0.11/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.11/0.13 % Command : run_vampire %s %d 0.13/0.35 % Computer : n011.cluster.edu 0.13/0.35 % Model : x86_64 x86_64 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.35 % Memory : 8042.1875MB 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.35 % CPULimit : 1200 0.13/0.35 % WCLimit : 120 0.13/0.35 % DateTime : Tue Jul 13 12:01:40 EDT 2021 0.13/0.35 % 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 0.13/0.36 Running in auto input_syntax mode. Trying TPTP 0.13/0.39 % (22029)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 0.13/0.40 % (22045)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 0.13/0.40 % (22028)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 0.13/0.41 % (22020)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 0.13/0.41 % (22030)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 0.13/0.41 % (22032)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 0.13/0.41 % (22031)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 0.13/0.41 % (22037)lrs+1011_5:1_acc=on:csup=on:inj=on:e2e=on:prag=on:cases=on:cnfonf=eager:amm=off:anc=all_dependent:bd=off:ccuc=small_ones:fde=unused:gs=on:gsaa=full_model:gsem=off:lcm=predicate:lwlo=on:nm=6:newcnf=on:nwc=2.5:stl=30:sp=occurrence:updr=off:thsq=on_30 on theBenchmark 0.13/0.41 % (22029)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs. 0.13/0.41 % (22025)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 0.13/0.41 % (22029)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs. 0.13/0.41 % (22042)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 0.13/0.41 % (22044)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 0.13/0.42 % (22021)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 0.21/0.42 % (22034)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 0.21/0.42 % (22028)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs. 0.21/0.42 % (22045)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs. 0.21/0.43 % (22024)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 0.21/0.43 % (22023)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 0.21/0.43 % (22022)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 0.21/0.43 % (22049)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 0.21/0.43 % (22037)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs. 0.21/0.43 % (22041)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 0.21/0.43 % (22026)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 0.21/0.44 % (22024)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs. 0.21/0.44 % (22042)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs. 0.21/0.44 % (22022)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs. 0.21/0.44 % (22048)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 0.21/0.44 % (22046)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 0.21/0.44 % (22047)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 0.21/0.45 % (22033)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 0.21/0.45 % (22043)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 0.21/0.45 % (22026)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs. 0.21/0.45 % (22044)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs. 0.21/0.45 % (22038)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 0.21/0.45 % (22040)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 0.21/0.45 % (22039)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 0.21/0.46 % (22030)Refutation not found, incomplete strategy% (22030)------------------------------ 0.21/0.46 % (22030)Version: Vampire 4.6.0 (commit 0afb7ed4a on 2021-06-23 15:27:21 +0100) 0.21/0.46 % (22030)Termination reason: Refutation not found, incomplete strategy 0.21/0.46 0.21/0.46 % (22030)Memory used [KB]: 10746 0.21/0.46 % (22030)Time elapsed: 0.081 s 0.21/0.46 % (22030)------------------------------ 0.21/0.46 % (22030)------------------------------ 0.21/0.46 % (22036)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 0.21/0.46 % (22023)Refutation not found, incomplete strategy% (22023)------------------------------ 0.21/0.46 % (22023)Version: Vampire 4.6.0 (commit 0afb7ed4a on 2021-06-23 15:27:21 +0100) 0.21/0.46 % (22023)Termination reason: Refutation not found, incomplete strategy 0.21/0.46 0.21/0.46 % (22023)Memory used [KB]: 10618 0.21/0.46 % (22023)Time elapsed: 0.090 s 0.21/0.46 % (22023)------------------------------ 0.21/0.46 % (22023)------------------------------ 0.21/0.47 % (22035)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 0.21/0.47 % (22033)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs. 0.21/0.47 % (22027)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 0.21/0.47 % (22043)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs. 0.21/0.48 % (22039)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs. 0.21/0.48 % (22035)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs. 0.21/0.49 % (22036)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs. 0.21/0.49 % (22036)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs. 0.21/0.50 % (22027)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs. 0.21/0.50 % (22050)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 0.21/0.52 % (22051)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 0.21/0.54 % (22051)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs. 0.21/0.56 % (22029)First to succeed. 0.21/0.62 % (22045)Also succeeded, but the first one will report. 0.21/0.62 % (22029)Refutation found. Thanks to Tanya! 0.21/0.62 % SZS status Theorem for theBenchmark 0.21/0.62 % SZS output start Proof for theBenchmark 0.21/0.62 thf(type_def_6, type, g: $tType). 0.21/0.62 thf(type_def_7, type, >: ($tType * $tType) > $tType). 0.21/0.62 thf(func_def_8, type, cGROUP2: (g > g > g) > g > $o). 0.21/0.62 thf(func_def_9, type, cGROUP3: (g > g > g) > g > $o). 0.21/0.62 thf(func_def_10, type, cGRP_ASSOC: (g > g > g) > $o). 0.21/0.62 thf(func_def_11, type, cGRP_LEFT_INVERSE: (g > g > g) > g > $o). 0.21/0.62 thf(func_def_12, type, cGRP_LEFT_UNIT: (g > g > g) > g > $o). 0.21/0.62 thf(func_def_13, type, cGRP_RIGHT_INVERSE: (g > g > g) > g > $o). 0.21/0.62 thf(func_def_14, type, cGRP_RIGHT_UNIT: (g > g > g) > g > $o). 0.21/0.62 thf(func_def_16, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)). 0.21/0.62 thf(func_def_19, type, vAND: $o > $o > $o). 0.21/0.62 thf(func_def_20, type, bCOMB: !>[X0: $tType, X1: $tType, X2: $tType]:((X1 > X2) > (X0 > X1) > X0 > X2)). 0.21/0.62 thf(func_def_21, type, sCOMB: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > (X0 > X1) > X0 > X2)). 0.21/0.62 thf(func_def_22, type, vEQ: !>[X0: $tType]:(X0 > X0 > $o)). 0.21/0.62 thf(func_def_23, type, vPI: !>[X0: $tType]:((X0 > $o) > $o)). 0.21/0.62 thf(func_def_24, type, iCOMB: !>[X0: $tType]:(X0 > X0)). 0.21/0.62 thf(func_def_25, type, cCOMB: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > X1 > X0 > X2)). 0.21/0.62 thf(func_def_26, type, vSIGMA: !>[X0: $tType]:((X0 > $o) > $o)). 0.21/0.62 thf(func_def_27, type, sK0: g > g > g). 0.21/0.62 thf(func_def_28, type, sK1: g). 0.21/0.62 thf(func_def_30, type, kCOMB: !>[X0: $tType, X1: $tType]:(X0 > X1 > X0)). 0.21/0.62 thf(func_def_31, type, sK3: g). 0.21/0.62 thf(func_def_32, type, sK4: g). 0.21/0.62 thf(func_def_33, type, sK5: g). 0.21/0.62 thf(func_def_34, type, sK6: g). 0.21/0.62 thf(func_def_35, type, sK7: g). 0.21/0.62 thf(func_def_36, type, sK8: g). 0.21/0.62 thf(func_def_37, type, sK9: g). 0.21/0.62 thf(func_def_38, type, sK10: g > g). 0.21/0.62 thf(func_def_39, type, sK11: g > g). 0.21/0.62 thf(func_def_40, type, sK12: g > g). 0.21/0.62 thf(func_def_41, type, sK13: g > g). 0.21/0.62 thf(f1031,plain,( 0.21/0.62 $false), 0.21/0.62 inference(avatar_sat_refutation,[],[f158,f162,f173,f174,f181,f200,f203,f218,f300,f333,f395,f411,f644,f719,f746,f1024,f1030])). 0.21/0.62 thf(f1030,plain,( 0.21/0.62 ~spl2_6 | ~spl2_12), 0.21/0.62 inference(avatar_contradiction_clause,[],[f1029])). 0.21/0.62 thf(f1029,plain,( 0.21/0.62 $false | (~spl2_6 | ~spl2_12)), 0.21/0.62 inference(trivial_inequality_removal,[],[f1027])). 0.21/0.62 thf(f1027,plain,( 0.21/0.62 (sK1 != sK1) | (~spl2_6 | ~spl2_12)), 0.21/0.62 inference(superposition,[],[f196,f169])). 0.21/0.62 thf(f169,plain,( 0.21/0.62 ( ! [X2 : g] : ((sK1 = ((sK0 @ (sK11 @ X2)) @ X2))) ) | ~spl2_6), 0.21/0.62 inference(avatar_component_clause,[],[f168])). 0.21/0.62 thf(f168,plain,( 0.21/0.62 spl2_6 <=> ! [X2 : g] : (sK1 = ((sK0 @ (sK11 @ X2)) @ X2))), 0.21/0.62 introduced(avatar_definition,[new_symbols(naming,[spl2_6])])). 0.21/0.62 thf(f196,plain,( 0.21/0.62 ( ! [X2 : g] : ((sK1 != ((sK0 @ X2) @ sK4))) ) | ~spl2_12), 0.21/0.62 inference(avatar_component_clause,[],[f195])). 0.21/0.62 thf(f195,plain,( 0.21/0.62 spl2_12 <=> ! [X2 : g] : (sK1 != ((sK0 @ X2) @ sK4))), 0.21/0.62 introduced(avatar_definition,[new_symbols(naming,[spl2_12])])). 0.21/0.62 thf(f1024,plain,( 0.21/0.62 ~spl2_3 | ~spl2_4 | ~spl2_5 | ~spl2_6 | spl2_11), 0.21/0.62 inference(avatar_contradiction_clause,[],[f1023])). 0.21/0.62 thf(f1023,plain,( 0.21/0.62 $false | (~spl2_3 | ~spl2_4 | ~spl2_5 | ~spl2_6 | spl2_11)), 0.21/0.62 inference(trivial_inequality_removal,[],[f1016])). 0.21/0.62 thf(f1016,plain,( 0.21/0.62 (sK5 != sK5) | (~spl2_3 | ~spl2_4 | ~spl2_5 | ~spl2_6 | spl2_11)), 0.21/0.62 inference(superposition,[],[f193,f942])). 0.21/0.62 thf(f942,plain,( 0.21/0.62 ( ! [X0 : g] : ((((sK0 @ X0) @ sK1) = X0)) ) | (~spl2_3 | ~spl2_4 | ~spl2_5 | ~spl2_6)), 0.21/0.62 inference(forward_demodulation,[],[f933,f813])). 