0.09/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.09/0.12 % Command : run_vampire %s %d 0.11/0.32 % Computer : n012.cluster.edu 0.11/0.32 % Model : x86_64 x86_64 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.11/0.32 % Memory : 8042.1875MB 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 0.11/0.32 % CPULimit : 960 0.11/0.32 % WCLimit : 120 0.11/0.32 % DateTime : Thu Jul 2 07:47:51 EDT 2020 0.11/0.33 % CPUTime : 0.11/0.35 % (18721)dis+10_4_av=off:bsr=on:csup=on:inj=on:chr=on:foolp=on:cnfonf=eager:cond=fast:er=filter:fde=none:gsp=input_only:lcm=reverse:lma=on:nwc=4:sp=occurrence:urr=on_8 on theBenchmark 0.11/0.36 % (18713)lrs+1002_1_av=off:er=filter:csup=on:inj=on:chr=on:foolp=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_1 on theBenchmark 0.11/0.36 % (18708)dis+1_2:3_acc=on:add=large:csup=on:inj=on:chr=on:foolp=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_3 on theBenchmark 0.11/0.37 % (18701)lrs+1011_8_add=large:csup=on:inj=on:chr=on:foolp=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_3 on theBenchmark 0.11/0.37 % (18705)lrs+1011_5:1_acc=on:csup=on:inj=on:chr=on:foolp=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_3 on theBenchmark 0.11/0.37 % (18716)lrs+1011_5:1_acc=on:csup=on:inj=on:e2e=on:prag=on:foolp=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_30 on theBenchmark 0.11/0.37 % (18700)lrs-11_4:1_afp=4000:csup=on:inj=on:chr=on:foolp=on:cnfonf=eager:afq=2.0:anc=none:br=off:gs=on:lwlo=on:nm=64:nwc=3:stl=30:urr=on_2 on theBenchmark 0.11/0.38 % (18699)ott+1002_2_av=off:bd=preordered:csup=on:inj=on:chr=on:foolp=on:cnfonf=eager:irw=on:lma=on:nm=64:nwc=10:sp=reverse_arity:updr=off_2 on theBenchmark 0.11/0.38 % (18707)dis+1010_3:2_av=off:csup=on:inj=on:chr=on:foolp=on:cnfonf=eager:gsp=input_only:nm=2:nwc=1:sp=reverse_arity:urr=ec_only_29 on theBenchmark 0.11/0.38 % (18709)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_40 on theBenchmark 0.11/0.38 % (18712)lrs+1010_3_av=off:fsr=off:csup=on:inj=on:chr=on:foolp=on:cnfonf=eager:gs=on:gsem=off:nm=2:newcnf=on:nwc=2:stl=30:sp=reverse_arity:urr=on:updr=off_9 on theBenchmark 0.11/0.39 % (18724)lrs+1010_8_add=off:afp=100000:csup=on:inj=off:foolp=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_13 on theBenchmark 0.11/0.39 % (18710)dis-11_3_add=off:afp=40000:csup=on:inj=on:chr=on:foolp=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_2 on theBenchmark 0.11/0.39 % (18718)dis+1002_3:1_acc=model:csup=on:inj=on:chr=on:foolp=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_8 on theBenchmark 0.11/0.40 % (18726)lrs-11_4:1_afp=4000:csup=on:inj=on:mXXn=1:foolp=on:e2e=on:cnfonf=eager:afq=2.0:anc=none:br=off:gs=on:lwlo=on:nm=64:nwc=3:stl=30:urr=on_186 on theBenchmark 0.11/0.40 % (18722)lrs+1002_1_add=large:csup=on:inj=on:fe=off:chr=on:foolp=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_50 on theBenchmark 0.11/0.40 % (18703)lrs+1010_8_add=off:afp=100000:csup=on:inj=on:chr=on:foolp=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_13 on theBenchmark 0.11/0.40 % (18702)dis+10_128_acc=on:add=off:csup=on:inj=on:chr=on:foolp=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_2 on theBenchmark 0.11/0.40 % (18720)lrs-11_4:1_afp=4000:csup=on:inj=on:chr=on:foolp=on:cnfonf=lazy_gen:afq=2.0:anc=none:br=off:gs=on:lwlo=on:nm=64:nwc=3:stl=30:urr=on_30 on theBenchmark 0.11/0.40 % (18704)ott+1002_8:1_add=off:csup=on:inj=on:chr=on:foolp=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_14 on theBenchmark 0.11/0.40 % (18727)dis+1002_4_add=large:csup=on:inj=on:chr=on:foolp=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 0.11/0.40 % (18719)lrs+10_12_add=off:afp=100000:csup=on:inj=on:chr=on:foolp=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_41 on theBenchmark 0.11/0.41 % (18711)dis+1002_6_add=large:csup=on:inj=on:chr=on:foolp=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_2 on theBenchmark 0.11/0.41 % (18714)ott+2_2_afp=10000:afq=1.4:csup=on:inj=on:chr=on:foolp=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_7 on theBenchmark 0.11/0.41 % (18725)lrs+1_4_afp=100000:afq=1.2:csup=on:inj=on:chr=on:foolp=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_300 on theBenchmark 0.11/0.41 % (18723)lrs+1011_5_add=large:csup=on:inj=on:chr=on:foolp=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_130 on theBenchmark 0.11/0.41 % (18728)dis-11_3_add=off:afp=40000:csup=on:inj=on:chr=on:e2e=on:prag=on:foolp=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_50 on theBenchmark 0.18/0.42 % (18706)lrs+4_3_av=off:br=off:csup=on:inj=on:chr=on:foolp=on:cnfonf=eager:nm=0:newcnf=on:nwc=1:stl=30:sp=occurrence:urr=on_32 on theBenchmark 0.18/0.42 % (18717)ott+11_20_afr=on:afp=100000:csup=on:inj=on:chr=on:foolp=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_6 on theBenchmark 