0.10/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.10/0.14 % Command : run_vampire %s %d 0.14/0.35 % Computer : n007.cluster.edu 0.14/0.35 % Model : x86_64 x86_64 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.35 % Memory : 8042.1875MB 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.35 % CPULimit : 1200 0.14/0.35 % WCLimit : 120 0.14/0.35 % DateTime : Tue Jul 13 12:59:19 EDT 2021 0.14/0.35 % CPUTime : 0.14/0.35 This is a THF_ problem 0.14/0.36 Running vampire --ignore_missing on --mode casc_hol --cores 0 -t 120 /export/starexec/sandbox/benchmark/theBenchmark.p 0.14/0.36 Running in auto input_syntax mode. Trying TPTP 0.22/0.43 % (23243)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 0.22/0.43 % (23245)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 0.22/0.43 % (23241)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 0.22/0.43 % (23238)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 0.22/0.43 % (23239)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 0.22/0.43 % (23251)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 0.22/0.44 % (23261)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 0.22/0.44 % (23253)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 0.22/0.45 % (23259)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 0.22/0.45 % (23240)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 0.22/0.45 % (23237)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 0.22/0.46 % (23249)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 0.22/0.46 % (23257)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 0.22/0.46 % (23266)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 0.22/0.46 % (23260)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 0.22/0.46 % (23258)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 0.22/0.47 % (23262)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 0.22/0.47 % (23250)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 0.22/0.47 % (23255)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 0.22/0.47 % (23252)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 0.22/0.47 % (23254)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 0.22/0.48 % (23247)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 0.22/0.48 % (23244)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 0.22/0.48 % (23242)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 0.22/0.48 % (23265)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 0.22/0.48 % (23246)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 0.22/0.48 % (23263)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 0.22/0.49 % (23256)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 0.22/0.49 % (23264)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 0.22/0.50 % (23248)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 0.22/0.60 % (23262)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs. 0.22/0.61 % (23254)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs. 4.67/1.02 % (23244)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs. 5.20/1.11 % (23241)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs. 6.10/1.29 % (23246)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs. 6.10/1.30 % (23250)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs. 6.10/1.31 % (23252)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs. 7.62/1.40 % (23253)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs. 7.62/1.40 % (23243)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs. 9.46/1.64 % (23256)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs. 10.00/1.68 % (23246)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs. 10.37/1.71 % (23260)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs. 10.37/1.74 % (23245)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs. 10.71/1.80 % (23251)Time limit reached! 10.71/1.80 % (23251)------------------------------ 10.71/1.80 % (23251)Version: Vampire 4.6.0 (commit 0afb7ed4a on 2021-06-23 15:27:21 +0100) 10.71/1.80 % (23251)Termination reason: Time limit 10.71/1.80 % (23251)Termination phase: Property scanning 10.71/1.80 10.71/1.80 % (23251)Memory used [KB]: 4349 10.71/1.80 % (23251)Time elapsed: 0.500 s 10.71/1.80 % (23251)------------------------------ 10.71/1.80 % (23251)------------------------------ 10.71/1.80 % (23261)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs. 10.71/1.81 % (23259)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs. 11.44/1.86 % (23267)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 11.44/1.88 % (23239)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs. 11.44/1.91 % (23253)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs. 15.29/2.33 % (23243)Time limit reached! 15.29/2.33 % (23243)------------------------------ 15.29/2.33 % (23243)Version: Vampire 4.6.0 (commit 0afb7ed4a on 2021-06-23 15:27:21 +0100) 15.29/2.33 % (23243)Termination reason: Time limit 15.29/2.33 % (23243)Termination phase: Saturation 15.29/2.33 15.29/2.33 % (23243)Memory used [KB]: 15479 15.29/2.33 % (23243)Time elapsed: 0.900 s 15.29/2.33 % (23243)------------------------------ 15.29/2.33 % (23243)------------------------------ 15.34/2.39 % (23268)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 16.42/2.59 % (23240)Time limit reached! 16.42/2.59 % (23240)------------------------------ 16.42/2.59 % (23240)Version: Vampire 4.6.0 (commit 0afb7ed4a on 2021-06-23 15:27:21 +0100) 16.42/2.59 % (23240)Termination reason: Time limit 16.42/2.59 16.42/2.59 % (23240)Memory used [KB]: 44135 16.42/2.59 % (23240)Time elapsed: 2.117 s 16.42/2.59 % (23240)------------------------------ 16.42/2.59 % (23240)------------------------------ 17.81/2.66 % (23269)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 18.58/2.76 % (23249)Time limit reached! 18.58/2.76 % (23249)------------------------------ 18.58/2.76 % (23249)Version: Vampire 4.6.0 (commit 0afb7ed4a on 2021-06-23 15:27:21 +0100) 18.58/2.76 % (23249)Termination reason: Time limit 18.58/2.76 % (23249)Termination phase: Saturation 18.58/2.76 18.58/2.76 % (23249)Memory used [KB]: 12409 18.58/2.76 % (23249)Time elapsed: 0.700 s 18.58/2.76 % (23249)------------------------------ 18.58/2.76 % (23249)------------------------------ 19.10/2.82 % (23270)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 19.42/2.91 % (23237)Time limit reached! 19.42/2.91 % (23237)------------------------------ 19.42/2.91 % (23237)Version: Vampire 4.6.0 (commit 0afb7ed4a on 2021-06-23 15:27:21 +0100) 19.42/2.92 % (23237)Termination reason: Time limit 19.42/2.92 % (23237)Termination phase: Saturation 19.42/2.92 19.42/2.92 % (23237)Memory used [KB]: 8059 19.42/2.92 % (23237)Time elapsed: 0.700 s 19.42/2.92 % (23237)------------------------------ 19.42/2.92 % (23237)------------------------------ 20.05/2.96 % (23248)Time limit reached! 20.05/2.96 % (23248)------------------------------ 20.05/2.96 % (23248)Version: Vampire 4.6.0 (commit 0afb7ed4a on 2021-06-23 15:27:21 +0100) 20.05/2.96 % (23248)Termination reason: Time limit 20.05/2.96 % (23248)Termination phase: Saturation 20.05/2.96 20.05/2.96 % (23248)Memory used [KB]: 17014 20.05/2.96 % (23248)Time elapsed: 0.700 s 20.05/2.96 % (23248)------------------------------ 20.05/2.96 % (23248)------------------------------ 20.05/2.96 % (23271)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 20.31/2.99 % (23238)Time limit reached! 20.31/2.99 % (23238)------------------------------ 20.31/2.99 % (23238)Version: Vampire 4.6.0 (commit 0afb7ed4a on 2021-06-23 15:27:21 +0100) 20.31/2.99 % (23238)Termination reason: Time limit 20.31/2.99 % (23238)Termination phase: Saturation 20.31/2.99 20.31/2.99 % (23238)Memory used [KB]: 17014 20.31/2.99 % (23238)Time elapsed: 0.700 s 20.31/2.99 % (23238)------------------------------ 20.31/2.99 % (23238)------------------------------ 20.31/3.01 % (23272)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 20.81/3.06 % (23273)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 23.61/3.45 % (23239)Time limit reached! 23.61/3.45 % (23239)------------------------------ 23.61/3.45 % (23239)Version: Vampire 4.6.0 (commit 0afb7ed4a on 2021-06-23 15:27:21 +0100) 23.61/3.46 % (23239)Termination reason: Time limit 23.61/3.46 23.61/3.46 % (23239)Memory used [KB]: 19317 23.61/3.46 % (23239)Time elapsed: 3.051 s 23.61/3.46 % (23239)------------------------------ 23.61/3.46 % (23239)------------------------------ 24.47/3.51 % (23274)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 24.82/3.56 % (23269)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs. 25.98/3.75 % (23246)Time limit reached! 25.98/3.75 % (23246)------------------------------ 25.98/3.75 % (23246)Version: Vampire 4.6.0 (commit 0afb7ed4a on 2021-06-23 15:27:21 +0100) 25.98/3.75 % (23246)Termination reason: Time limit 25.98/3.75 % (23246)Termination phase: Saturation 25.98/3.75 25.98/3.75 % (23246)Memory used [KB]: 20980 25.98/3.75 % (23246)Time elapsed: 0.900 s 25.98/3.75 % (23246)------------------------------ 25.98/3.75 % (23246)------------------------------ 26.63/3.81 % (23275)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 27.06/3.87 % (23268)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs. 28.62/4.02 % (23274)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs. 28.62/4.02 % (23270)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs. 29.22/4.14 % (23263)First to succeed. 29.22/4.16 % (23263)Refutation found. Thanks to Tanya! 29.22/4.16 % SZS status Theorem for theBenchmark 29.22/4.16 % SZS output start Proof for theBenchmark 29.22/4.16 thf(type_def_6, type, >: ($tType * $tType) > $tType). 29.22/4.16 thf(func_def_7, type, in: $i > $i > $o). 29.22/4.16 thf(func_def_8, type, exu: ($i > $o) > $o). 29.22/4.16 thf(func_def_13, type, setadjoin: $i > $i > $i). 29.22/4.16 thf(func_def_15, type, powerset: $i > $i). 29.22/4.16 thf(func_def_17, type, setunion: $i > $i). 29.22/4.16 thf(func_def_26, type, descr: ($i > $o) > $i). 29.22/4.16 thf(func_def_28, type, dsetconstr: $i > ($i > $o) > $i). 29.22/4.16 thf(func_def_33, type, prop2set: $o > $i). 29.22/4.16 thf(func_def_43, type, nonempty: $i > $o). 29.22/4.16 thf(func_def_76, type, set2prop: $i > $o). 29.22/4.16 thf(func_def_95, type, subset: $i > $i > $o). 