0.21/0.62 thf(f813,plain,( 0.21/0.62 ( ! [X0 : g] : (((sK12 @ (sK11 @ X0)) = X0)) ) | (~spl2_3 | ~spl2_4 | ~spl2_5 | ~spl2_6)), 0.21/0.62 inference(superposition,[],[f792,f242])). 0.21/0.62 thf(f242,plain,( 0.21/0.62 ( ! [X2 : g] : ((((sK0 @ (sK11 @ (sK11 @ X2))) @ sK1) = X2)) ) | (~spl2_4 | ~spl2_5 | ~spl2_6)), 0.21/0.62 inference(superposition,[],[f220,f169])). 0.21/0.62 thf(f220,plain,( 0.21/0.62 ( ! [X4 : g,X5 : g] : ((((sK0 @ (sK11 @ X4)) @ ((sK0 @ X4) @ X5)) = X5)) ) | (~spl2_4 | ~spl2_5 | ~spl2_6)), 0.21/0.62 inference(forward_demodulation,[],[f214,f161])). 0.21/0.62 thf(f161,plain,( 0.21/0.62 ( ! [X2 : g] : ((((sK0 @ sK1) @ X2) = X2)) ) | ~spl2_4), 0.21/0.62 inference(avatar_component_clause,[],[f160])). 0.21/0.62 thf(f160,plain,( 0.21/0.62 spl2_4 <=> ! [X2 : g] : (((sK0 @ sK1) @ X2) = X2)), 0.21/0.62 introduced(avatar_definition,[new_symbols(naming,[spl2_4])])). 0.21/0.62 thf(f214,plain,( 0.21/0.62 ( ! [X4 : g,X5 : g] : ((((sK0 @ (sK11 @ X4)) @ ((sK0 @ X4) @ X5)) = ((sK0 @ sK1) @ X5))) ) | (~spl2_5 | ~spl2_6)), 0.21/0.62 inference(superposition,[],[f165,f169])). 0.21/0.62 thf(f165,plain,( 0.21/0.62 ( ! [X4 : g,X2 : g,X3 : g] : ((((sK0 @ ((sK0 @ X4) @ X3)) @ X2) = ((sK0 @ X4) @ ((sK0 @ X3) @ X2)))) ) | ~spl2_5), 0.21/0.62 inference(avatar_component_clause,[],[f164])). 0.21/0.62 thf(f164,plain,( 0.21/0.62 spl2_5 <=> ! [X3 : g,X2 : g,X4 : g] : (((sK0 @ ((sK0 @ X4) @ X3)) @ X2) = ((sK0 @ X4) @ ((sK0 @ X3) @ X2)))), 0.21/0.62 introduced(avatar_definition,[new_symbols(naming,[spl2_5])])). 0.21/0.62 thf(f792,plain,( 0.21/0.62 ( ! [X6 : g] : (((sK12 @ X6) = ((sK0 @ (sK11 @ X6)) @ sK1))) ) | (~spl2_3 | ~spl2_4 | ~spl2_5 | ~spl2_6)), 0.21/0.62 inference(superposition,[],[f220,f157])). 0.21/0.62 thf(f157,plain,( 0.21/0.62 ( ! [X1 : g] : ((sK1 = ((sK0 @ X1) @ (sK12 @ X1)))) ) | ~spl2_3), 0.21/0.62 inference(avatar_component_clause,[],[f156])). 0.21/0.62 thf(f156,plain,( 0.21/0.62 spl2_3 <=> ! [X1 : g] : (sK1 = ((sK0 @ X1) @ (sK12 @ X1)))), 0.21/0.62 introduced(avatar_definition,[new_symbols(naming,[spl2_3])])). 0.21/0.62 thf(f933,plain,( 0.21/0.62 ( ! [X0 : g] : ((((sK0 @ X0) @ sK1) = (sK12 @ (sK11 @ X0)))) ) | (~spl2_3 | ~spl2_4 | ~spl2_5 | ~spl2_6)), 0.21/0.62 inference(backward_demodulation,[],[f867,f927])). 0.21/0.62 thf(f927,plain,( 0.21/0.62 ( ! [X0 : g] : (((sK12 @ X0) = (sK11 @ X0))) ) | (~spl2_3 | ~spl2_4 | ~spl2_5 | ~spl2_6)), 0.21/0.62 inference(forward_demodulation,[],[f919,f813])). 0.21/0.62 thf(f919,plain,( 0.21/0.62 ( ! [X0 : g] : (((sK12 @ X0) = (sK12 @ (sK11 @ (sK11 @ X0))))) ) | (~spl2_3 | ~spl2_4 | ~spl2_5 | ~spl2_6)), 0.21/0.62 inference(superposition,[],[f914,f242])). 0.21/0.62 thf(f914,plain,( 0.21/0.62 ( ! [X0 : g] : (((sK12 @ X0) = (sK12 @ ((sK0 @ X0) @ sK1)))) ) | (~spl2_3 | ~spl2_4 | ~spl2_5 | ~spl2_6)), 0.21/0.62 inference(forward_demodulation,[],[f904,f792])). 0.21/0.62 thf(f904,plain,( 0.21/0.62 ( ! [X0 : g] : (((sK12 @ ((sK0 @ X0) @ sK1)) = ((sK0 @ (sK11 @ X0)) @ sK1))) ) | (~spl2_3 | ~spl2_4 | ~spl2_5 | ~spl2_6)), 0.21/0.62 inference(superposition,[],[f220,f762])). 0.21/0.62 thf(f762,plain,( 0.21/0.62 ( ! [X3 : g] : ((sK1 = ((sK0 @ X3) @ (sK12 @ ((sK0 @ X3) @ sK1))))) ) | (~spl2_3 | ~spl2_4 | ~spl2_5)), 0.21/0.62 inference(superposition,[],[f412,f161])). 0.21/0.62 thf(f412,plain,( 0.21/0.62 ( ! [X2 : g,X1 : g] : ((sK1 = ((sK0 @ X1) @ ((sK0 @ X2) @ (sK12 @ ((sK0 @ X1) @ X2)))))) ) | (~spl2_3 | ~spl2_5)), 0.21/0.62 inference(superposition,[],[f157,f165])). 0.21/0.62 thf(f867,plain,( 0.21/0.62 ( ! [X0 : g] : ((((sK0 @ X0) @ sK1) = (sK12 @ (sK12 @ X0)))) ) | (~spl2_3 | ~spl2_4 | ~spl2_5)), 0.21/0.62 inference(superposition,[],[f862,f157])). 0.21/0.62 thf(f862,plain,( 0.21/0.62 ( ! [X0 : g,X1 : g] : ((((sK0 @ X0) @ ((sK0 @ (sK12 @ X0)) @ X1)) = X1)) ) | (~spl2_3 | ~spl2_4 | ~spl2_5)), 0.21/0.62 inference(forward_demodulation,[],[f413,f161])). 0.21/0.62 thf(f413,plain,( 0.21/0.62 ( ! [X0 : g,X1 : g] : ((((sK0 @ sK1) @ X1) = ((sK0 @ X0) @ ((sK0 @ (sK12 @ X0)) @ X1)))) ) | (~spl2_3 | ~spl2_5)), 0.21/0.62 inference(superposition,[],[f165,f157])). 0.21/0.62 thf(f193,plain,( 0.21/0.62 (sK5 != ((sK0 @ sK5) @ sK1)) | spl2_11), 0.21/0.62 inference(avatar_component_clause,[],[f191])). 0.21/0.62 thf(f191,plain,( 0.21/0.62 spl2_11 <=> (sK5 = ((sK0 @ sK5) @ sK1))), 0.21/0.62 introduced(avatar_definition,[new_symbols(naming,[spl2_11])])). 0.21/0.62 thf(f746,plain,( 0.21/0.62 ~spl2_3 | ~spl2_5 | ~spl2_7 | ~spl2_12), 0.21/0.62 inference(avatar_contradiction_clause,[],[f745])). 0.21/0.62 thf(f745,plain,( 0.21/0.62 $false | (~spl2_3 | ~spl2_5 | ~spl2_7 | ~spl2_12)), 0.21/0.62 inference(trivial_inequality_removal,[],[f739])). 0.21/0.62 thf(f739,plain,( 0.21/0.62 (sK1 != sK1) | (~spl2_3 | ~spl2_5 | ~spl2_7 | ~spl2_12)), 0.21/0.62 inference(superposition,[],[f331,f687])). 0.21/0.62 thf(f687,plain,( 0.21/0.62 ( ! [X0 : g] : ((sK1 = ((sK0 @ (sK12 @ X0)) @ X0))) ) | (~spl2_3 | ~spl2_5 | ~spl2_7)), 0.21/0.62 inference(superposition,[],[f447,f543])). 0.21/0.62 thf(f543,plain,( 0.21/0.62 ( ! [X0 : g] : ((((sK0 @ sK1) @ (sK12 @ (sK12 @ X0))) = X0)) ) | (~spl2_3 | ~spl2_5 | ~spl2_7)), 0.21/0.62 inference(forward_demodulation,[],[f529,f172])). 0.21/0.62 thf(f172,plain,( 0.21/0.62 ( ! [X1 : g] : ((((sK0 @ X1) @ sK1) = X1)) ) | ~spl2_7), 0.21/0.62 inference(avatar_component_clause,[],[f171])). 0.21/0.62 thf(f171,plain,( 0.21/0.62 spl2_7 <=> ! [X1 : g] : (((sK0 @ X1) @ sK1) = X1)), 0.21/0.62 introduced(avatar_definition,[new_symbols(naming,[spl2_7])])). 0.21/0.62 thf(f529,plain,( 0.21/0.62 ( ! [X0 : g] : ((((sK0 @ X0) @ sK1) = ((sK0 @ sK1) @ (sK12 @ (sK12 @ X0))))) ) | (~spl2_3 | ~spl2_5)), 0.21/0.62 inference(superposition,[],[f413,f157])). 0.21/0.62 thf(f447,plain,( 0.21/0.62 ( ! [X11 : g] : ((sK1 = ((sK0 @ X11) @ ((sK0 @ sK1) @ (sK12 @ X11))))) ) | (~spl2_3 | ~spl2_5 | ~spl2_7)), 0.21/0.62 inference(superposition,[],[f412,f172])). 0.21/0.62 thf(f331,plain,( 0.21/0.62 ( ! [X0 : g,X1 : g] : ((sK1 != ((sK0 @ X0) @ ((sK0 @ X1) @ sK4)))) ) | (~spl2_5 | ~spl2_12)), 0.21/0.62 inference(superposition,[],[f196,f165])). 0.21/0.62 thf(f719,plain,( 0.21/0.62 ~spl2_3 | ~spl2_5 | ~spl2_7 | spl2_10), 0.21/0.62 inference(avatar_contradiction_clause,[],[f718])). 0.21/0.62 thf(f718,plain,( 0.21/0.62 $false | (~spl2_3 | ~spl2_5 | ~spl2_7 | spl2_10)), 0.21/0.62 inference(trivial_inequality_removal,[],[f717])). 0.21/0.62 thf(f717,plain,( 0.21/0.62 (sK6 != sK6) | (~spl2_3 | ~spl2_5 | ~spl2_7 | spl2_10)), 0.21/0.62 inference(superposition,[],[f189,f704])). 0.21/0.62 thf(f704,plain,( 0.21/0.62 ( ! [X5 : g] : ((((sK0 @ sK1) @ X5) = X5)) ) | (~spl2_3 | ~spl2_5 | ~spl2_7)), 0.21/0.62 inference(forward_demodulation,[],[f703,f172])). 0.21/0.62 thf(f703,plain,( 0.21/0.62 ( ! [X5 : g] : ((((sK0 @ sK1) @ X5) = ((sK0 @ X5) @ sK1))) ) | (~spl2_3 | ~spl2_5 | ~spl2_7)), 0.21/0.62 inference(forward_demodulation,[],[f695,f543])). 0.21/0.62 thf(f695,plain,( 0.21/0.62 ( ! [X5 : g] : ((((sK0 @ X5) @ sK1) = ((sK0 @ sK1) @ ((sK0 @ sK1) @ (sK12 @ (sK12 @ X5)))))) ) | (~spl2_3 | ~spl2_5 | ~spl2_7)), 0.21/0.62 inference(superposition,[],[f413,f447])). 0.21/0.62 thf(f189,plain,( 0.21/0.62 (sK6 != ((sK0 @ sK1) @ sK6)) | spl2_10), 0.21/0.62 inference(avatar_component_clause,[],[f187])). 0.21/0.62 thf(f187,plain,( 0.21/0.62 spl2_10 <=> (sK6 = ((sK0 @ sK1) @ sK6))), 0.21/0.62 introduced(avatar_definition,[new_symbols(naming,[spl2_10])])). 0.21/0.62 thf(f644,plain,( 0.21/0.62 ~spl2_3 | ~spl2_13), 0.21/0.62 inference(avatar_contradiction_clause,[],[f643])). 0.21/0.62 thf(f643,plain,( 0.21/0.62 $false | (~spl2_3 | ~spl2_13)), 0.21/0.62 inference(trivial_inequality_removal,[],[f635])). 0.21/0.62 thf(f635,plain,( 0.21/0.62 (sK1 != sK1) | (~spl2_3 | ~spl2_13)), 0.21/0.62 inference(superposition,[],[f199,f157])). 0.21/0.62 thf(f199,plain,( 0.21/0.62 ( ! [X1 : g] : ((sK1 != ((sK0 @ sK3) @ X1))) ) | ~spl2_13), 0.21/0.62 inference(avatar_component_clause,[],[f198])). 0.21/0.62 thf(f198,plain,( 0.21/0.62 spl2_13 <=> ! [X1 : g] : (sK1 != ((sK0 @ sK3) @ X1))), 0.21/0.62 introduced(avatar_definition,[new_symbols(naming,[spl2_13])])). 0.21/0.62 thf(f411,plain,( 0.21/0.62 ~spl2_7 | spl2_11), 0.21/0.62 inference(avatar_contradiction_clause,[],[f410])). 0.21/0.62 thf(f410,plain,( 0.21/0.62 $false | (~spl2_7 | spl2_11)), 0.21/0.62 inference(trivial_inequality_removal,[],[f406])). 0.21/0.62 thf(f406,plain,( 0.21/0.62 (sK5 != sK5) | (~spl2_7 | spl2_11)), 0.21/0.62 inference(superposition,[],[f193,f172])). 0.21/0.62 thf(f395,plain,( 0.21/0.62 ~spl2_2 | ~spl2_4 | ~spl2_5 | ~spl2_13), 0.21/0.62 inference(avatar_contradiction_clause,[],[f394])). 0.21/0.62 thf(f394,plain,( 0.21/0.62 $false | (~spl2_2 | ~spl2_4 | ~spl2_5 | ~spl2_13)), 0.21/0.62 inference(trivial_inequality_removal,[],[f388])). 0.21/0.62 thf(f388,plain,( 0.21/0.62 (sK1 != sK1) | (~spl2_2 | ~spl2_4 | ~spl2_5 | ~spl2_13)), 0.21/0.62 inference(superposition,[],[f199,f265])). 0.21/0.62 thf(f265,plain,( 0.21/0.62 ( ! [X0 : g] : ((sK1 = ((sK0 @ X0) @ (sK13 @ X0)))) ) | (~spl2_2 | ~spl2_4 | ~spl2_5)), 0.21/0.62 inference(superposition,[],[f227,f154])). 0.21/0.62 thf(f154,plain,( 0.21/0.62 ( ! [X2 : g] : ((sK1 = ((sK0 @ (sK13 @ X2)) @ X2))) ) | ~spl2_2), 0.21/0.62 inference(avatar_component_clause,[],[f153])). 0.21/0.62 thf(f153,plain,( 0.21/0.62 spl2_2 <=> ! [X2 : g] : (sK1 = ((sK0 @ (sK13 @ X2)) @ X2))), 0.21/0.62 introduced(avatar_definition,[new_symbols(naming,[spl2_2])])). 