)) @ (cCOMB @ setminus)))) @ iCOMB))))), 14.98/2.30 inference(cnf_transformation,[],[f452])). 14.98/2.30 thf(f452,plain,( 14.98/2.30 (setminusLsub = (vPI($i) @ ((bCOMB @ vPI($i)) @ ((cCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ subset)) @ (cCOMB @ setminus)))) @ iCOMB))))), 14.98/2.30 inference(fool_elimination,[],[f451])). 14.98/2.30 thf(f451,plain,( 14.98/2.30 (setminusLsub = ! [X0,X1] : ((subset @ ((setminus @ X0) @ X1)) @ X0))), 14.98/2.30 inference(rectify,[],[f128])). 14.98/2.30 thf(f128,axiom,( 14.98/2.30 (setminusLsub = ! [X3,X4] : ((subset @ ((setminus @ X3) @ X4)) @ X3))), 14.98/2.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusLsub)). 14.98/2.30 thf(f7644,plain,( 14.98/2.30 ( ! [X57 : $i] : (($false = ((subset @ X57) @ sK1)) | ($true = ((subset @ X57) @ sK0))) )), 14.98/2.30 inference(trivial_inequality_removal,[],[f7525])). 14.98/2.30 thf(f7525,plain,( 14.98/2.30 ( ! [X57 : $i] : (($true = $false) | ($false = ((subset @ X57) @ sK1)) | ($true = ((subset @ X57) @ sK0))) )), 14.98/2.30 inference(superposition,[],[f2505,f5531])). 14.98/2.30 thf(f5531,plain,( 14.98/2.30 ($true = ((subset @ sK1) @ sK0))), 14.98/2.30 inference(trivial_inequality_removal,[],[f5496])). 14.98/2.30 thf(f5496,plain,( 14.98/2.30 ($true = $false) | ($true = ((subset @ sK1) @ sK0))), 14.98/2.30 inference(superposition,[],[f2779,f933])). 14.98/2.30 thf(f933,plain,( 14.98/2.30 ($true = ((in @ sK1) @ (powerset @ sK0)))), 14.98/2.30 inference(cnf_transformation,[],[f703])). 14.98/2.30 thf(f2779,plain,( 14.98/2.30 ( ! [X2 : $i,X1 : $i] : (($false = ((in @ X1) @ (powerset @ X2))) | ($true = ((subset @ X1) @ X2))) )), 14.98/2.30 inference(binary_proxy_clausification,[],[f2778])). 14.98/2.30 thf(f2778,plain,( 14.98/2.30 ( ! [X2 : $i,X1 : $i] : (($true = ((vIMP @ ((in @ X1) @ (powerset @ X2))) @ ((subset @ X1) @ X2)))) )), 14.98/2.30 inference(combinator_demodulation,[],[f2777])). 14.98/2.30 thf(f2777,plain,( 14.98/2.30 ( ! [X2 : $i,X1 : $i] : (($true = (((sCOMB @ ((bCOMB @ vIMP) @ ((bCOMB @ (in @ X1)) @ powerset))) @ (subset @ X1)) @ X2))) )), 14.98/2.30 inference(pi_clausification,[],[f2776])). 14.98/2.30 thf(f2776,plain,( 14.98/2.30 ( ! [X1 : $i] : (($true = (vPI($i) @ ((sCOMB @ ((bCOMB @ vIMP) @ ((bCOMB @ (in @ X1)) @ powerset))) @ (subset @ X1))))) )), 14.98/2.30 inference(combinator_demodulation,[],[f2775])). 14.98/2.30 thf(f2775,plain,( 14.98/2.30 ( ! [X1 : $i] : (($true = (((bCOMB @ vPI($i)) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vIMP)) @ ((cCOMB @ ((bCOMB @ bCOMB) @ in)) @ powerset)))) @ subset)) @ X1))) )), 14.98/2.30 inference(pi_clausification,[],[f1265])). 