0.07/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.13 % Command : run_vampire %s %d 0.13/0.34 % Computer : n021.cluster.edu 0.13/0.34 % Model : x86_64 x86_64 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.34 % Memory : 8042.1875MB 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.34 % CPULimit : 1200 0.13/0.34 % WCLimit : 120 0.13/0.34 % DateTime : Tue Jul 13 14:03:40 EDT 2021 0.13/0.34 % CPUTime : 0.13/0.35 This is a THF_ problem 0.13/0.35 Running vampire --ignore_missing on --mode casc_hol --cores 0 -t 120 /export/starexec/sandbox/benchmark/theBenchmark.p 0.13/0.35 Running in auto input_syntax mode. Trying TPTP 0.19/0.40 % (20543)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 0.19/0.41 % (20551)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 0.19/0.41 % (20539)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 0.19/0.41 % (20538)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 0.19/0.42 % (20537)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 0.19/0.42 % (20558)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 0.19/0.42 % (20540)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 0.19/0.43 % (20550)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 0.19/0.43 % (20536)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 0.19/0.43 % (20541)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 0.19/0.43 % (20559)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 0.19/0.44 % (20542)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 0.19/0.44 % (20560)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 0.19/0.44 % (20565)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 0.19/0.44 % (20564)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 0.19/0.44 % (20555)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 0.19/0.45 % (20554)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 0.19/0.45 % (20557)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 0.19/0.45 % (20552)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 0.19/0.45 % (20563)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 0.19/0.45 % (20556)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 0.19/0.45 % (20546)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 0.19/0.45 % (20544)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 0.19/0.45 % (20562)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 0.19/0.45 % (20561)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 0.19/0.45 % (20547)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 0.19/0.45 % (20549)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 0.19/0.45 % (20545)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 0.19/0.46 % (20548)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 0.19/0.46 % (20553)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 5.03/1.06 % (20542)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs. 6.36/1.18 % (20540)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs. 6.62/1.21 % (20552)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs. 6.62/1.21 % (20545)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs. 6.62/1.21 % (20553)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs. 6.62/1.22 % (20561)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs. 6.62/1.22 % (20549)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs. 6.91/1.27 % (20543)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs. 6.91/1.27 % (20550)Time limit reached! 6.91/1.27 % (20550)------------------------------ 6.91/1.27 % (20550)Version: Vampire 4.6.0 (commit 0afb7ed4a on 2021-06-23 15:27:21 +0100) 6.91/1.27 % (20550)Termination reason: Time limit 6.91/1.27 6.91/1.27 % (20550)Memory used [KB]: 11769 6.91/1.27 % (20550)Time elapsed: 0.869 s 6.91/1.27 % (20550)------------------------------ 6.91/1.27 % (20550)------------------------------ 6.91/1.29 % (20558)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs. 6.91/1.31 % (20538)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs. 6.91/1.32 % (20566)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 7.62/1.34 % (20560)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs. 7.62/1.36 % (20538)Time limit reached! 7.62/1.36 % (20538)------------------------------ 7.62/1.36 % (20538)Version: Vampire 4.6.0 (commit 0afb7ed4a on 2021-06-23 15:27:21 +0100) 7.62/1.36 % (20538)Termination reason: Time limit 7.62/1.36 7.62/1.36 % (20538)Memory used [KB]: 16247 7.62/1.36 % (20538)Time elapsed: 0.964 s 7.62/1.36 % (20538)------------------------------ 7.62/1.36 % (20538)------------------------------ 7.62/1.38 % (20542)Time limit reached! 7.62/1.38 % (20542)------------------------------ 7.62/1.38 % (20542)Version: Vampire 4.6.0 (commit 0afb7ed4a on 2021-06-23 15:27:21 +0100) 7.62/1.38 % (20542)Termination reason: Time limit 7.62/1.38 7.62/1.38 % (20542)Memory used [KB]: 14072 7.62/1.38 % (20542)Time elapsed: 0.968 s 7.62/1.38 % (20542)------------------------------ 7.62/1.38 % (20542)------------------------------ 8.08/1.40 % (20559)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs. 8.08/1.41 % (20567)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 8.08/1.42 % (20569)lrs+1011_8_add=large:csup=on:inj=on:prag=on:cases=on:cnfonf=eager:afp=100000:afq=1.1:er=filter:gsp=input_only:gs=on:gsem=on:lma=on:nm=6:nwc=1:stl=30:sd=2:ss=axioms:st=1.5:sos=on:thsq=on_26 on theBenchmark 9.15/1.59 % (20539)Time limit reached! 9.15/1.59 % (20539)------------------------------ 9.15/1.59 % (20539)Version: Vampire 4.6.0 (commit 0afb7ed4a on 2021-06-23 15:27:21 +0100) 9.15/1.59 % (20539)Termination reason: Time limit 9.15/1.59 9.15/1.59 % (20539)Memory used [KB]: 13432 9.15/1.59 % (20539)Time elapsed: 1.204 s 9.15/1.59 % (20539)------------------------------ 9.15/1.59 % (20539)------------------------------ 9.83/1.64 % (20570)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 10.22/1.70 % (20552)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs. 10.22/1.70 % (20544)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs. 10.22/1.71 % (20555)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs. 10.22/1.71 % (20545)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs. 11.64/1.91 % (20551)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs. 12.75/2.05 % (20547)Time limit reached! 12.75/2.05 % (20547)------------------------------ 12.75/2.05 % (20547)Version: Vampire 4.6.0 (commit 0afb7ed4a on 2021-06-23 15:27:21 +0100) 12.75/2.05 % (20547)Termination reason: Time limit 12.75/2.05 12.75/2.05 % (20547)Memory used [KB]: 29935 12.75/2.05 % (20547)Time elapsed: 1.655 s 12.75/2.05 % (20547)------------------------------ 12.75/2.05 % (20547)------------------------------ 13.37/2.07 % (20548)Time limit reached! 13.37/2.07 % (20548)------------------------------ 13.37/2.07 % (20548)Version: Vampire 4.6.0 (commit 0afb7ed4a on 2021-06-23 15:27:21 +0100) 13.45/2.08 % (20548)Termination reason: Time limit 13.45/2.08 13.45/2.08 % (20548)Memory used [KB]: 8059 13.45/2.08 % (20548)Time elapsed: 1.674 s 13.45/2.08 % (20548)------------------------------ 13.45/2.08 % (20548)------------------------------ 13.45/2.11 % (20545)Time limit reached! 13.45/2.11 % (20545)------------------------------ 13.45/2.11 % (20545)Version: Vampire 4.6.0 (commit 0afb7ed4a on 2021-06-23 15:27:21 +0100) 13.45/2.11 % (20545)Termination reason: Time limit 13.45/2.11 13.45/2.11 % (20545)Memory used [KB]: 12792 13.45/2.11 % (20545)Time elapsed: 1.710 s 13.45/2.11 % (20545)------------------------------ 13.45/2.11 % (20545)------------------------------ 13.45/2.11 % (20571)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 13.80/2.13 % (20572)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 13.96/2.16 % (20573)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 14.54/2.25 % (20569)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs. 14.54/2.28 % (20562)First to succeed. 15.18/2.32 % (20536)Time limit reached! 15.18/2.32 % (20536)------------------------------ 15.18/2.32 % (20536)Version: Vampire 4.6.0 (commit 0afb7ed4a on 2021-06-23 15:27:21 +0100) 15.18/2.33 % (20562)Refutation found. Thanks to Tanya! 15.18/2.33 % SZS status Theorem for theBenchmark 15.18/2.33 % SZS output start Proof for theBenchmark 15.18/2.33 thf(type_def_6, type, >: ($tType * $tType) > $tType). 15.18/2.33 thf(func_def_7, type, c_Eps_i: ($i > $o) > $i). 15.18/2.33 thf(func_def_10, type, c_not: $o > $o). 15.18/2.33 thf(func_def_11, type, c_and: $o > $o > $o). 15.18/2.33 thf(func_def_12, type, c_or: $o > $o > $o). 15.18/2.33 thf(func_def_13, type, c_iff: $o > $o > $o). 15.18/2.33 thf(func_def_14, type, c_In: $i > $i > $o). 15.18/2.33 thf(func_def_15, type, c_Subq: $i > $i > $o). 15.18/2.33 thf(func_def_17, type, c_Union: $i > $i). 15.18/2.33 thf(func_def_18, type, c_Power: $i > $i). 15.18/2.33 thf(func_def_19, type, c_Repl: $i > ($i > $i) > $i). 15.18/2.33 thf(func_def_20, type, c_TransSet: $i > $o). 15.18/2.33 thf(func_def_21, type, c_atleast2: $i > $o). 15.18/2.33 thf(func_def_22, type, c_atleast3: $i > $o). 15.18/2.33 thf(func_def_23, type, c_atleast4: $i > $o). 15.18/2.33 thf(func_def_24, type, c_atleast5: $i > $o). 15.18/2.33 thf(func_def_25, type, c_atleast6: $i > $o). 15.18/2.33 thf(func_def_26, type, c_exactly2: $i > $o). 15.18/2.33 thf(func_def_27, type, c_exactly3: $i > $o). 15.18/2.33 thf(func_def_28, type, c_exactly4: $i > $o). 15.18/2.33 thf(func_def_29, type, c_exactly5: $i > $o). 15.18/2.33 thf(func_def_30, type, c_exu_i: ($i > $o) > $o). 15.18/2.33 thf(func_def_31, type, c_reflexive_i: ($i > $i > $o) > $o). 15.18/2.33 thf(func_def_32, type, c_irreflexive_i: ($i > $i > $o) > $o). 15.18/2.33 thf(func_def_33, type, c_symmetric_i: ($i > $i > $o) > $o). 15.18/2.33 thf(func_def_34, type, c_antisymmetric_i: ($i > $i > $o) > $o). 15.18/2.33 thf(func_def_35, type, c_transitive_i: ($i > $i > $o) > $o). 15.18/2.33 thf(func_def_36, type, c_eqreln_i: ($i > $i > $o) > $o). 15.18/2.33 thf(func_def_37, type, c_per_i: ($i > $i > $o) > $o). 15.18/2.33 thf(func_def_38, type, c_linear_i: ($i > $i > $o) > $o). 15.18/2.33 thf(func_def_39, type, c_trichotomous_or_i: ($i > $i > $o) > $o). 15.18/2.33 thf(func_def_40, type, c_partialorder_i: ($i > $i > $o) > $o). 15.18/2.33 thf(func_def_41, type, c_totalorder_i: ($i > $i > $o) > $o). 15.18/2.33 thf(func_def_42, type, c_strictpartialorder_i: ($i > $i > $o) > $o). 15.18/2.33 thf(func_def_43, type, c_stricttotalorder_i: ($i > $i > $o) > $o). 15.18/2.33 thf(func_def_44, type, c_If_i: $o > $i > $i > $i). 15.18/2.33 thf(func_def_45, type, c_exactly1of2: $o > $o > $o). 15.18/2.33 thf(func_def_46, type, c_exactly1of3: $o > $o > $o > $o). 15.18/2.33 thf(func_def_47, type, c_nIn: $i > $i > $o). 15.18/2.33 thf(func_def_48, type, c_nSubq: $i > $i > $o). 15.18/2.33 thf(func_def_49, type, c_UPair: $i > $i > $i). 15.18/2.33 thf(func_def_50, type, c_Sing: $i > $i). 15.18/2.33 thf(func_def_51, type, c_binunion: $i > $i > $i). 15.18/2.33 thf(func_def_52, type, c_SetAdjoin: $i > $i > $i). 15.18/2.33 thf(func_def_53, type, c_famunion: $i > ($i > $i) > $i). 15.18/2.33 thf(func_def_54, type, c_Sep: $i > ($i > $o) > $i). 15.18/2.33 thf(func_def_55, type, c_ReplSep: $i > ($i > $o) > ($i > $i) > $i). 15.18/2.33 thf(func_def_56, type, c_binintersect: $i > $i > $i). 15.18/2.33 thf(func_def_57, type, c_setminus: $i > $i > $i). 15.18/2.33 thf(func_def_58, type, c_inj: $i > $i > ($i > $i) > $o). 15.18/2.33 thf(func_def_59, type, c_bij: $i > $i > ($i > $i) > $o). 15.18/2.33 thf(func_def_60, type, c_atleastp: $i > $i > $o). 