0.21/0.62 thf(f227,plain,( 0.21/0.62 ( ! [X6 : g,X7 : g] : ((((sK0 @ X6) @ X7) = ((sK0 @ (sK13 @ (sK13 @ X6))) @ X7))) ) | (~spl2_2 | ~spl2_4 | ~spl2_5)), 0.21/0.62 inference(superposition,[],[f219,f219])). 0.21/0.62 thf(f219,plain,( 0.21/0.62 ( ! [X2 : g,X3 : g] : ((((sK0 @ (sK13 @ X2)) @ ((sK0 @ X2) @ X3)) = X3)) ) | (~spl2_2 | ~spl2_4 | ~spl2_5)), 0.21/0.62 inference(forward_demodulation,[],[f213,f161])). 0.21/0.62 thf(f213,plain,( 0.21/0.62 ( ! [X2 : g,X3 : g] : ((((sK0 @ (sK13 @ X2)) @ ((sK0 @ X2) @ X3)) = ((sK0 @ sK1) @ X3))) ) | (~spl2_2 | ~spl2_5)), 0.21/0.62 inference(superposition,[],[f165,f154])). 0.21/0.62 thf(f333,plain,( 0.21/0.62 ~spl2_2 | ~spl2_12), 0.21/0.62 inference(avatar_contradiction_clause,[],[f332])). 0.21/0.62 thf(f332,plain,( 0.21/0.62 $false | (~spl2_2 | ~spl2_12)), 0.21/0.62 inference(trivial_inequality_removal,[],[f330])). 0.21/0.62 thf(f330,plain,( 0.21/0.62 (sK1 != sK1) | (~spl2_2 | ~spl2_12)), 0.21/0.62 inference(superposition,[],[f196,f154])). 0.21/0.62 thf(f300,plain,( 0.21/0.62 ~spl2_2 | ~spl2_4 | ~spl2_5 | spl2_11), 0.21/0.62 inference(avatar_contradiction_clause,[],[f299])). 0.21/0.62 thf(f299,plain,( 0.21/0.62 $false | (~spl2_2 | ~spl2_4 | ~spl2_5 | spl2_11)), 0.21/0.62 inference(trivial_inequality_removal,[],[f285])). 0.21/0.62 thf(f285,plain,( 0.21/0.62 (sK5 != sK5) | (~spl2_2 | ~spl2_4 | ~spl2_5 | spl2_11)), 0.21/0.62 inference(superposition,[],[f193,f267])). 0.21/0.62 thf(f267,plain,( 0.21/0.62 ( ! [X5 : g] : ((((sK0 @ X5) @ sK1) = X5)) ) | (~spl2_2 | ~spl2_4 | ~spl2_5)), 0.21/0.62 inference(superposition,[],[f227,f224])). 0.21/0.62 thf(f224,plain,( 0.21/0.62 ( ! [X1 : g] : ((((sK0 @ (sK13 @ (sK13 @ X1))) @ sK1) = X1)) ) | (~spl2_2 | ~spl2_4 | ~spl2_5)), 0.21/0.62 inference(superposition,[],[f219,f154])). 0.21/0.62 thf(f218,plain,( 0.21/0.62 ~spl2_5 | spl2_9), 0.21/0.62 inference(avatar_contradiction_clause,[],[f217])). 0.21/0.62 thf(f217,plain,( 0.21/0.62 $false | (~spl2_5 | spl2_9)), 0.21/0.62 inference(trivial_inequality_removal,[],[f216])). 0.21/0.62 thf(f216,plain,( 0.21/0.62 (((sK0 @ sK9) @ ((sK0 @ sK8) @ sK7)) != ((sK0 @ sK9) @ ((sK0 @ sK8) @ sK7))) | (~spl2_5 | spl2_9)), 0.21/0.62 inference(superposition,[],[f185,f165])). 0.21/0.62 thf(f185,plain,( 0.21/0.62 (((sK0 @ ((sK0 @ sK9) @ sK8)) @ sK7) != ((sK0 @ sK9) @ ((sK0 @ sK8) @ sK7))) | spl2_9), 0.21/0.62 inference(avatar_component_clause,[],[f183])). 0.21/0.62 thf(f183,plain,( 0.21/0.62 spl2_9 <=> (((sK0 @ ((sK0 @ sK9) @ sK8)) @ sK7) = ((sK0 @ sK9) @ ((sK0 @ sK8) @ sK7)))), 0.21/0.62 introduced(avatar_definition,[new_symbols(naming,[spl2_9])])). 0.21/0.62 thf(f203,plain,( 0.21/0.62 ~spl2_4 | spl2_10), 0.21/0.62 inference(avatar_contradiction_clause,[],[f202])). 0.21/0.62 thf(f202,plain,( 0.21/0.62 $false | (~spl2_4 | spl2_10)), 0.21/0.62 inference(trivial_inequality_removal,[],[f201])). 0.21/0.62 thf(f201,plain,( 0.21/0.62 (sK6 != sK6) | (~spl2_4 | spl2_10)), 0.21/0.62 inference(superposition,[],[f189,f161])). 0.21/0.62 thf(f200,plain,( 0.21/0.62 ~spl2_9 | ~spl2_10 | ~spl2_11 | spl2_12 | spl2_13), 0.21/0.62 inference(avatar_split_clause,[],[f70,f198,f195,f191,f187,f183])). 0.21/0.62 thf(f70,plain,( 0.21/0.62 ( ! [X2 : g,X1 : g] : ((sK1 != ((sK0 @ sK3) @ X1)) | (sK1 != ((sK0 @ X2) @ sK4)) | (sK5 != ((sK0 @ sK5) @ sK1)) | (sK6 != ((sK0 @ sK1) @ sK6)) | (((sK0 @ ((sK0 @ sK9) @ sK8)) @ sK7) != ((sK0 @ sK9) @ ((sK0 @ sK8) @ sK7)))) )), 0.21/0.62 inference(equality_proxy_clausification,[],[f69])). 0.21/0.62 thf(f69,plain,( 0.21/0.62 ( ! [X2 : g,X1 : g] : ((sK1 != ((sK0 @ sK3) @ X1)) | (sK1 != ((sK0 @ X2) @ sK4)) | (sK5 != ((sK0 @ sK5) @ sK1)) | (sK6 != ((sK0 @ sK1) @ sK6)) | ($false = ((vEQ(g) @ ((sK0 @ ((sK0 @ sK9) @ sK8)) @ sK7)) @ ((sK0 @ sK9) @ ((sK0 @ sK8) @ sK7))))) )), 0.21/0.62 inference(combinator_demodulation,[],[f68])). 0.21/0.62 thf(f68,plain,( 0.21/0.62 ( ! [X2 : g,X1 : g] : ((sK1 != ((sK0 @ sK3) @ X1)) | (sK1 != ((sK0 @ X2) @ sK4)) | (sK5 != ((sK0 @ sK5) @ sK1)) | (sK6 != ((sK0 @ sK1) @ sK6)) | ($false = (((sCOMB @ ((bCOMB @ vEQ(g)) @ ((cCOMB @ ((bCOMB @ sK0) @ ((cCOMB @ sK0) @ sK8))) @ sK7))) @ ((cCOMB @ sK0) @ ((sK0 @ sK8) @ sK7))) @ sK9))) )), 0.21/0.62 inference(sigma_clausification,[],[f67])). 0.21/0.62 thf(f67,plain,( 0.21/0.62 ( ! [X2 : g,X1 : g] : ((sK1 != ((sK0 @ sK3) @ X1)) | (sK1 != ((sK0 @ X2) @ sK4)) | (sK5 != ((sK0 @ sK5) @ sK1)) | (sK6 != ((sK0 @ sK1) @ sK6)) | ($false = (vPI(g) @ ((sCOMB @ ((bCOMB @ vEQ(g)) @ ((cCOMB @ ((bCOMB @ sK0) @ ((cCOMB @ sK0) @ sK8))) @ sK7))) @ ((cCOMB @ sK0) @ ((sK0 @ sK8) @ sK7)))))) )), 0.21/0.62 inference(combinator_demodulation,[],[f66])). 0.21/0.62 thf(f66,plain,( 0.21/0.62 ( ! [X2 : g,X1 : g] : ((sK1 != ((sK0 @ sK3) @ X1)) | (sK1 != ((sK0 @ X2) @ sK4)) | (sK5 != ((sK0 @ sK5) @ sK1)) | (sK6 != ((sK0 @ sK1) @ sK6)) | ($false = (((bCOMB @ vPI(g)) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vEQ(g))) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sK0)) @ (cCOMB @ sK0)))) @ sK7)))) @ ((bCOMB @ (cCOMB @ sK0)) @ ((cCOMB @ sK0) @ sK7)))) @ sK8))) )), 0.21/0.62 inference(sigma_clausification,[],[f65])). 0.21/0.62 thf(f65,plain,( 0.21/0.62 ( ! [X2 : g,X1 : g] : ((sK1 != ((sK0 @ sK3) @ X1)) | (sK1 != ((sK0 @ X2) @ sK4)) | (sK5 != ((sK0 @ sK5) @ sK1)) | (sK6 != ((sK0 @ sK1) @ sK6)) | ($false = (vPI(g) @ ((bCOMB @ vPI(g)) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vEQ(g))) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sK0)) @ (cCOMB @ sK0)))) @ sK7)))) @ ((bCOMB @ (cCOMB @ sK0)) @ ((cCOMB @ sK0) @ sK7))))))) )), 0.21/0.62 inference(combinator_demodulation,[],[f64])). 0.21/0.62 thf(f64,plain,( 0.21/0.62 ( ! [X2 : g,X1 : g] : ((sK1 != ((sK0 @ sK3) @ X1)) | (sK1 != ((sK0 @ X2) @ sK4)) | (sK5 != ((sK0 @ sK5) @ sK1)) | (sK6 != ((sK0 @ sK1) @ sK6)) | ($false = (((bCOMB @ vPI(g)) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vEQ(g)))) @ (cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sK0)) @ (cCOMB @ sK0)))))))) @ ((bCOMB @ (bCOMB @ (cCOMB @ sK0))) @ (cCOMB @ sK0))))) @ sK7))) )), 0.21/0.62 inference(sigma_clausification,[],[f63])). 0.21/0.62 thf(f63,plain,( 0.21/0.62 ( ! [X2 : g,X1 : g] : ((sK1 != ((sK0 @ sK3) @ X1)) | (sK1 != ((sK0 @ X2) @ sK4)) | (sK5 != ((sK0 @ sK5) @ sK1)) | (sK6 != ((sK0 @ sK1) @ sK6)) | ($false = (vPI(g) @ ((bCOMB @ vPI(g)) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vEQ(g)))) @ (cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sK0)) @ (cCOMB @ sK0)))))))) @ ((bCOMB @ (bCOMB @ (cCOMB @ sK0))) @ (cCOMB @ sK0)))))))) )), 0.21/0.62 inference(equality_proxy_clausification,[],[f62])). 0.21/0.62 thf(f62,plain,( 0.21/0.62 ( ! [X2 : g,X1 : g] : ((sK1 != ((sK0 @ sK3) @ X1)) | (sK1 != ((sK0 @ X2) @ sK4)) | (sK5 != ((sK0 @ sK5) @ sK1)) | ($false = ((vEQ(g) @ ((sK0 @ sK1) @ sK6)) @ sK6)) | ($false = (vPI(g) @ ((bCOMB @ vPI(g)) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vEQ(g)))) @ (cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sK0)) @ (cCOMB @ sK0)))))))) @ ((bCOMB @ (bCOMB @ (cCOMB @ sK0))) @ (cCOMB @ sK0)))))))) )), 0.21/0.62 inference(combinator_demodulation,[],[f61])). 0.21/0.62 thf(f61,plain,( 0.21/0.62 ( ! [X2 : g,X1 : g] : ((sK1 != ((sK0 @ sK3) @ X1)) | (sK1 != ((sK0 @ X2) @ sK4)) | (sK5 != ((sK0 @ sK5) @ sK1)) | ($false = (((sCOMB @ ((bCOMB @ vEQ(g)) @ (sK0 @ sK1))) @ iCOMB) @ sK6)) | ($false = (vPI(g) @ ((bCOMB @ vPI(g)) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vEQ(g)))) @ (cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sK0)) @ (cCOMB @ sK0)))))))) @ ((bCOMB @ (bCOMB @ (cCOMB @ sK0))) @ (cCOMB @ sK0)))))))) )), 0.21/0.62 inference(sigma_clausification,[],[f60])). 0.21/0.62 thf(f60,plain,( 0.21/0.62 ( ! [X2 : g,X1 : g] : ((sK1 != ((sK0 @ sK3) @ X1)) | (sK1 != ((sK0 @ X2) @ sK4)) | (sK5 != ((sK0 @ sK5) @ sK1)) | ($false = (vPI(g) @ ((sCOMB @ ((bCOMB @ vEQ(g)) @ (sK0 @ sK1))) @ iCOMB))) | ($false = (vPI(g) @ ((bCOMB @ vPI(g)) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vEQ(g)))) @ (cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sK0)) @ (cCOMB @ sK0)))))))) @ ((bCOMB @ (bCOMB @ (cCOMB @ sK0))) @ (cCOMB @ sK0)))))))) )), 0.21/0.62 inference(duplicate_literal_removal,[],[f59])). 0.21/0.62 thf(f59,plain,( 0.21/0.62 ( ! [X2 : g,X1 : g] : ((sK1 != ((sK0 @ sK3) @ X1)) | (sK1 != ((sK0 @ X2) @ sK4)) | (sK5 != ((sK0 @ sK5) @ sK1)) | ($false = (vPI(g) @ ((sCOMB @ ((bCOMB @ vEQ(g)) @ (sK0 @ sK1))) @ iCOMB))) | ($false = (vPI(g) @ ((bCOMB @ vPI(g)) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vEQ(g)))) @ (cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sK0)) @ (cCOMB @ sK0)))))))) @ ((bCOMB @ (bCOMB @ (cCOMB @ sK0))) @ (cCOMB @ sK0))))))) | ($false = (vPI(g) @ ((bCOMB @ vPI(g)) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vEQ(g)))) @ (cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sK0)) @ (cCOMB @ sK0)))))))) @ ((bCOMB @ (bCOMB @ (cCOMB @ sK0))) @ (cCOMB @ sK0)))))))) )), 0.21/0.62 inference(binary_proxy_clausification,[],[f58])). 0.21/0.62 thf(f58,plain,( 0.21/0.62 ( ! [X2 : g,X1 : g] : ((sK1 != ((sK0 @ sK3) @ X1)) | (sK1 != ((sK0 @ X2) @ sK4)) | (sK5 != ((sK0 @ sK5) @ sK1)) | ($false = ((vAND @ (vPI(g) @ ((bCOMB @ vPI(g)) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vEQ(g)))) @ (cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sK0)) @ (cCOMB @ sK0)))))))) @ ((bCOMB @ (bCOMB @ (cCOMB @ sK0))) @ (cCOMB @ sK0))))))) @ (vPI(g) @ ((sCOMB @ ((bCOMB @ vEQ(g)) @ (sK0 @ sK1))) @ iCOMB)))) | ($false = (vPI(g) @ ((bCOMB @ vPI(g)) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vEQ(g)))) @ (cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sK0)) @ (cCOMB @ sK0)))))))) @ ((bCOMB @ (bCOMB @ (cCOMB @ sK0))) @ (cCOMB @ sK0)))))))) )), 0.21/0.62 inference(equality_proxy_clausification,[],[f57])). 