0.18/0.42 % (18715)lrs+1010_3:2_afr=on:csup=on:inj=on:chr=on:foolp=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_300 on theBenchmark 0.18/0.57 % (18722)Refutation not found, incomplete strategy 0.18/0.57 % (18722)------------------------------ 0.18/0.57 % (18722)Version: Vampire 4.5.0 (commit 7ae30c7f on 2020-06-30 15:57:20 +0100) 0.18/0.57 % (18722)Termination reason: Refutation not found, incomplete strategy 0.18/0.57 0.18/0.57 % (18722)Memory used [KB]: 10618 0.18/0.57 % (18722)Time elapsed: 0.226 s 0.18/0.57 % (18722)------------------------------ 0.18/0.57 % (18722)------------------------------ 0.18/0.61 % (18729)dis+1011_10_add=large:csup=on:inj=on:chr=on:foolp=on:cnfonf=eager:afr=on:afp=4000:afq=1.0:amm=off:anc=none:lma=on:nm=64:nwc=4:sac=on:sp=occurrence_75 on theBenchmark 0.18/0.63 % (18709)Refutation not found, incomplete strategy 0.18/0.63 % (18709)------------------------------ 0.18/0.63 % (18709)Version: Vampire 4.5.0 (commit 7ae30c7f on 2020-06-30 15:57:20 +0100) 0.18/0.63 % (18709)Termination reason: Refutation not found, incomplete strategy 0.18/0.63 0.18/0.63 % (18709)Memory used [KB]: 11641 0.18/0.63 % (18709)Time elapsed: 0.287 s 0.18/0.63 % (18709)------------------------------ 0.18/0.63 % (18709)------------------------------ 0.18/0.68 % (18730)dis+1010_3:2_av=off:csup=on:prag=on:chr=on:foolp=on:bet=on:cnfonf=lazy_not_be_gen:gsp=input_only:nm=2:nwc=1:sp=reverse_arity:urr=ec_only_29 on theBenchmark 3.04/0.75 % (18713)Time limit reached! 3.04/0.75 % (18713)------------------------------ 3.04/0.75 % (18713)Version: Vampire 4.5.0 (commit 7ae30c7f on 2020-06-30 15:57:20 +0100) 3.04/0.75 % (18713)Termination reason: Time limit 3.04/0.75 % (18713)Termination phase: Saturation 3.04/0.75 3.04/0.75 % (18713)Memory used [KB]: 6908 3.04/0.75 % (18713)Time elapsed: 0.400 s 3.04/0.75 % (18713)------------------------------ 3.04/0.75 % (18713)------------------------------ 3.04/0.79 % (18731)lrs+1011_8_add=large:csup=on:inj=on:prag=on:foolp=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_26 on theBenchmark 3.81/0.85 % (18700)Time limit reached! 3.81/0.85 % (18700)------------------------------ 3.81/0.85 % (18700)Version: Vampire 4.5.0 (commit 7ae30c7f on 2020-06-30 15:57:20 +0100) 3.81/0.85 % (18699)Time limit reached! 3.81/0.85 % (18699)------------------------------ 3.81/0.85 % (18699)Version: Vampire 4.5.0 (commit 7ae30c7f on 2020-06-30 15:57:20 +0100) 3.81/0.85 % (18699)Termination reason: Time limit 3.81/0.85 3.81/0.85 % (18699)Memory used [KB]: 2686 3.81/0.85 % (18699)Time elapsed: 0.514 s 3.81/0.85 % (18699)------------------------------ 3.81/0.85 % (18699)------------------------------ 3.81/0.86 % (18710)Time limit reached! 3.81/0.86 % (18710)------------------------------ 3.81/0.86 % (18710)Version: Vampire 4.5.0 (commit 7ae30c7f on 2020-06-30 15:57:20 +0100) 3.81/0.86 % (18700)Termination reason: Time limit 3.81/0.86 3.81/0.86 % (18700)Memory used [KB]: 11257 3.81/0.86 % (18700)Time elapsed: 0.507 s 3.81/0.86 % (18700)------------------------------ 3.81/0.86 % (18700)------------------------------ 3.81/0.86 % (18710)Termination reason: Time limit 3.81/0.86 % (18710)Termination phase: Saturation 3.81/0.86 3.81/0.86 % (18710)Memory used [KB]: 12792 3.81/0.86 % (18710)Time elapsed: 0.500 s 3.81/0.86 % (18710)------------------------------ 3.81/0.86 % (18710)------------------------------ 3.81/0.86 % (18711)Time limit reached! 3.81/0.86 % (18711)------------------------------ 3.81/0.86 % (18711)Version: Vampire 4.5.0 (commit 7ae30c7f on 2020-06-30 15:57:20 +0100) 3.81/0.86 % (18711)Termination reason: Time limit 3.81/0.86 3.81/0.86 % (18711)Memory used [KB]: 7547 3.81/0.86 % (18711)Time elapsed: 0.516 s 3.81/0.86 % (18711)------------------------------ 3.81/0.86 % (18711)------------------------------ 3.81/0.87 % (18702)Time limit reached! 3.81/0.87 % (18702)------------------------------ 3.81/0.87 % (18702)Version: Vampire 4.5.0 (commit 7ae30c7f on 2020-06-30 15:57:20 +0100) 3.81/0.88 % (18702)Termination reason: Time limit 3.81/0.88 3.81/0.88 % (18702)Memory used [KB]: 14456 3.81/0.88 % (18702)Time elapsed: 0.534 s 3.81/0.88 % (18702)------------------------------ 3.81/0.88 % (18702)------------------------------ 3.81/0.89 % (18735)dis+1010_3:1_av=off:csup=on:inj=on:chr=on:foolp=on:cnfonf=eager:irw=on:nm=32:nwc=1:sos=all:urr=ec_only:updr=off_77 on theBenchmark 3.81/0.89 % (18732)lrs+1011_8_add=large:csup=on:fe=off:foolp=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_30 on theBenchmark 3.81/0.89 % (18733)dis+1002_4_add=large:csup=on:narr=off:inj=on:prag=on:cbe=off:foolp=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_27 on theBenchmark 4.38/0.91 % (18734)dis+1_3_add=large:afp=4000:csup=on:inj=on:chr=on:foolp=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:uwa=all:updr=off:uhcvi=on_125 on theBenchmark 4.38/0.94 % (18736)lrs+1011_5:4_acc=on:csup=on:inj=on:chr=on:foolp=on:cnfonf=eager:add=large:afr=on:afp=10000:afq=2.0:amm=sco:anc=none:bsr=on:ccuc=first:cond=on:fde=unused:gs=on:gsaa=from_current:gsem=off:irw=on:nm=2:newcnf=on:nwc=1.2:stl=30:sos=on:sac=on:sp=reverse_arity:updr=off_126 on theBenchmark 4.38/0.95 % (18708)Time limit reached! 