15.18/2.33 thf(func_def_61, type, c_equip: $i > $i > $o). 15.18/2.33 thf(func_def_62, type, c_In_rec_poly_G_i: ($i > ($i > $i) > $i) > $i > $i > $o). 15.18/2.33 thf(func_def_63, type, c_In_rec_poly_i: ($i > ($i > $i) > $i) > $i > $i). 15.18/2.33 thf(func_def_64, type, c_ordsucc: $i > $i). 15.18/2.33 thf(func_def_65, type, c_nat_p: $i > $o). 15.18/2.33 thf(func_def_66, type, c_nat_primrec: $i > ($i > $i > $i) > $i > $i). 15.18/2.33 thf(func_def_67, type, c_add_nat: $i > $i > $i). 15.18/2.33 thf(func_def_68, type, c_mul_nat: $i > $i > $i). 15.18/2.33 thf(func_def_69, type, c_ordinal: $i > $o). 15.18/2.33 thf(func_def_70, type, c_V_: $i > $i). 15.18/2.33 thf(func_def_71, type, c_Inj1: $i > $i). 15.18/2.33 thf(func_def_72, type, c_Inj0: $i > $i). 15.18/2.33 thf(func_def_73, type, c_Unj: $i > $i). 15.18/2.33 thf(func_def_74, type, c_combine_funcs: $i > $i > ($i > $i) > ($i > $i) > $i > $i). 15.18/2.33 thf(func_def_75, type, c_setsum: $i > $i > $i). 15.18/2.33 thf(func_def_76, type, c_proj0: $i > $i). 15.18/2.33 thf(func_def_77, type, c_proj1: $i > $i). 15.18/2.33 thf(func_def_78, type, c_binrep: $i > $i > $i). 15.18/2.33 thf(func_def_79, type, c_lam: $i > ($i > $i) > $i). 15.18/2.33 thf(func_def_80, type, c_setprod: $i > $i > $i). 15.18/2.33 thf(func_def_81, type, c_ap: $i > $i > $i). 15.18/2.33 thf(func_def_82, type, c_setsum_p: $i > $o). 15.18/2.33 thf(func_def_83, type, c_tuple_p: $i > $i > $o). 15.18/2.33 thf(func_def_84, type, c_Pi: $i > ($i > $i) > $i). 15.18/2.33 thf(func_def_85, type, c_setexp: $i > $i > $i). 15.18/2.33 thf(func_def_86, type, c_Sep2: $i > ($i > $i) > ($i > $i > $o) > $i). 15.18/2.33 thf(func_def_87, type, c_set_of_pairs: $i > $o). 15.18/2.33 thf(func_def_88, type, c_lam2: $i > ($i > $i) > ($i > $i > $i) > $i). 15.18/2.33 thf(func_def_89, type, c_PNoEq_: $i > ($i > $o) > ($i > $o) > $o). 15.18/2.33 thf(func_def_90, type, c_PNoLt_: $i > ($i > $o) > ($i > $o) > $o). 15.18/2.33 thf(func_def_91, type, c_PNoLt: $i > ($i > $o) > $i > ($i > $o) > $o). 15.18/2.33 thf(func_def_92, type, c_PNoLe: $i > ($i > $o) > $i > ($i > $o) > $o). 15.18/2.33 thf(func_def_93, type, c_PNo_downc: ($i > ($i > $o) > $o) > $i > ($i > $o) > $o). 15.18/2.33 thf(func_def_94, type, c_PNo_upc: ($i > ($i > $o) > $o) > $i > ($i > $o) > $o). 15.18/2.33 thf(func_def_95, type, c_SNoElts_: $i > $i). 15.18/2.33 thf(func_def_96, type, c_SNo_: $i > $i > $o). 15.18/2.33 thf(func_def_97, type, c_PSNo: $i > ($i > $o) > $i). 15.18/2.33 thf(func_def_98, type, c_SNo: $i > $o). 15.18/2.33 thf(func_def_99, type, c_SNoLev: $i > $i). 15.18/2.33 thf(func_def_100, type, c_SNoEq_: $i > $i > $i > $o). 15.18/2.33 thf(func_def_101, type, c_SNoLt: $i > $i > $o). 15.18/2.33 thf(func_def_102, type, c_SNoLe: $i > $i > $o). 15.18/2.33 thf(func_def_103, type, c_binop_on: $i > ($i > $i > $i) > $o). 15.18/2.33 thf(func_def_104, type, c_Loop: $i > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > $i > $o). 15.18/2.33 thf(func_def_105, type, c_Loop_with_defs: $i > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > $i > ($i > $i > $i) > ($i > $i > $i > $i) > ($i > $i > $i) > ($i > $i > $i > $i) > ($i > $i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > $o). 15.18/2.33 thf(func_def_106, type, c_Loop_with_defs_cex1: $i > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > $i > ($i > $i > $i) > ($i > $i > $i > $i) > ($i > $i > $i) > ($i > $i > $i > $i) > ($i > $i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > $o). 15.18/2.33 thf(func_def_107, type, c_Loop_with_defs_cex2: $i > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > $i > ($i > $i > $i) > ($i > $i > $i > $i) > ($i > $i > $i) > ($i > $i > $i > $i) > ($i > $i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > $o). 15.18/2.33 thf(func_def_108, type, c_combinator: $i > $o). 15.18/2.33 thf(func_def_109, type, c_combinator_equiv: $i > $i > $o). 15.18/2.33 thf(func_def_110, type, c_equip_mod: $i > $i > $i > $o). 15.18/2.33 thf(func_def_112, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)). 15.18/2.33 thf(func_def_115, type, kCOMB: !>[X0: $tType, X1: $tType]:(X0 > X1 > X0)). 15.18/2.33 thf(func_def_116, type, bCOMB: !>[X0: $tType, X1: $tType, X2: $tType]:((X1 > X2) > (X0 > X1) > X0 > X2)). 15.18/2.33 thf(func_def_117, type, cCOMB: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > X1 > X0 > X2)). 15.18/2.33 thf(func_def_118, type, iCOMB: !>[X0: $tType]:(X0 > X0)). 15.18/2.33 thf(func_def_119, type, vEQ: !>[X0: $tType]:(X0 > X0 > $o)). 15.18/2.33 thf(func_def_120, type, sCOMB: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > (X0 > X1) > X0 > X2)). 15.18/2.33 thf(func_def_121, type, vIMP: $o > $o > $o). 15.18/2.33 thf(func_def_122, type, vPI: !>[X0: $tType]:((X0 > $o) > $o)). 15.18/2.33 thf(func_def_123, type, vSIGMA: !>[X0: $tType]:((X0 > $o) > $o)). 15.18/2.33 thf(func_def_124, type, sK0: ($i > $i > $i > $i) > ($i > $i) > (($i > $i > $i) > $i) > $i). 15.18/2.33 thf(func_def_125, type, sK1: ($i > $i) > $i > $i). 15.18/2.33 thf(func_def_126, type, sK2: ((($i > $i > $i > $i) > $i) > $i > $i) > $i > $i). 15.18/2.33 thf(func_def_127, type, sK3: ($i > $i) > ($i > $i) > $i). 15.18/2.33 thf(func_def_128, type, sK4: ($i > $o) > $i). 15.18/2.33 thf(func_def_129, type, sK5: ($i > $o) > $i > $i). 15.18/2.33 thf(func_def_130, type, sK6: ($i > $o) > $i). 15.18/2.33 thf(func_def_131, type, sK7: ($i > $o) > $i). 15.18/2.33 thf(func_def_132, type, sK8: ($i > $o) > $i). 15.18/2.33 thf(func_def_133, type, sK9: ($i > $o) > $i). 15.18/2.33 thf(func_def_134, type, sK10: ($i > $o) > $i). 15.18/2.33 thf(func_def_136, type, vAND: $o > $o > $o). 15.18/2.33 thf(func_def_137, type, vOR: $o > $o > $o). 15.18/2.33 thf(func_def_138, type, vNOT: $o > $o). 15.18/2.33 thf(func_def_143, type, sK13: $i > $i > ($i > $i > $i > $i) > $i). 15.18/2.33 thf(func_def_144, type, sK14: $i > $i > $i). 15.18/2.33 thf(func_def_145, type, sK15: $i > $i). 15.18/2.33 thf(func_def_146, type, sK16: $i > $i > $o). 15.18/2.33 thf(func_def_147, type, sK17: $i > $i > $i). 15.18/2.33 thf(func_def_148, type, sK18: $i > $i > $i). 15.18/2.33 thf(func_def_149, type, sK19: $i > $i > $i > $o). 15.18/2.33 thf(func_def_150, type, sK20: $i > $i > $i). 15.18/2.33 thf(func_def_151, type, sK21: $i > ($i > $i) > $i > $i). 15.18/2.33 thf(func_def_152, type, sK22: $i > $i > $i). 15.18/2.33 thf(func_def_153, type, sK23: $i > $i > $i). 15.18/2.33 thf(func_def_154, type, sK24: $i > $i > $i). 15.18/2.33 thf(func_def_155, type, sK25: $i > $i > $i). 15.18/2.33 thf(func_def_156, type, sK26: $i > $i > $i). 15.18/2.33 thf(func_def_157, type, sK27: $i > $i > $i). 15.18/2.33 thf(func_def_158, type, sK28: $i > $i > $i). 15.18/2.33 thf(func_def_159, type, sK29: $i > $i > $i > $o). 15.18/2.33 thf(func_def_160, type, sK30: $i > $i > $i > $o). 15.18/2.33 thf(func_def_161, type, sK31: $i > $i > $i > $o). 15.18/2.33 thf(func_def_162, type, sK32: $i > $i > $i > $o). 15.18/2.33 thf(func_def_163, type, sK33: $i > $i > ($i > $i) > $i > $o). 15.18/2.33 thf(func_def_164, type, sK34: $i > $i > ($i > $i) > $i > $o). 15.18/2.33 thf(func_def_165, type, sK35: $i > $i > ($i > $i) > $i > $o). 15.18/2.33 thf(func_def_166, type, sK36: $i > ($i > $i) > $i > $i > $o). 15.18/2.33 thf(func_def_167, type, sK37: ($i > $i) > $i > $i > $i). 15.18/2.33 thf(func_def_168, type, sK38: ($i > $i) > $i > $i > $i). 15.18/2.33 thf(func_def_169, type, sK39: $i > ($i > $i) > $i > $i). 15.18/2.33 thf(func_def_173, type, sK43: $o > $o > $o). 15.18/2.33 thf(func_def_174, type, sK44: $o > $o > $o). 15.18/2.33 thf(func_def_175, type, sK45: $i > $i > $i > $o). 15.18/2.33 thf(func_def_176, type, sK46: $i > $i > $i > $o). 15.18/2.33 thf(func_def_177, type, sK47: $i > ($i > $i) > $i > $i > $o). 15.18/2.33 thf(func_def_178, type, sK48: $i > $i > ($i > $i) > $i > $o). 15.18/2.33 thf(func_def_179, type, sK49: $i > $i > $i). 15.18/2.33 thf(func_def_180, type, sK50: $i > $i > $i). 15.18/2.33 thf(func_def_181, type, sK51: $i > $i > $i). 15.18/2.33 thf(func_def_182, type, sK52: $i > $i > $i). 15.18/2.33 thf(func_def_183, type, sK53: $i > $i > $i). 15.18/2.33 thf(func_def_184, type, sK54: $i > $i > $i). 15.18/2.33 thf(func_def_185, type, sK55: $i > $i > $i). 15.18/2.33 thf(func_def_186, type, sK56: $i > $i > $i). 15.18/2.33 thf(func_def_187, type, sK57: $o > $o > $o). 15.18/2.33 thf(func_def_188, type, sK58: $o > $o > $o). 15.18/2.33 thf(func_def_198, type, sK68: ($i > $i) > ($i > $i) > $i). 15.18/2.33 thf(func_def_199, type, sK69: $i > $i > $i). 15.18/2.33 thf(func_def_200, type, sK70: $i > $i > $i). 15.18/2.33 thf(func_def_201, type, sK71: $i > $i > $i > $o). 15.18/2.33 thf(func_def_202, type, sK72: $i > $i > $i). 15.18/2.33 thf(func_def_203, type, sK73: $i > $i > $i). 15.18/2.33 thf(func_def_204, type, sK74: $i > $i > $i > $o). 15.18/2.33 thf(func_def_205, type, sK75: $i > $i > $i). 15.18/2.33 thf(func_def_206, type, sK76: $i > $i > $i). 15.18/2.33 thf(func_def_207, type, sK77: $i > $i > $i > $o). 15.18/2.33 thf(func_def_208, type, sK78: ($i > $i) > $i > $i > $i). 15.18/2.33 thf(func_def_209, type, sK79: $i > $i > ($i > $i) > $i > $o). 15.18/2.33 thf(func_def_210, type, sK80: $i > $i > $i). 15.18/2.33 thf(func_def_211, type, sK81: $i > $i > $i). 15.18/2.33 thf(func_def_212, type, sK82: $i > $i > $i > $o). 15.18/2.33 thf(func_def_213, type, sK83: ($i > $i) > $i > $i > $i). 15.18/2.33 thf(func_def_214, type, sK84: $i > $i > ($i > $i) > $i > $o). 15.18/2.33 thf(f3453,plain,( 15.18/2.33 $false), 15.18/2.33 inference(avatar_sat_refutation,[],[f1658,f1698,f1700,f3452])). 15.18/2.33 thf(f3452,plain,( 15.18/2.33 ~spl11_18), 15.18/2.33 inference(avatar_contradiction_clause,[],[f3451])). 15.18/2.33 thf(f3451,plain,( 15.18/2.33 $false | ~spl11_18), 15.18/2.33 inference(trivial_inequality_removal,[],[f3450])). 15.18/2.33 thf(f3450,plain,( 15.18/2.33 ($true = $false) | ~spl11_18), 15.18/2.33 inference(forward_demodulation,[],[f3449,f2301])). 15.18/2.33 thf(f2301,plain,( 15.18/2.33 ( ! [X0 : $i,X1 : $i] : ((((c_In @ X1) @ X0) = $false)) ) | ~spl11_18), 15.18/2.33 inference(superposition,[],[f1657,f2250])). 15.18/2.33 thf(f2250,plain,( 15.18/2.33 ( ! [X19 : $i,X18 : $i] : ((X18 = X19)) )), 15.18/2.33 inference(combinator_demodulation,[],[f1953])). 15.18/2.33 thf(f1953,plain,( 15.18/2.33 ( ! [X19 : $i,X18 : $i] : (((iCOMB @ X19) = X18)) )), 15.18/2.33 inference(i_narrow,[],[f1933])). 15.18/2.33 thf(f1933,plain,( 15.18/2.33 ( ! [X2 : $i,X0 : $i > $i,X1 : $i] : (((X0 @ X1) = (X0 @ X2))) )), 15.18/2.33 inference(equality_resolution,[],[f530])). 15.18/2.33 thf(f530,plain,( 15.18/2.33 ( ! [X6 : $i > $i,X4 : $i > $i,X7 : $i,X5 : $i] : (((kCOMB @ (X4 @ c_Empty)) != (kCOMB @ (X6 @ c_Empty))) | ((X6 @ X7) = (X4 @ X5))) )), 15.18/2.33 inference(constrained_superposition,[],[f450,f450])). 15.18/2.33 thf(f450,plain,( 15.18/2.33 ( ! [X4 : $i,X5 : $i > $i] : (((X5 @ X4) = (((sK0 @ (kCOMB @ (kCOMB @ ((cCOMB @ ((bCOMB @ sK1) @ ((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ sK2) @ ((bCOMB @ kCOMB) @ kCOMB)))) @ (sK2 @ (kCOMB @ (kCOMB @ (c_Union @ ((c_UPair @ ((c_Repl @ c_Empty) @ ((cCOMB @ c_Repl) @ (c_In_rec_poly_i @ ((bCOMB @ (bCOMB @ ((bCOMB @ c_Union) @ (c_UPair @ (c_Sing @ c_Empty))))) @ c_Repl))))) @ ((c_Repl @ c_Empty) @ (c_In_rec_poly_i @ ((bCOMB @ (bCOMB @ ((bCOMB @ c_Union) @ (c_UPair @ (c_Sing @ c_Empty))))) @ c_Repl))))))))))) @ ((c_In_rec_poly_i @ ((bCOMB @ (bCOMB @ ((bCOMB @ c_Union) @ (c_UPair @ (c_Sing @ c_Empty))))) @ c_Repl)) @ c_Empty))))) @ (kCOMB @ (X5 @ c_Empty))) @ (kCOMB @ c_Empty)))) )), 15.18/2.33 inference(combinator_demodulation,[],[f390])). 