0.21/0.62 thf(f57,plain,( 0.21/0.62 ( ! [X2 : g,X1 : g] : ((sK1 != ((sK0 @ sK3) @ X1)) | (sK1 != ((sK0 @ X2) @ sK4)) | ($false = ((vEQ(g) @ ((sK0 @ sK5) @ sK1)) @ sK5)) | ($false = ((vAND @ (vPI(g) @ ((bCOMB @ vPI(g)) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vEQ(g)))) @ (cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sK0)) @ (cCOMB @ sK0)))))))) @ ((bCOMB @ (bCOMB @ (cCOMB @ sK0))) @ (cCOMB @ sK0))))))) @ (vPI(g) @ ((sCOMB @ ((bCOMB @ vEQ(g)) @ (sK0 @ sK1))) @ iCOMB)))) | ($false = (vPI(g) @ ((bCOMB @ vPI(g)) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vEQ(g)))) @ (cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sK0)) @ (cCOMB @ sK0)))))))) @ ((bCOMB @ (bCOMB @ (cCOMB @ sK0))) @ (cCOMB @ sK0)))))))) )), 0.21/0.62 inference(combinator_demodulation,[],[f56])). 0.21/0.62 thf(f56,plain,( 0.21/0.62 ( ! [X2 : g,X1 : g] : ((sK1 != ((sK0 @ sK3) @ X1)) | (sK1 != ((sK0 @ X2) @ sK4)) | ($false = (((sCOMB @ ((bCOMB @ vEQ(g)) @ ((cCOMB @ sK0) @ sK1))) @ iCOMB) @ sK5)) | ($false = ((vAND @ (vPI(g) @ ((bCOMB @ vPI(g)) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vEQ(g)))) @ (cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sK0)) @ (cCOMB @ sK0)))))))) @ ((bCOMB @ (bCOMB @ (cCOMB @ sK0))) @ (cCOMB @ sK0))))))) @ (vPI(g) @ ((sCOMB @ ((bCOMB @ vEQ(g)) @ (sK0 @ sK1))) @ iCOMB)))) | ($false = (vPI(g) @ ((bCOMB @ vPI(g)) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vEQ(g)))) @ (cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sK0)) @ (cCOMB @ sK0)))))))) @ ((bCOMB @ (bCOMB @ (cCOMB @ sK0))) @ (cCOMB @ sK0)))))))) )), 0.21/0.62 inference(sigma_clausification,[],[f55])). 0.21/0.62 thf(f55,plain,( 0.21/0.62 ( ! [X2 : g,X1 : g] : ((sK1 != ((sK0 @ sK3) @ X1)) | (sK1 != ((sK0 @ X2) @ sK4)) | ($false = (vPI(g) @ ((sCOMB @ ((bCOMB @ vEQ(g)) @ ((cCOMB @ sK0) @ sK1))) @ iCOMB))) | ($false = ((vAND @ (vPI(g) @ ((bCOMB @ vPI(g)) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vEQ(g)))) @ (cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sK0)) @ (cCOMB @ sK0)))))))) @ ((bCOMB @ (bCOMB @ (cCOMB @ sK0))) @ (cCOMB @ sK0))))))) @ (vPI(g) @ ((sCOMB @ ((bCOMB @ vEQ(g)) @ (sK0 @ sK1))) @ iCOMB)))) | ($false = (vPI(g) @ ((bCOMB @ vPI(g)) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vEQ(g)))) @ (cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sK0)) @ (cCOMB @ sK0)))))))) @ ((bCOMB @ (bCOMB @ (cCOMB @ sK0))) @ (cCOMB @ sK0)))))))) )), 0.21/0.62 inference(binary_proxy_clausification,[],[f54])). 0.21/0.62 thf(f54,plain,( 0.21/0.62 ( ! [X2 : g,X1 : g] : ((sK1 != ((sK0 @ sK3) @ X1)) | (sK1 != ((sK0 @ X2) @ sK4)) | ($false = ((vAND @ (vPI(g) @ ((bCOMB @ vPI(g)) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vEQ(g)))) @ (cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sK0)) @ (cCOMB @ sK0)))))))) @ ((bCOMB @ (bCOMB @ (cCOMB @ sK0))) @ (cCOMB @ sK0))))))) @ (vPI(g) @ ((sCOMB @ ((bCOMB @ vEQ(g)) @ ((cCOMB @ sK0) @ sK1))) @ iCOMB)))) | ($false = ((vAND @ (vPI(g) @ ((bCOMB @ vPI(g)) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vEQ(g)))) @ (cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sK0)) @ (cCOMB @ sK0)))))))) @ ((bCOMB @ (bCOMB @ (cCOMB @ sK0))) @ (cCOMB @ sK0))))))) @ (vPI(g) @ ((sCOMB @ ((bCOMB @ vEQ(g)) @ (sK0 @ sK1))) @ iCOMB))))) )), 0.21/0.62 inference(equality_proxy_clausification,[],[f53])). 0.21/0.62 thf(f53,plain,( 0.21/0.62 ( ! [X2 : g,X1 : g] : ((sK1 != ((sK0 @ sK3) @ X1)) | ($false = ((vEQ(g) @ ((sK0 @ X2) @ sK4)) @ sK1)) | ($false = ((vAND @ (vPI(g) @ ((bCOMB @ vPI(g)) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vEQ(g)))) @ (cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sK0)) @ (cCOMB @ sK0)))))))) @ ((bCOMB @ (bCOMB @ (cCOMB @ sK0))) @ (cCOMB @ sK0))))))) @ (vPI(g) @ ((sCOMB @ ((bCOMB @ vEQ(g)) @ ((cCOMB @ sK0) @ sK1))) @ iCOMB)))) | ($false = ((vAND @ (vPI(g) @ ((bCOMB @ vPI(g)) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vEQ(g)))) @ (cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sK0)) @ (cCOMB @ sK0)))))))) @ ((bCOMB @ (bCOMB @ (cCOMB @ sK0))) @ (cCOMB @ sK0))))))) @ (vPI(g) @ ((sCOMB @ ((bCOMB @ vEQ(g)) @ (sK0 @ sK1))) @ iCOMB))))) )), 0.21/0.62 inference(combinator_demodulation,[],[f52])). 0.21/0.62 thf(f52,plain,( 0.21/0.62 ( ! [X2 : g,X1 : g] : ((sK1 != ((sK0 @ sK3) @ X1)) | ($false = (((cCOMB @ ((bCOMB @ vEQ(g)) @ ((cCOMB @ sK0) @ sK4))) @ sK1) @ X2)) | ($false = ((vAND @ (vPI(g) @ ((bCOMB @ vPI(g)) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vEQ(g)))) @ (cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sK0)) @ (cCOMB @ sK0)))))))) @ ((bCOMB @ (bCOMB @ (cCOMB @ sK0))) @ (cCOMB @ sK0))))))) @ (vPI(g) @ ((sCOMB @ ((bCOMB @ vEQ(g)) @ ((cCOMB @ sK0) @ sK1))) @ iCOMB)))) | ($false = ((vAND @ (vPI(g) @ ((bCOMB @ vPI(g)) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vEQ(g)))) @ (cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sK0)) @ (cCOMB @ sK0)))))))) @ ((bCOMB @ (bCOMB @ (cCOMB @ sK0))) @ (cCOMB @ sK0))))))) @ (vPI(g) @ ((sCOMB @ ((bCOMB @ vEQ(g)) @ (sK0 @ sK1))) @ iCOMB))))) )), 0.21/0.62 inference(pi_clausification,[],[f51])). 0.21/0.62 thf(f51,plain,( 0.21/0.62 ( ! [X1 : g] : ((sK1 != ((sK0 @ sK3) @ X1)) | ($false = (vSIGMA(g) @ ((cCOMB @ ((bCOMB @ vEQ(g)) @ ((cCOMB @ sK0) @ sK4))) @ sK1))) | ($false = ((vAND @ (vPI(g) @ ((bCOMB @ vPI(g)) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vEQ(g)))) @ (cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sK0)) @ (cCOMB @ sK0)))))))) @ ((bCOMB @ (bCOMB @ (cCOMB @ sK0))) @ (cCOMB @ sK0))))))) @ (vPI(g) @ ((sCOMB @ ((bCOMB @ vEQ(g)) @ ((cCOMB @ sK0) @ sK1))) @ iCOMB)))) | ($false = ((vAND @ (vPI(g) @ ((bCOMB @ vPI(g)) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vEQ(g)))) @ (cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sK0)) @ (cCOMB @ sK0)))))))) @ ((bCOMB @ (bCOMB @ (cCOMB @ sK0))) @ (cCOMB @ sK0))))))) @ (vPI(g) @ ((sCOMB @ ((bCOMB @ vEQ(g)) @ (sK0 @ sK1))) @ iCOMB))))) )), 0.21/0.62 inference(combinator_demodulation,[],[f50])). 0.21/0.62 thf(f50,plain,( 0.21/0.62 ( ! [X1 : g] : ((sK1 != ((sK0 @ sK3) @ X1)) | ($false = (((bCOMB @ vSIGMA(g)) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ vEQ(g))) @ (cCOMB @ sK0)))) @ sK1)) @ sK4)) | ($false = ((vAND @ (vPI(g) @ ((bCOMB @ vPI(g)) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vEQ(g)))) @ (cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sK0)) @ (cCOMB @ sK0)))))))) @ ((bCOMB @ (bCOMB @ (cCOMB @ sK0))) @ (cCOMB @ sK0))))))) @ (vPI(g) @ ((sCOMB @ ((bCOMB @ vEQ(g)) @ ((cCOMB @ sK0) @ sK1))) @ iCOMB)))) | ($false = ((vAND @ (vPI(g) @ ((bCOMB @ vPI(g)) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vEQ(g)))) @ (cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sK0)) @ (cCOMB @ sK0)))))))) @ ((bCOMB @ (bCOMB @ (cCOMB @ sK0))) @ (cCOMB @ sK0))))))) @ (vPI(g) @ ((sCOMB @ ((bCOMB @ vEQ(g)) @ (sK0 @ sK1))) @ iCOMB))))) )), 0.21/0.62 inference(sigma_clausification,[],[f49])). 0.21/0.62 thf(f49,plain,( 0.21/0.62 ( ! [X1 : g] : ((sK1 != ((sK0 @ sK3) @ X1)) | ($false = (vPI(g) @ ((bCOMB @ vSIGMA(g)) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ vEQ(g))) @ (cCOMB @ sK0)))) @ sK1)))) | ($false = ((vAND @ (vPI(g) @ ((bCOMB @ vPI(g)) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vEQ(g)))) @ (cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sK0)) @ (cCOMB @ sK0)))))))) @ ((bCOMB @ (bCOMB @ (cCOMB @ sK0))) @ (cCOMB @ sK0))))))) @ (vPI(g) @ ((sCOMB @ ((bCOMB @ vEQ(g)) @ ((cCOMB @ sK0) @ sK1))) @ iCOMB)))) | ($false = ((vAND @ (vPI(g) @ ((bCOMB @ vPI(g)) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vEQ(g)))) @ (cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sK0)) @ (cCOMB @ sK0)))))))) @ ((bCOMB @ (bCOMB @ (cCOMB @ sK0))) @ (cCOMB @ sK0))))))) @ (vPI(g) @ ((sCOMB @ ((bCOMB @ vEQ(g)) @ (sK0 @ sK1))) @ iCOMB))))) )), 0.21/0.62 inference(binary_proxy_clausification,[],[f48])). 0.21/0.62 thf(f48,plain,( 0.21/0.62 ( ! [X1 : g] : ((sK1 != ((sK0 @ sK3) @ X1)) | ($false = ((vAND @ ((vAND @ (vPI(g) @ ((bCOMB @ vPI(g)) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vEQ(g)))) @ (cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sK0)) @ (cCOMB @ sK0)))))))) @ ((bCOMB @ (bCOMB @ (cCOMB @ sK0))) @ (cCOMB @ sK0))))))) @ (vPI(g) @ ((sCOMB @ ((bCOMB @ vEQ(g)) @ (sK0 @ sK1))) @ iCOMB)))) @ (vPI(g) @ ((bCOMB @ vSIGMA(g)) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ vEQ(g))) @ (cCOMB @ sK0)))) @ sK1))))) | ($false = ((vAND @ (vPI(g) @ ((bCOMB @ vPI(g)) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vEQ(g)))) @ (cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sK0)) @ (cCOMB @ sK0)))))))) @ ((bCOMB @ (bCOMB @ (cCOMB @ sK0))) @ (cCOMB @ sK0))))))) @ (vPI(g) @ ((sCOMB @ ((bCOMB @ vEQ(g)) @ ((cCOMB @ sK0) @ sK1))) @ iCOMB))))) )), 0.21/0.62 inference(equality_proxy_clausification,[],[f47])). 