4.38/0.95 % (18708)------------------------------ 4.38/0.95 % (18708)Version: Vampire 4.5.0 (commit 7ae30c7f on 2020-06-30 15:57:20 +0100) 4.38/0.95 % (18705)Time limit reached! 4.38/0.95 % (18705)------------------------------ 4.38/0.95 % (18705)Version: Vampire 4.5.0 (commit 7ae30c7f on 2020-06-30 15:57:20 +0100) 4.38/0.95 % (18705)Termination reason: Time limit 4.38/0.95 4.38/0.95 % (18705)Memory used [KB]: 14711 4.38/0.95 % (18705)Time elapsed: 0.616 s 4.38/0.95 % (18705)------------------------------ 4.38/0.95 % (18705)------------------------------ 4.38/0.96 % (18701)Time limit reached! 4.38/0.96 % (18701)------------------------------ 4.38/0.96 % (18701)Version: Vampire 4.5.0 (commit 7ae30c7f on 2020-06-30 15:57:20 +0100) 4.38/0.96 % (18701)Termination reason: Time limit 4.38/0.96 4.38/0.96 % (18701)Memory used [KB]: 11513 4.38/0.96 % (18701)Time elapsed: 0.615 s 4.38/0.96 % (18701)------------------------------ 4.38/0.96 % (18701)------------------------------ 4.38/0.96 % (18708)Termination reason: Time limit 4.38/0.96 4.38/0.96 % (18708)Memory used [KB]: 12920 4.38/0.96 % (18708)Time elapsed: 0.609 s 4.38/0.96 % (18708)------------------------------ 4.38/0.96 % (18708)------------------------------ 4.84/0.99 % (18737)lrs+1002_1_add=large:csup=on:narr=off:inj=on:fe=off:chr=on:foolp=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_50 on theBenchmark 4.84/1.01 % (18738)lrs-3_4:1_afp=1000:afq=1.4:csup=on:inj=on:chr=on:foolp=on:cnfonf=eager:amm=sco:fde=none:gs=on:lcm=reverse:lma=on:nwc=1.5:stl=30:sd=1:ss=axioms:sp=reverse_arity:urr=on:updr=off:uhcvi=on_11 on theBenchmark 4.84/1.03 % (18739)ott+11_2:1_add=large:csup=on:inj=on:chr=on:foolp=on:cnfonf=eager:afp=40000:afq=2.0:amm=sco:anc=none:br=off:cond=on:irw=on:nwc=1:sd=2:ss=axioms:st=2.0:sos=all:urr=on:updr=off_9 on theBenchmark 5.54/1.12 % (18737)Refutation not found, incomplete strategy 5.54/1.12 % (18737)------------------------------ 5.54/1.12 % (18737)Version: Vampire 4.5.0 (commit 7ae30c7f on 2020-06-30 15:57:20 +0100) 5.54/1.12 % (18737)Termination reason: Refutation not found, incomplete strategy 5.54/1.12 5.54/1.12 % (18737)Memory used [KB]: 10618 5.54/1.12 % (18737)Time elapsed: 0.152 s 5.54/1.12 % (18737)------------------------------ 5.54/1.12 % (18737)------------------------------ 5.78/1.16 % (18740)lrs+1011_8_add=large:csup=off:foolp=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_13 on theBenchmark 6.16/1.21 % (18740)Refutation not found, incomplete strategy 6.16/1.21 % (18740)------------------------------ 6.16/1.21 % (18740)Version: Vampire 4.5.0 (commit 7ae30c7f on 2020-06-30 15:57:20 +0100) 6.16/1.21 % (18740)Termination reason: Refutation not found, incomplete strategy 6.16/1.21 6.16/1.21 % (18740)Memory used [KB]: 11385 6.16/1.21 % (18740)Time elapsed: 0.058 s 6.16/1.21 % (18740)------------------------------ 6.16/1.21 % (18740)------------------------------ 6.16/1.25 % (18741)lrs+1011_2:1_av=off:csup=on:inj=on:chr=on:foolp=on:cnfonf=eager:irw=on:lwlo=on:nm=16:newcnf=on:nwc=2:sd=4:ss=axioms:st=3.0:sp=occurrence_300 on theBenchmark 6.16/1.26 % (18717)Time limit reached! 6.16/1.26 % (18717)------------------------------ 6.16/1.26 % (18717)Version: Vampire 4.5.0 (commit 7ae30c7f on 2020-06-30 15:57:20 +0100) 6.16/1.26 % (18717)Termination reason: Time limit 6.16/1.26 % (18717)Termination phase: Saturation 6.16/1.26 6.16/1.26 % (18717)Memory used [KB]: 9083 6.16/1.26 % (18717)Time elapsed: 0.900 s 6.16/1.26 % (18717)------------------------------ 6.16/1.26 % (18717)------------------------------ 6.57/1.31 % (18742)dis+1011_4_av=off:cond=on:csup=on:inj=on:chr=on:foolp=on:cnfonf=eager:irw=on:lma=on:nm=2:nwc=1:sos=all:sp=occurrence_5 on theBenchmark 6.57/1.35 % (18714)Time limit reached! 6.57/1.35 % (18714)------------------------------ 6.57/1.35 % (18714)Version: Vampire 4.5.0 (commit 7ae30c7f on 2020-06-30 15:57:20 +0100) 6.57/1.35 % (18714)Termination reason: Time limit 6.57/1.35 6.57/1.35 % (18714)Memory used [KB]: 13176 6.57/1.35 % (18714)Time elapsed: 1.006 s 6.57/1.35 % (18714)------------------------------ 6.57/1.35 % (18714)------------------------------ 8.44/1.41 % (18743)lrs+10_3:1_av=off:bsr=on:csup=on:inj=on:chr=on:foolp=on:cnfonf=eager:cond=on:er=known:gs=on:lcm=reverse:nm=32:nwc=4:stl=30:sp=occurrence:urr=on:updr=off_73 on theBenchmark 8.69/1.44 % (18718)Time limit reached! 