29.22/4.16 thf(func_def_96, type, disjoint: $i > $i > $o). 29.22/4.16 thf(func_def_97, type, setsmeet: $i > $i > $o). 29.22/4.16 thf(func_def_121, type, binunion: $i > $i > $i). 29.22/4.16 thf(func_def_129, type, binintersect: $i > $i > $i). 29.22/4.16 thf(func_def_142, type, regular: $i > $o). 29.22/4.16 thf(func_def_143, type, setminus: $i > $i > $i). 29.22/4.16 thf(func_def_154, type, symdiff: $i > $i > $i). 29.22/4.16 thf(func_def_160, type, iskpair: $i > $o). 29.22/4.16 thf(func_def_165, type, kpair: $i > $i > $i). 29.22/4.16 thf(func_def_167, type, cartprod: $i > $i > $i). 29.22/4.16 thf(func_def_184, type, singleton: $i > $o). 29.22/4.16 thf(func_def_186, type, ex1: $i > ($i > $o) > $o). 29.22/4.16 thf(func_def_191, type, atmost1p: $i > $o). 29.22/4.16 thf(func_def_192, type, atleast2p: $i > $o). 29.22/4.16 thf(func_def_193, type, atmost2p: $i > $o). 29.22/4.16 thf(func_def_194, type, upairsetp: $i > $o). 29.22/4.16 thf(func_def_198, type, kfst: $i > $i). 29.22/4.16 thf(func_def_210, type, ksnd: $i > $i). 29.22/4.16 thf(func_def_220, type, breln: $i > $i > $i > $o). 29.22/4.16 thf(func_def_221, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i). 29.22/4.16 thf(func_def_229, type, func: $i > $i > $i > $o). 29.22/4.16 thf(func_def_230, type, funcSet: $i > $i > $i). 29.22/4.16 thf(func_def_233, type, ap: $i > $i > $i > $i > $i). 29.22/4.16 thf(func_def_239, type, lam: $i > $i > ($i > $i) > $i). 29.22/4.16 thf(func_def_266, type, if: $i > $o > $i > $i > $i). 29.22/4.16 thf(func_def_330, type, breln1: $i > $i > $o). 29.22/4.16 thf(func_def_332, type, breln1Set: $i > $i). 29.22/4.16 thf(func_def_334, type, transitive: $i > $i > $o). 29.22/4.16 thf(func_def_335, type, antisymmetric: $i > $i > $o). 29.22/4.16 thf(func_def_336, type, reflexive: $i > $i > $o). 29.22/4.16 thf(func_def_337, type, refltransitive: $i > $i > $o). 29.22/4.16 thf(func_def_338, type, refllinearorder: $i > $i > $o). 29.22/4.16 thf(func_def_339, type, reflwellordering: $i > $i > $o). 29.22/4.16 thf(func_def_345, type, breln1invset: $i > $i > $i). 29.22/4.16 thf(func_def_349, type, breln1compset: $i > $i > $i > $i). 29.22/4.16 thf(func_def_367, type, image1: $i > ($i > $i) > $i). 29.22/4.16 thf(func_def_371, type, injective: $i > $i > $i > $o). 29.22/4.16 thf(func_def_372, type, injFuncSet: $i > $i > $i). 29.22/4.16 thf(func_def_376, type, surjective: $i > $i > $i > $o). 29.22/4.16 thf(func_def_377, type, surjFuncSet: $i > $i > $i). 29.22/4.16 thf(func_def_385, type, omegaS: $i > $i). 29.22/4.16 thf(func_def_389, type, peano3: $i > $i > $i > $o). 29.22/4.16 thf(func_def_390, type, peano4: $i > $i > $i > $o). 29.22/4.16 thf(func_def_391, type, peano5: $i > $i > $i > $o). 29.22/4.16 thf(func_def_393, type, peano: $i > $i > $i > $o). 29.22/4.16 thf(func_def_394, type, transitiveset: $i > $o). 29.22/4.16 thf(func_def_399, type, stricttotalorderedByIn: $i > $o). 29.22/4.16 thf(func_def_400, type, wellorderedByIn: $i > $o). 29.22/4.16 thf(func_def_401, type, ordinal: $i > $o). 29.22/4.16 thf(func_def_402, type, limitOrdinal: $i > $o). 29.22/4.16 thf(func_def_404, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)). 29.22/4.16 thf(func_def_407, type, vAND: $o > $o > $o). 29.22/4.16 thf(func_def_408, type, vIMP: $o > $o > $o). 29.22/4.16 thf(func_def_409, type, vPI: !>[X0: $tType]:((X0 > $o) > $o)). 29.22/4.16 thf(func_def_410, type, cCOMB: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > X1 > X0 > X2)). 29.22/4.16 thf(func_def_411, type, bCOMB: !>[X0: $tType, X1: $tType, X2: $tType]:((X1 > X2) > (X0 > X1) > X0 > X2)). 29.22/4.16 thf(func_def_412, type, sCOMB: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > (X0 > X1) > X0 > X2)). 29.22/4.16 thf(func_def_413, type, vOR: $o > $o > $o). 29.22/4.16 thf(func_def_414, type, vEQ: !>[X0: $tType]:(X0 > X0 > $o)). 29.22/4.16 thf(func_def_415, type, vNOT: $o > $o). 29.22/4.16 thf(func_def_416, type, iCOMB: !>[X0: $tType]:(X0 > X0)). 29.22/4.16 thf(func_def_417, type, vSIGMA: !>[X0: $tType]:((X0 > $o) > $o)). 29.22/4.16 thf(func_def_418, type, kCOMB: !>[X0: $tType, X1: $tType]:(X0 > X1 > X0)). 29.22/4.16 thf(func_def_419, type, vIFF: $o > $o > $o). 29.22/4.16 thf(func_def_427, type, sK4: $i > $i > $i). 29.22/4.16 thf(func_def_428, type, sK5: $i > $i). 29.22/4.16 thf(func_def_429, type, sK6: ($i > $i > $o) > $i > $i). 29.22/4.16 thf(func_def_430, type, sK7: ($i > $i > $o) > $i > $i). 29.22/4.16 thf(func_def_431, type, sK8: $i > ($i > $i > $o) > $i > $i). 29.22/4.16 thf(func_def_432, type, sK9: ($i > $i > $o) > $i > $i). 29.22/4.16 thf(func_def_433, type, sK10: ($i > $i > $o) > $i > $i). 29.22/4.16 thf(func_def_434, type, sK11: $i > $i). 29.22/4.16 thf(func_def_435, type, sK12: $i > $i). 29.22/4.16 thf(func_def_436, type, sK13: $i > $i > $i > $i). 29.22/4.16 thf(func_def_437, type, sK14: $i > $i > $i). 29.22/4.16 thf(func_def_438, type, sK15: $i > $i > $i). 29.22/4.16 thf(func_def_439, type, sK16: $i > $i > $i). 29.22/4.16 thf(func_def_440, type, sK17: $i > $i > $i). 29.22/4.16 thf(func_def_441, type, sK18: $i > $i > $i). 29.22/4.16 thf(func_def_442, type, sK19: $i > $i > $i). 29.22/4.16 thf(func_def_443, type, sK20: $i > ($i > $o) > $i). 29.22/4.16 thf(func_def_444, type, sK21: $i > ($i > $o) > $i). 29.22/4.16 thf(func_def_445, type, sK22: ($i > $o) > $i). 29.22/4.16 thf(func_def_446, type, sK23: ($i > $o) > $i). 29.22/4.16 thf(func_def_447, type, sK24: $i > $i > $i). 29.22/4.16 thf(func_def_448, type, sK25: $i > $i > $i). 29.22/4.16 thf(func_def_449, type, sK26: $i > $i > $i). 29.22/4.16 thf(func_def_450, type, sK27: $i > $i). 29.22/4.16 thf(func_def_451, type, sK28: $i > $i). 29.22/4.16 thf(func_def_452, type, sK29: $i > $i). 29.22/4.16 thf(func_def_453, type, sK30: $i > $i > $i). 29.22/4.16 thf(func_def_454, type, sK31: $o > $i > $i > $i). 29.22/4.16 thf(func_def_455, type, sK32: $i > ($i > $o) > $i). 29.22/4.16 thf(func_def_456, type, sK33: ($i > $o) > $i). 29.22/4.16 thf(func_def_457, type, sK34: ($i > $o) > $i). 29.22/4.16 thf(func_def_458, type, sK35: $i > $i). 29.22/4.16 thf(func_def_459, type, sK36: $i > ($i > $o) > $i). 29.22/4.16 thf(func_def_460, type, sK37: $i > ($i > $o) > $i). 29.22/4.16 thf(func_def_461, type, sK38: $i > ($i > $o) > $i). 29.22/4.16 thf(func_def_462, type, sK39: $i > ($i > $o) > $i). 29.22/4.16 thf(func_def_463, type, sK40: $i > ($i > $o) > $i). 29.22/4.16 thf(func_def_464, type, sK41: $i > ($i > $o) > $i). 29.22/4.16 thf(func_def_465, type, sK42: ($i > $o) > $i). 29.22/4.16 thf(func_def_466, type, sK43: ($i > $o) > $i). 29.22/4.16 thf(func_def_467, type, sK44: ($i > $o) > $i). 29.22/4.16 thf(func_def_468, type, sK45: ($i > $o) > $i). 29.22/4.16 thf(func_def_469, type, sK46: ($i > $o) > $i). 29.22/4.16 thf(func_def_470, type, sK47: $i > ($i > $o) > $i). 29.22/4.16 thf(func_def_471, type, sK48: ($i > $o) > $i). 29.22/4.16 thf(func_def_472, type, sK49: $i > ($i > $o) > $i). 29.22/4.16 thf(func_def_473, type, sK50: ($i > $o) > ($i > $o) > $i). 29.22/4.16 thf(func_def_474, type, sK51: ($i > $o) > ($i > $o) > $i). 29.22/4.16 thf(func_def_475, type, sK52: $i > ($i > $o) > $i). 29.22/4.16 thf(func_def_476, type, sK53: ($i > $o) > ($i > $o) > $i). 29.22/4.16 thf(func_def_477, type, sK54: ($i > $o) > ($i > $o) > $i). 29.22/4.16 thf(func_def_478, type, sK55: $i > ($i > $o) > $i). 29.22/4.16 thf(func_def_479, type, sK56: $i > ($i > $o) > $i). 29.22/4.16 thf(func_def_480, type, sK57: $i > ($i > $o) > $i). 29.22/4.16 thf(func_def_481, type, sK58: $i > ($i > $o) > $i). 29.22/4.16 thf(func_def_482, type, sK59: $i > ($i > $o) > $i). 29.22/4.16 thf(func_def_483, type, sK60: $i > ($i > $o) > $i). 29.22/4.16 thf(func_def_484, type, sK61: ($i > $o) > ($i > $o) > $i > $i > $i). 29.22/4.16 thf(func_def_485, type, sK62: ($i > $o) > ($i > $o) > $i > $i > $i). 29.22/4.16 thf(func_def_486, type, sK63: $i > $i > $i). 29.22/4.16 thf(func_def_487, type, sK64: $i > $i > $i). 29.22/4.16 thf(func_def_488, type, sK65: $i > $i > $i). 29.22/4.16 thf(func_def_489, type, sK66: $i > $i > $i > $i). 29.22/4.16 thf(func_def_490, type, sK67: $i > $i > $i > $i). 29.22/4.16 thf(func_def_491, type, sK68: $i > $i > $i). 29.22/4.16 thf(func_def_492, type, sK69: $i > ($i > $o) > $i). 29.22/4.16 thf(func_def_493, type, sK70: $i > ($i > $o) > $i). 29.22/4.16 thf(func_def_494, type, sK71: $i > ($i > $o) > $i). 29.22/4.16 thf(func_def_495, type, sK72: $i > ($i > $o) > $i > $i). 29.22/4.16 thf(func_def_496, type, sK73: $i > ($i > $o) > $i). 29.22/4.16 thf(func_def_497, type, sK74: $i > ($i > $o) > $i). 29.22/4.16 thf(func_def_498, type, sK75: $i > $i > ($i > $i) > $i). 29.22/4.16 thf(func_def_499, type, sK76: $i > $i > ($i > $i) > $i). 29.22/4.16 thf(func_def_500, type, sK77: $i > $i > ($i > $i) > $i). 29.22/4.16 thf(func_def_501, type, sK78: ($i > $o) > $i > $i > $i > $i). 29.22/4.16 thf(func_def_502, type, sK79: ($i > $o) > $i > $i > $i > $i). 29.22/4.16 thf(func_def_503, type, sK80: ($i > $o) > $i > $i > $i > $i). 29.22/4.16 thf(func_def_504, type, sK81: ($i > $o) > $i > $i > $i > $i). 29.22/4.16 thf(func_def_505, type, sK82: $i > $i > $i > $i > $i). 29.22/4.16 thf(func_def_506, type, sK83: $i > $i > $i > $i > $i). 29.22/4.16 thf(func_def_507, type, sK84: $i > $i > $i > $i > $i). 29.22/4.16 thf(func_def_508, type, sK85: $i > $i > $i > $i > $i). 29.22/4.16 thf(func_def_509, type, sK86: $i > $i > $i > $i > $i). 29.22/4.16 thf(func_def_510, type, sK87: $i > $i > $i > $i > $i). 29.22/4.16 thf(func_def_511, type, sK88: $i > $i > $i > $i > $i). 29.22/4.16 thf(func_def_512, type, sK89: $i > $i > $i > $i > $i). 29.22/4.16 thf(func_def_513, type, sK90: $i > $i > $i > $i > $i). 29.22/4.16 thf(func_def_514, type, sK91: $i > $i > $i > $i > $i). 29.22/4.16 thf(func_def_515, type, sK92: $i > $i > $i > $i > $i). 29.22/4.16 thf(func_def_516, type, sK93: $i > $i > $i > $i > $i). 29.22/4.16 thf(func_def_517, type, sK94: $i > $i > $i > $i > $i). 29.22/4.16 thf(func_def_518, type, sK95: $i > $i > $i > $i > $i). 29.22/4.16 thf(func_def_519, type, sK96: $i > $i > $i > $i > $i). 29.22/4.16 thf(func_def_520, type, sK97: $i > $i > ($i > $i) > $i). 29.22/4.16 thf(func_def_521, type, sK98: $i > $i > ($i > $i) > $i). 29.22/4.16 thf(func_def_522, type, sK99: $i > $i > $i > $i). 29.22/4.16 thf(func_def_523, type, sK100: $i > $i > $i > $i). 29.22/4.16 thf(func_def_524, type, sK101: $i > $i > $i > $i). 