0.21/0.62 thf(f47,plain,( 0.21/0.62 ( ! [X1 : g] : (($false = ((vEQ(g) @ ((sK0 @ sK3) @ X1)) @ sK1)) | ($false = ((vAND @ ((vAND @ (vPI(g) @ ((bCOMB @ vPI(g)) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vEQ(g)))) @ (cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sK0)) @ (cCOMB @ sK0)))))))) @ ((bCOMB @ (bCOMB @ (cCOMB @ sK0))) @ (cCOMB @ sK0))))))) @ (vPI(g) @ ((sCOMB @ ((bCOMB @ vEQ(g)) @ (sK0 @ sK1))) @ iCOMB)))) @ (vPI(g) @ ((bCOMB @ vSIGMA(g)) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ vEQ(g))) @ (cCOMB @ sK0)))) @ sK1))))) | ($false = ((vAND @ (vPI(g) @ ((bCOMB @ vPI(g)) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vEQ(g)))) @ (cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sK0)) @ (cCOMB @ sK0)))))))) @ ((bCOMB @ (bCOMB @ (cCOMB @ sK0))) @ (cCOMB @ sK0))))))) @ (vPI(g) @ ((sCOMB @ ((bCOMB @ vEQ(g)) @ ((cCOMB @ sK0) @ sK1))) @ iCOMB))))) )), 0.21/0.62 inference(combinator_demodulation,[],[f46])). 0.21/0.62 thf(f46,plain,( 0.21/0.62 ( ! [X1 : g] : (($false = (((cCOMB @ ((bCOMB @ vEQ(g)) @ (sK0 @ sK3))) @ sK1) @ X1)) | ($false = ((vAND @ ((vAND @ (vPI(g) @ ((bCOMB @ vPI(g)) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vEQ(g)))) @ (cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sK0)) @ (cCOMB @ sK0)))))))) @ ((bCOMB @ (bCOMB @ (cCOMB @ sK0))) @ (cCOMB @ sK0))))))) @ (vPI(g) @ ((sCOMB @ ((bCOMB @ vEQ(g)) @ (sK0 @ sK1))) @ iCOMB)))) @ (vPI(g) @ ((bCOMB @ vSIGMA(g)) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ vEQ(g))) @ (cCOMB @ sK0)))) @ sK1))))) | ($false = ((vAND @ (vPI(g) @ ((bCOMB @ vPI(g)) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vEQ(g)))) @ (cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sK0)) @ (cCOMB @ sK0)))))))) @ ((bCOMB @ (bCOMB @ (cCOMB @ sK0))) @ (cCOMB @ sK0))))))) @ (vPI(g) @ ((sCOMB @ ((bCOMB @ vEQ(g)) @ ((cCOMB @ sK0) @ sK1))) @ iCOMB))))) )), 0.21/0.62 inference(pi_clausification,[],[f45])). 0.21/0.62 thf(f45,plain,( 0.21/0.62 ($false = (vSIGMA(g) @ ((cCOMB @ ((bCOMB @ vEQ(g)) @ (sK0 @ sK3))) @ sK1))) | ($false = ((vAND @ ((vAND @ (vPI(g) @ ((bCOMB @ vPI(g)) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vEQ(g)))) @ (cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sK0)) @ (cCOMB @ sK0)))))))) @ ((bCOMB @ (bCOMB @ (cCOMB @ sK0))) @ (cCOMB @ sK0))))))) @ (vPI(g) @ ((sCOMB @ ((bCOMB @ vEQ(g)) @ (sK0 @ sK1))) @ iCOMB)))) @ (vPI(g) @ ((bCOMB @ vSIGMA(g)) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ vEQ(g))) @ (cCOMB @ sK0)))) @ sK1))))) | ($false = ((vAND @ (vPI(g) @ ((bCOMB @ vPI(g)) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vEQ(g)))) @ (cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sK0)) @ (cCOMB @ sK0)))))))) @ ((bCOMB @ (bCOMB @ (cCOMB @ sK0))) @ (cCOMB @ sK0))))))) @ (vPI(g) @ ((sCOMB @ ((bCOMB @ vEQ(g)) @ ((cCOMB @ sK0) @ sK1))) @ iCOMB))))), 0.21/0.62 inference(combinator_demodulation,[],[f44])). 0.21/0.62 thf(f44,plain,( 0.21/0.62 ($false = (((bCOMB @ vSIGMA(g)) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ vEQ(g))) @ sK0))) @ sK1)) @ sK3)) | ($false = ((vAND @ ((vAND @ (vPI(g) @ ((bCOMB @ vPI(g)) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vEQ(g)))) @ (cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sK0)) @ (cCOMB @ sK0)))))))) @ ((bCOMB @ (bCOMB @ (cCOMB @ sK0))) @ (cCOMB @ sK0))))))) @ (vPI(g) @ ((sCOMB @ ((bCOMB @ vEQ(g)) @ (sK0 @ sK1))) @ iCOMB)))) @ (vPI(g) @ ((bCOMB @ vSIGMA(g)) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ vEQ(g))) @ (cCOMB @ sK0)))) @ sK1))))) | ($false = ((vAND @ (vPI(g) @ ((bCOMB @ vPI(g)) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vEQ(g)))) @ (cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sK0)) @ (cCOMB @ sK0)))))))) @ ((bCOMB @ (bCOMB @ (cCOMB @ sK0))) @ (cCOMB @ sK0))))))) @ (vPI(g) @ ((sCOMB @ ((bCOMB @ vEQ(g)) @ ((cCOMB @ sK0) @ sK1))) @ iCOMB))))), 0.21/0.62 inference(sigma_clausification,[],[f43])). 0.21/0.62 thf(f43,plain,( 0.21/0.62 ($false = (vPI(g) @ ((bCOMB @ vSIGMA(g)) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ vEQ(g))) @ sK0))) @ sK1)))) | ($false = ((vAND @ ((vAND @ (vPI(g) @ ((bCOMB @ vPI(g)) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vEQ(g)))) @ (cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sK0)) @ (cCOMB @ sK0)))))))) @ ((bCOMB @ (bCOMB @ (cCOMB @ sK0))) @ (cCOMB @ sK0))))))) @ (vPI(g) @ ((sCOMB @ ((bCOMB @ vEQ(g)) @ (sK0 @ sK1))) @ iCOMB)))) @ (vPI(g) @ ((bCOMB @ vSIGMA(g)) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ vEQ(g))) @ (cCOMB @ sK0)))) @ sK1))))) | ($false = ((vAND @ (vPI(g) @ ((bCOMB @ vPI(g)) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vEQ(g)))) @ (cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sK0)) @ (cCOMB @ sK0)))))))) @ ((bCOMB @ (bCOMB @ (cCOMB @ sK0))) @ (cCOMB @ sK0))))))) @ (vPI(g) @ ((sCOMB @ ((bCOMB @ vEQ(g)) @ ((cCOMB @ sK0) @ sK1))) @ iCOMB))))), 0.21/0.62 inference(binary_proxy_clausification,[],[f42])). 0.21/0.62 thf(f42,plain,( 0.21/0.62 ($false = ((vAND @ ((vAND @ (vPI(g) @ ((bCOMB @ vPI(g)) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vEQ(g)))) @ (cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sK0)) @ (cCOMB @ sK0)))))))) @ ((bCOMB @ (bCOMB @ (cCOMB @ sK0))) @ (cCOMB @ sK0))))))) @ (vPI(g) @ ((sCOMB @ ((bCOMB @ vEQ(g)) @ ((cCOMB @ sK0) @ sK1))) @ iCOMB)))) @ (vPI(g) @ ((bCOMB @ vSIGMA(g)) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ vEQ(g))) @ sK0))) @ sK1))))) | ($false = ((vAND @ ((vAND @ (vPI(g) @ ((bCOMB @ vPI(g)) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vEQ(g)))) @ (cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sK0)) @ (cCOMB @ sK0)))))))) @ ((bCOMB @ (bCOMB @ (cCOMB @ sK0))) @ (cCOMB @ sK0))))))) @ (vPI(g) @ ((sCOMB @ ((bCOMB @ vEQ(g)) @ (sK0 @ sK1))) @ iCOMB)))) @ (vPI(g) @ ((bCOMB @ vSIGMA(g)) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ vEQ(g))) @ (cCOMB @ sK0)))) @ sK1)))))), 0.21/0.62 inference(binary_proxy_clausification,[],[f40])). 0.21/0.62 thf(f40,plain,( 0.21/0.62 (((vAND @ ((vAND @ (vPI(g) @ ((bCOMB @ vPI(g)) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vEQ(g)))) @ (cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sK0)) @ (cCOMB @ sK0)))))))) @ ((bCOMB @ (bCOMB @ (cCOMB @ sK0))) @ (cCOMB @ sK0))))))) @ (vPI(g) @ ((sCOMB @ ((bCOMB @ vEQ(g)) @ ((cCOMB @ sK0) @ sK1))) @ iCOMB)))) @ (vPI(g) @ ((bCOMB @ vSIGMA(g)) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ vEQ(g))) @ sK0))) @ sK1)))) != ((vAND @ ((vAND @ (vPI(g) @ ((bCOMB @ vPI(g)) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vEQ(g)))) @ (cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sK0)) @ (cCOMB @ sK0)))))))) @ ((bCOMB @ (bCOMB @ (cCOMB @ sK0))) @ (cCOMB @ sK0))))))) @ (vPI(g) @ ((sCOMB @ ((bCOMB @ vEQ(g)) @ (sK0 @ sK1))) @ iCOMB)))) @ (vPI(g) @ ((bCOMB @ vSIGMA(g)) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ vEQ(g))) @ (cCOMB @ sK0)))) @ sK1)))))), 0.21/0.62 inference(combinator_demodulation,[],[f39])). 0.21/0.62 thf(f39,plain,( 0.21/0.62 (((((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vAND)) @ ((sCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ vAND) @ ((bCOMB @ vPI(g)) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((bCOMB @ (bCOMB @ (bCOMB @ vPI(g)))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ sCOMB))) @ ((bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vEQ(g))))) @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ cCOMB)) @ ((sCOMB @ ((bCOMB @ bCOMB) @ bCOMB)) @ cCOMB)))))))) @ ((sCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ bCOMB) @ cCOMB))) @ cCOMB)))))))) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vEQ(g)))) @ cCOMB)))) @ iCOMB)))))) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((bCOMB @ (bCOMB @ (bCOMB @ vSIGMA(g)))) @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ cCOMB)) @ (bCOMB @ (bCOMB @ vEQ(g)))))))) @ sK0) @ sK1) != ((((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vAND)) @ ((sCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ vAND) @ ((bCOMB @ vPI(g)) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((bCOMB @ (bCOMB @ (bCOMB @ vPI(g)))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ sCOMB))) @ ((bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vEQ(g))))) @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ cCOMB)) @ ((sCOMB @ ((bCOMB @ bCOMB) @ bCOMB)) @ cCOMB)))))))) @ ((sCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ bCOMB) @ cCOMB))) @ cCOMB)))))))) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ (bCOMB @ (bCOMB @ vEQ(g)))))) @ iCOMB)))))) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((bCOMB @ (bCOMB @ (bCOMB @ vSIGMA(g)))) @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ cCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vEQ(g)))) @ cCOMB)))))) @ sK0) @ sK1))), 0.21/0.62 inference(definition_unfolding,[],[f29,f38,f37])). 0.21/0.62 thf(f37,plain,( 0.21/0.62 (cGROUP2 = ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vAND)) @ ((sCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ vAND) @ ((bCOMB @ vPI(g)) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((bCOMB @ (bCOMB @ (bCOMB @ vPI(g)))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ sCOMB))) @ ((bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vEQ(g))))) @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ cCOMB)) @ ((sCOMB @ ((bCOMB @ bCOMB) @ bCOMB)) @ cCOMB)))))))) @ ((sCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ bCOMB) @ cCOMB))) @ cCOMB)))))))) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ (bCOMB @ (bCOMB @ vEQ(g)))))) @ iCOMB)))))) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((bCOMB @ (bCOMB @ (bCOMB @ vSIGMA(g)))) @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ cCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vEQ(g)))) @ cCOMB)))))))), 0.21/0.62 inference(definition_unfolding,[],[f30,f36,f32,f34])). 