14.98/2.30 thf(f1265,plain,( 14.98/2.30 ($true = (vPI($i) @ ((bCOMB @ vPI($i)) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vIMP)) @ ((cCOMB @ ((bCOMB @ bCOMB) @ in)) @ powerset)))) @ subset))))), 14.98/2.30 inference(definition_unfolding,[],[f1032,f797])). 14.98/2.30 thf(f797,plain,( 14.98/2.30 (powersetE1 = $true)), 14.98/2.30 inference(cnf_transformation,[],[f703])). 14.98/2.30 thf(f1032,plain,( 14.98/2.30 (powersetE1 = (vPI($i) @ ((bCOMB @ vPI($i)) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vIMP)) @ ((cCOMB @ ((bCOMB @ bCOMB) @ in)) @ powerset)))) @ subset))))), 14.98/2.30 inference(cnf_transformation,[],[f426])). 14.98/2.30 thf(f426,plain,( 14.98/2.30 (powersetE1 = (vPI($i) @ ((bCOMB @ vPI($i)) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vIMP)) @ ((cCOMB @ ((bCOMB @ bCOMB) @ in)) @ powerset)))) @ subset))))), 14.98/2.30 inference(fool_elimination,[],[f425])). 14.98/2.30 thf(f425,plain,( 14.98/2.30 (powersetE1 = ! [X0,X1] : (((in @ X1) @ (powerset @ X0)) => ((subset @ X1) @ X0)))), 14.98/2.30 inference(rectify,[],[f96])). 14.98/2.30 thf(f96,axiom,( 14.98/2.30 (powersetE1 = ! [X3,X4] : (((in @ X4) @ (powerset @ X3)) => ((subset @ X4) @ X3)))), 14.98/2.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetE1)). 14.98/2.30 thf(f2505,plain,( 14.98/2.30 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((subset @ X3) @ X2)) | ($false = ((subset @ X2) @ X1)) | ($true = ((subset @ X3) @ X1))) )), 14.98/2.30 inference(binary_proxy_clausification,[],[f2504])). 14.98/2.30 thf(f2504,plain,( 14.98/2.30 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((subset @ X3) @ X2)) | ($true = ((vIMP @ ((subset @ X2) @ X1)) @ ((subset @ X3) @ X1)))) )), 14.98/2.30 inference(binary_proxy_clausification,[],[f2503])). 14.98/2.30 thf(f2503,plain,( 14.98/2.30 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((vIMP @ ((subset @ X3) @ X2)) @ ((vIMP @ ((subset @ X2) @ X1)) @ ((subset @ X3) @ X1))))) )), 14.98/2.30 inference(combinator_demodulation,[],[f2502])). 14.98/2.30 thf(f2502,plain,( 14.98/2.30 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((sCOMB @ ((bCOMB @ vIMP) @ ((cCOMB @ subset) @ X2))) @ ((bCOMB @ (vIMP @ ((subset @ X2) @ X1))) @ ((cCOMB @ subset) @ X1))) @ X3))) )), 14.98/2.30 inference(pi_clausification,[],[f2501])). 14.98/2.30 thf(f2501,plain,( 14.98/2.30 ( ! [X2 : $i,X1 : $i] : (($true = (vPI($i) @ ((sCOMB @ ((bCOMB @ vIMP) @ ((cCOMB @ subset) @ X2))) @ ((bCOMB @ (vIMP @ ((subset @ X2) @ X1))) @ ((cCOMB @ subset) @ X1)))))) )), 14.98/2.30 inference(combinator_demodulation,[],[f2500])). 