8.69/1.44 % (18718)------------------------------ 8.69/1.44 % (18718)Version: Vampire 4.5.0 (commit 7ae30c7f on 2020-06-30 15:57:20 +0100) 8.69/1.45 % (18721)Time limit reached! 8.69/1.45 % (18721)------------------------------ 8.69/1.45 % (18721)Version: Vampire 4.5.0 (commit 7ae30c7f on 2020-06-30 15:57:20 +0100) 8.69/1.45 % (18721)Termination reason: Time limit 8.69/1.45 8.69/1.45 % (18721)Memory used [KB]: 11769 8.69/1.45 % (18721)Time elapsed: 1.107 s 8.69/1.45 % (18721)------------------------------ 8.69/1.45 % (18721)------------------------------ 8.69/1.45 % (18712)Time limit reached! 8.69/1.45 % (18712)------------------------------ 8.69/1.45 % (18712)Version: Vampire 4.5.0 (commit 7ae30c7f on 2020-06-30 15:57:20 +0100) 8.69/1.45 % (18712)Termination reason: Time limit 8.69/1.45 8.69/1.45 % (18712)Memory used [KB]: 8315 8.69/1.45 % (18712)Time elapsed: 1.105 s 8.69/1.45 % (18712)------------------------------ 8.69/1.45 % (18712)------------------------------ 8.69/1.45 % (18718)Termination reason: Time limit 8.69/1.45 % (18718)Termination phase: Saturation 8.69/1.45 8.69/1.45 % (18718)Memory used [KB]: 12792 8.69/1.45 % (18718)Time elapsed: 1.100 s 8.69/1.45 % (18718)------------------------------ 8.69/1.45 % (18718)------------------------------ 8.69/1.49 % (18744)dis+10_1_add=off:afp=4000:csup=on:inj=on:chr=on:e2e=on:foolp=on:cnfonf=eager:afq=1.2:anc=none:br=off:cond=on:gs=on:irw=on:lcm=reverse:nwc=10:sd=10:ss=axioms:sos=theory:sac=on:sp=occurrence:urr=on_12 on theBenchmark 8.69/1.49 % (18745)lrs+4_3_av=off:bd=preordered:csup=on:inj=on:chr=on:foolp=on:cnfonf=eager:bs=unit_only:cond=fast:fde=unused:gsp=input_only:gs=on:gsem=on:lma=on:lwlo=on:nm=6:nwc=1:stl=60:sp=occurrence:uhcvi=on_481 on theBenchmark 8.69/1.49 % (18746)lrs+1002_1_av=off:fde=unused:csup=on:inj=on:chr=on:foolp=on:cnfonf=eager:lwlo=on:nm=16:nwc=4:sp=occurrence_300 on theBenchmark 10.85/1.80 % (18715)Refutation found. Thanks to Tanya! 10.85/1.80 % SZS status Theorem for theBenchmark 10.85/1.80 % SZS output start Proof for theBenchmark 10.85/1.80 tff(func_def_0, type, mu: '$tType'). 10.85/1.80 tff(func_def_4, type, ->: ('$tType' * '$tType') > '$tType'). 10.85/1.80 tff(func_def_5, type, qmltpeq: mu -> mu -> '$i' -> '$o'). 10.85/1.80 tff(func_def_6, type, meq_prop: ('$i' -> '$o') -> ('$i' -> '$o') -> '$i' -> '$o'). 10.85/1.80 tff(func_def_7, type, vAPP: !>[X0: $ttype, X1: $ttype]:(X0 -> X1 * X0) > X1). 10.85/1.80 tff(func_def_8, type, mnot: ('$i' -> '$o') -> '$i' -> '$o'). 10.85/1.80 tff(func_def_9, type, mor: ('$i' -> '$o') -> ('$i' -> '$o') -> '$i' -> '$o'). 10.85/1.80 tff(func_def_10, type, mbox: ('$i' -> '$i' -> '$o') -> ('$i' -> '$o') -> '$i' -> '$o'). 10.85/1.80 tff(func_def_11, type, mforall_prop: (('$i' -> '$o') -> '$i' -> '$o') -> '$i' -> '$o'). 10.85/1.80 tff(func_def_12, type, mtrue: '$i' -> '$o'). 10.85/1.80 tff(func_def_13, type, mfalse: '$i' -> '$o'). 10.85/1.80 tff(func_def_14, type, mand: ('$i' -> '$o') -> ('$i' -> '$o') -> '$i' -> '$o'). 10.85/1.80 tff(func_def_15, type, mimplies: ('$i' -> '$o') -> ('$i' -> '$o') -> '$i' -> '$o'). 10.85/1.80 tff(func_def_16, type, mimplied: ('$i' -> '$o') -> ('$i' -> '$o') -> '$i' -> '$o'). 10.85/1.80 tff(func_def_17, type, mequiv: ('$i' -> '$o') -> ('$i' -> '$o') -> '$i' -> '$o'). 10.85/1.80 tff(func_def_18, type, mxor: ('$i' -> '$o') -> ('$i' -> '$o') -> '$i' -> '$o'). 10.85/1.80 tff(func_def_19, type, mdia: ('$i' -> '$i' -> '$o') -> ('$i' -> '$o') -> '$i' -> '$o'). 10.85/1.80 tff(func_def_20, type, exists_in_world: mu -> '$i' -> '$o'). 10.85/1.80 tff(func_def_21, type, mforall_ind: (mu -> '$i' -> '$o') -> '$i' -> '$o'). 10.85/1.80 tff(func_def_22, type, mexists_ind: (mu -> '$i' -> '$o') -> '$i' -> '$o'). 10.85/1.80 tff(func_def_23, type, mexists_prop: (('$i' -> '$o') -> '$i' -> '$o') -> '$i' -> '$o'). 10.85/1.80 tff(func_def_24, type, mreflexive: ('$i' -> '$i' -> '$o') -> '$o'). 10.85/1.80 tff(func_def_25, type, msymmetric: ('$i' -> '$i' -> '$o') -> '$o'). 10.85/1.80 tff(func_def_26, type, mserial: ('$i' -> '$i' -> '$o') -> '$o'). 10.85/1.80 tff(func_def_27, type, mtransitive: ('$i' -> '$i' -> '$o') -> '$o'). 10.85/1.80 tff(func_def_28, type, meuclidean: ('$i' -> '$i' -> '$o') -> '$o'). 10.85/1.80 tff(func_def_29, type, mpartially_functional: ('$i' -> '$i' -> '$o') -> '$o'). 10.85/1.80 tff(func_def_30, type, mfunctional: ('$i' -> '$i' -> '$o') -> '$o'). 10.85/1.80 tff(func_def_31, type, mweakly_dense: ('$i' -> '$i' -> '$o') -> '$o'). 10.85/1.80 tff(func_def_32, type, mweakly_connected: ('$i' -> '$i' -> '$o') -> '$o'). 10.85/1.80 tff(func_def_33, type, mweakly_directed: ('$i' -> '$i' -> '$o') -> '$o'). 10.85/1.80 tff(func_def_34, type, mvalid: ('$i' -> '$o') -> '$o'). 10.85/1.80 tff(func_def_35, type, msatisfiable: ('$i' -> '$o') -> '$o'). 10.85/1.80 tff(func_def_36, type, mcountersatisfiable: ('$i' -> '$o') -> '$o'). 