29.22/4.16 thf(func_def_525, type, sK102: $i > $i > $i > $i). 29.22/4.16 thf(func_def_526, type, sK103: $i > $i > $i > $i). 29.22/4.16 thf(func_def_527, type, sK104: $i > $i > $i > $i). 29.22/4.16 thf(func_def_528, type, sK105: ($i > $o) > $i > $i > $i). 29.22/4.16 thf(func_def_529, type, sK106: ($i > $o) > $i > $i > $i). 29.22/4.16 thf(func_def_530, type, sK107: $i > $i > ($i > $i > $o) > $i). 29.22/4.16 thf(func_def_531, type, sK108: ($i > $o) > $i > $i > $i). 29.22/4.16 thf(func_def_532, type, sK109: ($i > $o) > $i > $i > $i). 29.22/4.16 thf(func_def_533, type, sK110: $i > $i > $i > $i). 29.22/4.16 thf(func_def_534, type, sK111: $i > $i > $i > $i). 29.22/4.16 thf(func_def_535, type, sK112: $i > $i > $i > $i). 29.22/4.16 thf(func_def_536, type, sK113: $i > $i > $i > $i). 29.22/4.16 thf(func_def_537, type, sK114: $i > $i > $i > $i). 29.22/4.16 thf(func_def_538, type, sK115: $i > $i > $i > $i). 29.22/4.16 thf(func_def_539, type, sK116: $i > $i > $i > $i). 29.22/4.16 thf(func_def_540, type, sK117: $i > $i > $i > $i). 29.22/4.16 thf(func_def_541, type, sK118: $i > $i > $i > $i). 29.22/4.16 thf(func_def_542, type, sK119: $i > $i > $i > $i). 29.22/4.16 thf(func_def_543, type, sK120: $i > $i > $i > $i). 29.22/4.16 thf(func_def_544, type, sK121: $i > $i > $i > $i). 29.22/4.16 thf(func_def_545, type, sK122: $i > $i > $i > $i > $i > $i). 29.22/4.16 thf(func_def_546, type, sK123: $o > $i > $i > $i > $i > $i > $i). 29.22/4.16 thf(func_def_547, type, sK124: $i > ($i > $i) > $i). 29.22/4.16 thf(func_def_548, type, sK125: $i > ($i > $i) > $i). 29.22/4.16 thf(func_def_549, type, sK126: $i > $i > ($i > $i) > $i). 29.22/4.16 thf(func_def_550, type, sK127: $i > ($i > $i) > $i > $i). 29.22/4.16 thf(func_def_551, type, sK128: $i > $i > ($i > $i) > $i). 29.22/4.16 thf(func_def_552, type, sK129: $i > $i > $i > ($i > $i) > $i). 29.22/4.16 thf(func_def_553, type, sK130: $i > $i > $i > ($i > $i) > $i). 29.22/4.16 thf(func_def_554, type, sK131: $i > $i). 29.22/4.16 thf(func_def_555, type, sK132: $i > $i). 29.22/4.16 thf(func_def_556, type, sK133: $i > $i). 29.22/4.16 thf(func_def_557, type, sK134: $i > $i). 29.22/4.16 thf(func_def_558, type, sK135: $i > $i). 29.22/4.16 thf(func_def_559, type, sK136: $i > $i). 29.22/4.16 thf(func_def_560, type, sK137: $i > $i). 29.22/4.16 thf(func_def_561, type, sK138: $i > $i). 29.22/4.16 thf(func_def_562, type, sK139: $i > $i). 29.22/4.16 thf(func_def_563, type, sK140: $i > $i). 29.22/4.16 thf(func_def_564, type, sK141: $i > $i). 29.22/4.16 thf(func_def_565, type, sK142: $i > $i). 29.22/4.16 thf(func_def_566, type, sK143: $i > $i). 29.22/4.16 thf(func_def_567, type, sK144: $i > $i). 29.22/4.16 thf(func_def_568, type, sK145: $i > $i). 29.22/4.16 thf(func_def_569, type, sK146: $i > $i > $i). 29.22/4.16 thf(func_def_570, type, sK147: $i > $i). 29.22/4.16 thf(func_def_571, type, sK148: $i > $i). 29.22/4.16 thf(func_def_572, type, sK149: $i > $i). 29.22/4.16 thf(func_def_573, type, sK150: $i > $i). 29.22/4.16 thf(func_def_574, type, sK151: $i > $i). 29.22/4.16 thf(func_def_575, type, sK152: $i > $i). 29.22/4.16 thf(func_def_576, type, sK153: $i > $i). 29.22/4.16 thf(func_def_577, type, sK154: $i > $i). 29.22/4.16 thf(func_def_578, type, sK155: $i > $i). 29.22/4.16 thf(func_def_579, type, sK156: $i > $i). 29.22/4.16 thf(func_def_580, type, sK157: $i > $i). 29.22/4.16 thf(func_def_581, type, sK158: $i > $i). 29.22/4.16 thf(func_def_582, type, sK159: $i > $i). 29.22/4.16 thf(func_def_583, type, sK160: $i > $i). 29.22/4.16 thf(func_def_584, type, sK161: $i > $i). 29.22/4.16 thf(func_def_585, type, sK162: $i > $i). 29.22/4.16 thf(func_def_586, type, sK163: $i > $i > $i). 29.22/4.16 thf(func_def_587, type, sK164: $i > $i). 29.22/4.16 thf(func_def_588, type, sK165: $i > $i). 29.22/4.16 thf(func_def_589, type, sK166: $i > $i). 29.22/4.16 thf(func_def_590, type, sK167: $i > $i). 29.22/4.16 thf(func_def_591, type, sK168: $i > $i). 29.22/4.16 thf(func_def_592, type, sK169: $i > $i). 29.22/4.16 thf(func_def_593, type, sK170: $i > $i). 29.22/4.16 thf(func_def_594, type, sK171: $i > $i). 29.22/4.16 thf(func_def_595, type, sK172: $i > $i). 29.22/4.16 thf(func_def_596, type, sK173: $i > $i > $i). 29.22/4.16 thf(func_def_597, type, sK174: $i > $i). 29.22/4.16 thf(func_def_598, type, sK175: $i > $i). 29.22/4.16 thf(func_def_599, type, sK176: $i > $i). 29.22/4.16 thf(func_def_600, type, sK177: $i > $i). 29.22/4.16 thf(func_def_601, type, sK178: $i > $i). 29.22/4.16 thf(func_def_602, type, sK179: $i > $i). 29.22/4.16 thf(func_def_603, type, sK180: $i > $i). 29.22/4.16 thf(func_def_604, type, sK181: $i > $i > $i). 29.22/4.16 thf(func_def_605, type, sK182: $i > $i). 29.22/4.16 thf(func_def_606, type, sK183: $i > $i). 29.22/4.16 thf(func_def_607, type, sK184: $i > $i). 29.22/4.16 thf(func_def_608, type, sK185: $i > $i). 29.22/4.16 thf(func_def_609, type, sK186: $i > $i). 29.22/4.16 thf(func_def_610, type, sK187: $i > $i). 29.22/4.16 thf(func_def_611, type, sK188: $i > $i). 29.22/4.16 thf(func_def_612, type, sK189: $i > $i). 29.22/4.16 thf(func_def_613, type, sK190: $i > $i). 29.22/4.16 thf(func_def_614, type, sK191: $i > $i). 29.22/4.16 thf(func_def_615, type, sK192: $i > $i). 29.22/4.16 thf(func_def_616, type, sK193: $i > $i). 29.22/4.16 thf(func_def_617, type, sK194: $i > $i). 29.22/4.16 thf(func_def_618, type, sK195: $i > $i). 29.22/4.16 thf(func_def_619, type, sK196: $i > $i). 29.22/4.16 thf(func_def_620, type, sK197: $i > $i). 29.22/4.16 thf(func_def_621, type, sK198: $i > $i > $i). 29.22/4.16 thf(func_def_622, type, sK199: $i > $i). 29.22/4.16 thf(func_def_623, type, sK200: $i > $i). 29.22/4.16 thf(func_def_624, type, sK201: $i > $i). 29.22/4.16 thf(func_def_625, type, sK202: $i > $i). 29.22/4.16 thf(func_def_626, type, sK203: $i > $i). 29.22/4.16 thf(func_def_627, type, sK204: $i > $i). 29.22/4.16 thf(func_def_628, type, sK205: $i > $i). 29.22/4.16 thf(func_def_629, type, sK206: $i > $i). 29.22/4.16 thf(func_def_630, type, sK207: $i > $i). 29.22/4.16 thf(func_def_631, type, sK208: $i > $i). 29.22/4.16 thf(func_def_632, type, sK209: $i > $i). 29.22/4.16 thf(func_def_633, type, sK210: $i > $i). 29.22/4.16 thf(func_def_634, type, sK211: $i > $i). 29.22/4.16 thf(func_def_635, type, sK212: $i > $i). 29.22/4.16 thf(func_def_636, type, sK213: $i > $i). 29.22/4.16 thf(func_def_637, type, sK214: $i > $i). 29.22/4.16 thf(func_def_638, type, sK215: $i > $i > $i). 29.22/4.16 thf(func_def_639, type, sK216: $i > $i). 29.22/4.16 thf(func_def_640, type, sK217: $i > $i). 29.22/4.16 thf(func_def_641, type, sK218: $i > $i). 29.22/4.16 thf(func_def_642, type, sK219: $i > $i). 29.22/4.16 thf(func_def_643, type, sK220: $i > $i). 29.22/4.16 thf(func_def_644, type, sK221: $i > $i). 29.22/4.16 thf(func_def_645, type, sK222: $i > $i). 29.22/4.16 thf(func_def_646, type, sK223: $i > $i). 29.22/4.16 thf(func_def_647, type, sK224: $i > $i). 29.22/4.16 thf(func_def_648, type, sK225: $i > $i). 29.22/4.16 thf(func_def_650, type, sK227: $o > $i). 29.22/4.16 thf(f13880,plain,( 29.22/4.16 $false), 29.22/4.16 inference(trivial_inequality_removal,[],[f13871])). 29.22/4.16 thf(f13871,plain,( 29.22/4.16 ($true = $false)), 29.22/4.16 inference(superposition,[],[f1356,f13863])). 29.22/4.16 thf(f13863,plain,( 29.22/4.16 ($false = ((in @ sK2) @ sK0))), 29.22/4.16 inference(subsumption_resolution,[],[f13844,f1358])). 29.22/4.16 thf(f1358,plain,( 29.22/4.16 ($true != ((in @ sK1) @ sK0))), 29.22/4.16 inference(cnf_transformation,[],[f1021])). 29.22/4.16 thf(f1021,plain,( 29.22/4.16 ((($true != ((in @ sK1) @ sK0)) & ($true = ((in @ sK1) @ sK2)) & ($true = ((in @ sK2) @ sK0))) & ($true = (ordinal @ sK0))) & (ordinalMinLem1 = $true) & (setunionTransitive = $true) & (transitivesetOp2 = $true) & (binintTransitive = $true) & (transitivesetOp1 = $true) & (peanoSinj = $true) & (peano0notS = $true) & (omegaSclos = $true) & (omegaSp = $true) & (notinself2 = $true) & (notinself = $true) & (foundation2 = $true) & (surjCantorThm = $true) & (leftInvIsSurj = $true) & (surjFuncSetFuncSurj = $true) & (surjFuncSetFuncIn = $true) & (injFuncSetFuncInj = $true) & (injFuncSetFuncIn = $true) & (injFuncInInjFuncSet = $true) & (image1I = $true) & (image1E = $true) & (image1Equiv = $true) & (image1Ex1 = $true) & (image1Ex = $true) & (woz2B = $true) & (woz2A = $true) & (woz2W = $true) & (woz2Ex = $true) & (breln1unionCommutes = $true) & (breln1unionEcases = $true) & (breln1unionE = $true) & (breln1unionI = $true) & (breln1unionIR = $true) & (breln1unionIL = $true) & (breln1unionprop = $true) & (breln1compEex = $true) & (breln1compE = $true) & (breln1compI = $true) & (breln1compprop = $true) & (breln1invE = $true) & (breln1invI = $true) & (breln1invprop = $true) & (eqbreln1 = $true) & (subbreln1 = $true) & (breln1all1 = $true) & (setOfPairsIsBReln1 = $true) & (choice2fnsingleton = $true) & (breln1SetBreln1 = $true) & (breln1all2 = $true) & (woz1_5 = $true) & (woz1_4 = $true) & (woz1_3 = $true) & (woz1_2 = $true) & (woz1_1 = $true) & (woz13rule4 = $true) & (woz13rule3 = $true) & (woz13rule2 = $true) & (woz13rule1 = $true) & (woz13rule0 = $true) & (demorgan2 = $true) & (demorgan2b = $true) & (demorgan2b2 = $true) & (demorgan2a = $true) & (demorgan1 = $true) & (demorgan1b = $true) & (demorgan1a = $true) & (demorgan2a2 = $true) & (complementUnionInPowersetComplement = $true) & (demorgan2a1 = $true) & (binunionTEcontra = $true) & (binunionTE = $true) & (inComplementUnionImpInComplement1 = $true) & (inComplementUnionImpNotIn1 = $true) & (intersectInPowersetIntersectUnions = $true) & (inIntersectImpInIntersectUnions = $true) & (inIntersectImpInUnion2 = $true) & (inIntersectImpInUnion = $true) & (binunionTIRcontra = $true) & (binunionTILcontra = $true) & (complementTcontraSubset = $true) & (contraSubsetComplement = $true) & (complementInPowersetComplementIntersect = $true) & (complementSubsetComplementIntersect = $true) & (complementImpComplementIntersect = $true) & (complementTnotintersectT = $true) & (doubleComplementEq = $true) & (doubleComplementSub2 = $true) & (doubleComplementSub1 = $true) & (doubleComplementE1 = $true) & (doubleComplementI1 = $true) & (contrasubsetT3 = $true) & (contrasubsetT2 = $true) & (contrasubsetT1 = $true) & (contrasubsetT = $true) & (binintersectTERcontra = $true) & (binintersectTELcontra = $true) & (complementTE1 = $true) & (complementTI1 = $true) & (powersetTE1 = $true) & (powersetTI1 = $true) & (subsetTI = $true) & (setextT = $true) & (complementT_lem = $true) & (setminusT_lem = $true) & (powersetT_lem = $true) & (binunionT_lem = $true) & (binintersectT_lem = $true) & (iftrueorfalse = $true) & (iffalse = $true) & (iftrue = $true) & (theeq = $true) & (ifp = $true) & (ifSingleton = $true) & (iftrueProp2 = $true) & (iftrueProp1 = $true) & (iffalseProp2 = $true) & (iffalseProp1 = $true) & (eta2 = $true) & (beta2 = $true) & (lam2lamEq = $true) & (eta1 = $true) & (beta1 = $true) & (ap2apEq2 = $true) & (ap2apEq1 = $true) & (funcext2 = $true) & (funcext = $true) & (eqbreln = $true) & (subbreln = $true) & (funcGraphProp4 = $true) & (funcextLem = $true) & (funcGraphProp2 = $true) & (funcGraphProp3 = $true) & (funcGraphProp1 = $true) & (ex1E2 = $true) & (brelnall2 = $true) & (brelnall1 = $true) & (lam2p = $true) & (lamp = $true) & (lamProp = $true) & (funcinfuncset = $true) & (ap2p = $true) & (infuncsetfunc = $true) & (app = $true) & (apProp = $true) & (funcImageSingleton = $true) & (dpsetconstrER = $true) & (dpsetconstrEL2 = $true) & (dpsetconstrEL1 = $true) & (dpsetconstrERa = $true) & (setOfPairsIsBReln = $true) & (dpsetconstrSub = $true) & (dpsetconstrI = $true) & (cartprodpairsurjEq = $true) & (cartprodsndpairEq = $true) & (cartprodfstpairEq = $true) & (cartprodmempaircEq = $true) & (cartprodpairmemER = $true) & (cartprodpairmemEL = $true) & (cartprodsndin = $true) & (kpairsurjEq = $true) & (ksndpairEq = $true) & (ksndsingleton = $true) & (setukpairinjR = $true) & (setukpairinjR2 = $true) & (upairequniteq = $true) & (setukpairinjR1 = $true) & (setukpairinjR12 = $true) & (setukpairinjR11 = $true) & (setukpairinjL = $true) & (setukpairinjL2 = $true) & (cartprodfstin = $true) & (kfstpairEq = $true) & (theprop = $true) & (kfstsingleton = $true) & (setukpairinjL1 = $true) & (singletonsuniq = $true) & (ex1I2 = $true) & (ex1I = $true) & (ex1E1 = $true) & (singletonprop = $true) & (setunionsingleton = $true) & (setunionsingleton2 = $true) & (setunionsingleton1 = $true) & (setunionE2 = $true) & (cartprodmempair = $true) & (cartprodmempair1 = $true) & (cartprodpairin = $true) & (ubforcartprodlem3 = $true) & (ubforcartprodlem2 = $true) & (ubforcartprodlem1 = $true) & (upairinpowunion = $true) & (upairsubunion = $true) & (upairset2E = $true) & (singletoninpowunion = $true) & (singletoninpowerset = $true) & (singletonsubset = $true) & (kpairp = $true) & (kpairiskpair = $true) & (setukpairIR = $true) & (setukpairIL = $true) & (secondinupair = $true) & (symdiffIneg2 = $true) & (symdiffIneg1 = $true) & (symdiffI2 = $true) & (symdiffI1 = $true) & (symdiffE = $true) & (setminusSubset1 = $true) & (setminusLsub = $true) & (setminusIRneg = $true) & (setminusILneg = $true) & (setminusELneg = $true) & (setminusERneg = $true) & (setminusSubset2 = $true) & (setminusER = $true) & (setminusEL = $true) & (setminusI = $true) & (bs114d = $true) & (binintersectSubset1 = $true) & (binintersectSubset4 = $true) & (binintersectRsub = $true) & (disjointsetsI1 = $true) & (binintersectER = $true) & (binintersectSubset3 = $true) & (binintersectSubset2 = $true) & (binintersectLsub = $true) & (binintersectEL = $true) & (binintersectSubset5 = $true) & (binintersectI = $true) & (binunionRsub = $true) & (binunionLsub = $true) & (binunionE = $true) & (binunionEcases = $true) & (binunionIR = $true) & (upairset2IR = $true) & (binunionIL = $true) & (sepSubset = $true) & (sepInPowerset = $true) & (powersetsubset = $true) & (inPowerset = $true) & (powersetE1 = $true) & (powersetI1 = $true) & (subsetemptysetimpeq = $true) & (setextsub = $true) & (subset2powerset = $true) & (setadjoinSub2 = $true) & (setadjoinSub = $true) & (subsetTrans = $true) & (subsetRefl = $true) & (notequalI2 = $true) & (notequalI1 = $true) & (notsubsetI = $true) & (subsetE2 = $true) & (subsetE = $true) & (emptysetsubset = $true) & (subsetI2 = $true) & (eqimpsubset1 = $true) & (eqimpsubset2 = $true) & (subsetI1 = $true) & (dsetconstr__Cong = $true) & (descr__Cong = $true) & (exuEu = $true) & (omega__Cong = $true) & (setunion__Cong = $true) & (powerset__Cong = $true) & (setadjoin__Cong = $true) & (emptyset__Cong = $true) & (exu__Cong = $true) & (exuE3u = $true) & (in__Cong = $true) & (inCongP = $true) & (exuI2 = $true) & (exuI3 = $true) & (exuI1 = $true) & (notdallE = $true) & (notdexE = $true) & (prop2set2propI = $true) & (prop2setI = $true) & (quantDeMorgan4 = $true) & (quantDeMorgan3 = $true) & (quantDeMorgan2 = $true) & (quantDeMorgan1 = $true) & (vacuousDall = $true) & (emptyE1 = $true) & (upairsetIR = $true) & (upairsetIL = $true) & (upairsetE = $true) & (singletonsswitch = $true) & (eqinunit = $true) & (notinsingleton = $true) & (uniqinunit = $true) & (nonemptyImpWitness = $true) & (exuE2 = $true) & (subPowSU = $true) & (setunionE = $true) & (setunionI = $true) & (powersetE = $true) & (emptyInPowerset = $true) & (emptyinPowerset = $true) & (powersetI = $true) & (setoftrueEq = $true) & (setadjoinOr = $true) & (setadjoinE = $true) & (setadjoinIR = $true) & (emptyinunitempty = $true) & (setadjoinIL = $true) & (nonemptyI1 = $true) & (nonemptyI = $true) & (nonemptyE1 = $true) & (setbeta = $true) & (noeltsimpempty = $true) & (emptyI = $true) & (setext = $true) & (exuE3e = $true) & (notinemptyset = $true) & (emptysetimpfalse = $true) & (emptysetE = $true) & (prop2setE = $true) & (exuE1 = $true) & (dsetconstrER = $true) & (dsetconstrEL = $true) & (dsetconstrI = $true) & (descrp = $true) & (wellorderingAx = $true) & (foundationAx = $true) & (replAx = $true) & (omegaIndAx = $true) & (omegaSAx = $true) & (omega0Ax = $true) & (setunionAx = $true) & (powersetAx = $true) & (setadjoinAx = $true) & (emptysetAx = $true) & (setextAx = $true)), 29.22/4.16 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f1018,f1020,f1019])). 29.22/4.16 thf(f1019,plain,( 29.22/4.16 ? [X0] : (? [X1,X2] : (($true != ((in @ X1) @ X0)) & ($true = ((in @ X1) @ X2)) & ($true = ((in @ X2) @ X0))) & ($true = (ordinal @ X0))) => (? [X2,X1] : (($true != ((in @ X1) @ sK0)) & ($true = ((in @ X1) @ X2)) & ($true = ((in @ X2) @ sK0))) & ($true = (ordinal @ sK0)))), 29.22/4.16 introduced(choice_axiom,[])). 29.22/4.16 thf(f1020,plain,( 29.22/4.16 ? [X2,X1] : (($true != ((in @ X1) @ sK0)) & ($true = ((in @ X1) @ X2)) & ($true = ((in @ X2) @ sK0))) => (($true != ((in @ sK1) @ sK0)) & ($true = ((in @ sK1) @ sK2)) & ($true = ((in @ sK2) @ sK0)))), 29.22/4.16 introduced(choice_axiom,[])). 29.22/4.16 thf(f1018,plain,( 29.22/4.16 ? [X0] : (? [X1,X2] : (($true != ((in @ X1) @ X0)) & ($true = ((in @ X1) @ X2)) & ($true = ((in @ X2) @ X0))) & ($true = (ordinal @ X0))) & (ordinalMinLem1 = $true) & (setunionTransitive = $true) & (transitivesetOp2 = $true) & (binintTransitive = $true) & (transitivesetOp1 = $true) & (peanoSinj = $true) & (peano0notS = $true) & (omegaSclos = $true) & (omegaSp = $true) & (notinself2 = $true) & (notinself = $true) & (foundation2 = $true) & (surjCantorThm = $true) & (leftInvIsSurj = $true) & (surjFuncSetFuncSurj = $true) & (surjFuncSetFuncIn = $true) & (injFuncSetFuncInj = $true) & (injFuncSetFuncIn = $true) & (injFuncInInjFuncSet = $true) & (image1I = $true) & (image1E = $true) & (image1Equiv = $true) & (image1Ex1 = $true) & (image1Ex = $true) & (woz2B = $true) & (woz2A = $true) & (woz2W = $true) & (woz2Ex = $true) & (breln1unionCommutes = $true) & (breln1unionEcases = $true) & (breln1unionE = $true) & (breln1unionI = $true) & (breln1unionIR = $true) & (breln1unionIL = $true) & (breln1unionprop = $true) & (breln1compEex = $true) & (breln1compE = $true) & (breln1compI = $true) & (breln1compprop = $true) & (breln1invE = $true) & (breln1invI = $true) & (breln1invprop = $true) & (eqbreln1 = $true) & (subbreln1 = $true) & (breln1all1 = $true) & (setOfPairsIsBReln1 = $true) & (choice2fnsingleton = $true) & (breln1SetBreln1 = $true) & (breln1all2 = $true) & (woz1_5 = $true) & (woz1_4 = $true) & (woz1_3 = $true) & (woz1_2 = $true) & (woz1_1 = $true) & (woz13rule4 = $true) & (woz13rule3 = $true) & (woz13rule2 = $true) & (woz13rule1 = $true) & (woz13rule0 = $true) & (demorgan2 = $true) & (demorgan2b = $true) & (demorgan2b2 = $true) & (demorgan2a = $true) & (demorgan1 = $true) & (demorgan1b = $true) & (demorgan1a = $true) & (demorgan2a2 = $true) & (complementUnionInPowersetComplement = $true) & (demorgan2a1 = $true) & (binunionTEcontra = $true) & (binunionTE = $true) & (inComplementUnionImpInComplement1 = $true) & (inComplementUnionImpNotIn1 = $true) & (intersectInPowersetIntersectUnions = $true) & (inIntersectImpInIntersectUnions = $true) & (inIntersectImpInUnion2 = $true) & (inIntersectImpInUnion = $true) & (binunionTIRcontra = $true) & (binunionTILcontra = $true) & (complementTcontraSubset = $true) & (contraSubsetComplement = $true) & (complementInPowersetComplementIntersect = $true) & (complementSubsetComplementIntersect = $true) & (complementImpComplementIntersect = $true) & (complementTnotintersectT = $true) & (doubleComplementEq = $true) & (doubleComplementSub2 = $true) & (doubleComplementSub1 = $true) & (doubleComplementE1 = $true) & (doubleComplementI1 = $true) & (contrasubsetT3 = $true) & (contrasubsetT2 = $true) & (contrasubsetT1 = $true) & (contrasubsetT = $true) & (binintersectTERcontra = $true) & (binintersectTELcontra = $true) & (complementTE1 = $true) & (complementTI1 = $true) & (powersetTE1 = $true) & (powersetTI1 = $true) & (subsetTI = $true) & (setextT = $true) & (complementT_lem = $true) & (setminusT_lem = $true) & (powersetT_lem = $true) & (binunionT_lem = $true) & (binintersectT_lem = $true) & (iftrueorfalse = $true) & (iffalse = $true) & (iftrue = $true) & (theeq = $true) & (ifp = $true) & (ifSingleton = $true) & (iftrueProp2 = $true) & (iftrueProp1 = $true) & (iffalseProp2 = $true) & (iffalseProp1 = $true) & (eta2 = $true) & (beta2 = $true) & (lam2lamEq = $true) & (eta1 = $true) & (beta1 = $true) & (ap2apEq2 = $true) & (ap2apEq1 = $true) & (funcext2 = $true) & (funcext = $true) & (eqbreln = $true) & (subbreln = $true) & (funcGraphProp4 = $true) & (funcextLem = $true) & (funcGraphProp2 = $true) & (funcGraphProp3 = $true) & (funcGraphProp1 = $true) & (ex1E2 = $true) & (brelnall2 = $true) & (brelnall1 = $true) & (lam2p = $true) & (lamp = $true) & (lamProp = $true) & (funcinfuncset = $true) & (ap2p = $true) & (infuncsetfunc = $true) & (app = $true) & (apProp = $true) & (funcImageSingleton = $true) & (dpsetconstrER = $true) & (dpsetconstrEL2 = $true) & (dpsetconstrEL1 = $true) & (dpsetconstrERa = $true) & (setOfPairsIsBReln = $true) & (dpsetconstrSub = $true) & (dpsetconstrI = $true) & (cartprodpairsurjEq = $true) & (cartprodsndpairEq = $true) & (cartprodfstpairEq = $true) & (cartprodmempaircEq = $true) & (cartprodpairmemER = $true) & (cartprodpairmemEL = $true) & (cartprodsndin = $true) & (kpairsurjEq = $true) & (ksndpairEq = $true) & (ksndsingleton = $true) & (setukpairinjR = $true) & (setukpairinjR2 = $true) & (upairequniteq = $true) & (setukpairinjR1 = $true) & (setukpairinjR12 = $true) & (setukpairinjR11 = $true) & (setukpairinjL = $true) & (setukpairinjL2 = $true) & (cartprodfstin = $true) & (kfstpairEq = $true) & (theprop = $true) & (kfstsingleton = $true) & (setukpairinjL1 = $true) & (singletonsuniq = $true) & (ex1I2 = $true) & (ex1I = $true) & (ex1E1 = $true) & (singletonprop = $true) & (setunionsingleton = $true) & (setunionsingleton2 = $true) & (setunionsingleton1 = $true) & (setunionE2 = $true) & (cartprodmempair = $true) & (cartprodmempair1 = $true) & (cartprodpairin = $true) & (ubforcartprodlem3 = $true) & (ubforcartprodlem2 = $true) & (ubforcartprodlem1 = $true) & (upairinpowunion = $true) & (upairsubunion = $true) & (upairset2E = $true) & (singletoninpowunion = $true) & (singletoninpowerset = $true) & (singletonsubset = $true) & (kpairp = $true) & (kpairiskpair = $true) & (setukpairIR = $true) & (setukpairIL = $true) & (secondinupair = $true) & (symdiffIneg2 = $true) & (symdiffIneg1 = $true) & (symdiffI2 = $true) & (symdiffI1 = $true) & (symdiffE = $true) & (setminusSubset1 = $true) & (setminusLsub = $true) & (setminusIRneg = $true) & (setminusILneg = $true) & (setminusELneg = $true) & (setminusERneg = $true) & (setminusSubset2 = $true) & (setminusER = $true) & (setminusEL = $true) & (setminusI = $true) & (bs114d = $true) & (binintersectSubset1 = $true) & (binintersectSubset4 = $true) & (binintersectRsub = $true) & (disjointsetsI1 = $true) & (binintersectER = $true) & (binintersectSubset3 = $true) & (binintersectSubset2 = $true) & (binintersectLsub = $true) & (binintersectEL = $true) & (binintersectSubset5 = $true) & (binintersectI = $true) & (binunionRsub = $true) & (binunionLsub = $true) & (binunionE = $true) & (binunionEcases = $true) & (binunionIR = $true) & (upairset2IR = $true) & (binunionIL = $true) & (sepSubset = $true) & (sepInPowerset = $true) & (powersetsubset = $true) & (inPowerset = $true) & (powersetE1 = $true) & (powersetI1 = $true) & (subsetemptysetimpeq = $true) & (setextsub = $true) & (subset2powerset = $true) & (setadjoinSub2 = $true) & (setadjoinSub = $true) & (subsetTrans = $true) & (subsetRefl = $true) & (notequalI2 = $true) & (notequalI1 = $true) & (notsubsetI = $true) & (subsetE2 = $true) & (subsetE = $true) & (emptysetsubset = $true) & (subsetI2 = $true) & (eqimpsubset1 = $true) & (eqimpsubset2 = $true) & (subsetI1 = $true) & (dsetconstr__Cong = $true) & (descr__Cong = $true) & (exuEu = $true) & (omega__Cong = $true) & (setunion__Cong = $true) & (powerset__Cong = $true) & (setadjoin__Cong = $true) & (emptyset__Cong = $true) & (exu__Cong = $true) & (exuE3u = $true) & (in__Cong = $true) & (inCongP = $true) & (exuI2 = $true) & (exuI3 = $true) & (exuI1 = $true) & (notdallE = $true) & (notdexE = $true) & (prop2set2propI = $true) & (prop2setI = $true) & (quantDeMorgan4 = $true) & (quantDeMorgan3 = $true) & (quantDeMorgan2 = $true) & (quantDeMorgan1 = $true) & (vacuousDall = $true) & (emptyE1 = $true) & (upairsetIR = $true) & (upairsetIL = $true) & (upairsetE = $true) & (singletonsswitch = $true) & (eqinunit = $true) & (notinsingleton = $true) & (uniqinunit = $true) & (nonemptyImpWitness = $true) & (exuE2 = $true) & (subPowSU = $true) & (setunionE = $true) & (setunionI = $true) & (powersetE = $true) & (emptyInPowerset = $true) & (emptyinPowerset = $true) & (powersetI = $true) & (setoftrueEq = $true) & (setadjoinOr = $true) & (setadjoinE = $true) & (setadjoinIR = $true) & (emptyinunitempty = $true) & (setadjoinIL = $true) & (nonemptyI1 = $true) & (nonemptyI = $true) & (nonemptyE1 = $true) & (setbeta = $true) & (noeltsimpempty = $true) & (emptyI = $true) & (setext = $true) & (exuE3e = $true) & (notinemptyset = $true) & (emptysetimpfalse = $true) & (emptysetE = $true) & (prop2setE = $true) & (exuE1 = $true) & (dsetconstrER = $true) & (dsetconstrEL = $true) & (dsetconstrI = $true) & (descrp = $true) & (wellorderingAx = $true) & (foundationAx = $true) & (replAx = $true) & (omegaIndAx = $true) & (omegaSAx = $true) & (omega0Ax = $true) & (setunionAx = $true) & (powersetAx = $true) & (setadjoinAx = $true) & (emptysetAx = $true) & (setextAx = $true)), 29.22/4.16 inference(flattening,[],[f1017])). 29.22/4.16 thf(f1017,plain,( 29.22/4.16 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0] : (? [X1,X2] : ((($true != ((in @ X1) @ X0)) & ($true = ((in @ X1) @ X2))) & ($true = ((in @ X2) @ X0))) & ($true = (ordinal @ X0))) & (ordinalMinLem1 = $true)) & (setunionTransitive = $true)) & (transitivesetOp2 = $true)) & (binintTransitive = $true)) & (transitivesetOp1 = $true)) & (peanoSinj = $true)) & (peano0notS = $true)) & (omegaSclos = $true)) & (omegaSp = $true)) & (notinself2 = $true)) & (notinself = $true)) & (foundation2 = $true)) & (surjCantorThm = $true)) & (leftInvIsSurj = $true)) & (surjFuncSetFuncSurj = $true)) & (surjFuncSetFuncIn = $true)) & (injFuncSetFuncInj = $true)) & (injFuncSetFuncIn = $true)) & (injFuncInInjFuncSet = $true)) & (image1I = $true)) & (image1E = $true)) & (image1Equiv = $true)) & (image1Ex1 = $true)) & (image1Ex = $true)) & (woz2B = $true)) & (woz2A = $true)) & (woz2W = $true)) & (woz2Ex = $true)) & (breln1unionCommutes = $true)) & (breln1unionEcases = $true)) & (breln1unionE = $true)) & (breln1unionI = $true)) & (breln1unionIR = $true)) & (breln1unionIL = $true)) & (breln1unionprop = $true)) & (breln1compEex = $true)) & (breln1compE = $true)) & (breln1compI = $true)) & (breln1compprop = $true)) & (breln1invE = $true)) & (breln1invI = $true)) & (breln1invprop = $true)) & (eqbreln1 = $true)) & (subbreln1 = $true)) & (breln1all1 = $true)) & (setOfPairsIsBReln1 = $true)) & (choice2fnsingleton = $true)) & (breln1SetBreln1 = $true)) & (breln1all2 = $true)) & (woz1_5 = $true)) & (woz1_4 = $true)) & (woz1_3 = $true)) & (woz1_2 = $true)) & (woz1_1 = $true)) & (woz13rule4 = $true)) & (woz13rule3 = $true)) & (woz13rule2 = $true)) & (woz13rule1 = $true)) & (woz13rule0 = $true)) & (demorgan2 = $true)) & (demorgan2b = $true)) & (demorgan2b2 = $true)) & (demorgan2a = $true)) & (demorgan1 = $true)) & (demorgan1b = $true)) & (demorgan1a = $true)) & (demorgan2a2 = $true)) & (complementUnionInPowersetComplement = $true)) & (demorgan2a1 = $true)) & (binunionTEcontra = $true)) & (binunionTE = $true)) & (inComplementUnionImpInComplement1 = $true)) & (inComplementUnionImpNotIn1 = $true)) & (intersectInPowersetIntersectUnions = $true)) & (inIntersectImpInIntersectUnions = $true)) & (inIntersectImpInUnion2 = $true)) & (inIntersectImpInUnion = $true)) & (binunionTIRcontra = $true)) & (binunionTILcontra = $true)) & (complementTcontraSubset = $true)) & (contraSubsetComplement = $true)) & (complementInPowersetComplementIntersect = $true)) & (complementSubsetComplementIntersect = $true)) & (complementImpComplementIntersect = $true)) & (complementTnotintersectT = $true)) & (doubleComplementEq = $true)) & (doubleComplementSub2 = $true)) & (doubleComplementSub1 = $true)) & (doubleComplementE1 = $true)) & (doubleComplementI1 = $true)) & (contrasubsetT3 = $true)) & (contrasubsetT2 = $true)) & (contrasubsetT1 = $true)) & (contrasubsetT = $true)) & (binintersectTERcontra = $true)) & (binintersectTELcontra = $true)) & (complementTE1 = $true)) & (complementTI1 = $true)) & (powersetTE1 = $true)) & (powersetTI1 = $true)) & (subsetTI = $true)) & (setextT = $true)) & (complementT_lem = $true)) & (setminusT_lem = $true)) & (powersetT_lem = $true)) & (binunionT_lem = $true)) & (binintersectT_lem = $true)) & (iftrueorfalse = $true)) & (iffalse = $true)) & (iftrue = $true)) & (theeq = $true)) & (ifp = $true)) & (ifSingleton = $true)) & (iftrueProp2 = $true)) & (iftrueProp1 = $true)) & (iffalseProp2 = $true)) & (iffalseProp1 = $true)) & (eta2 = $true)) & (beta2 = $true)) & (lam2lamEq = $true)) & (eta1 = $true)) & (beta1 = $true)) & (ap2apEq2 = $true)) & (ap2apEq1 = $true)) & (funcext2 = $true)) & (funcext = $true)) & (eqbreln = $true)) & (subbreln = $true)) & (funcGraphProp4 = $true)) & (funcextLem = $true)) & (funcGraphProp2 = $true)) & (funcGraphProp3 = $true)) & (funcGraphProp1 = $true)) & (ex1E2 = $true)) & (brelnall2 = $true)) & (brelnall1 = $true)) & (lam2p = $true)) & (lamp = $true)) & (lamProp = $true)) & (funcinfuncset = $true)) & (ap2p = $true)) & (infuncsetfunc = $true)) & (app = $true)) & (apProp = $true)) & (funcImageSingleton = $true)) & (dpsetconstrER = $true)) & (dpsetconstrEL2 = $true)) & (dpsetconstrEL1 = $true)) & (dpsetconstrERa = $true)) & (setOfPairsIsBReln = $true)) & (dpsetconstrSub = $true)) & (dpsetconstrI = $true)) & (cartprodpairsurjEq = $true)) & (cartprodsndpairEq = $true)) & (cartprodfstpairEq = $true)) & (cartprodmempaircEq = $true)) & (cartprodpairmemER = $true)) & (cartprodpairmemEL = $true)) & (cartprodsndin = $true)) & (kpairsurjEq = $true)) & (ksndpairEq = $true)) & (ksndsingleton = $true)) & (setukpairinjR = $true)) & (setukpairinjR2 = $true)) & (upairequniteq = $true)) & (setukpairinjR1 = $true)) & (setukpairinjR12 = $true)) & (setukpairinjR11 = $true)) & (setukpairinjL = $true)) & (setukpairinjL2 = $true)) & (cartprodfstin = $true)) & (kfstpairEq = $true)) & (theprop = $true)) & (kfstsingleton = $true)) & (setukpairinjL1 = $true)) & (singletonsuniq = $true)) & (ex1I2 = $true)) & (ex1I = $true)) & (ex1E1 = $true)) & (singletonprop = $true)) & (setunionsingleton = $true)) & (setunionsingleton2 = $true)) & (setunionsingleton1 = $true)) & (setunionE2 = $true)) & (cartprodmempair = $true)) & (cartprodmempair1 = $true)) & (cartprodpairin = $true)) & (ubforcartprodlem3 = $true)) & (ubforcartprodlem2 = $true)) & (ubforcartprodlem1 = $true)) & (upairinpowunion = $true)) & (upairsubunion = $true)) & (upairset2E = $true)) & (singletoninpowunion = $true)) & (singletoninpowerset = $true)) & (singletonsubset = $true)) & (kpairp = $true)) & (kpairiskpair = $true)) & (setukpairIR = $true)) & (setukpairIL = $true)) & (secondinupair = $true)) & (symdiffIneg2 = $true)) & (symdiffIneg1 = $true)) & (symdiffI2 = $true)) & (symdiffI1 = $true)) & (symdiffE = $true)) & (setminusSubset1 = $true)) & (setminusLsub = $true)) & (setminusIRneg = $true)) & (setminusILneg = $true)) & (setminusELneg = $true)) & (setminusERneg = $true)) & (setminusSubset2 = $true)) & (setminusER = $true)) & (setminusEL = $true)) & (setminusI = $true)) & (bs114d = $true)) & (binintersectSubset1 = $true)) & (binintersectSubset4 = $true)) & (binintersectRsub = $true)) & (disjointsetsI1 = $true)) & (binintersectER = $true)) & (binintersectSubset3 = $true)) & (binintersectSubset2 = $true)) & (binintersectLsub = $true)) & (binintersectEL = $true)) & (binintersectSubset5 = $true)) & (binintersectI = $true)) & (binunionRsub = $true)) & (binunionLsub = $true)) & (binunionE = $true)) & (binunionEcases = $true)) & (binunionIR = $true)) & (upairset2IR = $true)) & (binunionIL = $true)) & (sepSubset = $true)) & (sepInPowerset = $true)) & (powersetsubset = $true)) & (inPowerset = $true)) & (powersetE1 = $true)) & (powersetI1 = $true)) & (subsetemptysetimpeq = $true)) & (setextsub = $true)) & (subset2powerset = $true)) & (setadjoinSub2 = $true)) & (setadjoinSub = $true)) & (subsetTrans = $true)) & (subsetRefl = $true)) & (notequalI2 = $true)) & (notequalI1 = $true)) & (notsubsetI = $true)) & (subsetE2 = $true)) & (subsetE = $true)) & (emptysetsubset = $true)) & (subsetI2 = $true)) & (eqimpsubset1 = $true)) & (eqimpsubset2 = $true)) & (subsetI1 = $true)) & (dsetconstr__Cong = $true)) & (descr__Cong = $true)) & (exuEu = $true)) & (omega__Cong = $true)) & (setunion__Cong = $true)) & (powerset__Cong = $true)) & (setadjoin__Cong = $true)) & (emptyset__Cong = $true)) & (exu__Cong = $true)) & (exuE3u = $true)) & (in__Cong = $true)) & (inCongP = $true)) & (exuI2 = $true)) & (exuI3 = $true)) & (exuI1 = $true)) & (notdallE = $true)) & (notdexE = $true)) & (prop2set2propI = $true)) & (prop2setI = $true)) & (quantDeMorgan4 = $true)) & (quantDeMorgan3 = $true)) & (quantDeMorgan2 = $true)) & (quantDeMorgan1 = $true)) & (vacuousDall = $true)) & (emptyE1 = $true)) & (upairsetIR = $true)) & (upairsetIL = $true)) & (upairsetE = $true)) & (singletonsswitch = $true)) & (eqinunit = $true)) & (notinsingleton = $true)) & (uniqinunit = $true)) & (nonemptyImpWitness = $true)) & (exuE2 = $true)) & (subPowSU = $true)) & (setunionE = $true)) & (setunionI = $true)) & (powersetE = $true)) & (emptyInPowerset = $true)) & (emptyinPowerset = $true)) & (powersetI = $true)) & (setoftrueEq = $true)) & (setadjoinOr = $true)) & (setadjoinE = $true)) & (setadjoinIR = $true)) & (emptyinunitempty = $true)) & (setadjoinIL = $true)) & (nonemptyI1 = $true)) & (nonemptyI = $true)) & (nonemptyE1 = $true)) & (setbeta = $true)) & (noeltsimpempty = $true)) & (emptyI = $true)) & (setext = $true)) & (exuE3e = $true)) & (notinemptyset = $true)) & (emptysetimpfalse = $true)) & (emptysetE = $true)) & (prop2setE = $true)) & (exuE1 = $true)) & (dsetconstrER = $true)) & (dsetconstrEL = $true)) & (dsetconstrI = $true)) & (descrp = $true)) & (wellorderingAx = $true)) & (foundationAx = $true)) & (replAx = $true)) & (omegaIndAx = $true)) & (omegaSAx = $true)) & (omega0Ax = $true)) & (setunionAx = $true)) & (powersetAx = $true)) & (setadjoinAx = $true)) & (emptysetAx = $true)) & (setextAx = $true)), 29.22/4.16 inference(ennf_transformation,[],[f344])). 29.22/4.16 thf(f344,plain,( 29.22/4.16 ~((setextAx = $true) => ((emptysetAx = $true) => ((setadjoinAx = $true) => ((powersetAx = $true) => ((setunionAx = $true) => ((omega0Ax = $true) => ((omegaSAx = $true) => ((omegaIndAx = $true) => ((replAx = $true) => ((foundationAx = $true) => ((wellorderingAx = $true) => ((descrp = $true) => ((dsetconstrI = $true) => ((dsetconstrEL = $true) => ((dsetconstrER = $true) => ((exuE1 = $true) => ((prop2setE = $true) => ((emptysetE = $true) => ((emptysetimpfalse = $true) => ((notinemptyset = $true) => ((exuE3e = $true) => ((setext = $true) => ((emptyI = $true) => ((noeltsimpempty = $true) => ((setbeta = $true) => ((nonemptyE1 = $true) => ((nonemptyI = $true) => ((nonemptyI1 = $true) => ((setadjoinIL = $true) => ((emptyinunitempty = $true) => ((setadjoinIR = $true) => ((setadjoinE = $true) => ((setadjoinOr = $true) => ((setoftrueEq = $true) => ((powersetI = $true) => ((emptyinPowerset = $true) => ((emptyInPowerset = $true) => ((powersetE = $true) => ((setunionI = $true) => ((setunionE = $true) => ((subPowSU = $true) => ((exuE2 = $true) => ((nonemptyImpWitness = $true) => ((uniqinunit = $true) => ((notinsingleton = $true) => ((eqinunit = $true) => ((singletonsswitch = $true) => ((upairsetE = $true) => ((upairsetIL = $true) => ((upairsetIR = $true) => ((emptyE1 = $true) => ((vacuousDall = $true) => ((quantDeMorgan1 = $true) => ((quantDeMorgan2 = $true) => ((quantDeMorgan3 = $true) => ((quantDeMorgan4 = $true) => ((prop2setI = $true) => ((prop2set2propI = $true) => ((notdexE = $true) => ((notdallE = $true) => ((exuI1 = $true) => ((exuI3 = $true) => ((exuI2 = $true) => ((inCongP = $true) => ((in__Cong = $true) => ((exuE3u = $true) => ((exu__Cong = $true) => ((emptyset__Cong = $true) => ((setadjoin__Cong = $true) => ((powerset__Cong = $true) => ((setunion__Cong = $true) => ((omega__Cong = $true) => ((exuEu = $true) => ((descr__Cong = $true) => ((dsetconstr__Cong = $true) => ((subsetI1 = $true) => ((eqimpsubset2 = $true) => ((eqimpsubset1 = $true) => ((subsetI2 = $true) => ((emptysetsubset = $true) => ((subsetE = $true) => ((subsetE2 = $true) => ((notsubsetI = $true) => ((notequalI1 = $true) => ((notequalI2 = $true) => ((subsetRefl = $true) => ((subsetTrans = $true) => ((setadjoinSub = $true) => ((setadjoinSub2 = $true) => ((subset2powerset = $true) => ((setextsub = $true) => ((subsetemptysetimpeq = $true) => ((powersetI1 = $true) => ((powersetE1 = $true) => ((inPowerset = $true) => ((powersetsubset = $true) => ((sepInPowerset = $true) => ((sepSubset = $true) => ((binunionIL = $true) => ((upairset2IR = $true) => ((binunionIR = $true) => ((binunionEcases = $true) => ((binunionE = $true) => ((binunionLsub = $true) => ((binunionRsub = $true) => ((binintersectI = $true) => ((binintersectSubset5 = $true) => ((binintersectEL = $true) => ((binintersectLsub = $true) => ((binintersectSubset2 = $true) => ((binintersectSubset3 = $true) => ((binintersectER = $true) => ((disjointsetsI1 = $true) => ((binintersectRsub = $true) => ((binintersectSubset4 = $true) => ((binintersectSubset1 = $true) => ((bs114d = $true) => ((setminusI = $true) => ((setminusEL = $true) => ((setminusER = $true) => ((setminusSubset2 = $true) => ((setminusERneg = $true) => ((setminusELneg = $true) => ((setminusILneg = $true) => ((setminusIRneg = $true) => ((setminusLsub = $true) => ((setminusSubset1 = $true) => ((symdiffE = $true) => ((symdiffI1 = $true) => ((symdiffI2 = $true) => ((symdiffIneg1 = $true) => ((symdiffIneg2 = $true) => ((secondinupair = $true) => ((setukpairIL = $true) => ((setukpairIR = $true) => ((kpairiskpair = $true) => ((kpairp = $true) => ((singletonsubset = $true) => ((singletoninpowerset = $true) => ((singletoninpowunion = $true) => ((upairset2E = $true) => ((upairsubunion = $true) => ((upairinpowunion = $true) => ((ubforcartprodlem1 = $true) => ((ubforcartprodlem2 = $true) => ((ubforcartprodlem3 = $true) => ((cartprodpairin = $true) => ((cartprodmempair1 = $true) => ((cartprodmempair = $true) => ((setunionE2 = $true) => ((setunionsingleton1 = $true) => ((setunionsingleton2 = $true) => ((setunionsingleton = $true) => ((singletonprop = $true) => ((ex1E1 = $true) => ((ex1I = $true) => ((ex1I2 = $true) => ((singletonsuniq = $true) => ((setukpairinjL1 = $true) => ((kfstsingleton = $true) => ((theprop = $true) => ((kfstpairEq = $true) => ((cartprodfstin = $true) => ((setukpairinjL2 = $true) => ((setukpairinjL = $true) => ((setukpairinjR11 = $true) => ((setukpairinjR12 = $true) => ((setukpairinjR1 = $true) => ((upairequniteq = $true) => ((setukpairinjR2 = $true) => ((setukpairinjR = $true) => ((ksndsingleton = $true) => ((ksndpairEq = $true) => ((kpairsurjEq = $true) => ((cartprodsndin = $true) => ((cartprodpairmemEL = $true) => ((cartprodpairmemER = $true) => ((cartprodmempaircEq = $true) => ((cartprodfstpairEq = $true) => ((cartprodsndpairEq = $true) => ((cartprodpairsurjEq = $true) => ((dpsetconstrI = $true) => ((dpsetconstrSub = $true) => ((setOfPairsIsBReln = $true) => ((dpsetconstrERa = $true) => ((dpsetconstrEL1 = $true) => ((dpsetconstrEL2 = $true) => ((dpsetconstrER = $true) => ((funcImageSingleton = $true) => ((apProp = $true) => ((app = $true) => ((infuncsetfunc = $true) => ((ap2p = $true) => ((funcinfuncset = $true) => ((lamProp = $true) => ((lamp = $true) => ((lam2p = $true) => ((brelnall1 = $true) => ((brelnall2 = $true) => ((ex1E2 = $true) => ((funcGraphProp1 = $true) => ((funcGraphProp3 = $true) => ((funcGraphProp2 = $true) => ((funcextLem = $true) => ((funcGraphProp4 = $true) => ((subbreln = $true) => ((eqbreln = $true) => ((funcext = $true) => ((funcext2 = $true) => ((ap2apEq1 = $true) => ((ap2apEq2 = $true) => ((beta1 = $true) => ((eta1 = $true) => ((lam2lamEq = $true) => ((beta2 = $true) => ((eta2 = $true) => ((iffalseProp1 = $true) => ((iffalseProp2 = $true) => ((iftrueProp1 = $true) => ((iftrueProp2 = $true) => ((ifSingleton = $true) => ((ifp = $true) => ((theeq = $true) => ((iftrue = $true) => ((iffalse = $true) => ((iftrueorfalse = $true) => ((binintersectT_lem = $true) => ((binunionT_lem = $true) => ((powersetT_lem = $true) => ((setminusT_lem = $true) => ((complementT_lem = $true) => ((setextT = $true) => ((subsetTI = $true) => ((powersetTI1 = $true) => ((powersetTE1 = $true) => ((complementTI1 = $true) => ((complementTE1 = $true) => ((binintersectTELcontra = $true) => ((binintersectTERcontra = $true) => ((contrasubsetT = $true) => ((contrasubsetT1 = $true) => ((contrasubsetT2 = $true) => ((contrasubsetT3 = $true) => ((doubleComplementI1 = $true) => ((doubleComplementE1 = $true) => ((doubleComplementSub1 = $true) => ((doubleComplementSub2 = $true) => ((doubleComplementEq = $true) => ((complementTnotintersectT = $true) => ((complementImpComplementIntersect = $true) => ((complementSubsetComplementIntersect = $true) => ((complementInPowersetComplementIntersect = $true) => ((contraSubsetComplement = $true) => ((complementTcontraSubset = $true) => ((binunionTILcontra = $true) => ((binunionTIRcontra = $true) => ((inIntersectImpInUnion = $true) => ((inIntersectImpInUnion2 = $true) => ((inIntersectImpInIntersectUnions = $true) => ((intersectInPowersetIntersectUnions = $true) => ((inComplementUnionImpNotIn1 = $true) => ((inComplementUnionImpInComplement1 = $true) => ((binunionTE = $true) => ((binunionTEcontra = $true) => ((demorgan2a1 = $true) => ((complementUnionInPowersetComplement = $true) => ((demorgan2a2 = $true) => ((demorgan1a = $true) => ((demorgan1b = $true) => ((demorgan1 = $true) => ((demorgan2a = $true) => ((demorgan2b2 = $true) => ((demorgan2b = $true) => ((demorgan2 = $true) => ((woz13rule0 = $true) => ((woz13rule1 = $true) => ((woz13rule2 = $true) => ((woz13rule3 = $true) => ((woz13rule4 = $true) => ((woz1_1 = $true) => ((woz1_2 = $true) => ((woz1_3 = $true) => ((woz1_4 = $true) => ((woz1_5 = $true) => ((breln1all2 = $true) => ((breln1SetBreln1 = $true) => ((choice2fnsingleton = $true) => ((setOfPairsIsBReln1 = $true) => ((breln1all1 = $true) => ((subbreln1 = $true) => ((eqbreln1 = $true) => ((breln1invprop = $true) => ((breln1invI = $true) => ((breln1invE = $true) => ((breln1compprop = $true) => ((breln1compI = $true) => ((breln1compE = $true) => ((breln1compEex = $true) => ((breln1unionprop = $true) => ((breln1unionIL = $true) => ((breln1unionIR = $true) => ((breln1unionI = $true) => ((breln1unionE = $true) => ((breln1unionEcases = $true) => ((breln1unionCommutes = $true) => ((woz2Ex = $true) => ((woz2W = $true) => ((woz2A = $true) => ((woz2B = $true) => ((image1Ex = $true) => ((image1Ex1 = $true) => ((image1Equiv = $true) => ((image1E = $true) => ((image1I = $true) => ((injFuncInInjFuncSet = $true) => ((injFuncSetFuncIn = $true) => ((injFuncSetFuncInj = $true) => ((surjFuncSetFuncIn = $true) => ((surjFuncSetFuncSurj = $true) => ((leftInvIsSurj = $true) => ((surjCantorThm = $true) => ((foundation2 = $true) => ((notinself = $true) => ((notinself2 = $true) => ((omegaSp = $true) => ((omegaSclos = $true) => ((peano0notS = $true) => ((peanoSinj = $true) => ((transitivesetOp1 = $true) => ((binintTransitive = $true) => ((transitivesetOp2 = $true) => ((setunionTransitive = $true) => ((ordinalMinLem1 = $true) => ! [X0] : (($true = (ordinal @ X0)) => ! [X1,X2] : (($true = ((in @ X2) @ X0)) => (($true = ((in @ X1) @ X2)) => ($true = ((in @ X1) @ X0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 29.22/4.16 inference(fool_elimination,[],[f343])). 29.22/4.16 thf(f343,plain,( 29.22/4.16 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (subbreln1 => (eqbreln1 => (breln1invprop => (breln1invI => (breln1invE => (breln1compprop => (breln1compI => (breln1compE => (breln1compEex => (breln1unionprop => (breln1unionIL => (breln1unionIR => (breln1unionI => (breln1unionE => (breln1unionEcases => (breln1unionCommutes => (woz2Ex => (woz2W => (woz2A => (woz2B => (image1Ex => (image1Ex1 => (image1Equiv => (image1E => (image1I => (injFuncInInjFuncSet => (injFuncSetFuncIn => (injFuncSetFuncInj => (surjFuncSetFuncIn => (surjFuncSetFuncSurj => (leftInvIsSurj => (surjCantorThm => (foundation2 => (notinself => (notinself2 => (omegaSp => (omegaSclos => (peano0notS => (peanoSinj => (transitivesetOp1 => (binintTransitive => (transitivesetOp2 => (setunionTransitive => (ordinalMinLem1 => ! [X0] : ((ordinal @ X0) => ! [X1,X2] : (((in @ X2) @ X0) => (((in @ X1) @ X2) => ((in @ X1) @ X0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 29.22/4.16 inference(rectify,[],[f341])). 29.22/4.16 thf(f341,negated_conjecture,( 29.22/4.16 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (subbreln1 => (eqbreln1 => (breln1invprop => (breln1invI => (breln1invE => (breln1compprop => (breln1compI => (breln1compE => (breln1compEex => (breln1unionprop => (breln1unionIL => (breln1unionIR => (breln1unionI => (breln1unionE => (breln1unionEcases => (breln1unionCommutes => (woz2Ex => (woz2W => (woz2A => (woz2B => (image1Ex => (image1Ex1 => (image1Equiv => (image1E => (image1I => (injFuncInInjFuncSet => (injFuncSetFuncIn => (injFuncSetFuncInj => (surjFuncSetFuncIn => (surjFuncSetFuncSurj => (leftInvIsSurj => (surjCantorThm => (foundation2 => (notinself => (notinself2 => (omegaSp => (omegaSclos => (peano0notS => (peanoSinj => (transitivesetOp1 => (binintTransitive => (transitivesetOp2 => (setunionTransitive => (ordinalMinLem1 => ! [X11] : ((ordinal @ X11) => ! [X1,X3] : (((in @ X3) @ X11) => (((in @ X1) @ X3) => ((in @ X1) @ X11)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 29.22/4.16 inference(negated_conjecture,[],[f340])). 29.22/4.16 thf(f340,conjecture,( 29.22/4.16 setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (subbreln1 => (eqbreln1 => (breln1invprop => (breln1invI => (breln1invE => (breln1compprop => (breln1compI => (breln1compE => (breln1compEex => (breln1unionprop => (breln1unionIL => (breln1unionIR => (breln1unionI => (breln1unionE => (breln1unionEcases => (breln1unionCommutes => (woz2Ex => (woz2W => (woz2A => (woz2B => (image1Ex => (image1Ex1 => (image1Equiv => (image1E => (image1I => (injFuncInInjFuncSet => (injFuncSetFuncIn => (injFuncSetFuncInj => (surjFuncSetFuncIn => (surjFuncSetFuncSurj => (leftInvIsSurj => (surjCantorThm => (foundation2 => (notinself => (notinself2 => (omegaSp => (omegaSclos => (peano0notS => (peanoSinj => (transitivesetOp1 => (binintTransitive => (transitivesetOp2 => (setunionTransitive => (ordinalMinLem1 => ! [X11] : ((ordinal @ X11) => ! [X1,X3] : (((in @ X3) @ X11) => (((in @ X1) @ X3) => ((in @ X1) @ X11))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 29.22/4.17 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordinalTransSet)). 29.22/4.17 thf(f13844,plain,( 29.22/4.17 ($true = ((in @ sK1) @ sK0)) | ($false = ((in @ sK2) @ sK0))), 29.22/4.17 inference(trivial_inequality_removal,[],[f13823])). 29.22/4.17 thf(f13823,plain,( 29.22/4.17 ($true = $false) | ($true = ((in @ sK1) @ sK0)) | ($false = ((in @ sK2) @ sK0))), 29.22/4.17 inference(superposition,[],[f11850,f6382])). 29.22/4.17 thf(f6382,plain,( 29.22/4.17 ( ! [X1 : $i] : (($true = ((subset @ X1) @ sK0)) | ($false = ((in @ X1) @ sK0))) )), 29.22/4.17 inference(binary_proxy_clausification,[],[f6381])). 29.22/4.17 thf(f6381,plain,( 29.22/4.17 ( ! [X1 : $i] : (($true = ((vIMP @ ((in @ X1) @ sK0)) @ ((subset @ X1) @ sK0)))) )), 29.22/4.17 inference(combinator_demodulation,[],[f6380])). 29.22/4.17 thf(f6380,plain,( 29.22/4.17 ( ! [X1 : $i] : (($true = (((sCOMB @ ((bCOMB @ vIMP) @ ((cCOMB @ in) @ sK0))) @ ((cCOMB @ subset) @ sK0)) @ X1))) )), 29.22/4.17 inference(pi_clausification,[],[f6379])). 29.22/4.17 thf(f6379,plain,( 29.22/4.17 ($true = (vPI($i) @ ((sCOMB @ ((bCOMB @ vIMP) @ ((cCOMB @ in) @ sK0))) @ ((cCOMB @ subset) @ sK0))))), 29.22/4.17 inference(binary_proxy_clausification,[],[f6377])). 29.22/4.17 thf(f6377,plain,( 29.22/4.17 ($true = ((vAND @ (vPI($i) @ ((sCOMB @ ((bCOMB @ vIMP) @ ((cCOMB @ in) @ sK0))) @ ((cCOMB @ subset) @ sK0)))) @ ((vAND @ (stricttotalorderedByIn @ sK0)) @ (vPI($i) @ ((sCOMB @ ((bCOMB @ vIMP) @ ((cCOMB @ in) @ (powerset @ sK0)))) @ ((sCOMB @ ((bCOMB @ vIMP) @ ((bCOMB @ vNOT) @ (vEQ($i) @ emptyset)))) @ ((bCOMB @ vSIGMA($i)) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vAND)) @ (cCOMB @ in)))) @ ((bCOMB @ (bCOMB @ vPI($i))) @ ((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vIMP)) @ (cCOMB @ in))))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vOR)) @ vEQ($i)))) @ in)))))))))))), 29.22/4.17 inference(combinator_demodulation,[],[f1699])). 29.22/4.17 thf(f1699,plain,( 29.22/4.17 ($true = (((sCOMB @ ((bCOMB @ vAND) @ ((bCOMB @ vPI($i)) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vIMP)) @ (cCOMB @ in)))) @ (cCOMB @ subset))))) @ ((sCOMB @ ((bCOMB @ vAND) @ stricttotalorderedByIn)) @ ((bCOMB @ vPI($i)) @ ((cCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vIMP)) @ ((bCOMB @ (cCOMB @ in)) @ powerset)))) @ ((sCOMB @ ((bCOMB @ vIMP) @ ((bCOMB @ vNOT) @ (vEQ($i) @ emptyset)))) @ ((bCOMB @ vSIGMA($i)) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vAND)) @ (cCOMB @ in)))) @ ((bCOMB @ (bCOMB @ vPI($i))) @ ((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vIMP)) @ (cCOMB @ in))))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vOR)) @ vEQ($i)))) @ in)))))))))) @ sK0))), 29.22/4.17 inference(definition_unfolding,[],[f1355,f1698])). 29.22/4.17 thf(f1698,plain,( 29.22/4.17 (ordinal = ((sCOMB @ ((bCOMB @ vAND) @ ((bCOMB @ vPI($i)) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vIMP)) @ (cCOMB @ in)))) @ (cCOMB @ subset))))) @ ((sCOMB @ ((bCOMB @ vAND) @ stricttotalorderedByIn)) @ ((bCOMB @ vPI($i)) @ ((cCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vIMP)) @ ((bCOMB @ (cCOMB @ in)) @ powerset)))) @ ((sCOMB @ ((bCOMB @ vIMP) @ ((bCOMB @ vNOT) @ (vEQ($i) @ emptyset)))) @ ((bCOMB @ vSIGMA($i)) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vAND)) @ (cCOMB @ in)))) @ ((bCOMB @ (bCOMB @ vPI($i))) @ ((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vIMP)) @ (cCOMB @ in))))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vOR)) @ vEQ($i)))) @ in)))))))))))), 29.22/4.17 inference(definition_unfolding,[],[f1359,f1694,f1697])). 29.22/4.17 thf(f1697,plain,( 29.22/4.17 (wellorderedByIn = ((sCOMB @ ((bCOMB @ vAND) @ stricttotalorderedByIn)) @ ((bCOMB @ vPI($i)) @ ((cCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vIMP)) @ ((bCOMB @ (cCOMB @ in)) @ powerset)))) @ ((sCOMB @ ((bCOMB @ vIMP) @ ((bCOMB @ vNOT) @ (vEQ($i) @ emptyset)))) @ ((bCOMB @ vSIGMA($i)) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vAND)) @ (cCOMB @ in)))) @ ((bCOMB @ (bCOMB @ vPI($i))) @ ((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vIMP)) @ (cCOMB @ in))))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vOR)) @ vEQ($i)))) @ in))))))))))), 29.22/4.17 inference(definition_unfolding,[],[f1693,f1695])). 29.22/4.17 thf(f1695,plain,( 29.22/4.17 (nonempty = ((bCOMB @ vNOT) @ (vEQ($i) @ emptyset)))), 29.22/4.17 inference(cnf_transformation,[],[f1012])). 