15.18/2.33 thf(f390,plain,( 15.18/2.33 ( ! [X4 : $i,X5 : $i > $i] : (((X5 @ X4) = (((sK0 @ (kCOMB @ (kCOMB @ ((cCOMB @ ((bCOMB @ sK1) @ ((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ sK2) @ ((bCOMB @ kCOMB) @ kCOMB)))) @ (sK2 @ (kCOMB @ (kCOMB @ ((((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ ((bCOMB @ (bCOMB @ c_Union)) @ c_UPair)) @ ((cCOMB @ c_Repl) @ ((cCOMB @ c_Repl) @ (c_In_rec_poly_i @ ((bCOMB @ (bCOMB @ (((bCOMB @ (bCOMB @ c_Union)) @ c_UPair) @ (c_Sing @ c_Empty)))) @ c_Repl))))))) @ ((cCOMB @ c_Repl) @ (c_In_rec_poly_i @ ((bCOMB @ (bCOMB @ (((bCOMB @ (bCOMB @ c_Union)) @ c_UPair) @ (c_Sing @ c_Empty)))) @ c_Repl)))) @ c_Empty) @ c_Empty))))))) @ ((c_In_rec_poly_i @ ((bCOMB @ (bCOMB @ (((bCOMB @ (bCOMB @ c_Union)) @ c_UPair) @ (c_Sing @ c_Empty)))) @ c_Repl)) @ c_Empty))))) @ (kCOMB @ (X5 @ c_Empty))) @ (kCOMB @ c_Empty)))) )), 15.18/2.33 inference(definition_unfolding,[],[f320,f384,f382])). 15.18/2.33 thf(f382,plain,( 15.18/2.33 (c_Inj1 = (c_In_rec_poly_i @ ((bCOMB @ (bCOMB @ (((bCOMB @ (bCOMB @ c_Union)) @ c_UPair) @ (c_Sing @ c_Empty)))) @ c_Repl)))), 15.18/2.33 inference(definition_unfolding,[],[f372,f375])). 15.18/2.33 thf(f375,plain,( 15.18/2.33 (c_binunion = ((bCOMB @ (bCOMB @ c_Union)) @ c_UPair))), 15.18/2.33 inference(cnf_transformation,[],[f233])). 15.18/2.33 thf(f233,plain,( 15.18/2.33 (c_binunion = ((bCOMB @ (bCOMB @ c_Union)) @ c_UPair))), 15.18/2.33 inference(fool_elimination,[],[f42])). 15.18/2.33 thf(f42,axiom,( 15.18/2.33 (c_binunion = (^[X0 : $i, X1 : $i] : ((c_Union @ ((c_UPair @ X0) @ X1)))))), 15.18/2.33 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax49)). 15.18/2.33 thf(f372,plain,( 15.18/2.33 (c_Inj1 = (c_In_rec_poly_i @ ((bCOMB @ (bCOMB @ (c_binunion @ (c_Sing @ c_Empty)))) @ c_Repl)))), 15.18/2.33 inference(cnf_transformation,[],[f263])). 15.18/2.33 thf(f263,plain,( 15.18/2.33 (c_Inj1 = (c_In_rec_poly_i @ ((bCOMB @ (bCOMB @ (c_binunion @ (c_Sing @ c_Empty)))) @ c_Repl)))), 15.18/2.33 inference(fool_elimination,[],[f82])). 15.18/2.33 thf(f82,axiom,( 15.18/2.33 (c_Inj1 = (c_In_rec_poly_i @ (^[X0 : $i, X1 : $i > $i] : (((c_binunion @ (c_Sing @ c_Empty)) @ ((c_Repl @ X0) @ (^[X2 : $i] : ((X1 @ X2)))))))))), 15.18/2.33 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax69)). 15.18/2.33 thf(f384,plain,( 15.18/2.33 (c_setsum = ((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ ((bCOMB @ (bCOMB @ c_Union)) @ c_UPair)) @ ((cCOMB @ c_Repl) @ ((cCOMB @ c_Repl) @ (c_In_rec_poly_i @ ((bCOMB @ (bCOMB @ (((bCOMB @ (bCOMB @ c_Union)) @ c_UPair) @ (c_Sing @ c_Empty)))) @ c_Repl))))))) @ ((cCOMB @ c_Repl) @ (c_In_rec_poly_i @ ((bCOMB @ (bCOMB @ (((bCOMB @ (bCOMB @ c_Union)) @ c_UPair) @ (c_Sing @ c_Empty)))) @ c_Repl)))))), 15.18/2.33 inference(definition_unfolding,[],[f370,f375,f383,f382])). 15.18/2.33 thf(f383,plain,( 15.18/2.33 (c_Inj0 = ((cCOMB @ c_Repl) @ (c_In_rec_poly_i @ ((bCOMB @ (bCOMB @ (((bCOMB @ (bCOMB @ c_Union)) @ c_UPair) @ (c_Sing @ c_Empty)))) @ c_Repl))))), 15.18/2.33 inference(definition_unfolding,[],[f371,f382])). 15.18/2.33 thf(f371,plain,( 15.18/2.33 (c_Inj0 = ((cCOMB @ c_Repl) @ c_Inj1))), 15.18/2.33 inference(cnf_transformation,[],[f260])). 15.18/2.33 thf(f260,plain,( 15.18/2.33 (c_Inj0 = ((cCOMB @ c_Repl) @ c_Inj1))), 15.18/2.33 inference(fool_elimination,[],[f62])). 15.18/2.33 thf(f62,axiom,( 15.18/2.33 (c_Inj0 = (^[X0 : $i] : (((c_Repl @ X0) @ (^[X1 : $i] : ((c_Inj1 @ X1)))))))), 15.18/2.33 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax70)). 15.18/2.33 thf(f370,plain,( 15.18/2.33 (c_setsum = ((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ c_binunion) @ ((cCOMB @ c_Repl) @ c_Inj0)))) @ ((cCOMB @ c_Repl) @ c_Inj1)))), 15.18/2.33 inference(cnf_transformation,[],[f262])). 15.18/2.33 thf(f262,plain,( 15.18/2.33 (c_setsum = ((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ c_binunion) @ ((cCOMB @ c_Repl) @ c_Inj0)))) @ ((cCOMB @ c_Repl) @ c_Inj1)))), 15.18/2.33 inference(fool_elimination,[],[f261])). 15.18/2.33 thf(f261,plain,( 15.18/2.33 (c_setsum = (^[X0 : $i, X1 : $i] : (((c_binunion @ ((c_Repl @ X0) @ (^[X2 : $i] : ((c_Inj0 @ X2))))) @ ((c_Repl @ X1) @ (^[X3 : $i] : ((c_Inj1 @ X3))))))))), 15.18/2.33 inference(rectify,[],[f88])). 15.18/2.33 thf(f88,axiom,( 15.18/2.33 (c_setsum = (^[X0 : $i, X1 : $i] : (((c_binunion @ ((c_Repl @ X0) @ (^[X2 : $i] : ((c_Inj0 @ X2))))) @ ((c_Repl @ X1) @ (^[X2 : $i] : ((c_Inj1 @ X2))))))))), 15.18/2.33 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax73)). 15.18/2.33 thf(f320,plain,( 15.18/2.33 ( ! [X4 : $i,X5 : $i > $i] : (((X5 @ X4) = (((sK0 @ (kCOMB @ (kCOMB @ ((cCOMB @ ((bCOMB @ sK1) @ ((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ sK2) @ ((bCOMB @ kCOMB) @ kCOMB)))) @ (sK2 @ (kCOMB @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty))))))) @ (c_Inj1 @ c_Empty))))) @ (kCOMB @ (X5 @ c_Empty))) @ (kCOMB @ c_Empty)))) )), 15.18/2.33 inference(cnf_transformation,[],[f301])). 15.18/2.33 thf(f301,plain,( 15.18/2.33 (c_False != $true) & ! [X4,X5 : $i > $i] : ((X5 @ X4) = (((sK0 @ (kCOMB @ (kCOMB @ ((cCOMB @ ((bCOMB @ sK1) @ ((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ sK2) @ ((bCOMB @ kCOMB) @ kCOMB)))) @ (sK2 @ (kCOMB @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty))))))) @ (c_Inj1 @ c_Empty))))) @ (kCOMB @ (X5 @ c_Empty))) @ (kCOMB @ c_Empty))) & ! [X6,X7] : ((((sK0 @ (kCOMB @ (kCOMB @ (kCOMB @ X7)))) @ (kCOMB @ X6)) @ (kCOMB @ c_Empty)) = X6) & ! [X8,X9 : ($i > $i) > ($i > $i) > $i] : (((sK1 @ ((cCOMB @ ((bCOMB @ X9) @ (cCOMB @ c_setsum))) @ (kCOMB @ c_Empty))) @ c_Empty) = ((X9 @ (kCOMB @ ((c_setsum @ ((sK2 @ (kCOMB @ (kCOMB @ c_Empty))) @ ((sK3 @ (kCOMB @ ((sK2 @ (kCOMB @ (kCOMB @ c_Empty))) @ c_Empty))) @ (kCOMB @ ((sK1 @ (kCOMB @ c_Empty)) @ c_Empty))))) @ ((sK2 @ (kCOMB @ (kCOMB @ c_Empty))) @ ((sK2 @ (kCOMB @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty)))) @ ((sK2 @ (kCOMB @ (kCOMB @ c_Empty))) @ c_Empty)))))) @ (kCOMB @ (c_Inj1 @ ((sK1 @ (kCOMB @ ((X9 @ (kCOMB @ ((sK1 @ (kCOMB @ c_Empty)) @ c_Empty))) @ (kCOMB @ (c_Inj1 @ c_Empty))))) @ X8))))) & ! [X10,X11] : (((sK1 @ (kCOMB @ (c_Inj1 @ ((sK1 @ (kCOMB @ (c_Inj0 @ (((sK0 @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))) @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty))))) @ (c_Inj1 @ X11))))) @ (c_Inj0 @ ((sK2 @ (kCOMB @ iCOMB)) @ X10))) = (c_Inj0 @ ((sK2 @ (kCOMB @ (kCOMB @ X11))) @ ((c_setsum @ c_Empty) @ c_Empty)))) & ! [X12 : $i > ($i > $i > $i) > $i,X13 : $i > $i,X14 : $i > $i] : (((sK2 @ (kCOMB @ (kCOMB @ (X14 @ ((sK2 @ (kCOMB @ (kCOMB @ (((sK0 @ (kCOMB @ (kCOMB @ (kCOMB @ (c_Inj1 @ c_Empty))))) @ (kCOMB @ (c_Inj0 @ c_Empty))) @ (kCOMB @ ((sK3 @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty))))))) @ (c_Inj0 @ (((sK0 @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))) @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty)))))))) @ ((sK3 @ ((cCOMB @ c_setsum) @ c_Empty)) @ (kCOMB @ c_Empty))) = ((c_setsum @ (X14 @ (X13 @ (((sK0 @ (kCOMB @ (kCOMB @ (kCOMB @ (c_Inj1 @ c_Empty))))) @ (kCOMB @ (((sK0 @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))) @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty)))) @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty)))))) @ ((sK1 @ (kCOMB @ (X14 @ c_Empty))) @ (X13 @ ((X12 @ ((sK1 @ (kCOMB @ c_Empty)) @ c_Empty)) @ (kCOMB @ (kCOMB @ c_Empty))))))) & ! [X15] : (((sK2 @ (kCOMB @ (kCOMB @ X15))) @ c_Empty) = X15) & ! [X16,X17] : (((c_setsum @ ((sK2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (((sK0 @ (kCOMB @ (kCOMB @ ((cCOMB @ ((bCOMB @ sK3) @ kCOMB)) @ (kCOMB @ c_Empty))))) @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty)))) @ c_Empty) = ((sK3 @ (kCOMB @ X16)) @ (kCOMB @ X17))) & ((c_Inj1 @ c_Empty) = ((sK3 @ (kCOMB @ (c_Inj1 @ c_Empty))) @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty))))), 15.18/2.33 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f299,f300])). 15.18/2.33 thf(f300,plain,( 15.18/2.33 ? [X0 : ($i > $i > $i > $i) > ($i > $i) > (($i > $i > $i) > $i) > $i,X1 : ($i > $i) > $i > $i,X2 : ((($i > $i > $i > $i) > $i) > $i > $i) > $i > $i,X3 : ($i > $i) > ($i > $i) > $i] : ((c_False != $true) & ! [X4,X5 : $i > $i] : ((X5 @ X4) = (((X0 @ (kCOMB @ (kCOMB @ ((cCOMB @ ((bCOMB @ X1) @ ((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ X2) @ ((bCOMB @ kCOMB) @ kCOMB)))) @ (X2 @ (kCOMB @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty))))))) @ (c_Inj1 @ c_Empty))))) @ (kCOMB @ (X5 @ c_Empty))) @ (kCOMB @ c_Empty))) & ! [X6,X7] : ((((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ X7)))) @ (kCOMB @ X6)) @ (kCOMB @ c_Empty)) = X6) & ! [X8,X9 : ($i > $i) > ($i > $i) > $i] : (((X1 @ ((cCOMB @ ((bCOMB @ X9) @ (cCOMB @ c_setsum))) @ (kCOMB @ c_Empty))) @ c_Empty) = ((X9 @ (kCOMB @ ((c_setsum @ ((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ ((X3 @ (kCOMB @ ((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ c_Empty))) @ (kCOMB @ ((X1 @ (kCOMB @ c_Empty)) @ c_Empty))))) @ ((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ ((X2 @ (kCOMB @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty)))) @ ((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ c_Empty)))))) @ (kCOMB @ (c_Inj1 @ ((X1 @ (kCOMB @ ((X9 @ (kCOMB @ ((X1 @ (kCOMB @ c_Empty)) @ c_Empty))) @ (kCOMB @ (c_Inj1 @ c_Empty))))) @ X8))))) & ! [X10,X11] : (((X1 @ (kCOMB @ (c_Inj1 @ ((X1 @ (kCOMB @ (c_Inj0 @ (((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))) @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty))))) @ (c_Inj1 @ X11))))) @ (c_Inj0 @ ((X2 @ (kCOMB @ iCOMB)) @ X10))) = (c_Inj0 @ ((X2 @ (kCOMB @ (kCOMB @ X11))) @ ((c_setsum @ c_Empty) @ c_Empty)))) & ! [X12 : $i > ($i > $i > $i) > $i,X13 : $i > $i,X14 : $i > $i] : (((X2 @ (kCOMB @ (kCOMB @ (X14 @ ((X2 @ (kCOMB @ (kCOMB @ (((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (c_Inj1 @ c_Empty))))) @ (kCOMB @ (c_Inj0 @ c_Empty))) @ (kCOMB @ ((X3 @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty))))))) @ (c_Inj0 @ (((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))) @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty)))))))) @ ((X3 @ ((cCOMB @ c_setsum) @ c_Empty)) @ (kCOMB @ c_Empty))) = ((c_setsum @ (X14 @ (X13 @ (((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (c_Inj1 @ c_Empty))))) @ (kCOMB @ (((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))) @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty)))) @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty)))))) @ ((X1 @ (kCOMB @ (X14 @ c_Empty))) @ (X13 @ ((X12 @ ((X1 @ (kCOMB @ c_Empty)) @ c_Empty)) @ (kCOMB @ (kCOMB @ c_Empty))))))) & ! [X15] : (((X2 @ (kCOMB @ (kCOMB @ X15))) @ c_Empty) = X15) & ! [X16,X17] : (((c_setsum @ ((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (((X0 @ (kCOMB @ (kCOMB @ ((cCOMB @ ((bCOMB @ X3) @ kCOMB)) @ (kCOMB @ c_Empty))))) @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty)))) @ c_Empty) = ((X3 @ (kCOMB @ X16)) @ (kCOMB @ X17))) & ((c_Inj1 @ c_Empty) = ((X3 @ (kCOMB @ (c_Inj1 @ c_Empty))) @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty))))) => ((c_False != $true) & ! [X5 : $i > $i,X4] : ((X5 @ X4) = (((sK0 @ (kCOMB @ (kCOMB @ ((cCOMB @ ((bCOMB @ sK1) @ ((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ sK2) @ ((bCOMB @ kCOMB) @ kCOMB)))) @ (sK2 @ (kCOMB @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty))))))) @ (c_Inj1 @ c_Empty))))) @ (kCOMB @ (X5 @ c_Empty))) @ (kCOMB @ c_Empty))) & ! [X7,X6] : ((((sK0 @ (kCOMB @ (kCOMB @ (kCOMB @ X7)))) @ (kCOMB @ X6)) @ (kCOMB @ c_Empty)) = X6) & ! [X9 : ($i > $i) > ($i > $i) > $i,X8] : (((sK1 @ ((cCOMB @ ((bCOMB @ X9) @ (cCOMB @ c_setsum))) @ (kCOMB @ c_Empty))) @ c_Empty) = ((X9 @ (kCOMB @ ((c_setsum @ ((sK2 @ (kCOMB @ (kCOMB @ c_Empty))) @ ((sK3 @ (kCOMB @ ((sK2 @ (kCOMB @ (kCOMB @ c_Empty))) @ c_Empty))) @ (kCOMB @ ((sK1 @ (kCOMB @ c_Empty)) @ c_Empty))))) @ ((sK2 @ (kCOMB @ (kCOMB @ c_Empty))) @ ((sK2 @ (kCOMB @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty)))) @ ((sK2 @ (kCOMB @ (kCOMB @ c_Empty))) @ c_Empty)))))) @ (kCOMB @ (c_Inj1 @ ((sK1 @ (kCOMB @ ((X9 @ (kCOMB @ ((sK1 @ (kCOMB @ c_Empty)) @ c_Empty))) @ (kCOMB @ (c_Inj1 @ c_Empty))))) @ X8))))) & ! [X11,X10] : (((sK1 @ (kCOMB @ (c_Inj1 @ ((sK1 @ (kCOMB @ (c_Inj0 @ (((sK0 @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))) @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty))))) @ (c_Inj1 @ X11))))) @ (c_Inj0 @ ((sK2 @ (kCOMB @ iCOMB)) @ X10))) = (c_Inj0 @ ((sK2 @ (kCOMB @ (kCOMB @ X11))) @ ((c_setsum @ c_Empty) @ c_Empty)))) & ! [X14 : $i > $i,X13 : $i > $i,X12 : $i > ($i > $i > $i) > $i] : (((sK2 @ (kCOMB @ (kCOMB @ (X14 @ ((sK2 @ (kCOMB @ (kCOMB @ (((sK0 @ (kCOMB @ (kCOMB @ (kCOMB @ (c_Inj1 @ c_Empty))))) @ (kCOMB @ (c_Inj0 @ c_Empty))) @ (kCOMB @ ((sK3 @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty))))))) @ (c_Inj0 @ (((sK0 @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))) @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty)))))))) @ ((sK3 @ ((cCOMB @ c_setsum) @ c_Empty)) @ (kCOMB @ c_Empty))) = ((c_setsum @ (X14 @ (X13 @ (((sK0 @ (kCOMB @ (kCOMB @ (kCOMB @ (c_Inj1 @ c_Empty))))) @ (kCOMB @ (((sK0 @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))) @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty)))) @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty)))))) @ ((sK1 @ (kCOMB @ (X14 @ c_Empty))) @ (X13 @ ((X12 @ ((sK1 @ (kCOMB @ c_Empty)) @ c_Empty)) @ (kCOMB @ (kCOMB @ c_Empty))))))) & ! [X15] : (((sK2 @ (kCOMB @ (kCOMB @ X15))) @ c_Empty) = X15) & ! [X17,X16] : (((c_setsum @ ((sK2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (((sK0 @ (kCOMB @ (kCOMB @ ((cCOMB @ ((bCOMB @ sK3) @ kCOMB)) @ (kCOMB @ c_Empty))))) @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty)))) @ c_Empty) = ((sK3 @ (kCOMB @ X16)) @ (kCOMB @ X17))) & ((c_Inj1 @ c_Empty) = ((sK3 @ (kCOMB @ (c_Inj1 @ c_Empty))) @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty)))))), 15.18/2.33 introduced(choice_axiom,[])). 15.18/2.33 thf(f299,plain,( 15.18/2.33 ? [X0 : ($i > $i > $i > $i) > ($i > $i) > (($i > $i > $i) > $i) > $i,X1 : ($i > $i) > $i > $i,X2 : ((($i > $i > $i > $i) > $i) > $i > $i) > $i > $i,X3 : ($i > $i) > ($i > $i) > $i] : ((c_False != $true) & ! [X4,X5 : $i > $i] : ((X5 @ X4) = (((X0 @ (kCOMB @ (kCOMB @ ((cCOMB @ ((bCOMB @ X1) @ ((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ X2) @ ((bCOMB @ kCOMB) @ kCOMB)))) @ (X2 @ (kCOMB @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty))))))) @ (c_Inj1 @ c_Empty))))) @ (kCOMB @ (X5 @ c_Empty))) @ (kCOMB @ c_Empty))) & ! [X6,X7] : ((((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ X7)))) @ (kCOMB @ X6)) @ (kCOMB @ c_Empty)) = X6) & ! [X8,X9 : ($i > $i) > ($i > $i) > $i] : (((X1 @ ((cCOMB @ ((bCOMB @ X9) @ (cCOMB @ c_setsum))) @ (kCOMB @ c_Empty))) @ c_Empty) = ((X9 @ (kCOMB @ ((c_setsum @ ((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ ((X3 @ (kCOMB @ ((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ c_Empty))) @ (kCOMB @ ((X1 @ (kCOMB @ c_Empty)) @ c_Empty))))) @ ((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ ((X2 @ (kCOMB @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty)))) @ ((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ c_Empty)))))) @ (kCOMB @ (c_Inj1 @ ((X1 @ (kCOMB @ ((X9 @ (kCOMB @ ((X1 @ (kCOMB @ c_Empty)) @ c_Empty))) @ (kCOMB @ (c_Inj1 @ c_Empty))))) @ X8))))) & ! [X10,X11] : (((X1 @ (kCOMB @ (c_Inj1 @ ((X1 @ (kCOMB @ (c_Inj0 @ (((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))) @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty))))) @ (c_Inj1 @ X11))))) @ (c_Inj0 @ ((X2 @ (kCOMB @ iCOMB)) @ X10))) = (c_Inj0 @ ((X2 @ (kCOMB @ (kCOMB @ X11))) @ ((c_setsum @ c_Empty) @ c_Empty)))) & ! [X12 : $i > ($i > $i > $i) > $i,X13 : $i > $i,X14 : $i > $i] : (((X2 @ (kCOMB @ (kCOMB @ (X14 @ ((X2 @ (kCOMB @ (kCOMB @ (((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (c_Inj1 @ c_Empty))))) @ (kCOMB @ (c_Inj0 @ c_Empty))) @ (kCOMB @ ((X3 @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty))))))) @ (c_Inj0 @ (((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))) @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty)))))))) @ ((X3 @ ((cCOMB @ c_setsum) @ c_Empty)) @ (kCOMB @ c_Empty))) = ((c_setsum @ (X14 @ (X13 @ (((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (c_Inj1 @ c_Empty))))) @ (kCOMB @ (((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))) @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty)))) @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty)))))) @ ((X1 @ (kCOMB @ (X14 @ c_Empty))) @ (X13 @ ((X12 @ ((X1 @ (kCOMB @ c_Empty)) @ c_Empty)) @ (kCOMB @ (kCOMB @ c_Empty))))))) & ! [X15] : (((X2 @ (kCOMB @ (kCOMB @ X15))) @ c_Empty) = X15) & ! [X16,X17] : (((c_setsum @ ((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (((X0 @ (kCOMB @ (kCOMB @ ((cCOMB @ ((bCOMB @ X3) @ kCOMB)) @ (kCOMB @ c_Empty))))) @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty)))) @ c_Empty) = ((X3 @ (kCOMB @ X16)) @ (kCOMB @ X17))) & ((c_Inj1 @ c_Empty) = ((X3 @ (kCOMB @ (c_Inj1 @ c_Empty))) @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty)))))), 15.18/2.33 inference(rectify,[],[f291])). 15.18/2.33 thf(f291,plain,( 15.18/2.33 ? [X0 : ($i > $i > $i > $i) > ($i > $i) > (($i > $i > $i) > $i) > $i,X1 : ($i > $i) > $i > $i,X2 : ((($i > $i > $i > $i) > $i) > $i > $i) > $i > $i,X3 : ($i > $i) > ($i > $i) > $i] : ((c_False != $true) & ! [X16,X17 : $i > $i] : ((X17 @ X16) = (((X0 @ (kCOMB @ (kCOMB @ ((cCOMB @ ((bCOMB @ X1) @ ((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ X2) @ ((bCOMB @ kCOMB) @ kCOMB)))) @ (X2 @ (kCOMB @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty))))))) @ (c_Inj1 @ c_Empty))))) @ (kCOMB @ (X17 @ c_Empty))) @ (kCOMB @ c_Empty))) & ! [X14,X15] : ((((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ X15)))) @ (kCOMB @ X14)) @ (kCOMB @ c_Empty)) = X14) & ! [X12,X13 : ($i > $i) > ($i > $i) > $i] : (((X1 @ ((cCOMB @ ((bCOMB @ X13) @ (cCOMB @ c_setsum))) @ (kCOMB @ c_Empty))) @ c_Empty) = ((X13 @ (kCOMB @ ((c_setsum @ ((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ ((X3 @ (kCOMB @ ((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ c_Empty))) @ (kCOMB @ ((X1 @ (kCOMB @ c_Empty)) @ c_Empty))))) @ ((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ ((X2 @ (kCOMB @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty)))) @ ((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ c_Empty)))))) @ (kCOMB @ (c_Inj1 @ ((X1 @ (kCOMB @ ((X13 @ (kCOMB @ ((X1 @ (kCOMB @ c_Empty)) @ c_Empty))) @ (kCOMB @ (c_Inj1 @ c_Empty))))) @ X12))))) & ! [X10,X11] : (((X1 @ (kCOMB @ (c_Inj1 @ ((X1 @ (kCOMB @ (c_Inj0 @ (((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))) @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty))))) @ (c_Inj1 @ X11))))) @ (c_Inj0 @ ((X2 @ (kCOMB @ iCOMB)) @ X10))) = (c_Inj0 @ ((X2 @ (kCOMB @ (kCOMB @ X11))) @ ((c_setsum @ c_Empty) @ c_Empty)))) & ! [X7 : $i > ($i > $i > $i) > $i,X8 : $i > $i,X9 : $i > $i] : (((X2 @ (kCOMB @ (kCOMB @ (X9 @ ((X2 @ (kCOMB @ (kCOMB @ (((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (c_Inj1 @ c_Empty))))) @ (kCOMB @ (c_Inj0 @ c_Empty))) @ (kCOMB @ ((X3 @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty))))))) @ (c_Inj0 @ (((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))) @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty)))))))) @ ((X3 @ ((cCOMB @ c_setsum) @ c_Empty)) @ (kCOMB @ c_Empty))) = ((c_setsum @ (X9 @ (X8 @ (((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (c_Inj1 @ c_Empty))))) @ (kCOMB @ (((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))) @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty)))) @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty)))))) @ ((X1 @ (kCOMB @ (X9 @ c_Empty))) @ (X8 @ ((X7 @ ((X1 @ (kCOMB @ c_Empty)) @ c_Empty)) @ (kCOMB @ (kCOMB @ c_Empty))))))) & ! [X6] : (((X2 @ (kCOMB @ (kCOMB @ X6))) @ c_Empty) = X6) & ! [X4,X5] : (((c_setsum @ ((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (((X0 @ (kCOMB @ (kCOMB @ ((cCOMB @ ((bCOMB @ X3) @ kCOMB)) @ (kCOMB @ c_Empty))))) @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty)))) @ c_Empty) = ((X3 @ (kCOMB @ X4)) @ (kCOMB @ X5))) & ((c_Inj1 @ c_Empty) = ((X3 @ (kCOMB @ (c_Inj1 @ c_Empty))) @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty)))))), 15.18/2.33 inference(flattening,[],[f290])). 15.18/2.33 thf(f290,plain,( 15.18/2.33 ? [X0 : ($i > $i > $i > $i) > ($i > $i) > (($i > $i > $i) > $i) > $i,X1 : ($i > $i) > $i > $i,X2 : ((($i > $i > $i > $i) > $i) > $i > $i) > $i > $i,X3 : ($i > $i) > ($i > $i) > $i] : (((((((((c_False != $true) & ! [X16,X17 : $i > $i] : ((X17 @ X16) = (((X0 @ (kCOMB @ (kCOMB @ ((cCOMB @ ((bCOMB @ X1) @ ((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ X2) @ ((bCOMB @ kCOMB) @ kCOMB)))) @ (X2 @ (kCOMB @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty))))))) @ (c_Inj1 @ c_Empty))))) @ (kCOMB @ (X17 @ c_Empty))) @ (kCOMB @ c_Empty)))) & ! [X14,X15] : ((((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ X15)))) @ (kCOMB @ X14)) @ (kCOMB @ c_Empty)) = X14)) & ! [X12,X13 : ($i > $i) > ($i > $i) > $i] : (((X1 @ ((cCOMB @ ((bCOMB @ X13) @ (cCOMB @ c_setsum))) @ (kCOMB @ c_Empty))) @ c_Empty) = ((X13 @ (kCOMB @ ((c_setsum @ ((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ ((X3 @ (kCOMB @ ((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ c_Empty))) @ (kCOMB @ ((X1 @ (kCOMB @ c_Empty)) @ c_Empty))))) @ ((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ ((X2 @ (kCOMB @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty)))) @ ((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ c_Empty)))))) @ (kCOMB @ (c_Inj1 @ ((X1 @ (kCOMB @ ((X13 @ (kCOMB @ ((X1 @ (kCOMB @ c_Empty)) @ c_Empty))) @ (kCOMB @ (c_Inj1 @ c_Empty))))) @ X12)))))) & ! [X10,X11] : (((X1 @ (kCOMB @ (c_Inj1 @ ((X1 @ (kCOMB @ (c_Inj0 @ (((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))) @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty))))) @ (c_Inj1 @ X11))))) @ (c_Inj0 @ ((X2 @ (kCOMB @ iCOMB)) @ X10))) = (c_Inj0 @ ((X2 @ (kCOMB @ (kCOMB @ X11))) @ ((c_setsum @ c_Empty) @ c_Empty))))) & ! [X7 : $i > ($i > $i > $i) > $i,X8 : $i > $i,X9 : $i > $i] : (((X2 @ (kCOMB @ (kCOMB @ (X9 @ ((X2 @ (kCOMB @ (kCOMB @ (((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (c_Inj1 @ c_Empty))))) @ (kCOMB @ (c_Inj0 @ c_Empty))) @ (kCOMB @ ((X3 @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty))))))) @ (c_Inj0 @ (((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))) @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty)))))))) @ ((X3 @ ((cCOMB @ c_setsum) @ c_Empty)) @ (kCOMB @ c_Empty))) = ((c_setsum @ (X9 @ (X8 @ (((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (c_Inj1 @ c_Empty))))) @ (kCOMB @ (((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))) @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty)))) @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty)))))) @ ((X1 @ (kCOMB @ (X9 @ c_Empty))) @ (X8 @ ((X7 @ ((X1 @ (kCOMB @ c_Empty)) @ c_Empty)) @ (kCOMB @ (kCOMB @ c_Empty)))))))) & ! [X6] : (((X2 @ (kCOMB @ (kCOMB @ X6))) @ c_Empty) = X6)) & ! [X4,X5] : (((c_setsum @ ((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (((X0 @ (kCOMB @ (kCOMB @ ((cCOMB @ ((bCOMB @ X3) @ kCOMB)) @ (kCOMB @ c_Empty))))) @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty)))) @ c_Empty) = ((X3 @ (kCOMB @ X4)) @ (kCOMB @ X5)))) & ((c_Inj1 @ c_Empty) = ((X3 @ (kCOMB @ (c_Inj1 @ c_Empty))) @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty)))))), 15.18/2.33 inference(ennf_transformation,[],[f288])). 