10.85/1.80 tff(func_def_37, type, minvalid: ('$i' -> '$o') -> '$o'). 10.85/1.80 tff(func_def_38, type, rel_s4: '$i' -> '$i' -> '$o'). 10.85/1.80 tff(func_def_39, type, mbox_s4: ('$i' -> '$o') -> '$i' -> '$o'). 10.85/1.80 tff(func_def_40, type, mdia_s4: ('$i' -> '$o') -> '$i' -> '$o'). 10.85/1.80 tff(func_def_41, type, p: '$i' -> '$o'). 10.85/1.80 tff(func_def_42, type, big_r: mu -> '$i' -> '$o'). 10.85/1.80 tff(func_def_43, type, big_q: mu -> '$i' -> '$o'). 10.85/1.80 tff(func_def_44, type, vEPSILON: !>[X0: $ttype]:(X0 -> '$o') -> X0). 10.85/1.80 tff(func_def_45, type, bCOMB: !>[X0: $ttype, X1: $ttype, X2: $ttype]:(X1 -> X2) -> (X0 -> X1) -> X0 -> X2). 10.85/1.80 tff(func_def_46, type, sCOMB: !>[X0: $ttype, X1: $ttype, X2: $ttype]:(X0 -> X1 -> X2) -> (X0 -> X1) -> X0 -> X2). 10.85/1.80 tff(func_def_49, type, vNOT: '$o' -> '$o'). 10.85/1.80 tff(func_def_50, type, vPI: !>[X0: $ttype]:(X0 -> '$o') -> '$o'). 10.85/1.80 tff(func_def_51, type, vAND: '$o' -> '$o' -> '$o'). 10.85/1.80 tff(func_def_52, type, vIMP: '$o' -> '$o' -> '$o'). 10.85/1.80 tff(func_def_53, type, vEQ: !>[X0: $ttype]:X0 -> X0 -> '$o'). 10.85/1.80 tff(func_def_54, type, vSIGMA: !>[X0: $ttype]:(X0 -> '$o') -> '$o'). 10.85/1.80 tff(func_def_55, type, cCOMB: !>[X0: $ttype, X1: $ttype, X2: $ttype]:(X0 -> X1 -> X2) -> X1 -> X0 -> X2). 10.85/1.80 tff(func_def_56, type, iCOMB: !>[X2: $ttype]:X2 -> X2). 10.85/1.80 tff(func_def_57, type, vOR: '$o' -> '$o' -> '$o'). 10.85/1.80 tff(func_def_58, type, kCOMB: !>[X1: $ttype, X2: $ttype]:X1 -> X2 -> X1). 10.85/1.80 tff(func_def_59, type, sK0: '$i' -> mu). 10.85/1.80 tff(func_def_64, type, sK5: mu). 10.85/1.80 tff(func_def_67, type, sK8: mu). 10.85/1.80 tff(func_def_69, type, sK10: '$i' -> '$i'). 10.85/1.80 tff(func_def_70, type, sK11: '$i' -> '$i'). 10.85/1.80 tff(f2,axiom,( 10.85/1.80 mnot = (^[X3 : '$i' -> '$o', X2 : '$i'] : ~X3 @ X2)), 10.85/1.80 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot)). 10.85/1.80 tff(f3,axiom,( 10.85/1.80 mor = (^[X3 : '$i' -> '$o', X4 : '$i' -> '$o', X2 : '$i'] : X4 @ X2 | X3 @ X2)), 10.85/1.80 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor)). 10.85/1.80 tff(f8,axiom,( 10.85/1.80 mand = (^[X3 : '$i' -> '$o', X4 : '$i' -> '$o'] : mnot @ (mor @ (mnot @ X3) @ (mnot @ X4)))), 10.85/1.80 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mand)). 10.85/1.80 tff(f9,axiom,( 10.85/1.80 mimplies = (^[X3 : '$i' -> '$o', X4 : '$i' -> '$o'] : mor @ (mnot @ X3) @ X4)), 10.85/1.80 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies)). 10.85/1.80 tff(f14,axiom,( 10.85/1.80 mforall_ind = (^[X3 : mu -> '$i' -> '$o', X2 : '$i'] : ! [X0 : mu] : (exists_in_world @ X0 @ X2 => X3 @ X0 @ X2))), 10.85/1.80 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_ind)). 10.85/1.80 tff(f17,axiom,( 10.85/1.80 mreflexive = (^[X5 : '$i' -> '$i' -> '$o'] : ! [X8] : X5 @ X8 @ X8)), 10.85/1.80 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mreflexive)). 10.85/1.80 tff(f20,axiom,( 10.85/1.80 mtransitive = (^[X5 : '$i' -> '$i' -> '$o'] : ! [X8,X9,X10] : ((X5 @ X9 @ X10 & X5 @ X8 @ X9) => X5 @ X8 @ X10))), 10.85/1.80 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mtransitive)). 10.85/1.80 tff(f27,axiom,( 10.85/1.80 mvalid = (^[X3 : '$i' -> '$o'] : ! [X2] : X3 @ X2)), 10.85/1.80 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mvalid)). 10.85/1.80 tff(f31,axiom,( 10.85/1.80 ! [X6] : ? [X0 : mu] : exists_in_world @ X0 @ X6), 10.85/1.80 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonempty_ax)). 10.85/1.80 tff(f32,axiom,( 10.85/1.80 mbox_s4 = (^[X3 : '$i' -> '$o', X2 : '$i'] : ! [X6] : (X3 @ X6 | ~rel_s4 @ X2 @ X6))), 10.85/1.80 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_s4)). 10.85/1.80 tff(f34,axiom,( 10.85/1.80 mtransitive @ rel_s4), 10.85/1.80 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2)). 10.85/1.81 tff(f35,axiom,( 10.85/1.81 mreflexive @ rel_s4), 10.85/1.81 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a1)). 10.85/1.81 tff(f36,axiom,( 10.85/1.81 ! [X0 : mu,X6,X2] : ((exists_in_world @ X0 @ X6 & rel_s4 @ X6 @ X2) => exists_in_world @ X0 @ X2)), 10.85/1.81 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cumulative_ax)). 10.85/1.81 tff(f37,conjecture,( 10.85/1.81 mvalid @ (mbox_s4 @ (mimplies @ (mbox_s4 @ (mforall_ind @ (^[X0 : mu] : mor @ (mand @ (mbox_s4 @ p) @ (mbox_s4 @ (big_q @ X0))) @ (mand @ (mbox_s4 @ (mnot @ (mbox_s4 @ p))) @ (mbox_s4 @ (big_r @ X0)))))) @ (mor @ (mbox_s4 @ (mforall_ind @ (^[X0 : mu] : mbox_s4 @ (big_q @ X0)))) @ (mbox_s4 @ (mforall_ind @ (^[X0 : mu] : mbox_s4 @ (big_r @ X0)))))))), 10.85/1.81 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x2118)). 