0.21/0.62 thf(f34,plain,( 0.21/0.62 (cGRP_LEFT_INVERSE = ((bCOMB @ (bCOMB @ vPI(g))) @ ((bCOMB @ (bCOMB @ (bCOMB @ vSIGMA(g)))) @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ cCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vEQ(g)))) @ cCOMB))))))), 0.21/0.62 inference(cnf_transformation,[],[f22])). 0.21/0.62 thf(f22,plain,( 0.21/0.62 (cGRP_LEFT_INVERSE = ((bCOMB @ (bCOMB @ vPI(g))) @ ((bCOMB @ (bCOMB @ (bCOMB @ vSIGMA(g)))) @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ cCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vEQ(g)))) @ cCOMB))))))), 0.21/0.62 inference(fool_elimination,[],[f21])). 0.21/0.62 thf(f21,plain,( 0.21/0.62 (cGRP_LEFT_INVERSE = (^[X0 : g > g > g, X1 : g] : (! [X2 : g] : ? [X3 : g] : (((X0 @ X3) @ X2) = X1))))), 0.21/0.62 inference(rectify,[],[f2])). 0.21/0.62 thf(f2,axiom,( 0.21/0.62 (cGRP_LEFT_INVERSE = (^[X0 : g > g > g, X4 : g] : (! [X1 : g] : ? [X2 : g] : (((X0 @ X2) @ X1) = X4))))), 0.21/0.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cGRP_LEFT_INVERSE_def)). 0.21/0.62 thf(f32,plain,( 0.21/0.62 (cGRP_LEFT_UNIT = ((bCOMB @ (bCOMB @ vPI(g))) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ (bCOMB @ (bCOMB @ vEQ(g)))))) @ iCOMB)))), 0.21/0.62 inference(cnf_transformation,[],[f18])). 0.21/0.62 thf(f18,plain,( 0.21/0.62 (cGRP_LEFT_UNIT = ((bCOMB @ (bCOMB @ vPI(g))) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ (bCOMB @ (bCOMB @ vEQ(g)))))) @ iCOMB)))), 0.21/0.62 inference(fool_elimination,[],[f17])). 0.21/0.62 thf(f17,plain,( 0.21/0.62 (cGRP_LEFT_UNIT = (^[X0 : g > g > g, X1 : g] : (! [X2 : g] : (((X0 @ X1) @ X2) = X2))))), 0.21/0.62 inference(rectify,[],[f3])). 0.21/0.62 thf(f3,axiom,( 0.21/0.62 (cGRP_LEFT_UNIT = (^[X0 : g > g > g, X4 : g] : (! [X1 : g] : (((X0 @ X4) @ X1) = X1))))), 0.21/0.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cGRP_LEFT_UNIT_def)). 0.21/0.62 thf(f36,plain,( 0.21/0.62 (cGRP_ASSOC = ((bCOMB @ vPI(g)) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((bCOMB @ (bCOMB @ (bCOMB @ vPI(g)))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ sCOMB))) @ ((bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vEQ(g))))) @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ cCOMB)) @ ((sCOMB @ ((bCOMB @ bCOMB) @ bCOMB)) @ cCOMB)))))))) @ ((sCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ bCOMB) @ cCOMB))) @ cCOMB))))))), 0.21/0.62 inference(cnf_transformation,[],[f25])). 0.21/0.62 thf(f25,plain,( 0.21/0.62 (cGRP_ASSOC = ((bCOMB @ vPI(g)) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((bCOMB @ (bCOMB @ (bCOMB @ vPI(g)))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ sCOMB))) @ ((bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vEQ(g))))) @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ cCOMB)) @ ((sCOMB @ ((bCOMB @ bCOMB) @ bCOMB)) @ cCOMB)))))))) @ ((sCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ bCOMB) @ cCOMB))) @ cCOMB))))))), 0.21/0.62 inference(fool_elimination,[],[f1])). 0.21/0.62 thf(f1,axiom,( 0.21/0.62 (cGRP_ASSOC = (^[X0 : g > g > g] : (! [X1 : g,X2 : g,X3 : g] : (((X0 @ ((X0 @ X1) @ X2)) @ X3) = ((X0 @ X1) @ ((X0 @ X2) @ X3))))))), 0.21/0.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cGRP_ASSOC_def)). 0.21/0.62 thf(f30,plain,( 0.21/0.62 (cGROUP2 = ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vAND)) @ ((sCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ vAND) @ cGRP_ASSOC))) @ cGRP_LEFT_UNIT)))) @ cGRP_LEFT_INVERSE))), 0.21/0.62 inference(cnf_transformation,[],[f14])). 0.21/0.62 thf(f14,plain,( 0.21/0.62 (cGROUP2 = ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vAND)) @ ((sCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ vAND) @ cGRP_ASSOC))) @ cGRP_LEFT_UNIT)))) @ cGRP_LEFT_INVERSE))), 0.21/0.62 inference(fool_elimination,[],[f13])). 0.21/0.62 thf(f13,plain,( 0.21/0.62 (cGROUP2 = (^[X0 : g > g > g, X1 : g] : (((cGRP_LEFT_INVERSE @ X0) @ X1) & ((cGRP_LEFT_UNIT @ X0) @ X1) & (cGRP_ASSOC @ X0))))), 0.21/0.62 inference(rectify,[],[f6])). 0.21/0.62 thf(f6,axiom,( 0.21/0.62 (cGROUP2 = (^[X0 : g > g > g, X4 : g] : (((cGRP_LEFT_INVERSE @ X0) @ X4) & ((cGRP_LEFT_UNIT @ X0) @ X4) & (cGRP_ASSOC @ X0))))), 0.21/0.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cGROUP2_def)). 0.21/0.62 thf(f38,plain,( 0.21/0.62 (cGROUP3 = ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vAND)) @ ((sCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ vAND) @ ((bCOMB @ vPI(g)) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((bCOMB @ (bCOMB @ (bCOMB @ vPI(g)))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ sCOMB))) @ ((bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vEQ(g))))) @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ cCOMB)) @ ((sCOMB @ ((bCOMB @ bCOMB) @ bCOMB)) @ cCOMB)))))))) @ ((sCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ bCOMB) @ cCOMB))) @ cCOMB)))))))) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vEQ(g)))) @ cCOMB)))) @ iCOMB)))))) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((bCOMB @ (bCOMB @ (bCOMB @ vSIGMA(g)))) @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ cCOMB)) @ (bCOMB @ (bCOMB @ vEQ(g)))))))))), 0.21/0.62 inference(definition_unfolding,[],[f31,f36,f33,f35])). 0.21/0.62 thf(f35,plain,( 0.21/0.62 (cGRP_RIGHT_INVERSE = ((bCOMB @ (bCOMB @ vPI(g))) @ ((bCOMB @ (bCOMB @ (bCOMB @ vSIGMA(g)))) @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ cCOMB)) @ (bCOMB @ (bCOMB @ vEQ(g))))))))), 0.21/0.62 inference(cnf_transformation,[],[f24])). 0.21/0.62 thf(f24,plain,( 0.21/0.62 (cGRP_RIGHT_INVERSE = ((bCOMB @ (bCOMB @ vPI(g))) @ ((bCOMB @ (bCOMB @ (bCOMB @ vSIGMA(g)))) @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ cCOMB)) @ (bCOMB @ (bCOMB @ vEQ(g))))))))), 0.21/0.62 inference(fool_elimination,[],[f23])). 0.21/0.62 thf(f23,plain,( 0.21/0.62 (cGRP_RIGHT_INVERSE = (^[X0 : g > g > g, X1 : g] : (! [X2 : g] : ? [X3 : g] : (((X0 @ X2) @ X3) = X1))))), 0.21/0.62 inference(rectify,[],[f4])). 0.21/0.62 thf(f4,axiom,( 0.21/0.62 (cGRP_RIGHT_INVERSE = (^[X0 : g > g > g, X4 : g] : (! [X1 : g] : ? [X2 : g] : (((X0 @ X1) @ X2) = X4))))), 0.21/0.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cGRP_RIGHT_INVERSE_def)). 0.21/0.62 thf(f33,plain,( 0.21/0.62 (cGRP_RIGHT_UNIT = ((bCOMB @ (bCOMB @ vPI(g))) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vEQ(g)))) @ cCOMB)))) @ iCOMB)))), 0.21/0.62 inference(cnf_transformation,[],[f20])). 0.21/0.62 thf(f20,plain,( 0.21/0.62 (cGRP_RIGHT_UNIT = ((bCOMB @ (bCOMB @ vPI(g))) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vEQ(g)))) @ cCOMB)))) @ iCOMB)))), 0.21/0.62 inference(fool_elimination,[],[f19])). 0.21/0.62 thf(f19,plain,( 0.21/0.62 (cGRP_RIGHT_UNIT = (^[X0 : g > g > g, X1 : g] : (! [X2 : g] : (((X0 @ X2) @ X1) = X2))))), 0.21/0.62 inference(rectify,[],[f5])). 0.21/0.62 thf(f5,axiom,( 0.21/0.62 (cGRP_RIGHT_UNIT = (^[X0 : g > g > g, X4 : g] : (! [X1 : g] : (((X0 @ X1) @ X4) = X1))))), 0.21/0.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cGRP_RIGHT_UNIT_def)). 0.21/0.62 thf(f31,plain,( 0.21/0.62 (cGROUP3 = ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vAND)) @ ((sCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ vAND) @ cGRP_ASSOC))) @ cGRP_RIGHT_UNIT)))) @ cGRP_RIGHT_INVERSE))), 0.21/0.62 inference(cnf_transformation,[],[f16])). 0.21/0.62 thf(f16,plain,( 0.21/0.62 (cGROUP3 = ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vAND)) @ ((sCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ vAND) @ cGRP_ASSOC))) @ cGRP_RIGHT_UNIT)))) @ cGRP_RIGHT_INVERSE))), 0.21/0.62 inference(fool_elimination,[],[f15])). 0.21/0.62 thf(f15,plain,( 0.21/0.62 (cGROUP3 = (^[X0 : g > g > g, X1 : g] : (((cGRP_RIGHT_INVERSE @ X0) @ X1) & ((cGRP_RIGHT_UNIT @ X0) @ X1) & (cGRP_ASSOC @ X0))))), 0.21/0.62 inference(rectify,[],[f7])). 0.21/0.62 thf(f7,axiom,( 0.21/0.62 (cGROUP3 = (^[X0 : g > g > g, X4 : g] : (((cGRP_RIGHT_INVERSE @ X0) @ X4) & ((cGRP_RIGHT_UNIT @ X0) @ X4) & (cGRP_ASSOC @ X0))))), 0.21/0.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cGROUP3_def)). 0.21/0.62 thf(f29,plain,( 0.21/0.62 (((cGROUP3 @ sK0) @ sK1) != ((cGROUP2 @ sK0) @ sK1))), 0.21/0.62 inference(cnf_transformation,[],[f28])). 0.21/0.62 thf(f28,plain,( 0.21/0.62 (((cGROUP3 @ sK0) @ sK1) != ((cGROUP2 @ sK0) @ sK1))), 0.21/0.62 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f26,f27])). 0.21/0.62 thf(f27,plain,( 0.21/0.62 ? [X0 : g > g > g,X1 : g] : (((cGROUP3 @ X0) @ X1) != ((cGROUP2 @ X0) @ X1)) => (((cGROUP3 @ sK0) @ sK1) != ((cGROUP2 @ sK0) @ sK1))), 0.21/0.62 introduced(choice_axiom,[])). 0.21/0.62 thf(f26,plain,( 0.21/0.62 ? [X0 : g > g > g,X1 : g] : (((cGROUP3 @ X0) @ X1) != ((cGROUP2 @ X0) @ X1))), 0.21/0.62 inference(ennf_transformation,[],[f12])). 0.21/0.62 thf(f12,plain,( 0.21/0.62 ~! [X0 : g > g > g,X1 : g] : (((cGROUP3 @ X0) @ X1) = ((cGROUP2 @ X0) @ X1))), 0.21/0.62 inference(fool_elimination,[],[f11])). 0.21/0.62 thf(f11,plain,( 0.21/0.62 ~! [X0 : g > g > g,X1 : g] : (((cGROUP3 @ X0) @ X1) <=> ((cGROUP2 @ X0) @ X1))), 0.21/0.62 inference(rectify,[],[f9])). 0.21/0.62 thf(f9,negated_conjecture,( 0.21/0.62 ~! [X0 : g > g > g,X4 : g] : (((cGROUP3 @ X0) @ X4) <=> ((cGROUP2 @ X0) @ X4))), 0.21/0.62 inference(negated_conjecture,[],[f8])). 0.21/0.62 thf(f8,conjecture,( 0.21/0.62 ! [X0 : g > g > g,X4 : g] : (((cGROUP3 @ X0) @ X4) <=> ((cGROUP2 @ X0) @ X4))), 0.21/0.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cEQUIV_02_03)). 0.21/0.62 thf(f181,plain,( 0.21/0.62 spl2_5 | spl2_5), 0.21/0.62 inference(avatar_split_clause,[],[f92,f164,f164])). 