14.98/2.30 thf(f2500,plain,( 14.98/2.30 ( ! [X2 : $i,X1 : $i] : (($true = (((bCOMB @ vPI($i)) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vIMP)) @ (cCOMB @ subset)))) @ ((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ vIMP) @ ((cCOMB @ subset) @ X1)))) @ ((cCOMB @ subset) @ X1)))) @ X2))) )), 14.98/2.30 inference(pi_clausification,[],[f2499])). 14.98/2.30 thf(f2499,plain,( 14.98/2.30 ( ! [X1 : $i] : (($true = (vPI($i) @ ((bCOMB @ vPI($i)) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vIMP)) @ (cCOMB @ subset)))) @ ((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ vIMP) @ ((cCOMB @ subset) @ X1)))) @ ((cCOMB @ subset) @ X1))))))) )), 14.98/2.30 inference(combinator_demodulation,[],[f2498])). 14.98/2.30 thf(f2498,plain,( 14.98/2.30 ( ! [X1 : $i] : (($true = (((bCOMB @ vPI($i)) @ ((bCOMB @ (bCOMB @ vPI($i))) @ ((bCOMB @ (sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vIMP)) @ (cCOMB @ subset))))) @ ((sCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ bCOMB)) @ ((bCOMB @ (bCOMB @ vIMP)) @ (cCOMB @ subset))))) @ (cCOMB @ subset))))) @ X1))) )), 14.98/2.30 inference(pi_clausification,[],[f1304])). 14.98/2.30 thf(f1304,plain,( 14.98/2.30 ($true = (vPI($i) @ ((bCOMB @ vPI($i)) @ ((bCOMB @ (bCOMB @ vPI($i))) @ ((bCOMB @ (sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vIMP)) @ (cCOMB @ subset))))) @ ((sCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ bCOMB)) @ ((bCOMB @ (bCOMB @ vIMP)) @ (cCOMB @ subset))))) @ (cCOMB @ subset)))))))), 14.98/2.30 inference(definition_unfolding,[],[f1071,f790])). 14.98/2.30 thf(f790,plain,( 14.98/2.30 (subsetTrans = $true)), 14.98/2.30 inference(cnf_transformation,[],[f703])). 14.98/2.30 thf(f1071,plain,( 14.98/2.30 (subsetTrans = (vPI($i) @ ((bCOMB @ vPI($i)) @ ((bCOMB @ (bCOMB @ vPI($i))) @ ((bCOMB @ (sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vIMP)) @ (cCOMB @ subset))))) @ ((sCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ bCOMB)) @ ((bCOMB @ (bCOMB @ vIMP)) @ (cCOMB @ subset))))) @ (cCOMB @ subset)))))))), 14.98/2.30 inference(cnf_transformation,[],[f504])). 14.98/2.30 thf(f504,plain,( 14.98/2.30 (subsetTrans = (vPI($i) @ ((bCOMB @ vPI($i)) @ ((bCOMB @ (bCOMB @ vPI($i))) @ ((bCOMB @ (sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vIMP)) @ (cCOMB @ subset))))) @ ((sCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ bCOMB)) @ ((bCOMB @ (bCOMB @ vIMP)) @ (cCOMB @ subset))))) @ (cCOMB @ subset)))))))), 14.98/2.30 inference(fool_elimination,[],[f503])). 14.98/2.30 thf(f503,plain,( 14.98/2.30 (subsetTrans = ! [X0,X1,X2] : (((subset @ X0) @ X1) => (((subset @ X1) @ X2) => ((subset @ X0) @ X2))))), 14.98/2.30 inference(rectify,[],[f89])). 