10.85/1.81 tff(f38,negated_conjecture,( 10.85/1.81 ~mvalid @ (mbox_s4 @ (mimplies @ (mbox_s4 @ (mforall_ind @ (^[X0 : mu] : mor @ (mand @ (mbox_s4 @ p) @ (mbox_s4 @ (big_q @ X0))) @ (mand @ (mbox_s4 @ (mnot @ (mbox_s4 @ p))) @ (mbox_s4 @ (big_r @ X0)))))) @ (mor @ (mbox_s4 @ (mforall_ind @ (^[X0 : mu] : mbox_s4 @ (big_q @ X0)))) @ (mbox_s4 @ (mforall_ind @ (^[X0 : mu] : mbox_s4 @ (big_r @ X0)))))))), 10.85/1.81 inference(negated_conjecture,[],[f37])). 10.85/1.81 tff(f39,plain,( 10.85/1.81 ~mvalid @ (mbox_s4 @ (mimplies @ (mbox_s4 @ (mforall_ind @ (^[X0 : mu] : mor @ (mand @ (mbox_s4 @ p) @ (mbox_s4 @ (big_q @ X0))) @ (mand @ (mbox_s4 @ (mnot @ (mbox_s4 @ p))) @ (mbox_s4 @ (big_r @ X0)))))) @ (mor @ (mbox_s4 @ (mforall_ind @ (^[X1 : mu] : mbox_s4 @ (big_q @ X1)))) @ (mbox_s4 @ (mforall_ind @ (^[X2 : mu] : mbox_s4 @ (big_r @ X2)))))))), 10.85/1.81 inference(rectify,[],[f38])). 10.85/1.81 tff(f40,plain,( 10.85/1.81 ~(mvalid @ (mbox_s4 @ (mimplies @ (mbox_s4 @ (mforall_ind @ (sCOMB @ (bCOMB @ mor @ (bCOMB @ (mand @ (mbox_s4 @ p)) @ (bCOMB @ mbox_s4 @ big_q))) @ (bCOMB @ (mand @ (mbox_s4 @ (mnot @ (mbox_s4 @ p)))) @ (bCOMB @ mbox_s4 @ big_r))))) @ (mor @ (mbox_s4 @ (mforall_ind @ (bCOMB @ mbox_s4 @ big_q))) @ (mbox_s4 @ (mforall_ind @ (bCOMB @ mbox_s4 @ big_r)))))) = $true)), 10.85/1.81 inference(fool_elimination,[],[f39])). 10.85/1.81 tff(f76,plain,( 10.85/1.81 mvalid = (^[X0 : '$i' -> '$o'] : ! [X1] : X0 @ X1)), 10.85/1.81 inference(rectify,[],[f27])). 10.85/1.81 tff(f77,plain,( 10.85/1.81 mvalid = vPI('$i')), 10.85/1.81 inference(fool_elimination,[],[f76])). 10.85/1.81 tff(f78,plain,( 10.85/1.81 mreflexive = (^[X0 : '$i' -> '$i' -> '$o'] : ! [X1] : X0 @ X1 @ X1)), 10.85/1.81 inference(rectify,[],[f17])). 10.85/1.81 tff(f79,plain,( 10.85/1.81 bCOMB @ vPI('$i') @ (cCOMB @ sCOMB @ iCOMB) = mreflexive), 10.85/1.81 inference(fool_elimination,[],[f78])). 10.85/1.81 tff(f80,plain,( 10.85/1.81 mtransitive = (^[X0 : '$i' -> '$i' -> '$o'] : ! [X1,X2,X3] : ((X0 @ X2 @ X3 & X0 @ X1 @ X2) => X0 @ X1 @ X3))), 10.85/1.81 inference(rectify,[],[f20])). 10.85/1.81 tff(f81,plain,( 10.85/1.81 bCOMB @ vPI('$i') @ (bCOMB @ (bCOMB @ vPI('$i')) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i'))) @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ cCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ sCOMB)) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vIMP))) @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ cCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vAND)) @ cCOMB)))) @ cCOMB))))) @ cCOMB))) = mtransitive), 10.85/1.81 inference(fool_elimination,[],[f80])). 10.85/1.81 tff(f90,plain,( 10.85/1.81 mimplies = (^[X0 : '$i' -> '$o', X1 : '$i' -> '$o'] : mor @ (mnot @ X0) @ X1)), 10.85/1.81 inference(rectify,[],[f9])). 10.85/1.81 tff(f91,plain,( 10.85/1.81 bCOMB @ mor @ mnot = mimplies), 10.85/1.81 inference(fool_elimination,[],[f90])). 10.85/1.81 tff(f92,plain,( 10.85/1.81 mnot = (^[X0 : '$i' -> '$o', X1 : '$i'] : ~X0 @ X1)), 10.85/1.81 inference(rectify,[],[f2])). 10.85/1.81 tff(f93,plain,( 10.85/1.81 bCOMB @ vNOT = mnot), 10.85/1.81 inference(fool_elimination,[],[f92])). 10.85/1.81 tff(f94,plain,( 10.85/1.81 mor = (^[X0 : '$i' -> '$o', X1 : '$i' -> '$o', X2 : '$i'] : X1 @ X2 | X0 @ X2)), 10.85/1.81 inference(rectify,[],[f3])). 10.85/1.81 tff(f95,plain,( 10.85/1.81 bCOMB @ sCOMB @ (bCOMB @ vOR) = mor), 10.85/1.81 inference(fool_elimination,[],[f94])). 10.85/1.81 tff(f96,plain,( 10.85/1.81 mand = (^[X0 : '$i' -> '$o', X1 : '$i' -> '$o'] : mnot @ (mor @ (mnot @ X0) @ (mnot @ X1)))), 10.85/1.81 inference(rectify,[],[f8])). 10.85/1.81 tff(f97,plain,( 10.85/1.81 bCOMB @ (bCOMB @ mnot) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ mor @ mnot)) @ mnot) = mand), 10.85/1.81 inference(fool_elimination,[],[f96])). 10.85/1.81 tff(f98,plain,( 10.85/1.81 mforall_ind = (^[X0 : mu -> '$i' -> '$o', X1 : '$i'] : ! [X2 : mu] : (exists_in_world @ X2 @ X1 => X0 @ X2 @ X1))), 10.85/1.81 inference(rectify,[],[f14])). 10.85/1.81 tff(f99,plain,( 10.85/1.81 bCOMB @ (bCOMB @ vPI(mu)) @ (bCOMB @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ exists_in_world)))) @ cCOMB) = mforall_ind), 10.85/1.81 inference(fool_elimination,[],[f98])). 10.85/1.81 tff(f100,plain,( 10.85/1.81 mbox_s4 = (^[X0 : '$i' -> '$o', X1 : '$i'] : ! [X2] : (X0 @ X2 | ~rel_s4 @ X1 @ X2))), 10.85/1.81 inference(rectify,[],[f32])). 10.85/1.81 tff(f101,plain,( 10.85/1.81 bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4)))) = mbox_s4), 10.85/1.81 inference(fool_elimination,[],[f100])). 10.85/1.81 tff(f102,plain,( 10.85/1.81 ! [X0] : ? [X1 : mu] : exists_in_world @ X1 @ X0), 10.85/1.81 inference(rectify,[],[f31])). 10.85/1.81 tff(f103,plain,( 10.85/1.81 ! [X0] : ? [X1 : mu] : (exists_in_world @ X1 @ X0 = $true)), 10.85/1.81 inference(fool_elimination,[],[f102])). 