15.18/2.33 thf(f288,plain,( 15.18/2.33 ~! [X0 : ($i > $i > $i > $i) > ($i > $i) > (($i > $i > $i) > $i) > $i,X1 : ($i > $i) > $i > $i,X2 : ((($i > $i > $i > $i) > $i) > $i > $i) > $i > $i,X3 : ($i > $i) > ($i > $i) > $i] : (((c_Inj1 @ c_Empty) = ((X3 @ (kCOMB @ (c_Inj1 @ c_Empty))) @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty)))) => (! [X4,X5] : (((c_setsum @ ((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (((X0 @ (kCOMB @ (kCOMB @ ((cCOMB @ ((bCOMB @ X3) @ kCOMB)) @ (kCOMB @ c_Empty))))) @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty)))) @ c_Empty) = ((X3 @ (kCOMB @ X4)) @ (kCOMB @ X5))) => (! [X6] : (((X2 @ (kCOMB @ (kCOMB @ X6))) @ c_Empty) = X6) => (! [X7 : $i > ($i > $i > $i) > $i,X8 : $i > $i,X9 : $i > $i] : (((X2 @ (kCOMB @ (kCOMB @ (X9 @ ((X2 @ (kCOMB @ (kCOMB @ (((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (c_Inj1 @ c_Empty))))) @ (kCOMB @ (c_Inj0 @ c_Empty))) @ (kCOMB @ ((X3 @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty))))))) @ (c_Inj0 @ (((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))) @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty)))))))) @ ((X3 @ ((cCOMB @ c_setsum) @ c_Empty)) @ (kCOMB @ c_Empty))) = ((c_setsum @ (X9 @ (X8 @ (((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (c_Inj1 @ c_Empty))))) @ (kCOMB @ (((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))) @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty)))) @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty)))))) @ ((X1 @ (kCOMB @ (X9 @ c_Empty))) @ (X8 @ ((X7 @ ((X1 @ (kCOMB @ c_Empty)) @ c_Empty)) @ (kCOMB @ (kCOMB @ c_Empty))))))) => (! [X10,X11] : (((X1 @ (kCOMB @ (c_Inj1 @ ((X1 @ (kCOMB @ (c_Inj0 @ (((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))) @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty))))) @ (c_Inj1 @ X11))))) @ (c_Inj0 @ ((X2 @ (kCOMB @ iCOMB)) @ X10))) = (c_Inj0 @ ((X2 @ (kCOMB @ (kCOMB @ X11))) @ ((c_setsum @ c_Empty) @ c_Empty)))) => (! [X12,X13 : ($i > $i) > ($i > $i) > $i] : (((X1 @ ((cCOMB @ ((bCOMB @ X13) @ (cCOMB @ c_setsum))) @ (kCOMB @ c_Empty))) @ c_Empty) = ((X13 @ (kCOMB @ ((c_setsum @ ((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ ((X3 @ (kCOMB @ ((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ c_Empty))) @ (kCOMB @ ((X1 @ (kCOMB @ c_Empty)) @ c_Empty))))) @ ((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ ((X2 @ (kCOMB @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty)))) @ ((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ c_Empty)))))) @ (kCOMB @ (c_Inj1 @ ((X1 @ (kCOMB @ ((X13 @ (kCOMB @ ((X1 @ (kCOMB @ c_Empty)) @ c_Empty))) @ (kCOMB @ (c_Inj1 @ c_Empty))))) @ X12))))) => (! [X14,X15] : ((((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ X15)))) @ (kCOMB @ X14)) @ (kCOMB @ c_Empty)) = X14) => (! [X16,X17 : $i > $i] : ((X17 @ X16) = (((X0 @ (kCOMB @ (kCOMB @ ((cCOMB @ ((bCOMB @ X1) @ ((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ X2) @ ((bCOMB @ kCOMB) @ kCOMB)))) @ (X2 @ (kCOMB @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty))))))) @ (c_Inj1 @ c_Empty))))) @ (kCOMB @ (X17 @ c_Empty))) @ (kCOMB @ c_Empty))) => (c_False = $true)))))))))), 15.18/2.33 inference(rectify,[],[f113])). 15.18/2.33 thf(f113,plain,( 15.18/2.33 ~! [X0 : ($i > $i > $i > $i) > ($i > $i) > (($i > $i > $i) > $i) > $i,X1 : ($i > $i) > $i > $i,X2 : ((($i > $i > $i > $i) > $i) > $i > $i) > $i > $i,X3 : ($i > $i) > ($i > $i) > $i] : (((c_Inj1 @ c_Empty) = ((X3 @ (kCOMB @ (c_Inj1 @ c_Empty))) @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty)))) => (! [X12,X13] : (((X3 @ (kCOMB @ X12)) @ (kCOMB @ X13)) = ((c_setsum @ ((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (((X0 @ (kCOMB @ (kCOMB @ ((cCOMB @ ((bCOMB @ X3) @ kCOMB)) @ (kCOMB @ c_Empty))))) @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty)))) @ c_Empty)) => (! [X28] : (((X2 @ (kCOMB @ (kCOMB @ X28))) @ c_Empty) = X28) => (! [X31 : $i > ($i > $i > $i) > $i,X32 : $i > $i,X34 : $i > $i] : (((X2 @ (kCOMB @ (kCOMB @ (X34 @ ((X2 @ (kCOMB @ (kCOMB @ (((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (c_Inj1 @ c_Empty))))) @ (kCOMB @ (c_Inj0 @ c_Empty))) @ (kCOMB @ ((X3 @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty))))))) @ (c_Inj0 @ (((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))) @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty)))))))) @ ((X3 @ ((cCOMB @ c_setsum) @ c_Empty)) @ (kCOMB @ c_Empty))) = ((c_setsum @ (X34 @ (X32 @ (((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ (c_Inj1 @ c_Empty))))) @ (kCOMB @ (((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))) @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty)))) @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty)))))) @ ((X1 @ (kCOMB @ (X34 @ c_Empty))) @ (X32 @ ((X31 @ ((X1 @ (kCOMB @ c_Empty)) @ c_Empty)) @ (kCOMB @ (kCOMB @ c_Empty))))))) => (! [X68,X70] : (((X1 @ (kCOMB @ (c_Inj1 @ ((X1 @ (kCOMB @ (c_Inj0 @ (((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ c_Empty)))) @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty))))) @ (c_Inj1 @ X70))))) @ (c_Inj0 @ ((X2 @ (kCOMB @ iCOMB)) @ X68))) = (c_Inj0 @ ((X2 @ (kCOMB @ (kCOMB @ X70))) @ ((c_setsum @ c_Empty) @ c_Empty)))) => (! [X84,X85 : ($i > $i) > ($i > $i) > $i] : (((X1 @ ((cCOMB @ ((bCOMB @ X85) @ (cCOMB @ c_setsum))) @ (kCOMB @ c_Empty))) @ c_Empty) = ((X85 @ (kCOMB @ ((c_setsum @ ((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ ((X3 @ (kCOMB @ ((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ c_Empty))) @ (kCOMB @ ((X1 @ (kCOMB @ c_Empty)) @ c_Empty))))) @ ((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ ((X2 @ (kCOMB @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty)))) @ ((X2 @ (kCOMB @ (kCOMB @ c_Empty))) @ c_Empty)))))) @ (kCOMB @ (c_Inj1 @ ((X1 @ (kCOMB @ ((X85 @ (kCOMB @ ((X1 @ (kCOMB @ c_Empty)) @ c_Empty))) @ (kCOMB @ (c_Inj1 @ c_Empty))))) @ X84))))) => (! [X110,X111] : ((((X0 @ (kCOMB @ (kCOMB @ (kCOMB @ X111)))) @ (kCOMB @ X110)) @ (kCOMB @ c_Empty)) = X110) => (! [X117,X120 : $i > $i] : ((X120 @ X117) = (((X0 @ (kCOMB @ (kCOMB @ ((cCOMB @ ((bCOMB @ X1) @ ((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ X2) @ ((bCOMB @ kCOMB) @ kCOMB)))) @ (X2 @ (kCOMB @ (kCOMB @ ((c_setsum @ c_Empty) @ c_Empty))))))) @ (c_Inj1 @ c_Empty))))) @ (kCOMB @ (X120 @ c_Empty))) @ (kCOMB @ c_Empty))) => (c_False = $true)))))))))), 15.18/2.33 inference(fool_elimination,[],[f112])). 15.18/2.33 thf(f112,plain,( 15.18/2.33 ~! [X0 : ($i > $i > $i > $i) > ($i > $i) > (($i > $i > $i) > $i) > $i,X1 : ($i > $i) > $i > $i,X2 : ((($i > $i > $i > $i) > $i) > $i > $i) > $i > $i,X3 : ($i > $i) > ($i > $i) > $i] : ((((X3 @ (^[X8 : $i] : ((c_Inj1 @ c_Empty)))) @ (^[X9 : $i] : (((c_setsum @ c_Empty) @ c_Empty)))) = (c_Inj1 @ c_Empty)) => (! [X12,X13] : (((X3 @ (^[X14 : $i] : (X12))) @ (^[X15 : $i] : (X13))) = ((c_setsum @ ((X2 @ (^[X16 : ($i > $i > $i > $i) > $i, X17 : $i] : (c_Empty))) @ (((X0 @ (^[X18 : $i, X19 : $i, X20 : $i] : (((X3 @ (^[X21 : $i] : (X20))) @ (^[X22 : $i] : (c_Empty)))))) @ (^[X23 : $i] : (c_Empty))) @ (^[X24 : $i > $i > $i] : (c_Empty))))) @ c_Empty)) => (! [X28] : (((X2 @ (^[X29 : ($i > $i > $i > $i) > $i, X30 : $i] : (X28))) @ c_Empty) = X28) => (! [X31 : $i > ($i > $i > $i) > $i,X32 : $i > $i,X34 : $i > $i] : (((X2 @ (^[X35 : ($i > $i > $i > $i) > $i, X36 : $i] : ((X34 @ ((X2 @ (^[X37 : ($i > $i > $i > $i) > $i, X38 : $i] : ((((X0 @ (^[X39 : $i, X40 : $i, X41 : $i] : ((c_Inj1 @ c_Empty)))) @ (^[X42 : $i] : ((c_Inj0 @ c_Empty)))) @ (^[X43 : $i > $i > $i] : (((X3 @ (^[X44 : $i] : (c_Empty))) @ (^[X45 : $i] : (c_Empty))))))))) @ (c_Inj0 @ (((X0 @ (^[X46 : $i, X47 : $i, X48 : $i] : (c_Empty))) @ (^[X49 : $i] : (c_Empty))) @ (^[X50 : $i > $i > $i] : (c_Empty))))))))) @ ((X3 @ (^[X51 : $i] : (((c_setsum @ X51) @ c_Empty)))) @ (^[X52 : $i] : (c_Empty)))) = ((c_setsum @ (X34 @ (X32 @ (((X0 @ (^[X53 : $i, X54 : $i, X55 : $i] : ((c_Inj1 @ c_Empty)))) @ (^[X56 : $i] : ((((X0 @ (^[X57 : $i, X58 : $i, X59 : $i] : (c_Empty))) @ (^[X60 : $i] : (c_Empty))) @ (^[X61 : $i > $i > $i] : (c_Empty)))))) @ (^[X62 : $i > $i > $i] : (((c_setsum @ c_Empty) @ c_Empty))))))) @ ((X1 @ (^[X63 : $i] : ((X34 @ c_Empty)))) @ (X32 @ ((X31 @ ((X1 @ (^[X64 : $i] : (c_Empty))) @ c_Empty)) @ (^[X65 : $i, X66 : $i] : (c_Empty))))))) => (! [X68,X70] : (((X1 @ (^[X71 : $i] : ((c_Inj1 @ ((X1 @ (^[X72 : $i] : ((c_Inj0 @ (((X0 @ (^[X73 : $i, X74 : $i, X75 : $i] : (c_Empty))) @ (^[X76 : $i] : (c_Empty))) @ (^[X77 : $i > $i > $i] : (c_Empty))))))) @ (c_Inj1 @ X70)))))) @ (c_Inj0 @ ((X2 @ (^[X78 : ($i > $i > $i > $i) > $i, X79 : $i] : (X79))) @ X68))) = (c_Inj0 @ ((X2 @ (^[X80 : ($i > $i > $i > $i) > $i, X81 : $i] : (X70))) @ ((c_setsum @ c_Empty) @ c_Empty)))) => (! [X84,X85 : ($i > $i) > ($i > $i) > $i] : (((X1 @ (^[X86 : $i] : (((X85 @ (^[X87 : $i] : (((c_setsum @ X87) @ X86)))) @ (^[X88 : $i] : (c_Empty)))))) @ c_Empty) = ((X85 @ (^[X89 : $i] : (((c_setsum @ ((X2 @ (^[X90 : ($i > $i > $i > $i) > $i, X91 : $i] : (c_Empty))) @ ((X3 @ (^[X92 : $i] : (((X2 @ (^[X93 : ($i > $i > $i > $i) > $i, X94 : $i] : (c_Empty))) @ c_Empty)))) @ (^[X95 : $i] : (((X1 @ (^[X96 : $i] : (c_Empty))) @ c_Empty)))))) @ ((X2 @ (^[X97 : ($i > $i > $i > $i) > $i, X98 : $i] : (c_Empty))) @ ((X2 @ (^[X99 : ($i > $i > $i > $i) > $i, X100 : $i] : (((c_setsum @ c_Empty) @ c_Empty)))) @ ((X2 @ (^[X101 : ($i > $i > $i > $i) > $i, X102 : $i] : (c_Empty))) @ c_Empty))))))) @ (^[X103 : $i] : ((c_Inj1 @ ((X1 @ (^[X104 : $i] : (((X85 @ (^[X105 : $i] : (((X1 @ (^[X106 : $i] : (c_Empty))) @ c_Empty)))) @ (^[X107 : $i] : ((c_Inj1 @ c_Empty))))))) @ X84)))))) => (! [X110,X111] : ((((X0 @ (^[X112 : $i, X113 : $i, X114 : $i] : (X111))) @ (^[X115 : $i] : (X110))) @ (^[X116 : $i > $i > $i] : (c_Empty))) = X110) => (! [X117,X120 : $i > $i] : ((((X0 @ (^[X121 : $i, X122 : $i, X123 : $i] : (((X1 @ (^[X124 : $i] : (((X2 @ (^[X125 : ($i > $i > $i > $i) > $i, X126 : $i] : (X123))) @ ((X2 @ (^[X127 : ($i > $i > $i > $i) > $i, X128 : $i] : (((c_setsum @ c_Empty) @ c_Empty)))) @ X124))))) @ (c_Inj1 @ c_Empty))))) @ (^[X129 : $i] : ((X120 @ c_Empty)))) @ (^[X130 : $i > $i > $i] : (c_Empty))) = (X120 @ X117)) => c_False))))))))), 15.18/2.33 inference(rectify,[],[f14])). 