14.98/2.30 thf(f89,axiom,( 14.98/2.30 (subsetTrans = ! [X3,X4,X5] : (((subset @ X3) @ X4) => (((subset @ X4) @ X5) => ((subset @ X3) @ X5))))), 14.98/2.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetTrans)). 14.98/2.30 thf(f5548,plain,( 14.98/2.30 ($false = ((subset @ ((setminus @ sK1) @ sK2)) @ sK0))), 14.98/2.30 inference(trivial_inequality_removal,[],[f5537])). 14.98/2.30 thf(f5537,plain,( 14.98/2.30 ($true = $false) | ($false = ((subset @ ((setminus @ sK1) @ sK2)) @ sK0))), 14.98/2.30 inference(superposition,[],[f2853,f4480])). 14.98/2.30 thf(f4480,plain,( 14.98/2.30 ($false = ((in @ ((setminus @ sK1) @ sK2)) @ (powerset @ sK0)))), 14.98/2.30 inference(unit_resulting_resolution,[],[f935,f3979])). 14.98/2.30 thf(f3979,plain,( 14.98/2.30 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )), 14.98/2.30 inference(trivial_inequality_removal,[],[f3978])). 14.98/2.30 thf(f3978,plain,( 14.98/2.30 ( ! [X0 : $o] : (($true = $false) | ($false = X0) | ($true = X0)) )), 14.98/2.30 inference(forward_demodulation,[],[f3972,f3620])). 14.98/2.30 thf(f3620,plain,( 14.98/2.30 ( ! [X1 : $i] : ((((in @ X1) @ emptyset) = $false)) )), 14.98/2.30 inference(not_proxy_clausification,[],[f3619])). 14.98/2.30 thf(f3619,plain,( 14.98/2.30 ( ! [X1 : $i] : (($true = (vNOT @ ((in @ X1) @ emptyset)))) )), 14.98/2.30 inference(boolean_simplification,[],[f3618])). 14.98/2.30 thf(f3618,plain,( 14.98/2.30 ( ! [X1 : $i] : (($true = ((vIMP @ ((in @ X1) @ emptyset)) @ $false))) )), 14.98/2.30 inference(combinator_demodulation,[],[f3617])). 14.98/2.30 thf(f3617,plain,( 14.98/2.30 ( ! [X1 : $i] : (($true = (((cCOMB @ ((bCOMB @ vIMP) @ ((cCOMB @ in) @ emptyset))) @ $false) @ X1))) )), 14.98/2.30 inference(pi_clausification,[],[f1195])). 14.98/2.30 thf(f1195,plain,( 14.98/2.30 ($true = (vPI($i) @ ((cCOMB @ ((bCOMB @ vIMP) @ ((cCOMB @ in) @ emptyset))) @ $false)))), 14.98/2.30 inference(definition_unfolding,[],[f962,f722])). 14.98/2.30 thf(f722,plain,( 14.98/2.30 (emptysetimpfalse = $true)), 14.98/2.30 inference(cnf_transformation,[],[f703])). 14.98/2.30 thf(f962,plain,( 14.98/2.30 (emptysetimpfalse = (vPI($i) @ ((cCOMB @ ((bCOMB @ vIMP) @ ((cCOMB @ in) @ emptyset))) @ $false)))), 14.98/2.30 inference(cnf_transformation,[],[f286])). 14.98/2.30 thf(f286,plain,( 14.98/2.30 (emptysetimpfalse = (vPI($i) @ ((cCOMB @ ((bCOMB @ vIMP) @ ((cCOMB @ in) @ emptyset))) @ $false)))), 14.98/2.30 inference(fool_elimination,[],[f285])). 14.98/2.30 thf(f285,plain,( 14.98/2.30 (emptysetimpfalse = ! [X0] : (((in @ X0) @ emptyset) => $false))), 14.98/2.30 inference(rectify,[],[f20])). 14.98/2.30 thf(f20,axiom,( 14.98/2.30 (emptysetimpfalse = ! [X1] : (((in @ X1) @ emptyset) => $false))), 14.98/2.