29.22/4.17 thf(f1012,plain,( 29.22/4.17 (nonempty = ((bCOMB @ vNOT) @ (vEQ($i) @ emptyset)))), 29.22/4.17 inference(fool_elimination,[],[f1011])). 29.22/4.17 thf(f1011,plain,( 29.22/4.17 (nonempty = (^[X0 : $i] : ((emptyset != X0))))), 29.22/4.17 inference(rectify,[],[f27])). 29.22/4.17 thf(f27,axiom,( 29.22/4.17 (nonempty = (^[X1 : $i] : ((emptyset != X1))))), 29.22/4.17 file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonempty)). 29.22/4.17 thf(f1693,plain,( 29.22/4.17 (wellorderedByIn = ((sCOMB @ ((bCOMB @ vAND) @ stricttotalorderedByIn)) @ ((bCOMB @ vPI($i)) @ ((cCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vIMP)) @ ((bCOMB @ (cCOMB @ in)) @ powerset)))) @ ((sCOMB @ ((bCOMB @ vIMP) @ nonempty)) @ ((bCOMB @ vSIGMA($i)) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vAND)) @ (cCOMB @ in)))) @ ((bCOMB @ (bCOMB @ vPI($i))) @ ((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vIMP)) @ (cCOMB @ in))))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vOR)) @ vEQ($i)))) @ in))))))))))), 29.22/4.17 inference(cnf_transformation,[],[f348])). 29.22/4.17 thf(f348,plain,( 29.22/4.17 (wellorderedByIn = ((sCOMB @ ((bCOMB @ vAND) @ stricttotalorderedByIn)) @ ((bCOMB @ vPI($i)) @ ((cCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vIMP)) @ ((bCOMB @ (cCOMB @ in)) @ powerset)))) @ ((sCOMB @ ((bCOMB @ vIMP) @ nonempty)) @ ((bCOMB @ vSIGMA($i)) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vAND)) @ (cCOMB @ in)))) @ ((bCOMB @ (bCOMB @ vPI($i))) @ ((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vIMP)) @ (cCOMB @ in))))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vOR)) @ vEQ($i)))) @ in))))))))))), 29.22/4.17 inference(fool_elimination,[],[f347])). 29.22/4.17 thf(f347,plain,( 29.22/4.17 (wellorderedByIn = (^[X0 : $i] : (! [X1] : (((in @ X1) @ (powerset @ X0)) => ((nonempty @ X1) => ? [X2] : (! [X3] : (((in @ X3) @ X1) => (((in @ X2) @ X3) | (X2 = X3))) & ((in @ X2) @ X1)))) & (stricttotalorderedByIn @ X0))))), 29.22/4.17 inference(rectify,[],[f337])). 29.22/4.17 thf(f337,axiom,( 29.22/4.17 (wellorderedByIn = (^[X3 : $i] : (! [X11] : (((in @ X11) @ (powerset @ X3)) => ((nonempty @ X11) => ? [X1] : (! [X16] : (((in @ X16) @ X11) => (((in @ X1) @ X16) | (X1 = X16))) & ((in @ X1) @ X11)))) & (stricttotalorderedByIn @ X3))))), 29.22/4.17 file('/export/starexec/sandbox/benchmark/theBenchmark.p',wellorderedByIn)). 29.22/4.17 thf(f1694,plain,( 29.22/4.17 (transitiveset = ((bCOMB @ vPI($i)) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vIMP)) @ (cCOMB @ in)))) @ (cCOMB @ subset))))), 29.22/4.17 inference(cnf_transformation,[],[f1014])). 29.22/4.17 thf(f1014,plain,( 29.22/4.17 (transitiveset = ((bCOMB @ vPI($i)) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vIMP)) @ (cCOMB @ in)))) @ (cCOMB @ subset))))), 29.22/4.17 inference(fool_elimination,[],[f1013])). 29.22/4.17 thf(f1013,plain,( 29.22/4.17 (transitiveset = (^[X0 : $i] : (! [X1] : (((in @ X1) @ X0) => ((subset @ X1) @ X0)))))), 29.22/4.17 inference(rectify,[],[f331])). 29.22/4.17 thf(f331,axiom,( 29.22/4.17 (transitiveset = (^[X3 : $i] : (! [X11] : (((in @ X11) @ X3) => ((subset @ X11) @ X3)))))), 29.22/4.17 file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitiveset)). 29.22/4.17 thf(f1359,plain,( 29.22/4.17 (ordinal = ((sCOMB @ ((bCOMB @ vAND) @ transitiveset)) @ wellorderedByIn))), 29.22/4.17 inference(cnf_transformation,[],[f1010])). 29.22/4.17 thf(f1010,plain,( 29.22/4.17 (ordinal = ((sCOMB @ ((bCOMB @ vAND) @ transitiveset)) @ wellorderedByIn))), 29.22/4.17 inference(fool_elimination,[],[f1009])). 29.22/4.17 thf(f1009,plain,( 29.22/4.17 (ordinal = (^[X0 : $i] : ((wellorderedByIn @ X0) & (transitiveset @ X0))))), 29.22/4.17 inference(rectify,[],[f338])). 29.22/4.17 thf(f338,axiom,( 29.22/4.17 (ordinal = (^[X1 : $i] : ((wellorderedByIn @ X1) & (transitiveset @ X1))))), 29.22/4.17 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordinal)). 29.22/4.17 thf(f1355,plain,( 29.22/4.17 ($true = (ordinal @ sK0))), 29.22/4.17 inference(cnf_transformation,[],[f1021])). 29.22/4.17 thf(f11850,plain,( 29.22/4.17 ( ! [X149 : $i] : (($false = ((subset @ sK2) @ X149)) | ($true = ((in @ sK1) @ X149))) )), 29.22/4.17 inference(trivial_inequality_removal,[],[f11449])). 29.22/4.17 thf(f11449,plain,( 29.22/4.17 ( ! [X149 : $i] : (($true = $false) | ($true = ((in @ sK1) @ X149)) | ($false = ((subset @ sK2) @ X149))) )), 29.22/4.17 inference(superposition,[],[f2960,f1357])). 29.22/4.17 thf(f1357,plain,( 29.22/4.17 ($true = ((in @ sK1) @ sK2))), 29.22/4.17 inference(cnf_transformation,[],[f1021])). 29.22/4.17 thf(f2960,plain,( 29.22/4.17 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((in @ X1) @ X3) = $false) | ($true = ((in @ X1) @ X2)) | ($false = ((subset @ X3) @ X2))) )), 29.22/4.17 inference(not_proxy_clausification,[],[f2959])). 29.22/4.17 thf(f2959,plain,( 29.22/4.17 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((in @ X1) @ X3) = $false) | ($true = ((in @ X1) @ X2)) | ($true = (vNOT @ ((subset @ X3) @ X2)))) )), 29.22/4.17 inference(not_proxy_clausification,[],[f2958])). 29.22/4.17 thf(f2958,plain,( 29.22/4.17 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((in @ X1) @ X3) = $false) | ($false = (vNOT @ ((in @ X1) @ X2))) | ($true = (vNOT @ ((subset @ X3) @ X2)))) )), 29.22/4.17 inference(binary_proxy_clausification,[],[f2957])). 29.22/4.17 thf(f2957,plain,( 29.22/4.17 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((in @ X1) @ X3) = $false) | ($true = ((vIMP @ (vNOT @ ((in @ X1) @ X2))) @ (vNOT @ ((subset @ X3) @ X2))))) )), 29.22/4.17 inference(binary_proxy_clausification,[],[f2956])). 29.22/4.17 thf(f2956,plain,( 29.22/4.17 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((vIMP @ ((in @ X1) @ X3)) @ ((vIMP @ (vNOT @ ((in @ X1) @ X2))) @ (vNOT @ ((subset @ X3) @ X2)))))) )), 29.22/4.17 inference(combinator_demodulation,[],[f2955])). 29.22/4.17 thf(f2955,plain,( 29.22/4.17 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((sCOMB @ ((bCOMB @ vIMP) @ (in @ X1))) @ ((bCOMB @ (vIMP @ (vNOT @ ((in @ X1) @ X2)))) @ ((bCOMB @ vNOT) @ ((cCOMB @ subset) @ X2)))) @ X3))) )), 29.22/4.17 inference(pi_clausification,[],[f2954])). 29.22/4.17 thf(f2954,plain,( 29.22/4.17 ( ! [X2 : $i,X1 : $i] : (($true = (vPI($i) @ ((sCOMB @ ((bCOMB @ vIMP) @ (in @ X1))) @ ((bCOMB @ (vIMP @ (vNOT @ ((in @ X1) @ X2)))) @ ((bCOMB @ vNOT) @ ((cCOMB @ subset) @ X2))))))) )), 29.22/4.17 inference(combinator_demodulation,[],[f2953])). 29.22/4.17 thf(f2953,plain,( 29.22/4.17 ( ! [X2 : $i,X1 : $i] : (($true = (((bCOMB @ vPI($i)) @ ((bCOMB @ (sCOMB @ ((bCOMB @ vIMP) @ (in @ X1)))) @ ((sCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ vIMP) @ ((bCOMB @ vNOT) @ (in @ X1))))) @ ((bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ subset))))) @ X2))) )), 29.22/4.17 inference(pi_clausification,[],[f2952])). 29.22/4.17 thf(f2952,plain,( 29.22/4.17 ( ! [X1 : $i] : (($true = (vPI($i) @ ((bCOMB @ vPI($i)) @ ((bCOMB @ (sCOMB @ ((bCOMB @ vIMP) @ (in @ X1)))) @ ((sCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ vIMP) @ ((bCOMB @ vNOT) @ (in @ X1))))) @ ((bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ subset)))))))) )), 29.22/4.17 inference(combinator_demodulation,[],[f2951])). 29.22/4.17 thf(f2951,plain,( 29.22/4.17 ( ! [X1 : $i] : (($true = (((bCOMB @ vPI($i)) @ ((bCOMB @ (bCOMB @ vPI($i))) @ ((sCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vIMP)) @ in)))) @ ((cCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ bCOMB)) @ ((bCOMB @ (bCOMB @ vIMP)) @ ((bCOMB @ (bCOMB @ vNOT)) @ in))))) @ ((bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ subset)))))) @ X1))) )), 29.22/4.17 inference(pi_clausification,[],[f1950])). 29.22/4.17 thf(f1950,plain,( 29.22/4.17 ($true = (vPI($i) @ ((bCOMB @ vPI($i)) @ ((bCOMB @ (bCOMB @ vPI($i))) @ ((sCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vIMP)) @ in)))) @ ((cCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ bCOMB)) @ ((bCOMB @ (bCOMB @ vIMP)) @ ((bCOMB @ (bCOMB @ vNOT)) @ in))))) @ ((bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ subset))))))))), 29.22/4.17 inference(definition_unfolding,[],[f1610,f1104])). 29.22/4.17 thf(f1104,plain,( 29.22/4.17 (notsubsetI = $true)), 29.22/4.17 inference(cnf_transformation,[],[f1021])). 29.22/4.17 thf(f1610,plain,( 29.22/4.17 (notsubsetI = (vPI($i) @ ((bCOMB @ vPI($i)) @ ((bCOMB @ (bCOMB @ vPI($i))) @ ((sCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vIMP)) @ in)))) @ ((cCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ bCOMB)) @ ((bCOMB @ (bCOMB @ vIMP)) @ ((bCOMB @ (bCOMB @ vNOT)) @ in))))) @ ((bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ subset))))))))), 29.22/4.17 inference(cnf_transformation,[],[f818])). 29.22/4.17 thf(f818,plain,( 29.22/4.17 (notsubsetI = (vPI($i) @ ((bCOMB @ vPI($i)) @ ((bCOMB @ (bCOMB @ vPI($i))) @ ((sCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vIMP)) @ in)))) @ ((cCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ bCOMB)) @ ((bCOMB @ (bCOMB @ vIMP)) @ ((bCOMB @ (bCOMB @ vNOT)) @ in))))) @ ((bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ subset))))))))), 29.22/4.17 inference(fool_elimination,[],[f817])). 29.22/4.17 thf(f817,plain,( 29.22/4.17 (notsubsetI = ! [X0,X1,X2] : (((in @ X2) @ X0) => (~((in @ X2) @ X1) => ~((subset @ X0) @ X1))))), 29.22/4.17 inference(rectify,[],[f85])). 29.22/4.17 thf(f85,axiom,( 29.22/4.17 (notsubsetI = ! [X3,X4,X1] : (((in @ X1) @ X3) => (~((in @ X1) @ X4) => ~((subset @ X3) @ X4))))), 29.22/4.17 file('/export/starexec/sandbox/benchmark/theBenchmark.p',notsubsetI)). 29.22/4.17 thf(f1356,plain,( 29.22/4.17 ($true = ((in @ sK2) @ sK0))), 29.22/4.17 inference(cnf_transformation,[],[f1021])). 29.22/4.17 % SZS output end Proof for theBenchmark 29.22/4.17 % (23263)------------------------------ 29.22/4.17 % (23263)Version: Vampire 4.6.0 (commit 0afb7ed4a on 2021-06-23 15:27:21 +0100) 29.22/4.17 % (23263)Termination reason: Refutation 29.22/4.17 29.22/4.17 % (23263)Memory used [KB]: 23666 29.22/4.17 % (23263)Time elapsed: 3.722 s 29.22/4.17 % (23263)------------------------------ 29.22/4.17 % (23263)------------------------------ 29.22/4.17 % (23236)Success in time 3.795 s 29.22/4.18 EOF