15.18/2.33 thf(f14,negated_conjecture,( 15.18/2.33 ~! [X0 : ($i > $i > $i > $i) > ($i > $i) > (($i > $i > $i) > $i) > $i,X1 : ($i > $i) > $i > $i,X2 : ((($i > $i > $i > $i) > $i) > $i > $i) > $i > $i,X3 : ($i > $i) > ($i > $i) > $i] : (! [X4 : $i > (($i > $i) > $i) > $i,X5 : ($i > $i) > $i,X6 : (($i > $i > $i) > ($i > $i) > $i) > $i,X7] : (((X3 @ (^[X8 : $i] : ((c_Inj1 @ c_Empty)))) @ (^[X8 : $i] : (((c_setsum @ c_Empty) @ c_Empty)))) = (c_Inj1 @ c_Empty)) => (! [X4,X5,X6,X7] : (((X3 @ (^[X8 : $i] : (X6))) @ (^[X8 : $i] : (X7))) = ((c_setsum @ ((X2 @ (^[X8 : ($i > $i > $i > $i) > $i, X9 : $i] : (c_Empty))) @ (((X0 @ (^[X8 : $i, X9 : $i, X10 : $i] : (((X3 @ (^[X11 : $i] : (X10))) @ (^[X11 : $i] : (c_Empty)))))) @ (^[X8 : $i] : (c_Empty))) @ (^[X8 : $i > $i > $i] : (c_Empty))))) @ c_Empty)) => (! [X4 : $i > $i,X5 : $i > $i > $i,X6 : $i > $i,X7] : (((X2 @ (^[X8 : ($i > $i > $i > $i) > $i, X9 : $i] : (X7))) @ c_Empty) = X7) => (! [X4 : $i > ($i > $i > $i) > $i,X5 : $i > $i,X6 : ((($i > $i) > $i) > $i) > $i,X7 : $i > $i] : (((X2 @ (^[X8 : ($i > $i > $i > $i) > $i, X9 : $i] : ((X7 @ ((X2 @ (^[X10 : ($i > $i > $i > $i) > $i, X11 : $i] : ((((X0 @ (^[X12 : $i, X13 : $i, X14 : $i] : ((c_Inj1 @ c_Empty)))) @ (^[X12 : $i] : ((c_Inj0 @ c_Empty)))) @ (^[X12 : $i > $i > $i] : (((X3 @ (^[X13 : $i] : (c_Empty))) @ (^[X13 : $i] : (c_Empty))))))))) @ (c_Inj0 @ (((X0 @ (^[X10 : $i, X11 : $i, X12 : $i] : (c_Empty))) @ (^[X10 : $i] : (c_Empty))) @ (^[X10 : $i > $i > $i] : (c_Empty))))))))) @ ((X3 @ (^[X8 : $i] : (((c_setsum @ X8) @ c_Empty)))) @ (^[X8 : $i] : (c_Empty)))) = ((c_setsum @ (X7 @ (X5 @ (((X0 @ (^[X8 : $i, X9 : $i, X10 : $i] : ((c_Inj1 @ c_Empty)))) @ (^[X8 : $i] : ((((X0 @ (^[X9 : $i, X10 : $i, X11 : $i] : (c_Empty))) @ (^[X9 : $i] : (c_Empty))) @ (^[X9 : $i > $i > $i] : (c_Empty)))))) @ (^[X8 : $i > $i > $i] : (((c_setsum @ c_Empty) @ c_Empty))))))) @ ((X1 @ (^[X8 : $i] : ((X7 @ c_Empty)))) @ (X5 @ ((X4 @ ((X1 @ (^[X8 : $i] : (c_Empty))) @ c_Empty)) @ (^[X8 : $i, X9 : $i] : (c_Empty))))))) => (! [X4 : (($i > $i) > $i > $i) > $i,X5,X6,X7] : (((X1 @ (^[X8 : $i] : ((c_Inj1 @ ((X1 @ (^[X9 : $i] : ((c_Inj0 @ (((X0 @ (^[X10 : $i, X11 : $i, X12 : $i] : (c_Empty))) @ (^[X10 : $i] : (c_Empty))) @ (^[X10 : $i > $i > $i] : (c_Empty))))))) @ (c_Inj1 @ X7)))))) @ (c_Inj0 @ ((X2 @ (^[X8 : ($i > $i > $i > $i) > $i, X9 : $i] : (X9))) @ X5))) = (c_Inj0 @ ((X2 @ (^[X8 : ($i > $i > $i > $i) > $i, X9 : $i] : (X7))) @ ((c_setsum @ c_Empty) @ c_Empty)))) => (! [X4 : (($i > $i) > $i) > $i,X5 : $i > $i > ($i > $i) > $i,X6,X7 : ($i > $i) > ($i > $i) > $i] : (((X1 @ (^[X8 : $i] : (((X7 @ (^[X9 : $i] : (((c_setsum @ X9) @ X8)))) @ (^[X9 : $i] : (c_Empty)))))) @ c_Empty) = ((X7 @ (^[X8 : $i] : (((c_setsum @ ((X2 @ (^[X9 : ($i > $i > $i > $i) > $i, X10 : $i] : (c_Empty))) @ ((X3 @ (^[X9 : $i] : (((X2 @ (^[X10 : ($i > $i > $i > $i) > $i, X11 : $i] : (c_Empty))) @ c_Empty)))) @ (^[X9 : $i] : (((X1 @ (^[X10 : $i] : (c_Empty))) @ c_Empty)))))) @ ((X2 @ (^[X9 : ($i > $i > $i > $i) > $i, X10 : $i] : (c_Empty))) @ ((X2 @ (^[X9 : ($i > $i > $i > $i) > $i, X10 : $i] : (((c_setsum @ c_Empty) @ c_Empty)))) @ ((X2 @ (^[X9 : ($i > $i > $i > $i) > $i, X10 : $i] : (c_Empty))) @ c_Empty))))))) @ (^[X8 : $i] : ((c_Inj1 @ ((X1 @ (^[X9 : $i] : (((X7 @ (^[X10 : $i] : (((X1 @ (^[X11 : $i] : (c_Empty))) @ c_Empty)))) @ (^[X10 : $i] : ((c_Inj1 @ c_Empty))))))) @ X6)))))) => (! [X4 : $i > (($i > $i) > $i > $i) > $i,X5,X6,X7] : ((((X0 @ (^[X8 : $i, X9 : $i, X10 : $i] : (X7))) @ (^[X8 : $i] : (X6))) @ (^[X8 : $i > $i > $i] : (c_Empty))) = X6) => (! [X4,X5,X6 : $i > ($i > $i) > $i,X7 : $i > $i] : ((((X0 @ (^[X8 : $i, X9 : $i, X10 : $i] : (((X1 @ (^[X11 : $i] : (((X2 @ (^[X12 : ($i > $i > $i > $i) > $i, X13 : $i] : (X10))) @ ((X2 @ (^[X12 : ($i > $i > $i > $i) > $i, X13 : $i] : (((c_setsum @ c_Empty) @ c_Empty)))) @ X11))))) @ (c_Inj1 @ c_Empty))))) @ (^[X8 : $i] : ((X7 @ c_Empty)))) @ (^[X8 : $i > $i > $i] : (c_Empty))) = (X7 @ X4)) => c_False))))))))), 15.18/2.33 inference(negated_conjecture,[],[f13])). 15.18/2.33 thf(f13,conjecture,( 15.18/2.33 ! [X0 : ($i > $i > $i > $i) > ($i > $i) > (($i > $i > $i) > $i) > $i,X1 : ($i > $i) > $i > $i,X2 : ((($i > $i > $i > $i) > $i) > $i > $i) > $i > $i,X3 : ($i > $i) > ($i > $i) > $i] : (! [X4 : $i > (($i > $i) > $i) > $i,X5 : ($i > $i) > $i,X6 : (($i > $i > $i) > ($i > $i) > $i) > $i,X7] : (((X3 @ (^[X8 : $i] : ((c_Inj1 @ c_Empty)))) @ (^[X8 : $i] : (((c_setsum @ c_Empty) @ c_Empty)))) = (c_Inj1 @ c_Empty)) => (! [X4,X5,X6,X7] : (((X3 @ (^[X8 : $i] : (X6))) @ (^[X8 : $i] : (X7))) = ((c_setsum @ ((X2 @ (^[X8 : ($i > $i > $i > $i) > $i, X9 : $i] : (c_Empty))) @ (((X0 @ (^[X8 : $i, X9 : $i, X10 : $i] : (((X3 @ (^[X11 : $i] : (X10))) @ (^[X11 : $i] : (c_Empty)))))) @ (^[X8 : $i] : (c_Empty))) @ (^[X8 : $i > $i > $i] : (c_Empty))))) @ c_Empty)) => (! [X4 : $i > $i,X5 : $i > $i > $i,X6 : $i > $i,X7] : (((X2 @ (^[X8 : ($i > $i > $i > $i) > $i, X9 : $i] : (X7))) @ c_Empty) = X7) => (! [X4 : $i > ($i > $i > $i) > $i,X5 : $i > $i,X6 : ((($i > $i) > $i) > $i) > $i,X7 : $i > $i] : (((X2 @ (^[X8 : ($i > $i > $i > $i) > $i, X9 : $i] : ((X7 @ ((X2 @ (^[X10 : ($i > $i > $i > $i) > $i, X11 : $i] : ((((X0 @ (^[X12 : $i, X13 : $i, X14 : $i] : ((c_Inj1 @ c_Empty)))) @ (^[X12 : $i] : ((c_Inj0 @ c_Empty)))) @ (^[X12 : $i > $i > $i] : (((X3 @ (^[X13 : $i] : (c_Empty))) @ (^[X13 : $i] : (c_Empty))))))))) @ (c_Inj0 @ (((X0 @ (^[X10 : $i, X11 : $i, X12 : $i] : (c_Empty))) @ (^[X10 : $i] : (c_Empty))) @ (^[X10 : $i > $i > $i] : (c_Empty))))))))) @ ((X3 @ (^[X8 : $i] : (((c_setsum @ X8) @ c_Empty)))) @ (^[X8 : $i] : (c_Empty)))) = ((c_setsum @ (X7 @ (X5 @ (((X0 @ (^[X8 : $i, X9 : $i, X10 : $i] : ((c_Inj1 @ c_Empty)))) @ (^[X8 : $i] : ((((X0 @ (^[X9 : $i, X10 : $i, X11 : $i] : (c_Empty))) @ (^[X9 : $i] : (c_Empty))) @ (^[X9 : $i > $i > $i] : (c_Empty)))))) @ (^[X8 : $i > $i > $i] : (((c_setsum @ c_Empty) @ c_Empty))))))) @ ((X1 @ (^[X8 : $i] : ((X7 @ c_Empty)))) @ (X5 @ ((X4 @ ((X1 @ (^[X8 : $i] : (c_Empty))) @ c_Empty)) @ (^[X8 : $i, X9 : $i] : (c_Empty))))))) => (! [X4 : (($i > $i) > $i > $i) > $i,X5,X6,X7] : (((X1 @ (^[X8 : $i] : ((c_Inj1 @ ((X1 @ (^[X9 : $i] : ((c_Inj0 @ (((X0 @ (^[X10 : $i, X11 : $i, X12 : $i] : (c_Empty))) @ (^[X10 : $i] : (c_Empty))) @ (^[X10 : $i > $i > $i] : (c_Empty))))))) @ (c_Inj1 @ X7)))))) @ (c_Inj0 @ ((X2 @ (^[X8 : ($i > $i > $i > $i) > $i, X9 : $i] : (X9))) @ X5))) = (c_Inj0 @ ((X2 @ (^[X8 : ($i > $i > $i > $i) > $i, X9 : $i] : (X7))) @ ((c_setsum @ c_Empty) @ c_Empty)))) => (! [X4 : (($i > $i) > $i) > $i,X5 : $i > $i > ($i > $i) > $i,X6,X7 : ($i > $i) > ($i > $i) > $i] : (((X1 @ (^[X8 : $i] : (((X7 @ (^[X9 : $i] : (((c_setsum @ X9) @ X8)))) @ (^[X9 : $i] : (c_Empty)))))) @ c_Empty) = ((X7 @ (^[X8 : $i] : (((c_setsum @ ((X2 @ (^[X9 : ($i > $i > $i > $i) > $i, X10 : $i] : (c_Empty))) @ ((X3 @ (^[X9 : $i] : (((X2 @ (^[X10 : ($i > $i > $i > $i) > $i, X11 : $i] : (c_Empty))) @ c_Empty)))) @ (^[X9 : $i] : (((X1 @ (^[X10 : $i] : (c_Empty))) @ c_Empty)))))) @ ((X2 @ (^[X9 : ($i > $i > $i > $i) > $i, X10 : $i] : (c_Empty))) @ ((X2 @ (^[X9 : ($i > $i > $i > $i) > $i, X10 : $i] : (((c_setsum @ c_Empty) @ c_Empty)))) @ ((X2 @ (^[X9 : ($i > $i > $i > $i) > $i, X10 : $i] : (c_Empty))) @ c_Empty))))))) @ (^[X8 : $i] : ((c_Inj1 @ ((X1 @ (^[X9 : $i] : (((X7 @ (^[X10 : $i] : (((X1 @ (^[X11 : $i] : (c_Empty))) @ c_Empty)))) @ (^[X10 : $i] : ((c_Inj1 @ c_Empty))))))) @ X6)))))) => (! [X4 : $i > (($i > $i) > $i > $i) > $i,X5,X6,X7] : ((((X0 @ (^[X8 : $i, X9 : $i, X10 : $i] : (X7))) @ (^[X8 : $i] : (X6))) @ (^[X8 : $i > $i > $i] : (c_Empty))) = X6) => (! [X4,X5,X6 : $i > ($i > $i) > $i,X7 : $i > $i] : ((((X0 @ (^[X8 : $i, X9 : $i, X10 : $i] : (((X1 @ (^[X11 : $i] : (((X2 @ (^[X12 : ($i > $i > $i > $i) > $i, X13 : $i] : (X10))) @ ((X2 @ (^[X12 : ($i > $i > $i > $i) > $i, X13 : $i] : (((c_setsum @ c_Empty) @ c_Empty)))) @ X11))))) @ (c_Inj1 @ c_Empty))))) @ (^[X8 : $i] : ((X7 @ c_Empty)))) @ (^[X8 : $i > $i > $i] : (c_Empty))) = (X7 @ X4)) => c_False))))))))), 15.18/2.33 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj)). 15.18/2.33 thf(f1657,plain,( 15.18/2.33 ( ! [X2 : $i] : (($false = ((c_In @ X2) @ c_Empty))) ) | ~spl11_18), 15.18/2.33 inference(avatar_component_clause,[],[f1656])). 15.18/2.33 thf(f1656,plain,( 15.18/2.33 spl11_18 <=> ! [X2] : ($false = ((c_In @ X2) @ c_Empty))), 15.18/2.33 introduced(avatar_definition,[new_symbols(naming,[spl11_18])])). 15.18/2.33 thf(f3449,plain,( 15.18/2.33 ( ! [X2 : $i,X0 : $i] : ((((c_In @ X0) @ X2) = $true)) ) | ~spl11_18), 15.18/2.33 inference(trivial_inequality_removal,[],[f3448])). 15.18/2.33 thf(f3448,plain,( 15.18/2.33 ( ! [X2 : $i,X0 : $i] : (($true = $false) | (((c_In @ X0) @ X2) = $true)) ) | ~spl11_18), 15.18/2.33 inference(forward_demodulation,[],[f2976,f2301])). 15.18/2.33 thf(f2976,plain,( 15.18/2.33 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((c_In @ ((sK75 @ X1) @ X0)) @ X0)) | (((c_In @ X0) @ X2) = $true)) )), 15.18/2.33 inference(binary_proxy_clausification,[],[f2974])). 15.18/2.33 thf(f2974,plain,( 15.18/2.33 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($false = ((vIMP @ ((c_In @ ((sK75 @ X1) @ X0)) @ X0)) @ ((c_In @ ((sK75 @ X1) @ X0)) @ X1))) | (((c_In @ X0) @ X2) = $true)) )), 15.18/2.33 inference(combinator_demodulation,[],[f2973])). 15.18/2.33 thf(f2973,plain,( 15.18/2.33 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($false = (((sCOMB @ ((bCOMB @ vIMP) @ ((cCOMB @ c_In) @ X0))) @ ((cCOMB @ c_In) @ X1)) @ ((sK75 @ X1) @ X0))) | (((c_In @ X0) @ X2) = $true)) )), 15.18/2.33 inference(sigma_clausification,[],[f2972])). 15.18/2.33 thf(f2972,plain,( 15.18/2.33 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($false = (vPI($i) @ ((sCOMB @ ((bCOMB @ vIMP) @ ((cCOMB @ c_In) @ X0))) @ ((cCOMB @ c_In) @ X1)))) | (((c_In @ X0) @ X2) = $true)) )), 15.18/2.33 inference(binary_proxy_clausification,[],[f2971])). 15.18/2.33 thf(f2971,plain,( 15.18/2.33 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((vIMP @ (vPI($i) @ ((sCOMB @ ((bCOMB @ vIMP) @ ((cCOMB @ c_In) @ X0))) @ ((cCOMB @ c_In) @ X1)))) @ ((c_In @ X0) @ X2)))) )), 15.18/2.33 inference(condensation,[],[f2970])). 15.18/2.33 thf(f2970,plain,( 15.18/2.33 ( ! [X2 : $i,X0 : $i,X3 : $o,X1 : $i] : (($true = ((vIMP @ (vPI($i) @ ((sCOMB @ ((bCOMB @ vIMP) @ ((cCOMB @ c_In) @ X2))) @ ((cCOMB @ c_In) @ X0)))) @ ((c_In @ X2) @ X1))) | ($true = X3)) )), 15.18/2.33 inference(binary_proxy_clausification,[],[f2962])). 15.18/2.33 thf(f2962,plain,( 15.18/2.33 ( ! [X2 : $i,X0 : $i,X3 : $o,X1 : $i] : (($false = ((vIMP @ ((vIMP @ (vPI($i) @ ((sCOMB @ ((bCOMB @ vIMP) @ ((cCOMB @ c_In) @ X2))) @ ((cCOMB @ c_In) @ X0)))) @ ((c_In @ X2) @ X1))) @ X3)) | ($true = X3)) )), 15.18/2.33 inference(binary_proxy_clausification,[],[f2961])). 15.18/2.33 thf(f2961,plain,( 15.18/2.33 ( ! [X2 : $i,X0 : $i,X3 : $o,X1 : $i] : (($false = ((vIMP @ ((vIMP @ ((c_In @ X2) @ X1)) @ (vPI($i) @ ((sCOMB @ ((bCOMB @ vIMP) @ ((cCOMB @ c_In) @ X2))) @ ((cCOMB @ c_In) @ X0))))) @ ((vIMP @ ((vIMP @ (vPI($i) @ ((sCOMB @ ((bCOMB @ vIMP) @ ((cCOMB @ c_In) @ X2))) @ ((cCOMB @ c_In) @ X0)))) @ ((c_In @ X2) @ X1))) @ X3))) | ($true = X3)) )), 15.18/2.33 inference(binary_proxy_clausification,[],[f2960])). 15.18/2.33 thf(f2960,plain,( 15.18/2.33 ( ! [X2 : $i,X0 : $i,X3 : $o,X1 : $i] : (($true = ((vIMP @ ((vIMP @ ((vIMP @ ((c_In @ X2) @ X1)) @ (vPI($i) @ ((sCOMB @ ((bCOMB @ vIMP) @ ((cCOMB @ c_In) @ X2))) @ ((cCOMB @ c_In) @ X0))))) @ ((vIMP @ ((vIMP @ (vPI($i) @ ((sCOMB @ ((bCOMB @ vIMP) @ ((cCOMB @ c_In) @ X2))) @ ((cCOMB @ c_In) @ X0)))) @ ((c_In @ X2) @ X1))) @ X3))) @ X3))) )), 15.18/2.33 inference(combinator_demodulation,[],[f2959])). 15.18/2.33 thf(f2959,plain,( 15.18/2.33 ( ! [X2 : $i,X0 : $i,X3 : $o,X1 : $i] : (($true = (((sCOMB @ ((bCOMB @ vIMP) @ ((bCOMB @ (vIMP @ ((vIMP @ ((c_In @ X2) @ X1)) @ (vPI($i) @ ((sCOMB @ ((bCOMB @ vIMP) @ ((cCOMB @ c_In) @ X2))) @ ((cCOMB @ c_In) @ X0)))))) @ (vIMP @ ((vIMP @ (vPI($i) @ ((sCOMB @ ((bCOMB @ vIMP) @ ((cCOMB @ c_In) @ X2))) @ ((cCOMB @ c_In) @ X0)))) @ ((c_In @ X2) @ X1)))))) @ iCOMB) @ X3))) )), 15.18/2.33 inference(pi_clausification,[],[f2825])). 