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetimpfalse)). 14.98/2.30 thf(f3972,plain,( 14.98/2.30 ( ! [X0 : $o] : (($true = ((in @ emptyset) @ emptyset)) | ($false = X0) | ($true = X0)) )), 14.98/2.30 inference(superposition,[],[f3670,f3874])). 14.98/2.30 thf(f3874,plain,( 14.98/2.30 ( ! [X1 : $o] : ((emptyset = (prop2set @ X1)) | ($true = X1)) )), 14.98/2.30 inference(trivial_inequality_removal,[],[f3867])). 14.98/2.30 thf(f3867,plain,( 14.98/2.30 ( ! [X1 : $o] : (($true = $false) | (emptyset = (prop2set @ X1)) | ($true = X1)) )), 14.98/2.30 inference(superposition,[],[f3659,f2823])). 14.98/2.30 thf(f2823,plain,( 14.98/2.30 ( ! [X2 : $o,X1 : $i] : (($false = ((in @ X1) @ (prop2set @ X2))) | ($true = X2)) )), 14.98/2.30 inference(binary_proxy_clausification,[],[f2822])). 14.98/2.30 thf(f2822,plain,( 14.98/2.30 ( ! [X2 : $o,X1 : $i] : (($true = ((vIMP @ ((in @ X1) @ (prop2set @ X2))) @ X2))) )), 14.98/2.30 inference(combinator_demodulation,[],[f2821])). 14.98/2.30 thf(f2821,plain,( 14.98/2.30 ( ! [X2 : $o,X1 : $i] : (($true = (((sCOMB @ ((bCOMB @ vIMP) @ ((bCOMB @ (in @ X1)) @ prop2set))) @ iCOMB) @ X2))) )), 14.98/2.30 inference(pi_clausification,[],[f2820])). 14.98/2.30 thf(f2820,plain,( 14.98/2.30 ( ! [X1 : $i] : (($true = (vPI($o) @ ((sCOMB @ ((bCOMB @ vIMP) @ ((bCOMB @ (in @ X1)) @ prop2set))) @ iCOMB)))) )), 14.98/2.30 inference(combinator_demodulation,[],[f2819])). 14.98/2.30 thf(f2819,plain,( 14.98/2.30 ( ! [X1 : $i] : (($true = (((bCOMB @ vPI($o)) @ ((cCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vIMP)) @ ((cCOMB @ ((bCOMB @ bCOMB) @ in)) @ prop2set)))) @ iCOMB)) @ X1))) )), 14.98/2.30 inference(pi_clausification,[],[f1260])). 14.98/2.30 thf(f1260,plain,( 14.98/2.30 ($true = (vPI($i) @ ((bCOMB @ vPI($o)) @ ((cCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vIMP)) @ ((cCOMB @ ((bCOMB @ bCOMB) @ in)) @ prop2set)))) @ iCOMB))))), 14.98/2.30 inference(definition_unfolding,[],[f1027,f720])). 14.98/2.30 thf(f720,plain,( 14.98/2.30 (prop2setE = $true)), 14.98/2.30 inference(cnf_transformation,[],[f703])). 14.98/2.30 thf(f1027,plain,( 14.98/2.30 (prop2setE = (vPI($i) @ ((bCOMB @ vPI($o)) @ ((cCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vIMP)) @ ((cCOMB @ ((bCOMB @ bCOMB) @ in)) @ prop2set)))) @ iCOMB))))), 14.98/2.30 inference(cnf_transformation,[],[f416])). 14.98/2.30 thf(f416,plain,( 14.98/2.30 (prop2setE = (vPI($i) @ ((bCOMB @ vPI($o)) @ ((cCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vIMP)) @ ((cCOMB @ ((bCOMB @ bCOMB) @ in)) @ prop2set)))) @ iCOMB))))), 14.98/2.30 inference(fool_elimination,[],[f415])). 