10.85/1.81 tff(f104,plain,( 10.85/1.81 ! [X0 : mu,X1,X2] : ((exists_in_world @ X0 @ X1 & rel_s4 @ X1 @ X2) => exists_in_world @ X0 @ X2)), 10.85/1.81 inference(rectify,[],[f36])). 10.85/1.81 tff(f105,plain,( 10.85/1.81 ! [X0 : mu,X1,X2] : (((exists_in_world @ X0 @ X1 = $true) & (rel_s4 @ X1 @ X2 = $true)) => (exists_in_world @ X0 @ X2 = $true))), 10.85/1.81 inference(fool_elimination,[],[f104])). 10.85/1.81 tff(f106,plain,( 10.85/1.81 mtransitive @ rel_s4), 10.85/1.81 inference(rectify,[],[f34])). 10.85/1.81 tff(f107,plain,( 10.85/1.81 (mtransitive @ rel_s4 = $true)), 10.85/1.81 inference(fool_elimination,[],[f106])). 10.85/1.81 tff(f108,plain,( 10.85/1.81 mreflexive @ rel_s4), 10.85/1.81 inference(rectify,[],[f35])). 10.85/1.81 tff(f109,plain,( 10.85/1.81 (mreflexive @ rel_s4 = $true)), 10.85/1.81 inference(fool_elimination,[],[f108])). 10.85/1.81 tff(f110,plain,( 10.85/1.81 (mvalid @ (mbox_s4 @ (mimplies @ (mbox_s4 @ (mforall_ind @ (sCOMB @ (bCOMB @ mor @ (bCOMB @ (mand @ (mbox_s4 @ p)) @ (bCOMB @ mbox_s4 @ big_q))) @ (bCOMB @ (mand @ (mbox_s4 @ (mnot @ (mbox_s4 @ p)))) @ (bCOMB @ mbox_s4 @ big_r))))) @ (mor @ (mbox_s4 @ (mforall_ind @ (bCOMB @ mbox_s4 @ big_q))) @ (mbox_s4 @ (mforall_ind @ (bCOMB @ mbox_s4 @ big_r)))))) != $true)), 10.85/1.81 inference(flattening,[],[f40])). 10.85/1.81 tff(f111,plain,( 10.85/1.81 ! [X0 : mu,X1,X2] : ((exists_in_world @ X0 @ X2 = $true) | ((exists_in_world @ X0 @ X1 != $true) | (rel_s4 @ X1 @ X2 != $true)))), 10.85/1.81 inference(ennf_transformation,[],[f105])). 10.85/1.81 tff(f112,plain,( 10.85/1.81 ! [X0 : mu,X1,X2] : ((exists_in_world @ X0 @ X2 = $true) | (exists_in_world @ X0 @ X1 != $true) | (rel_s4 @ X1 @ X2 != $true))), 10.85/1.81 inference(flattening,[],[f111])). 10.85/1.81 tff(f113,plain,( 10.85/1.81 ! [X0] : (? [X1 : mu] : (exists_in_world @ X1 @ X0 = $true) => (exists_in_world @ (sK0 @ X0) @ X0 = $true))), 10.85/1.81 introduced(choice_axiom,[])). 10.85/1.81 tff(f114,plain,( 10.85/1.81 ! [X0] : (exists_in_world @ (sK0 @ X0) @ X0 = $true)), 10.85/1.81 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f103,f113])). 10.85/1.81 tff(f115,plain,( 10.85/1.81 (mvalid @ (mbox_s4 @ (mimplies @ (mbox_s4 @ (mforall_ind @ (sCOMB @ (bCOMB @ mor @ (bCOMB @ (mand @ (mbox_s4 @ p)) @ (bCOMB @ mbox_s4 @ big_q))) @ (bCOMB @ (mand @ (mbox_s4 @ (mnot @ (mbox_s4 @ p)))) @ (bCOMB @ mbox_s4 @ big_r))))) @ (mor @ (mbox_s4 @ (mforall_ind @ (bCOMB @ mbox_s4 @ big_q))) @ (mbox_s4 @ (mforall_ind @ (bCOMB @ mbox_s4 @ big_r)))))) != $true)), 10.85/1.81 inference(cnf_transformation,[],[f110])). 10.85/1.81 tff(f135,plain,( 10.85/1.81 mvalid = vPI('$i')), 10.85/1.81 inference(cnf_transformation,[],[f77])). 10.85/1.81 tff(f136,plain,( 10.85/1.81 bCOMB @ vPI('$i') @ (cCOMB @ sCOMB @ iCOMB) = mreflexive), 10.85/1.81 inference(cnf_transformation,[],[f79])). 10.85/1.81 tff(f137,plain,( 10.85/1.81 bCOMB @ vPI('$i') @ (bCOMB @ (bCOMB @ vPI('$i')) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i'))) @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ cCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ sCOMB)) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vIMP))) @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ cCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vAND)) @ cCOMB)))) @ cCOMB))))) @ cCOMB))) = mtransitive), 10.85/1.81 inference(cnf_transformation,[],[f81])). 10.85/1.81 tff(f142,plain,( 10.85/1.81 bCOMB @ mor @ mnot = mimplies), 10.85/1.81 inference(cnf_transformation,[],[f91])). 10.85/1.81 tff(f143,plain,( 10.85/1.81 bCOMB @ vNOT = mnot), 10.85/1.81 inference(cnf_transformation,[],[f93])). 10.85/1.81 tff(f144,plain,( 10.85/1.81 bCOMB @ sCOMB @ (bCOMB @ vOR) = mor), 10.85/1.81 inference(cnf_transformation,[],[f95])). 10.85/1.81 tff(f145,plain,( 10.85/1.81 bCOMB @ (bCOMB @ mnot) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ mor @ mnot)) @ mnot) = mand), 10.85/1.81 inference(cnf_transformation,[],[f97])). 10.85/1.81 tff(f146,plain,( 10.85/1.81 bCOMB @ (bCOMB @ vPI(mu)) @ (bCOMB @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ exists_in_world)))) @ cCOMB) = mforall_ind), 10.85/1.81 inference(cnf_transformation,[],[f99])). 10.85/1.81 tff(f147,plain,( 10.85/1.81 bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4)))) = mbox_s4), 10.85/1.81 inference(cnf_transformation,[],[f101])). 10.85/1.81 tff(f148,plain,( 10.85/1.81 ( ! [X0] : ((exists_in_world @ (sK0 @ X0) @ X0 = $true)) )), 10.85/1.81 inference(cnf_transformation,[],[f114])). 10.85/1.81 tff(f149,plain,( 10.85/1.81 ( ! [X2,X0:mu,X1] : ((rel_s4 @ X1 @ X2 != $true) | (exists_in_world @ X0 @ X1 != $true) | (exists_in_world @ X0 @ X2 = $true)) )), 10.85/1.81 inference(cnf_transformation,[],[f112])). 10.85/1.81 tff(f150,plain,( 10.85/1.81 (mtransitive @ rel_s4 = $true)), 10.85/1.81 inference(cnf_transformation,[],[f107])). 