15.18/2.33 thf(f2825,plain,( 15.18/2.33 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (vPI($o) @ ((sCOMB @ ((bCOMB @ vIMP) @ ((bCOMB @ (vIMP @ ((vIMP @ ((c_In @ X2) @ X1)) @ (vPI($i) @ ((sCOMB @ ((bCOMB @ vIMP) @ ((cCOMB @ c_In) @ X2))) @ ((cCOMB @ c_In) @ X0)))))) @ (vIMP @ ((vIMP @ (vPI($i) @ ((sCOMB @ ((bCOMB @ vIMP) @ ((cCOMB @ c_In) @ X2))) @ ((cCOMB @ c_In) @ X0)))) @ ((c_In @ X2) @ X1)))))) @ iCOMB)))) )), 15.18/2.33 inference(superposition,[],[f406,f2250])). 15.18/2.33 thf(f406,plain,( 15.18/2.33 ( ! [X0 : $i,X1 : $i] : (($true = (vPI($o) @ ((sCOMB @ ((bCOMB @ vIMP) @ ((bCOMB @ (vIMP @ ((vIMP @ ((c_In @ X1) @ (c_Power @ X0))) @ (vPI($i) @ ((sCOMB @ ((bCOMB @ vIMP) @ ((cCOMB @ c_In) @ X1))) @ ((cCOMB @ c_In) @ X0)))))) @ (vIMP @ ((vIMP @ (vPI($i) @ ((sCOMB @ ((bCOMB @ vIMP) @ ((cCOMB @ c_In) @ X1))) @ ((cCOMB @ c_In) @ X0)))) @ ((c_In @ X1) @ (c_Power @ X0))))))) @ iCOMB)))) )), 15.18/2.33 inference(combinator_demodulation,[],[f399])). 15.18/2.33 thf(f399,plain,( 15.18/2.33 ( ! [X0 : $i,X1 : $i] : (($true = ((((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ ((bCOMB @ (bCOMB @ vPI($o))) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vIMP))) @ ((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ bCOMB) @ vIMP))) @ vIMP))))) @ iCOMB)))) @ vIMP))) @ (cCOMB @ vIMP)) @ ((c_In @ X1) @ (c_Power @ X0))) @ ((((bCOMB @ (bCOMB @ vPI($i))) @ ((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vIMP)) @ (cCOMB @ c_In))))) @ (cCOMB @ c_In))) @ X1) @ X0)))) )), 15.18/2.33 inference(definition_unfolding,[],[f325,f385,f378])). 15.18/2.33 thf(f378,plain,( 15.18/2.33 (c_Subq = ((bCOMB @ (bCOMB @ vPI($i))) @ ((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vIMP)) @ (cCOMB @ c_In))))) @ (cCOMB @ c_In))))), 15.18/2.33 inference(cnf_transformation,[],[f239])). 15.18/2.33 thf(f239,plain,( 15.18/2.33 (c_Subq = ((bCOMB @ (bCOMB @ vPI($i))) @ ((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vIMP)) @ (cCOMB @ c_In))))) @ (cCOMB @ c_In))))), 15.18/2.33 inference(fool_elimination,[],[f238])). 15.18/2.33 thf(f238,plain,( 15.18/2.33 (c_Subq = (^[X0 : $i, X1 : $i] : (! [X2] : (((c_In @ X2) @ X0) => ((c_In @ X2) @ X1)))))), 15.18/2.33 inference(rectify,[],[f33])). 15.18/2.33 thf(f33,axiom,( 15.18/2.33 (c_Subq = (^[X0 : $i, X1 : $i] : (! [X2] : (((c_In @ X2) @ X0) => ((c_In @ X2) @ X1)))))), 15.18/2.33 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax17)). 15.18/2.33 thf(f385,plain,( 15.18/2.33 (c_iff = ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ ((bCOMB @ (bCOMB @ vPI($o))) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vIMP))) @ ((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ bCOMB) @ vIMP))) @ vIMP))))) @ iCOMB)))) @ vIMP))) @ (cCOMB @ vIMP)))), 15.18/2.33 inference(definition_unfolding,[],[f374,f369])). 15.18/2.33 thf(f369,plain,( 15.18/2.33 (c_and = ((bCOMB @ (bCOMB @ vPI($o))) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vIMP))) @ ((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ bCOMB) @ vIMP))) @ vIMP))))) @ iCOMB)))), 15.18/2.33 inference(cnf_transformation,[],[f267])). 15.18/2.33 thf(f267,plain,( 15.18/2.33 (c_and = ((bCOMB @ (bCOMB @ vPI($o))) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vIMP))) @ ((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ bCOMB) @ vIMP))) @ vIMP))))) @ iCOMB)))), 15.18/2.33 inference(fool_elimination,[],[f266])). 15.18/2.33 thf(f266,plain,( 15.18/2.33 (c_and = (^[X0 : $o, X1 : $o] : (! [X2 : $o] : ((X0 => (X1 => X2)) => X2))))), 15.18/2.33 inference(rectify,[],[f66])). 15.18/2.33 thf(f66,axiom,( 15.18/2.33 (c_and = (^[X0 : $o, X1 : $o] : (! [X2 : $o] : ((X0 => (X1 => X2)) => X2))))), 15.18/2.33 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax14)). 15.18/2.33 thf(f374,plain,( 15.18/2.33 (c_iff = ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ c_and)) @ vIMP))) @ (cCOMB @ vIMP)))), 15.18/2.33 inference(cnf_transformation,[],[f226])). 15.18/2.33 thf(f226,plain,( 15.18/2.33 (c_iff = ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ c_and)) @ vIMP))) @ (cCOMB @ vIMP)))), 15.18/2.33 inference(fool_elimination,[],[f225])). 15.18/2.33 thf(f225,plain,( 15.18/2.33 (c_iff = (^[X0 : $o, X1 : $o] : (((c_and @ X0 => X1) @ X1 => X0))))), 15.18/2.33 inference(rectify,[],[f6])). 15.18/2.33 thf(f6,axiom,( 15.18/2.33 (c_iff = (^[X0 : $o, X1 : $o] : (((c_and @ X0 => X1) @ X1 => X0))))), 15.18/2.33 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax16)). 15.18/2.33 thf(f325,plain,( 15.18/2.33 ( ! [X0 : $i,X1 : $i] : ((((c_iff @ ((c_In @ X1) @ (c_Power @ X0))) @ ((c_Subq @ X1) @ X0)) = $true)) )), 15.18/2.33 inference(cnf_transformation,[],[f281])). 15.18/2.33 thf(f281,plain,( 15.18/2.33 ! [X0,X1] : (((c_iff @ ((c_In @ X1) @ (c_Power @ X0))) @ ((c_Subq @ X1) @ X0)) = $true)), 15.18/2.33 inference(fool_elimination,[],[f280])). 15.18/2.33 thf(f280,plain,( 15.18/2.33 ! [X0,X1] : ((c_iff @ ((c_In @ X1) @ (c_Power @ X0))) @ ((c_Subq @ X1) @ X0))), 15.18/2.33 inference(rectify,[],[f73])). 15.18/2.33 thf(f73,axiom,( 15.18/2.33 ! [X0,X1] : ((c_iff @ ((c_In @ X1) @ (c_Power @ X0))) @ ((c_Subq @ X1) @ X0))), 15.18/2.33 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax7)). 15.18/2.33 thf(f1700,plain,( 15.18/2.33 ~spl11_12 | spl11_23), 15.18/2.33 inference(avatar_contradiction_clause,[],[f1699])). 15.18/2.33 thf(f1699,plain,( 15.18/2.33 $false | (~spl11_12 | spl11_23)), 15.18/2.33 inference(subsumption_resolution,[],[f1680,f1629])). 15.18/2.33 thf(f1629,plain,( 15.18/2.33 ( ! [X0 : $o] : (($true = X0)) ) | ~spl11_12), 15.18/2.33 inference(avatar_component_clause,[],[f1628])). 15.18/2.33 thf(f1628,plain,( 15.18/2.33 spl11_12 <=> ! [X0 : $o] : ($true = X0)), 15.18/2.33 introduced(avatar_definition,[new_symbols(naming,[spl11_12])])). 15.18/2.33 thf(f1680,plain,( 15.18/2.33 ($true != $false) | spl11_23), 15.18/2.33 inference(avatar_component_clause,[],[f1678])). 15.18/2.33 thf(f1678,plain,( 15.18/2.33 spl11_23 <=> ($true = $false)), 15.18/2.33 introduced(avatar_definition,[new_symbols(naming,[spl11_23])])). 15.18/2.33 thf(f1698,plain,( 15.18/2.33 ~spl11_23), 15.18/2.33 inference(avatar_contradiction_clause,[],[f1697])). 15.18/2.33 thf(f1697,plain,( 15.18/2.33 $false | ~spl11_23), 15.18/2.33 inference(trivial_inequality_removal,[],[f1679])). 15.18/2.33 thf(f1679,plain,( 15.18/2.33 ($true = $false) | ~spl11_23), 15.18/2.33 inference(avatar_component_clause,[],[f1678])). 15.18/2.33 thf(f1658,plain,( 15.18/2.33 spl11_18 | spl11_12), 15.18/2.33 inference(avatar_split_clause,[],[f1431,f1628,f1656])). 15.18/2.33 thf(f1431,plain,( 15.18/2.33 ( ! [X2 : $i,X1 : $o] : (($true = X1) | ($false = ((c_In @ X2) @ c_Empty))) )), 15.18/2.33 inference(combinator_demodulation,[],[f1430])). 15.18/2.33 thf(f1430,plain,( 15.18/2.33 ( ! [X2 : $i,X1 : $o] : (($true = X1) | ($false = (((cCOMB @ c_In) @ c_Empty) @ X2))) )), 15.18/2.33 inference(pi_clausification,[],[f1429])). 15.18/2.33 thf(f1429,plain,( 15.18/2.33 ( ! [X1 : $o] : (($true = X1) | ($false = (vSIGMA($i) @ ((cCOMB @ c_In) @ c_Empty)))) )), 15.18/2.33 inference(combinator_demodulation,[],[f1428])). 15.18/2.33 thf(f1428,plain,( 15.18/2.33 ( ! [X1 : $o] : (($true = (iCOMB @ X1)) | ($false = (vSIGMA($i) @ ((cCOMB @ c_In) @ c_Empty)))) )), 15.18/2.33 inference(pi_clausification,[],[f1427])). 15.18/2.33 thf(f1427,plain,( 15.18/2.33 ($true = (vPI($o) @ iCOMB)) | ($false = (vSIGMA($i) @ ((cCOMB @ c_In) @ c_Empty)))), 15.18/2.33 inference(boolean_simplification,[],[f736])). 15.18/2.33 thf(f736,plain,( 15.18/2.33 ($true = ((vIMP @ $true) @ (vPI($o) @ iCOMB))) | ($false = (vSIGMA($i) @ ((cCOMB @ c_In) @ c_Empty)))), 15.18/2.33 inference(superposition,[],[f403,f487])). 15.18/2.33 thf(f487,plain,( 15.18/2.33 ( ! [X3 : $o] : (($true = X3) | ($false = X3)) )), 15.18/2.33 inference(binary_proxy_clausification,[],[f472])). 15.18/2.33 thf(f472,plain,( 15.18/2.33 ( ! [X2 : $i,X0 : $i,X3 : $o,X1 : $i] : (($false = ((vIMP @ ((vIMP @ (vSIGMA($i) @ ((sCOMB @ ((bCOMB @ ((bCOMB @ (bCOMB @ vPI($o))) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vIMP))) @ ((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ bCOMB) @ vIMP))) @ vIMP))))) @ iCOMB))) @ (c_In @ X2))) @ ((cCOMB @ c_In) @ ((c_UPair @ ((c_Repl @ ((sK2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (((sK0 @ (kCOMB @ (kCOMB @ ((cCOMB @ ((bCOMB @ sK3) @ kCOMB)) @ (kCOMB @ c_Empty))))) @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty)))) @ ((cCOMB @ c_Repl) @ (c_In_rec_poly_i @ ((bCOMB @ (bCOMB @ ((bCOMB @ c_Union) @ (c_UPair @ (c_Sing @ c_Empty))))) @ c_Repl))))) @ ((c_Repl @ c_Empty) @ (c_In_rec_poly_i @ ((bCOMB @ (bCOMB @ ((bCOMB @ c_Union) @ (c_UPair @ (c_Sing @ c_Empty))))) @ c_Repl)))))))) @ ((c_In @ X2) @ ((sK3 @ (kCOMB @ X0)) @ (kCOMB @ X1))))) @ X3)) | ($true = X3)) )), 15.18/2.33 inference(binary_proxy_clausification,[],[f471])). 15.18/2.33 thf(f471,plain,( 15.18/2.33 ( ! [X2 : $i,X0 : $i,X3 : $o,X1 : $i] : (($false = ((vIMP @ ((vIMP @ ((c_In @ X2) @ ((sK3 @ (kCOMB @ X0)) @ (kCOMB @ X1)))) @ (vSIGMA($i) @ ((sCOMB @ ((bCOMB @ ((bCOMB @ (bCOMB @ vPI($o))) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vIMP))) @ ((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ bCOMB) @ vIMP))) @ vIMP))))) @ iCOMB))) @ (c_In @ X2))) @ ((cCOMB @ c_In) @ ((c_UPair @ ((c_Repl @ ((sK2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (((sK0 @ (kCOMB @ (kCOMB @ ((cCOMB @ ((bCOMB @ sK3) @ kCOMB)) @ (kCOMB @ c_Empty))))) @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty)))) @ ((cCOMB @ c_Repl) @ (c_In_rec_poly_i @ ((bCOMB @ (bCOMB @ ((bCOMB @ c_Union) @ (c_UPair @ (c_Sing @ c_Empty))))) @ c_Repl))))) @ ((c_Repl @ c_Empty) @ (c_In_rec_poly_i @ ((bCOMB @ (bCOMB @ ((bCOMB @ c_Union) @ (c_UPair @ (c_Sing @ c_Empty))))) @ c_Repl))))))))) @ ((vIMP @ ((vIMP @ (vSIGMA($i) @ ((sCOMB @ ((bCOMB @ ((bCOMB @ (bCOMB @ vPI($o))) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vIMP))) @ ((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ bCOMB) @ vIMP))) @ vIMP))))) @ iCOMB))) @ (c_In @ X2))) @ ((cCOMB @ c_In) @ ((c_UPair @ ((c_Repl @ ((sK2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (((sK0 @ (kCOMB @ (kCOMB @ ((cCOMB @ ((bCOMB @ sK3) @ kCOMB)) @ (kCOMB @ c_Empty))))) @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty)))) @ ((cCOMB @ c_Repl) @ (c_In_rec_poly_i @ ((bCOMB @ (bCOMB @ ((bCOMB @ c_Union) @ (c_UPair @ (c_Sing @ c_Empty))))) @ c_Repl))))) @ ((c_Repl @ c_Empty) @ (c_In_rec_poly_i @ ((bCOMB @ (bCOMB @ ((bCOMB @ c_Union) @ (c_UPair @ (c_Sing @ c_Empty))))) @ c_Repl)))))))) @ ((c_In @ X2) @ ((sK3 @ (kCOMB @ X0)) @ (kCOMB @ X1))))) @ X3))) | ($true = X3)) )), 15.18/2.33 inference(binary_proxy_clausification,[],[f470])). 15.18/2.33 thf(f470,plain,( 15.18/2.33 ( ! [X2 : $i,X0 : $i,X3 : $o,X1 : $i] : (($true = ((vIMP @ ((vIMP @ ((vIMP @ ((c_In @ X2) @ ((sK3 @ (kCOMB @ X0)) @ (kCOMB @ X1)))) @ (vSIGMA($i) @ ((sCOMB @ ((bCOMB @ ((bCOMB @ (bCOMB @ vPI($o))) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vIMP))) @ ((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ bCOMB) @ vIMP))) @ vIMP))))) @ iCOMB))) @ (c_In @ X2))) @ ((cCOMB @ c_In) @ ((c_UPair @ ((c_Repl @ ((sK2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (((sK0 @ (kCOMB @ (kCOMB @ ((cCOMB @ ((bCOMB @ sK3) @ kCOMB)) @ (kCOMB @ c_Empty))))) @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty)))) @ ((cCOMB @ c_Repl) @ (c_In_rec_poly_i @ ((bCOMB @ (bCOMB @ ((bCOMB @ c_Union) @ (c_UPair @ (c_Sing @ c_Empty))))) @ c_Repl))))) @ ((c_Repl @ c_Empty) @ (c_In_rec_poly_i @ ((bCOMB @ (bCOMB @ ((bCOMB @ c_Union) @ (c_UPair @ (c_Sing @ c_Empty))))) @ c_Repl))))))))) @ ((vIMP @ ((vIMP @ (vSIGMA($i) @ ((sCOMB @ ((bCOMB @ ((bCOMB @ (bCOMB @ vPI($o))) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vIMP))) @ ((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ bCOMB) @ vIMP))) @ vIMP))))) @ iCOMB))) @ (c_In @ X2))) @ ((cCOMB @ c_In) @ ((c_UPair @ ((c_Repl @ ((sK2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (((sK0 @ (kCOMB @ (kCOMB @ ((cCOMB @ ((bCOMB @ sK3) @ kCOMB)) @ (kCOMB @ c_Empty))))) @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty)))) @ ((cCOMB @ c_Repl) @ (c_In_rec_poly_i @ ((bCOMB @ (bCOMB @ ((bCOMB @ c_Union) @ (c_UPair @ (c_Sing @ c_Empty))))) @ c_Repl))))) @ ((c_Repl @ c_Empty) @ (c_In_rec_poly_i @ ((bCOMB @ (bCOMB @ ((bCOMB @ c_Union) @ (c_UPair @ (c_Sing @ c_Empty))))) @ c_Repl)))))))) @ ((c_In @ X2) @ ((sK3 @ (kCOMB @ X0)) @ (kCOMB @ X1))))) @ X3))) @ X3))) )), 15.18/2.33 inference(combinator_demodulation,[],[f469])). 