14.98/2.30 thf(f415,plain,( 14.98/2.30 (prop2setE = ! [X0 : $o,X1] : (((in @ X1) @ (prop2set @ X0)) => X0))), 14.98/2.30 inference(rectify,[],[f18])). 14.98/2.30 thf(f18,axiom,( 14.98/2.30 (prop2setE = ! [X0 : $o,X1] : (((in @ X1) @ (prop2set @ X0)) => X0))), 14.98/2.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2setE)). 14.98/2.30 thf(f3659,plain,( 14.98/2.30 ( ! [X1 : $i] : (($true = ((in @ (sK85 @ X1)) @ X1)) | (emptyset = X1)) )), 14.98/2.30 inference(combinator_demodulation,[],[f3658])). 14.98/2.30 thf(f3658,plain,( 14.98/2.30 ( ! [X1 : $i] : ((emptyset = X1) | ($true = (((cCOMB @ in) @ X1) @ (sK85 @ X1)))) )), 14.98/2.30 inference(sigma_clausification,[],[f3657])). 14.98/2.30 thf(f3657,plain,( 14.98/2.30 ( ! [X1 : $i] : ((emptyset = X1) | ($true = (vSIGMA($i) @ ((cCOMB @ in) @ X1)))) )), 14.98/2.30 inference(equality_proxy_clausification,[],[f3656])). 14.98/2.30 thf(f3656,plain,( 14.98/2.30 ( ! [X1 : $i] : (($true = ((vEQ($i) @ emptyset) @ X1)) | ($true = (vSIGMA($i) @ ((cCOMB @ in) @ X1)))) )), 14.98/2.30 inference(not_proxy_clausification,[],[f3655])). 14.98/2.30 thf(f3655,plain,( 14.98/2.30 ( ! [X1 : $i] : (($false = (vNOT @ ((vEQ($i) @ emptyset) @ X1))) | ($true = (vSIGMA($i) @ ((cCOMB @ in) @ X1)))) )), 14.98/2.30 inference(binary_proxy_clausification,[],[f3654])). 14.98/2.30 thf(f3654,plain,( 14.98/2.30 ( ! [X1 : $i] : (($true = ((vIMP @ (vNOT @ ((vEQ($i) @ emptyset) @ X1))) @ (vSIGMA($i) @ ((cCOMB @ in) @ X1))))) )), 14.98/2.30 inference(combinator_demodulation,[],[f3653])). 14.98/2.30 thf(f3653,plain,( 14.98/2.30 ( ! [X1 : $i] : (($true = (((sCOMB @ ((bCOMB @ vIMP) @ ((bCOMB @ vNOT) @ (vEQ($i) @ emptyset)))) @ ((bCOMB @ vSIGMA($i)) @ (cCOMB @ in))) @ X1))) )), 14.98/2.30 inference(pi_clausification,[],[f1186])). 14.98/2.30 thf(f1186,plain,( 14.98/2.30 ($true = (vPI($i) @ ((sCOMB @ ((bCOMB @ vIMP) @ ((bCOMB @ vNOT) @ (vEQ($i) @ emptyset)))) @ ((bCOMB @ vSIGMA($i)) @ (cCOMB @ in)))))), 14.98/2.30 inference(definition_unfolding,[],[f953,f729,f1165])). 14.98/2.30 thf(f1165,plain,( 14.98/2.30 (nonempty = ((bCOMB @ vNOT) @ (vEQ($i) @ emptyset)))), 14.98/2.30 inference(cnf_transformation,[],[f692])). 14.98/2.30 thf(f692,plain,( 14.98/2.30 (nonempty = ((bCOMB @ vNOT) @ (vEQ($i) @ emptyset)))), 14.98/2.30 inference(fool_elimination,[],[f691])). 14.98/2.30 thf(f691,plain,( 14.98/2.30 (nonempty = (^[X0 : $i] : ((emptyset != X0))))), 14.98/2.30 inference(rectify,[],[f27])). 14.98/2.30 thf(f27,axiom,( 14.98/2.30 (nonempty = (^[X1 : $i] : ((emptyset != X1))))), 14.98/2.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonempty)). 14.98/2.30 thf(f729,plain,( 14.98/2.30 (nonemptyE1 = $true)), 14.98/2.30 inference(cnf_transformation,[],[f703])). 