0.21/0.62 thf(f92,plain,( 0.21/0.62 ( ! [X6 : g,X4 : g,X2 : g,X5 : g,X3 : g,X1 : g] : ((((sK0 @ ((sK0 @ X3) @ X2)) @ X1) = ((sK0 @ X3) @ ((sK0 @ X2) @ X1))) | (((sK0 @ ((sK0 @ X6) @ X5)) @ X4) = ((sK0 @ X6) @ ((sK0 @ X5) @ X4)))) )), 0.21/0.62 inference(equality_proxy_clausification,[],[f91])). 0.21/0.62 thf(f91,plain,( 0.21/0.62 ( ! [X6 : g,X4 : g,X2 : g,X5 : g,X3 : g,X1 : g] : ((((sK0 @ ((sK0 @ X3) @ X2)) @ X1) = ((sK0 @ X3) @ ((sK0 @ X2) @ X1))) | ($true = ((vEQ(g) @ ((sK0 @ ((sK0 @ X6) @ X5)) @ X4)) @ ((sK0 @ X6) @ ((sK0 @ X5) @ X4))))) )), 0.21/0.62 inference(combinator_demodulation,[],[f90])). 0.21/0.62 thf(f90,plain,( 0.21/0.62 ( ! [X6 : g,X4 : g,X2 : g,X5 : g,X3 : g,X1 : g] : ((((sK0 @ ((sK0 @ X3) @ X2)) @ X1) = ((sK0 @ X3) @ ((sK0 @ X2) @ X1))) | ($true = (((sCOMB @ ((bCOMB @ vEQ(g)) @ ((cCOMB @ ((bCOMB @ sK0) @ ((cCOMB @ sK0) @ X5))) @ X4))) @ ((cCOMB @ sK0) @ ((sK0 @ X5) @ X4))) @ X6))) )), 0.21/0.62 inference(pi_clausification,[],[f89])). 0.21/0.62 thf(f89,plain,( 0.21/0.62 ( ! [X4 : g,X2 : g,X5 : g,X3 : g,X1 : g] : ((((sK0 @ ((sK0 @ X3) @ X2)) @ X1) = ((sK0 @ X3) @ ((sK0 @ X2) @ X1))) | ($true = (vPI(g) @ ((sCOMB @ ((bCOMB @ vEQ(g)) @ ((cCOMB @ ((bCOMB @ sK0) @ ((cCOMB @ sK0) @ X5))) @ X4))) @ ((cCOMB @ sK0) @ ((sK0 @ X5) @ X4)))))) )), 0.21/0.62 inference(combinator_demodulation,[],[f88])). 0.21/0.62 thf(f88,plain,( 0.21/0.62 ( ! [X4 : g,X2 : g,X5 : g,X3 : g,X1 : g] : ((((sK0 @ ((sK0 @ X3) @ X2)) @ X1) = ((sK0 @ X3) @ ((sK0 @ X2) @ X1))) | ($true = (((bCOMB @ vPI(g)) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vEQ(g))) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sK0)) @ (cCOMB @ sK0)))) @ X4)))) @ ((bCOMB @ (cCOMB @ sK0)) @ ((cCOMB @ sK0) @ X4)))) @ X5))) )), 0.21/0.62 inference(pi_clausification,[],[f87])). 0.21/0.62 thf(f87,plain,( 0.21/0.62 ( ! [X4 : g,X2 : g,X3 : g,X1 : g] : ((((sK0 @ ((sK0 @ X3) @ X2)) @ X1) = ((sK0 @ X3) @ ((sK0 @ X2) @ X1))) | ($true = (vPI(g) @ ((bCOMB @ vPI(g)) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vEQ(g))) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sK0)) @ (cCOMB @ sK0)))) @ X4)))) @ ((bCOMB @ (cCOMB @ sK0)) @ ((cCOMB @ sK0) @ X4))))))) )), 0.21/0.62 inference(combinator_demodulation,[],[f86])). 0.21/0.62 thf(f86,plain,( 0.21/0.62 ( ! [X4 : g,X2 : g,X3 : g,X1 : g] : ((((sK0 @ ((sK0 @ X3) @ X2)) @ X1) = ((sK0 @ X3) @ ((sK0 @ X2) @ X1))) | ($true = (((bCOMB @ vPI(g)) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vEQ(g)))) @ (cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sK0)) @ (cCOMB @ sK0)))))))) @ ((bCOMB @ (bCOMB @ (cCOMB @ sK0))) @ (cCOMB @ sK0))))) @ X4))) )), 0.21/0.62 inference(pi_clausification,[],[f85])). 0.21/0.62 thf(f85,plain,( 0.21/0.62 ( ! [X2 : g,X3 : g,X1 : g] : ((((sK0 @ ((sK0 @ X3) @ X2)) @ X1) = ((sK0 @ X3) @ ((sK0 @ X2) @ X1))) | ($true = (vPI(g) @ ((bCOMB @ vPI(g)) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vEQ(g)))) @ (cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sK0)) @ (cCOMB @ sK0)))))))) @ ((bCOMB @ (bCOMB @ (cCOMB @ sK0))) @ (cCOMB @ sK0)))))))) )), 0.21/0.62 inference(binary_proxy_clausification,[],[f83])). 0.21/0.62 thf(f83,plain,( 0.21/0.62 ( ! [X2 : g,X3 : g,X1 : g] : ((((sK0 @ ((sK0 @ X3) @ X2)) @ X1) = ((sK0 @ X3) @ ((sK0 @ X2) @ X1))) | ($true = ((vAND @ (vPI(g) @ ((bCOMB @ vPI(g)) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vEQ(g)))) @ (cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sK0)) @ (cCOMB @ sK0)))))))) @ ((bCOMB @ (bCOMB @ (cCOMB @ sK0))) @ (cCOMB @ sK0))))))) @ (vPI(g) @ ((sCOMB @ ((bCOMB @ vEQ(g)) @ (sK0 @ sK1))) @ iCOMB))))) )), 0.21/0.62 inference(binary_proxy_clausification,[],[f81])). 0.21/0.62 thf(f81,plain,( 0.21/0.62 ( ! [X2 : g,X3 : g,X1 : g] : ((((sK0 @ ((sK0 @ X3) @ X2)) @ X1) = ((sK0 @ X3) @ ((sK0 @ X2) @ X1))) | ($true = ((vAND @ ((vAND @ (vPI(g) @ ((bCOMB @ vPI(g)) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vEQ(g)))) @ (cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sK0)) @ (cCOMB @ sK0)))))))) @ ((bCOMB @ (bCOMB @ (cCOMB @ sK0))) @ (cCOMB @ sK0))))))) @ (vPI(g) @ ((sCOMB @ ((bCOMB @ vEQ(g)) @ (sK0 @ sK1))) @ iCOMB)))) @ (vPI(g) @ ((bCOMB @ vSIGMA(g)) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ vEQ(g))) @ (cCOMB @ sK0)))) @ sK1)))))) )), 0.21/0.62 inference(equality_proxy_clausification,[],[f80])). 0.21/0.62 thf(f80,plain,( 0.21/0.62 ( ! [X2 : g,X3 : g,X1 : g] : (($true = ((vEQ(g) @ ((sK0 @ ((sK0 @ X3) @ X2)) @ X1)) @ ((sK0 @ X3) @ ((sK0 @ X2) @ X1)))) | ($true = ((vAND @ ((vAND @ (vPI(g) @ ((bCOMB @ vPI(g)) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vEQ(g)))) @ (cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sK0)) @ (cCOMB @ sK0)))))))) @ ((bCOMB @ (bCOMB @ (cCOMB @ sK0))) @ (cCOMB @ sK0))))))) @ (vPI(g) @ ((sCOMB @ ((bCOMB @ vEQ(g)) @ (sK0 @ sK1))) @ iCOMB)))) @ (vPI(g) @ ((bCOMB @ vSIGMA(g)) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ vEQ(g))) @ (cCOMB @ sK0)))) @ sK1)))))) )), 0.21/0.62 inference(combinator_demodulation,[],[f79])). 0.21/0.62 thf(f79,plain,( 0.21/0.62 ( ! 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[X1 : g] : (($true = (vPI(g) @ ((bCOMB @ vPI(g)) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vEQ(g))) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sK0)) @ (cCOMB @ sK0)))) @ X1)))) @ ((bCOMB @ (cCOMB @ sK0)) @ ((cCOMB @ sK0) @ X1)))))) | ($true = ((vAND @ ((vAND @ (vPI(g) @ ((bCOMB @ vPI(g)) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vEQ(g)))) @ (cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sK0)) @ (cCOMB @ sK0)))))))) @ ((bCOMB @ (bCOMB @ (cCOMB @ sK0))) @ (cCOMB @ sK0))))))) @ (vPI(g) @ ((sCOMB @ ((bCOMB @ vEQ(g)) @ (sK0 @ sK1))) @ iCOMB)))) @ (vPI(g) @ ((bCOMB @ vSIGMA(g)) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ vEQ(g))) @ (cCOMB @ sK0)))) @ sK1)))))) )), 0.21/0.62 inference(combinator_demodulation,[],[f75])). 0.21/0.62 thf(f75,plain,( 0.21/0.62 ( ! [X1 : g] : (($true = (((bCOMB @ vPI(g)) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vEQ(g)))) @ (cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sK0)) @ (cCOMB @ sK0)))))))) @ ((bCOMB @ (bCOMB @ (cCOMB @ sK0))) @ (cCOMB @ sK0))))) @ X1)) | ($true = ((vAND @ ((vAND @ (vPI(g) @ ((bCOMB @ vPI(g)) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vEQ(g)))) @ (cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sK0)) @ (cCOMB @ sK0)))))))) @ ((bCOMB @ (bCOMB @ (cCOMB @ sK0))) @ (cCOMB @ sK0))))))) @ (vPI(g) @ ((sCOMB @ ((bCOMB @ vEQ(g)) @ (sK0 @ sK1))) @ iCOMB)))) @ (vPI(g) @ ((bCOMB @ vSIGMA(g)) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ vEQ(g))) @ (cCOMB @ sK0)))) @ sK1)))))) )), 0.21/0.62 inference(pi_clausification,[],[f74])). 0.21/0.62 thf(f74,plain,( 0.21/0.62 ($true = (vPI(g) @ ((bCOMB @ vPI(g)) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vEQ(g)))) @ (cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sK0)) @ (cCOMB @ sK0)))))))) @ ((bCOMB @ (bCOMB @ (cCOMB @ sK0))) @ (cCOMB @ sK0))))))) | ($true = ((vAND @ ((vAND @ (vPI(g) @ ((bCOMB @ vPI(g)) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vEQ(g)))) @ (cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sK0)) @ (cCOMB @ sK0)))))))) @ ((bCOMB @ (bCOMB @ (cCOMB @ sK0))) @ (cCOMB @ sK0))))))) @ (vPI(g) @ ((sCOMB @ ((bCOMB @ vEQ(g)) @ (sK0 @ sK1))) @ iCOMB)))) @ (vPI(g) @ ((bCOMB @ vSIGMA(g)) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ vEQ(g))) @ (cCOMB @ sK0)))) @ sK1)))))), 0.21/0.62 inference(binary_proxy_clausification,[],[f72])). 0.21/0.62 thf(f72,plain,( 0.21/0.62 ($true = ((vAND @ (vPI(g) @ ((bCOMB @ vPI(g)) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vEQ(g)))) @ (cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sK0)) @ (cCOMB @ sK0)))))))) @ ((bCOMB @ (bCOMB @ (cCOMB @ sK0))) @ (cCOMB @ sK0))))))) @ (vPI(g) @ ((sCOMB @ ((bCOMB @ vEQ(g)) @ ((cCOMB @ sK0) @ sK1))) @ iCOMB)))) | ($true = ((vAND @ ((vAND @ (vPI(g) @ ((bCOMB @ vPI(g)) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vEQ(g)))) @ (cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sK0)) @ (cCOMB @ sK0)))))))) @ ((bCOMB @ (bCOMB @ (cCOMB @ sK0))) @ (cCOMB @ sK0))))))) @ (vPI(g) @ ((sCOMB @ ((bCOMB @ vEQ(g)) @ (sK0 @ sK1))) @ iCOMB)))) @ (vPI(g) @ ((bCOMB @ vSIGMA(g)) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ vEQ(g))) @ (cCOMB @ sK0)))) @ sK1)))))), 0.21/0.62 inference(binary_proxy_clausification,[],[f41])). 0.21/0.62 thf(f41,plain,( 0.21/0.62 ($true = ((vAND @ ((vAND @ (vPI(g) @ ((bCOMB @ vPI(g)) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vEQ(g)))) @ (cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sK0)) @ (cCOMB @ sK0)))))))) @ ((bCOMB @ (bCOMB @ (cCOMB @ sK0))) @ (cCOMB @ sK0))))))) @ (vPI(g) @ ((sCOMB @ ((bCOMB @ vEQ(g)) @ ((cCOMB @ sK0) @ sK1))) @ iCOMB)))) @ (vPI(g) @ ((bCOMB @ vSIGMA(g)) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ vEQ(g))) @ sK0))) @ sK1))))) | ($true = ((vAND @ ((vAND @ (vPI(g) @ ((bCOMB @ vPI(g)) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vEQ(g)))) @ (cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sK0)) @ (cCOMB @ sK0)))))))) @ ((bCOMB @ (bCOMB @ (cCOMB @ sK0))) @ (cCOMB @ sK0))))))) @ (vPI(g) @ ((sCOMB @ ((bCOMB @ vEQ(g)) @ (sK0 @ sK1))) @ iCOMB)))) @ (vPI(g) @ ((bCOMB @ vSIGMA(g)) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ vEQ(g))) @ (cCOMB @ sK0)))) @ sK1)))))), 0.21/0.62 inference(binary_proxy_clausification,[],[f40])). 0.21/0.62 thf(f174,plain,( 0.21/0.62 spl2_4 | spl2_7), 0.21/0.62 inference(avatar_split_clause,[],[f117,f171,f160])). 