15.18/2.33 thf(f469,plain,( 15.18/2.33 ( ! [X2 : $i,X0 : $i,X3 : $o,X1 : $i] : (($true = (((sCOMB @ ((bCOMB @ vIMP) @ ((bCOMB @ (vIMP @ ((vIMP @ ((c_In @ X2) @ ((sK3 @ (kCOMB @ X0)) @ (kCOMB @ X1)))) @ (vSIGMA($i) @ ((sCOMB @ ((bCOMB @ ((bCOMB @ (bCOMB @ vPI($o))) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vIMP))) @ ((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ bCOMB) @ vIMP))) @ vIMP))))) @ iCOMB))) @ (c_In @ X2))) @ ((cCOMB @ c_In) @ ((c_UPair @ ((c_Repl @ ((sK2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (((sK0 @ (kCOMB @ (kCOMB @ ((cCOMB @ ((bCOMB @ sK3) @ kCOMB)) @ (kCOMB @ c_Empty))))) @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty)))) @ ((cCOMB @ c_Repl) @ (c_In_rec_poly_i @ ((bCOMB @ (bCOMB @ ((bCOMB @ c_Union) @ (c_UPair @ (c_Sing @ c_Empty))))) @ c_Repl))))) @ ((c_Repl @ c_Empty) @ (c_In_rec_poly_i @ ((bCOMB @ (bCOMB @ ((bCOMB @ c_Union) @ (c_UPair @ (c_Sing @ c_Empty))))) @ c_Repl)))))))))) @ (vIMP @ ((vIMP @ (vSIGMA($i) @ ((sCOMB @ ((bCOMB @ ((bCOMB @ (bCOMB @ vPI($o))) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vIMP))) @ ((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ bCOMB) @ vIMP))) @ vIMP))))) @ iCOMB))) @ (c_In @ X2))) @ ((cCOMB @ c_In) @ ((c_UPair @ ((c_Repl @ ((sK2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (((sK0 @ (kCOMB @ (kCOMB @ ((cCOMB @ ((bCOMB @ sK3) @ kCOMB)) @ (kCOMB @ c_Empty))))) @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty)))) @ ((cCOMB @ c_Repl) @ (c_In_rec_poly_i @ ((bCOMB @ (bCOMB @ ((bCOMB @ c_Union) @ (c_UPair @ (c_Sing @ c_Empty))))) @ c_Repl))))) @ ((c_Repl @ c_Empty) @ (c_In_rec_poly_i @ ((bCOMB @ (bCOMB @ ((bCOMB @ c_Union) @ (c_UPair @ (c_Sing @ c_Empty))))) @ c_Repl)))))))) @ ((c_In @ X2) @ ((sK3 @ (kCOMB @ X0)) @ (kCOMB @ X1)))))))) @ iCOMB) @ X3))) )), 15.18/2.33 inference(pi_clausification,[],[f468])). 15.18/2.33 thf(f468,plain,( 15.18/2.33 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (vPI($o) @ ((sCOMB @ ((bCOMB @ vIMP) @ ((bCOMB @ (vIMP @ ((vIMP @ ((c_In @ X2) @ ((sK3 @ (kCOMB @ X0)) @ (kCOMB @ X1)))) @ (vSIGMA($i) @ ((sCOMB @ ((bCOMB @ ((bCOMB @ (bCOMB @ vPI($o))) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vIMP))) @ ((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ bCOMB) @ vIMP))) @ vIMP))))) @ iCOMB))) @ (c_In @ X2))) @ ((cCOMB @ c_In) @ ((c_UPair @ ((c_Repl @ ((sK2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (((sK0 @ (kCOMB @ (kCOMB @ ((cCOMB @ ((bCOMB @ sK3) @ kCOMB)) @ (kCOMB @ c_Empty))))) @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty)))) @ ((cCOMB @ c_Repl) @ (c_In_rec_poly_i @ ((bCOMB @ (bCOMB @ ((bCOMB @ c_Union) @ (c_UPair @ (c_Sing @ c_Empty))))) @ c_Repl))))) @ ((c_Repl @ c_Empty) @ (c_In_rec_poly_i @ ((bCOMB @ (bCOMB @ ((bCOMB @ c_Union) @ (c_UPair @ (c_Sing @ c_Empty))))) @ c_Repl)))))))))) @ (vIMP @ ((vIMP @ (vSIGMA($i) @ ((sCOMB @ ((bCOMB @ ((bCOMB @ (bCOMB @ vPI($o))) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vIMP))) @ ((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ bCOMB) @ vIMP))) @ vIMP))))) @ iCOMB))) @ (c_In @ X2))) @ ((cCOMB @ c_In) @ ((c_UPair @ ((c_Repl @ ((sK2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (((sK0 @ (kCOMB @ (kCOMB @ ((cCOMB @ ((bCOMB @ sK3) @ kCOMB)) @ (kCOMB @ c_Empty))))) @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty)))) @ ((cCOMB @ c_Repl) @ (c_In_rec_poly_i @ ((bCOMB @ (bCOMB @ ((bCOMB @ c_Union) @ (c_UPair @ (c_Sing @ c_Empty))))) @ c_Repl))))) @ ((c_Repl @ c_Empty) @ (c_In_rec_poly_i @ ((bCOMB @ (bCOMB @ ((bCOMB @ c_Union) @ (c_UPair @ (c_Sing @ c_Empty))))) @ c_Repl)))))))) @ ((c_In @ X2) @ ((sK3 @ (kCOMB @ X0)) @ (kCOMB @ X1)))))))) @ iCOMB)))) )), 15.18/2.33 inference(superposition,[],[f405,f446])). 15.18/2.33 thf(f446,plain,( 15.18/2.33 ( ! [X17 : $i,X16 : $i] : ((((sK3 @ (kCOMB @ X16)) @ (kCOMB @ X17)) = (c_Union @ ((c_UPair @ ((c_Repl @ ((sK2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (((sK0 @ (kCOMB @ (kCOMB @ ((cCOMB @ ((bCOMB @ sK3) @ kCOMB)) @ (kCOMB @ c_Empty))))) @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty)))) @ ((cCOMB @ c_Repl) @ (c_In_rec_poly_i @ ((bCOMB @ (bCOMB @ ((bCOMB @ c_Union) @ (c_UPair @ (c_Sing @ c_Empty))))) @ c_Repl))))) @ ((c_Repl @ c_Empty) @ (c_In_rec_poly_i @ ((bCOMB @ (bCOMB @ ((bCOMB @ c_Union) @ (c_UPair @ (c_Sing @ c_Empty))))) @ c_Repl))))))) )), 15.18/2.33 inference(combinator_demodulation,[],[f394])). 15.18/2.33 thf(f394,plain,( 15.18/2.33 ( ! [X17 : $i,X16 : $i] : ((((sK3 @ (kCOMB @ X16)) @ (kCOMB @ X17)) = ((((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ ((bCOMB @ (bCOMB @ c_Union)) @ c_UPair)) @ ((cCOMB @ c_Repl) @ ((cCOMB @ c_Repl) @ (c_In_rec_poly_i @ ((bCOMB @ (bCOMB @ (((bCOMB @ (bCOMB @ c_Union)) @ c_UPair) @ (c_Sing @ c_Empty)))) @ c_Repl))))))) @ ((cCOMB @ c_Repl) @ (c_In_rec_poly_i @ ((bCOMB @ (bCOMB @ (((bCOMB @ (bCOMB @ c_Union)) @ c_UPair) @ (c_Sing @ c_Empty)))) @ c_Repl)))) @ ((sK2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (((sK0 @ (kCOMB @ (kCOMB @ ((cCOMB @ ((bCOMB @ sK3) @ kCOMB)) @ (kCOMB @ c_Empty))))) @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty)))) @ c_Empty))) )), 15.18/2.33 inference(definition_unfolding,[],[f314,f384])). 15.18/2.33 thf(f314,plain,( 15.18/2.33 ( ! [X17 : $i,X16 : $i] : ((((c_setsum @ ((sK2 @ (kCOMB @ (kCOMB @ c_Empty))) @ (((sK0 @ (kCOMB @ (kCOMB @ ((cCOMB @ ((bCOMB @ sK3) @ kCOMB)) @ (kCOMB @ c_Empty))))) @ (kCOMB @ c_Empty)) @ (kCOMB @ c_Empty)))) @ c_Empty) = ((sK3 @ (kCOMB @ X16)) @ (kCOMB @ X17)))) )), 15.18/2.33 inference(cnf_transformation,[],[f301])). 15.18/2.33 thf(f405,plain,( 15.18/2.33 ( ! [X0 : $i,X1 : $i] : (($true = (vPI($o) @ ((sCOMB @ ((bCOMB @ vIMP) @ ((bCOMB @ (vIMP @ ((vIMP @ ((c_In @ X1) @ (c_Union @ X0))) @ (vSIGMA($i) @ ((sCOMB @ ((bCOMB @ ((bCOMB @ (bCOMB @ vPI($o))) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vIMP))) @ ((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ bCOMB) @ vIMP))) @ vIMP))))) @ iCOMB))) @ (c_In @ X1))) @ ((cCOMB @ c_In) @ X0)))))) @ (vIMP @ ((vIMP @ (vSIGMA($i) @ ((sCOMB @ ((bCOMB @ ((bCOMB @ (bCOMB @ vPI($o))) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vIMP))) @ ((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ bCOMB) @ vIMP))) @ vIMP))))) @ iCOMB))) @ (c_In @ X1))) @ ((cCOMB @ c_In) @ X0)))) @ ((c_In @ X1) @ (c_Union @ X0))))))) @ iCOMB)))) )), 15.18/2.33 inference(combinator_demodulation,[],[f398])). 15.18/2.33 thf(f398,plain,( 15.18/2.33 ( ! [X0 : $i,X1 : $i] : (($true = ((((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ ((bCOMB @ (bCOMB @ vPI($o))) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vIMP))) @ ((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ bCOMB) @ vIMP))) @ vIMP))))) @ iCOMB)))) @ vIMP))) @ (cCOMB @ vIMP)) @ ((c_In @ X1) @ (c_Union @ X0))) @ (vSIGMA($i) @ ((sCOMB @ ((bCOMB @ ((bCOMB @ (bCOMB @ vPI($o))) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vIMP))) @ ((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ bCOMB) @ vIMP))) @ vIMP))))) @ iCOMB))) @ (c_In @ X1))) @ ((cCOMB @ c_In) @ X0)))))) )), 15.18/2.33 inference(definition_unfolding,[],[f324,f385,f369])). 15.18/2.33 thf(f324,plain,( 15.18/2.33 ( ! [X0 : $i,X1 : $i] : (($true = ((c_iff @ ((c_In @ X1) @ (c_Union @ X0))) @ (vSIGMA($i) @ ((sCOMB @ ((bCOMB @ c_and) @ (c_In @ X1))) @ ((cCOMB @ c_In) @ X0)))))) )), 15.18/2.33 inference(cnf_transformation,[],[f283])). 15.18/2.33 thf(f283,plain,( 15.18/2.33 ! [X0,X1] : ($true = ((c_iff @ ((c_In @ X1) @ (c_Union @ X0))) @ (vSIGMA($i) @ ((sCOMB @ ((bCOMB @ c_and) @ (c_In @ X1))) @ ((cCOMB @ c_In) @ X0)))))), 15.18/2.33 inference(fool_elimination,[],[f282])). 15.18/2.33 thf(f282,plain,( 15.18/2.33 ! [X0,X1] : ((c_iff @ ((c_In @ X1) @ (c_Union @ X0))) @ ? [X2] : ((c_and @ ((c_In @ X1) @ X2)) @ ((c_In @ X2) @ X0)))), 15.18/2.33 inference(rectify,[],[f26])). 15.18/2.33 thf(f26,axiom,( 15.18/2.33 ! [X0,X1] : ((c_iff @ ((c_In @ X1) @ (c_Union @ X0))) @ ? [X2] : ((c_and @ ((c_In @ X1) @ X2)) @ ((c_In @ X2) @ X0)))), 15.18/2.33 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax6)). 15.18/2.33 thf(f403,plain,( 15.18/2.33 ($true = ((vIMP @ (vSIGMA($i) @ ((cCOMB @ c_In) @ c_Empty))) @ (vPI($o) @ iCOMB)))), 15.18/2.33 inference(combinator_demodulation,[],[f396])). 15.18/2.33 thf(f396,plain,( 15.18/2.33 ($true = (((cCOMB @ vIMP) @ (vPI($o) @ iCOMB)) @ (vSIGMA($i) @ ((cCOMB @ c_In) @ c_Empty))))), 15.18/2.33 inference(definition_unfolding,[],[f322,f386])). 15.18/2.33 thf(f386,plain,( 15.18/2.33 (c_not = ((cCOMB @ vIMP) @ (vPI($o) @ iCOMB)))), 15.18/2.33 inference(definition_unfolding,[],[f367,f368])). 15.18/2.33 thf(f368,plain,( 15.18/2.33 (c_False = (vPI($o) @ iCOMB))), 15.18/2.33 inference(cnf_transformation,[],[f204])). 15.18/2.33 thf(f204,plain,( 15.18/2.33 (c_False = (vPI($o) @ iCOMB))), 15.18/2.33 inference(fool_elimination,[],[f203])). 15.18/2.33 thf(f203,plain,( 15.18/2.33 (c_False = ! [X0 : $o] : X0)), 15.18/2.33 inference(rectify,[],[f89])). 15.18/2.33 thf(f89,axiom,( 15.18/2.33 (c_False = ! [X0 : $o] : X0)), 15.18/2.33 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax11)). 15.18/2.33 thf(f367,plain,( 15.18/2.33 (c_not = ((cCOMB @ vIMP) @ c_False))), 15.18/2.33 inference(cnf_transformation,[],[f255])). 15.18/2.33 thf(f255,plain,( 15.18/2.33 (c_not = ((cCOMB @ vIMP) @ c_False))), 15.18/2.33 inference(fool_elimination,[],[f254])). 15.18/2.33 thf(f254,plain,( 15.18/2.33 (c_not = (^[X0 : $o] : (X0 => c_False)))), 15.18/2.33 inference(rectify,[],[f100])). 15.18/2.33 thf(f100,axiom,( 15.18/2.33 (c_not = (^[X0 : $o] : (X0 => c_False)))), 15.18/2.33 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax13)). 15.18/2.33 thf(f322,plain,( 15.18/2.33 ($true = (c_not @ (vSIGMA($i) @ ((cCOMB @ c_In) @ c_Empty))))), 15.18/2.33 inference(cnf_transformation,[],[f287])). 15.18/2.33 thf(f287,plain,( 15.18/2.33 ($true = (c_not @ (vSIGMA($i) @ ((cCOMB @ c_In) @ c_Empty))))), 15.18/2.33 inference(fool_elimination,[],[f286])). 15.18/2.33 thf(f286,plain,( 15.18/2.33 (c_not @ ? [X0] : ((c_In @ X0) @ c_Empty))), 15.18/2.33 inference(rectify,[],[f54])). 15.18/2.33 thf(f54,axiom,( 15.18/2.33 (c_not @ ? [X0] : ((c_In @ X0) @ c_Empty))), 15.18/2.33 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax5)). 15.18/2.33 % SZS output end Proof for theBenchmark 15.18/2.33 % (20562)------------------------------ 15.18/2.33 % (20562)Version: Vampire 4.6.0 (commit 0afb7ed4a on 2021-06-23 15:27:21 +0100) 15.18/2.33 % (20562)Termination reason: Refutation 15.18/2.33 15.18/2.33 % (20562)Memory used [KB]: 20724 15.18/2.33 % (20562)Time elapsed: 1.771 s 15.18/2.33 % (20562)------------------------------ 15.18/2.33 % (20562)------------------------------ 15.18/2.33 % (20535)Success in time 1.97 s 15.18/2.34 EOF