14.98/2.30 thf(f953,plain,( 14.98/2.30 (nonemptyE1 = (vPI($i) @ ((sCOMB @ ((bCOMB @ vIMP) @ nonempty)) @ ((bCOMB @ vSIGMA($i)) @ (cCOMB @ in)))))), 14.98/2.30 inference(cnf_transformation,[],[f268])). 14.98/2.30 thf(f268,plain,( 14.98/2.30 (nonemptyE1 = (vPI($i) @ ((sCOMB @ ((bCOMB @ vIMP) @ nonempty)) @ ((bCOMB @ vSIGMA($i)) @ (cCOMB @ in)))))), 14.98/2.30 inference(fool_elimination,[],[f267])). 14.98/2.30 thf(f267,plain,( 14.98/2.30 (nonemptyE1 = ! [X0] : ((nonempty @ X0) => ? [X1] : ((in @ X1) @ X0)))), 14.98/2.30 inference(rectify,[],[f28])). 14.98/2.30 thf(f28,axiom,( 14.98/2.30 (nonemptyE1 = ! [X3] : ((nonempty @ X3) => ? [X1] : ((in @ X1) @ X3)))), 14.98/2.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyE1)). 14.98/2.30 thf(f3670,plain,( 14.98/2.30 ( ! [X1 : $o] : (($true = ((in @ emptyset) @ (prop2set @ X1))) | ($false = X1)) )), 14.98/2.30 inference(binary_proxy_clausification,[],[f3669])). 14.98/2.30 thf(f3669,plain,( 14.98/2.30 ( ! [X1 : $o] : (($true = ((vIMP @ X1) @ ((in @ emptyset) @ (prop2set @ X1))))) )), 14.98/2.30 inference(combinator_demodulation,[],[f3668])). 14.98/2.30 thf(f3668,plain,( 14.98/2.30 ( ! [X1 : $o] : (($true = (((sCOMB @ vIMP) @ ((bCOMB @ (in @ emptyset)) @ prop2set)) @ X1))) )), 14.98/2.30 inference(pi_clausification,[],[f1184])). 14.98/2.30 thf(f1184,plain,( 14.98/2.30 ($true = (vPI($o) @ ((sCOMB @ vIMP) @ ((bCOMB @ (in @ emptyset)) @ prop2set))))), 14.98/2.30 inference(definition_unfolding,[],[f951,f760])). 14.98/2.30 thf(f760,plain,( 14.98/2.30 (prop2setI = $true)), 14.98/2.30 inference(cnf_transformation,[],[f703])). 14.98/2.30 thf(f951,plain,( 14.98/2.30 (prop2setI = (vPI($o) @ ((sCOMB @ vIMP) @ ((bCOMB @ (in @ emptyset)) @ prop2set))))), 14.98/2.30 inference(cnf_transformation,[],[f264])). 14.98/2.30 thf(f264,plain,( 14.98/2.30 (prop2setI = (vPI($o) @ ((sCOMB @ vIMP) @ ((bCOMB @ (in @ emptyset)) @ prop2set))))), 14.98/2.30 inference(fool_elimination,[],[f263])). 14.98/2.30 thf(f263,plain,( 14.98/2.30 (prop2setI = ! [X0 : $o] : (X0 => ((in @ emptyset) @ (prop2set @ X0))))), 14.98/2.30 inference(rectify,[],[f59])). 14.98/2.30 thf(f59,axiom,( 14.98/2.30 (prop2setI = ! [X0 : $o] : (X0 => ((in @ emptyset) @ (prop2set @ X0))))), 14.98/2.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2setI)). 14.98/2.30 thf(f935,plain,( 14.98/2.30 ($true != ((in @ ((setminus @ sK1) @ sK2)) @ (powerset @ sK0)))), 14.98/2.30 inference(cnf_transformation,[],[f703])). 14.98/2.30 thf(f2853,plain,( 14.98/2.30 ( ! [X2 : $i,X1 : $i] : (($true = ((in @ X1) @ (powerset @ X2))) | ($false = ((subset @ X1) @ X2))) )), 14.98/2.30 inference(binary_proxy_clausification,[],[f2852])). 