0.21/0.62 thf(f117,plain,( 0.21/0.62 ( ! 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[X1 : g] : ((((sK0 @ X1) @ sK1) = X1) | ($true = ((vAND @ (vPI(g) @ ((bCOMB @ vPI(g)) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vEQ(g)))) @ (cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sK0)) @ (cCOMB @ sK0)))))))) @ ((bCOMB @ (bCOMB @ (cCOMB @ sK0))) @ (cCOMB @ sK0))))))) @ (vPI(g) @ ((sCOMB @ ((bCOMB @ vEQ(g)) @ (sK0 @ sK1))) @ iCOMB))))) )), 0.21/0.62 inference(binary_proxy_clausification,[],[f103])). 0.21/0.62 thf(f103,plain,( 0.21/0.62 ( ! 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[X2 : g,X1 : g] : ((((sK0 @ X1) @ sK1) = X1) | (sK1 = ((sK0 @ (sK11 @ X2)) @ X2))) )), 0.21/0.62 inference(equality_proxy_clausification,[],[f121])). 0.21/0.62 thf(f121,plain,( 0.21/0.62 ( ! [X2 : g,X1 : g] : ((((sK0 @ X1) @ sK1) = X1) | ($true = ((vEQ(g) @ ((sK0 @ (sK11 @ X2)) @ X2)) @ sK1))) )), 0.21/0.62 inference(combinator_demodulation,[],[f120])). 0.21/0.62 thf(f120,plain,( 0.21/0.62 ( ! [X2 : g,X1 : g] : ((((sK0 @ X1) @ sK1) = X1) | ($true = (((cCOMB @ ((bCOMB @ vEQ(g)) @ ((cCOMB @ sK0) @ X2))) @ sK1) @ (sK11 @ X2)))) )), 0.21/0.62 inference(sigma_clausification,[],[f119])). 0.21/0.62 thf(f119,plain,( 0.21/0.62 ( ! [X2 : g,X1 : g] : ((((sK0 @ X1) @ sK1) = X1) | ($true = (vSIGMA(g) @ ((cCOMB @ ((bCOMB @ vEQ(g)) @ ((cCOMB @ sK0) @ X2))) @ sK1)))) )), 0.21/0.62 inference(combinator_demodulation,[],[f118])). 0.21/0.62 thf(f118,plain,( 0.21/0.62 ( ! [X2 : g,X1 : g] : ((((sK0 @ X1) @ sK1) = X1) | ($true = (((bCOMB @ vSIGMA(g)) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ vEQ(g))) @ (cCOMB @ sK0)))) @ sK1)) @ X2))) )), 0.21/0.62 inference(pi_clausification,[],[f104])). 0.21/0.62 thf(f104,plain,( 0.21/0.62 ( ! [X1 : g] : ((((sK0 @ X1) @ sK1) = X1) | ($true = (vPI(g) @ ((bCOMB @ vSIGMA(g)) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ vEQ(g))) @ (cCOMB @ sK0)))) @ sK1))))) )), 0.21/0.62 inference(binary_proxy_clausification,[],[f103])). 0.21/0.62 thf(f162,plain,( 0.21/0.62 spl2_4 | spl2_3), 0.21/0.62 inference(avatar_split_clause,[],[f141,f156,f160])). 0.21/0.62 thf(f141,plain,( 0.21/0.62 ( ! [X2 : g,X1 : g] : ((sK1 = ((sK0 @ X1) @ (sK12 @ X1))) | (((sK0 @ sK1) @ X2) = X2)) )), 0.21/0.62 inference(equality_proxy_clausification,[],[f140])). 0.21/0.62 thf(f140,plain,( 0.21/0.62 ( ! [X2 : g,X1 : g] : ((sK1 = ((sK0 @ X1) @ (sK12 @ X1))) | ($true = ((vEQ(g) @ ((sK0 @ sK1) @ X2)) @ X2))) )), 0.21/0.62 inference(combinator_demodulation,[],[f139])). 0.21/0.62 thf(f139,plain,( 0.21/0.62 ( ! [X2 : g,X1 : g] : ((sK1 = ((sK0 @ X1) @ (sK12 @ X1))) | ($true = (((sCOMB @ ((bCOMB @ vEQ(g)) @ (sK0 @ sK1))) @ iCOMB) @ X2))) )), 0.21/0.62 inference(pi_clausification,[],[f130])). 0.21/0.62 thf(f130,plain,( 0.21/0.62 ( ! [X1 : g] : ((sK1 = ((sK0 @ X1) @ (sK12 @ X1))) | ($true = (vPI(g) @ ((sCOMB @ ((bCOMB @ vEQ(g)) @ (sK0 @ sK1))) @ iCOMB)))) )), 0.21/0.62 inference(binary_proxy_clausification,[],[f129])). 0.21/0.62 thf(f129,plain,( 0.21/0.62 ( ! [X1 : g] : ((sK1 = ((sK0 @ X1) @ (sK12 @ X1))) | ($true = ((vAND @ (vPI(g) @ ((bCOMB @ vPI(g)) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vEQ(g)))) @ (cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sK0)) @ (cCOMB @ sK0)))))))) @ ((bCOMB @ (bCOMB @ (cCOMB @ sK0))) @ (cCOMB @ sK0))))))) @ (vPI(g) @ ((sCOMB @ ((bCOMB @ vEQ(g)) @ (sK0 @ sK1))) @ iCOMB))))) )), 0.21/0.62 inference(binary_proxy_clausification,[],[f127])). 0.21/0.62 thf(f127,plain,( 0.21/0.62 ( ! [X1 : g] : ((sK1 = ((sK0 @ X1) @ (sK12 @ X1))) | ($true = ((vAND @ ((vAND @ (vPI(g) @ ((bCOMB @ vPI(g)) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vEQ(g)))) @ (cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sK0)) @ (cCOMB @ sK0)))))))) @ ((bCOMB @ (bCOMB @ (cCOMB @ sK0))) @ (cCOMB @ sK0))))))) @ (vPI(g) @ ((sCOMB @ ((bCOMB @ vEQ(g)) @ (sK0 @ sK1))) @ iCOMB)))) @ (vPI(g) @ ((bCOMB @ vSIGMA(g)) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ vEQ(g))) @ (cCOMB @ sK0)))) @ sK1)))))) )), 0.21/0.62 inference(equality_proxy_clausification,[],[f126])). 0.21/0.62 thf(f126,plain,( 0.21/0.62 ( ! [X1 : g] : (($true = ((vEQ(g) @ ((sK0 @ X1) @ (sK12 @ X1))) @ sK1)) | ($true = ((vAND @ ((vAND @ (vPI(g) @ ((bCOMB @ vPI(g)) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vEQ(g)))) @ (cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sK0)) @ (cCOMB @ sK0)))))))) @ ((bCOMB @ (bCOMB @ (cCOMB @ sK0))) @ (cCOMB @ sK0))))))) @ (vPI(g) @ ((sCOMB @ ((bCOMB @ vEQ(g)) @ (sK0 @ sK1))) @ iCOMB)))) @ (vPI(g) @ ((bCOMB @ vSIGMA(g)) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ vEQ(g))) @ (cCOMB @ sK0)))) @ sK1)))))) )), 0.21/0.62 inference(combinator_demodulation,[],[f125])). 0.21/0.62 thf(f125,plain,( 0.21/0.62 ( ! [X1 : g] : (($true = (((cCOMB @ ((bCOMB @ vEQ(g)) @ (sK0 @ X1))) @ sK1) @ (sK12 @ X1))) | ($true = ((vAND @ ((vAND @ (vPI(g) @ ((bCOMB @ vPI(g)) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vEQ(g)))) @ (cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sK0)) @ (cCOMB @ sK0)))))))) @ ((bCOMB @ (bCOMB @ (cCOMB @ sK0))) @ (cCOMB @ sK0))))))) @ (vPI(g) @ ((sCOMB @ ((bCOMB @ vEQ(g)) @ (sK0 @ sK1))) @ iCOMB)))) @ (vPI(g) @ ((bCOMB @ vSIGMA(g)) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ vEQ(g))) @ (cCOMB @ sK0)))) @ sK1)))))) )), 0.21/0.62 inference(sigma_clausification,[],[f124])). 0.21/0.62 thf(f124,plain,( 0.21/0.62 ( ! [X1 : g] : (($true = (vSIGMA(g) @ ((cCOMB @ ((bCOMB @ vEQ(g)) @ (sK0 @ X1))) @ sK1))) | ($true = ((vAND @ ((vAND @ (vPI(g) @ ((bCOMB @ vPI(g)) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vEQ(g)))) @ (cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sK0)) @ (cCOMB @ sK0)))))))) @ ((bCOMB @ (bCOMB @ (cCOMB @ sK0))) @ (cCOMB @ sK0))))))) @ (vPI(g) @ ((sCOMB @ ((bCOMB @ vEQ(g)) @ (sK0 @ sK1))) @ iCOMB)))) @ (vPI(g) @ ((bCOMB @ vSIGMA(g)) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ vEQ(g))) @ (cCOMB @ sK0)))) @ sK1)))))) )), 0.21/0.62 inference(combinator_demodulation,[],[f123])). 0.21/0.62 thf(f123,plain,( 0.21/0.62 ( ! [X1 : g] : (($true = (((bCOMB @ vSIGMA(g)) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ vEQ(g))) @ sK0))) @ sK1)) @ X1)) | ($true = ((vAND @ ((vAND @ (vPI(g) @ ((bCOMB @ vPI(g)) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vEQ(g)))) @ (cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sK0)) @ (cCOMB @ sK0)))))))) @ ((bCOMB @ (bCOMB @ (cCOMB @ sK0))) @ (cCOMB @ sK0))))))) @ (vPI(g) @ ((sCOMB @ ((bCOMB @ vEQ(g)) @ (sK0 @ sK1))) @ iCOMB)))) @ (vPI(g) @ ((bCOMB @ vSIGMA(g)) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ vEQ(g))) @ (cCOMB @ sK0)))) @ sK1)))))) )), 0.21/0.62 inference(pi_clausification,[],[f71])). 0.21/0.62 thf(f71,plain,( 0.21/0.62 ($true = (vPI(g) @ ((bCOMB @ vSIGMA(g)) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ vEQ(g))) @ sK0))) @ sK1)))) | ($true = ((vAND @ ((vAND @ (vPI(g) @ ((bCOMB @ vPI(g)) @ ((bCOMB @ (bCOMB @ vPI(g))) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vEQ(g)))) @ (cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sK0)) @ (cCOMB @ sK0)))))))) @ ((bCOMB @ (bCOMB @ (cCOMB @ sK0))) @ (cCOMB @ sK0))))))) @ (vPI(g) @ ((sCOMB @ ((bCOMB @ vEQ(g)) @ (sK0 @ sK1))) @ iCOMB)))) @ (vPI(g) @ ((bCOMB @ vSIGMA(g)) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ vEQ(g))) @ (cCOMB @ sK0)))) @ sK1)))))), 0.21/0.62 inference(binary_proxy_clausification,[],[f41])). 0.21/0.62 thf(f158,plain,( 0.21/0.62 spl2_2 | spl2_3), 0.21/0.62 inference(avatar_split_clause,[],[f146,f156,f153])). 0.21/0.62 thf(f146,plain,( 0.21/0.62 ( ! [X2 : g,X1 : g] : ((sK1 = ((sK0 @ X1) @ (sK12 @ X1))) | (sK1 = ((sK0 @ (sK13 @ X2)) @ X2))) )), 0.21/0.62 inference(equality_proxy_clausification,[],[f145])). 0.21/0.62 thf(f145,plain,( 0.21/0.62 ( ! [X2 : g,X1 : g] : ((sK1 = ((sK0 @ X1) @ (sK12 @ X1))) | ($true = ((vEQ(g) @ ((sK0 @ (sK13 @ X2)) @ X2)) @ sK1))) )), 0.21/0.62 inference(combinator_demodulation,[],[f144])). 0.21/0.62 thf(f144,plain,( 0.21/0.62 ( ! [X2 : g,X1 : g] : ((sK1 = ((sK0 @ X1) @ (sK12 @ X1))) | ($true = (((cCOMB @ ((bCOMB @ vEQ(g)) @ ((cCOMB @ sK0) @ X2))) @ sK1) @ (sK13 @ X2)))) )), 0.21/0.62 inference(sigma_clausification,[],[f143])). 0.21/0.62 thf(f143,plain,( 0.21/0.62 ( ! [X2 : g,X1 : g] : ((sK1 = ((sK0 @ X1) @ (sK12 @ X1))) | ($true = (vSIGMA(g) @ ((cCOMB @ ((bCOMB @ vEQ(g)) @ ((cCOMB @ sK0) @ X2))) @ sK1)))) )), 0.21/0.62 inference(combinator_demodulation,[],[f142])). 0.21/0.62 thf(f142,plain,( 0.21/0.62 ( ! [X2 : g,X1 : g] : ((sK1 = ((sK0 @ X1) @ (sK12 @ X1))) | ($true = (((bCOMB @ vSIGMA(g)) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ vEQ(g))) @ (cCOMB @ sK0)))) @ sK1)) @ X2))) )), 0.21/0.62 inference(pi_clausification,[],[f128])). 0.21/0.62 thf(f128,plain,( 0.21/0.62 ( ! [X1 : g] : ((sK1 = ((sK0 @ X1) @ (sK12 @ X1))) | ($true = (vPI(g) @ ((bCOMB @ vSIGMA(g)) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ vEQ(g))) @ (cCOMB @ sK0)))) @ sK1))))) )), 0.21/0.62 inference(binary_proxy_clausification,[],[f127])). 0.21/0.62 % SZS output end Proof for theBenchmark 0.21/0.62 % (22029)------------------------------ 0.21/0.62 % (22029)Version: Vampire 4.6.0 (commit 0afb7ed4a on 2021-06-23 15:27:21 +0100) 0.21/0.62 % (22029)Termination reason: Refutation 0.21/0.62 0.21/0.62 % (22029)Memory used [KB]: 11129 0.21/0.62 % (22029)Time elapsed: 0.182 s 0.21/0.62 % (22029)------------------------------ 0.21/0.62 % (22029)------------------------------ 0.21/0.62 % (22019)Success in time 0.258 s 0.21/0.62 EOF