14.98/2.30 thf(f2852,plain,( 14.98/2.30 ( ! [X2 : $i,X1 : $i] : (($true = ((vIMP @ ((subset @ X1) @ X2)) @ ((in @ X1) @ (powerset @ X2))))) )), 14.98/2.30 inference(combinator_demodulation,[],[f2851])). 14.98/2.30 thf(f2851,plain,( 14.98/2.30 ( ! [X2 : $i,X1 : $i] : (($true = (((sCOMB @ ((bCOMB @ vIMP) @ (subset @ X1))) @ ((bCOMB @ (in @ X1)) @ powerset)) @ X2))) )), 14.98/2.30 inference(pi_clausification,[],[f2850])). 14.98/2.30 thf(f2850,plain,( 14.98/2.30 ( ! [X1 : $i] : (($true = (vPI($i) @ ((sCOMB @ ((bCOMB @ vIMP) @ (subset @ X1))) @ ((bCOMB @ (in @ X1)) @ powerset))))) )), 14.98/2.30 inference(combinator_demodulation,[],[f2849])). 14.98/2.30 thf(f2849,plain,( 14.98/2.30 ( ! [X1 : $i] : (($true = (((bCOMB @ vPI($i)) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vIMP)) @ subset))) @ ((cCOMB @ ((bCOMB @ bCOMB) @ in)) @ powerset))) @ X1))) )), 14.98/2.30 inference(pi_clausification,[],[f1254])). 14.98/2.30 thf(f1254,plain,( 14.98/2.30 ($true = (vPI($i) @ ((bCOMB @ vPI($i)) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vIMP)) @ subset))) @ ((cCOMB @ ((bCOMB @ bCOMB) @ in)) @ powerset)))))), 14.98/2.30 inference(definition_unfolding,[],[f1021,f796])). 14.98/2.30 thf(f796,plain,( 14.98/2.30 (powersetI1 = $true)), 14.98/2.30 inference(cnf_transformation,[],[f703])). 14.98/2.30 thf(f1021,plain,( 14.98/2.30 (powersetI1 = (vPI($i) @ ((bCOMB @ vPI($i)) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vIMP)) @ subset))) @ ((cCOMB @ ((bCOMB @ bCOMB) @ in)) @ powerset)))))), 14.98/2.30 inference(cnf_transformation,[],[f404])). 14.98/2.30 thf(f404,plain,( 14.98/2.30 (powersetI1 = (vPI($i) @ ((bCOMB @ vPI($i)) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vIMP)) @ subset))) @ ((cCOMB @ ((bCOMB @ bCOMB) @ in)) @ powerset)))))), 14.98/2.30 inference(fool_elimination,[],[f403])). 14.98/2.30 thf(f403,plain,( 14.98/2.30 (powersetI1 = ! [X0,X1] : (((subset @ X1) @ X0) => ((in @ X1) @ (powerset @ X0))))), 14.98/2.30 inference(rectify,[],[f95])). 14.98/2.30 thf(f95,axiom,( 14.98/2.30 (powersetI1 = ! [X3,X4] : (((subset @ X4) @ X3) => ((in @ X4) @ (powerset @ X3))))), 14.98/2.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetI1)). 14.98/2.30 % SZS output end Proof for theBenchmark 14.98/2.30 % (6040)------------------------------ 14.98/2.30 % (6040)Version: Vampire 4.6.0 (commit 0afb7ed4a on 2021-06-23 15:27:21 +0100) 14.98/2.30 % (6040)Termination reason: Refutation 14.98/2.30 14.98/2.30 % (6040)Memory used [KB]: 8955 14.98/2.30 % (6040)Time elapsed: 2.013 s 14.98/2.30 % (6040)------------------------------ 14.98/2.30 % (6040)------------------------------ 14.98/2.30 % (6032)Success in time 2.041 s 14.98/2.31 EOF