10.85/1.81 tff(f151,plain,( 10.85/1.81 (mreflexive @ rel_s4 = $true)), 10.85/1.81 inference(cnf_transformation,[],[f109])). 10.85/1.81 tff(f153,plain,( 10.85/1.81 bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ vNOT)) = mand), 10.85/1.81 inference(definition_unfolding,[],[f145,f143,f144,f143,f143])). 10.85/1.81 tff(f154,plain,( 10.85/1.81 bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT) = mimplies), 10.85/1.81 inference(definition_unfolding,[],[f142,f144,f143])). 10.85/1.81 tff(f162,plain,( 10.85/1.81 (vPI('$i') @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4)))) @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT) @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4)))) @ (bCOMB @ (bCOMB @ vPI(mu)) @ (bCOMB @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ exists_in_world)))) @ cCOMB) @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ vNOT)) @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4)))) @ p)) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ big_q))) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ vNOT)) @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4)))) @ (bCOMB @ vNOT @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4)))) @ p)))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ big_r))))) @ (bCOMB @ sCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4)))) @ (bCOMB @ (bCOMB @ vPI(mu)) @ (bCOMB @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ exists_in_world)))) @ cCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ big_q))) @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4)))) @ (bCOMB @ (bCOMB @ vPI(mu)) @ (bCOMB @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ exists_in_world)))) @ cCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ big_r)))))) != $true)), 10.85/1.81 inference(definition_unfolding,[],[f115,f135,f147,f154,f147,f146,f144,f153,f147,f147,f153,f147,f143,f147,f147,f144,f147,f146,f147,f147,f146,f147])). 10.85/1.81 tff(f163,plain,( 10.85/1.81 (bCOMB @ vPI('$i') @ (bCOMB @ (bCOMB @ vPI('$i')) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i'))) @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ cCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ sCOMB)) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vIMP))) @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ cCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vAND)) @ cCOMB)))) @ cCOMB))))) @ cCOMB))) @ rel_s4 = $true)), 10.85/1.81 inference(definition_unfolding,[],[f150,f137])). 10.85/1.81 tff(f164,plain,( 10.85/1.81 (bCOMB @ vPI('$i') @ (cCOMB @ sCOMB @ iCOMB) @ rel_s4 = $true)), 10.85/1.81 inference(definition_unfolding,[],[f151,f136])). 10.85/1.81 tff(f165,plain,( 10.85/1.81 (vPI('$i') @ (sCOMB @ rel_s4 @ iCOMB) = $true)), 10.85/1.81 inference(combinator_demodulation,[],[f164])). 10.85/1.81 tff(f166,plain,( 10.85/1.81 ( ! [X1] : ((sCOMB @ rel_s4 @ iCOMB @ X1 = $true)) )), 10.85/1.81 inference(pi_clausification,[],[f165])). 10.85/1.81 tff(f167,plain,( 10.85/1.81 ( ! [X1] : ((rel_s4 @ X1 @ X1 = $true)) )), 10.85/1.81 inference(combinator_demodulation,[],[f166])). 10.85/1.81 tff(f168,plain,( 10.85/1.81 (vPI('$i') @ (bCOMB @ vPI('$i') @ (bCOMB @ (bCOMB @ vPI('$i')) @ (sCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ sCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vIMP)) @ (bCOMB @ (sCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ vAND) @ (cCOMB @ rel_s4)))) @ (cCOMB @ rel_s4))))) @ (cCOMB @ rel_s4)))) = $true)), 10.85/1.81 inference(combinator_demodulation,[],[f163])). 10.85/1.81 tff(f169,plain,( 10.85/1.81 ( ! [X1] : ((bCOMB @ vPI('$i') @ (bCOMB @ (bCOMB @ vPI('$i')) @ (sCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ sCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vIMP)) @ (bCOMB @ (sCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ vAND) @ (cCOMB @ rel_s4)))) @ (cCOMB @ rel_s4))))) @ (cCOMB @ rel_s4))) @ X1 = $true)) )), 10.85/1.81 inference(pi_clausification,[],[f168])). 10.85/1.81 tff(f170,plain,( 10.85/1.81 ( ! [X1] : ((vPI('$i') @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (sCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ vAND) @ (cCOMB @ rel_s4))) @ (cCOMB @ rel_s4 @ X1)))) @ (cCOMB @ rel_s4 @ X1))) = $true)) )), 10.85/1.81 inference(combinator_demodulation,[],[f169])). 10.85/1.81 tff(f171,plain,( 10.85/1.81 ( ! [X2,X1] : ((bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (sCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ vAND) @ (cCOMB @ rel_s4))) @ (cCOMB @ rel_s4 @ X1)))) @ (cCOMB @ rel_s4 @ X1)) @ X2 = $true)) )), 10.85/1.81 inference(pi_clausification,[],[f170])). 10.85/1.81 tff(f172,plain,( 10.85/1.81 ( ! [X2,X1] : ((vPI('$i') @ (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ (bCOMB @ vAND @ (cCOMB @ rel_s4 @ X2)) @ (rel_s4 @ X2 @ X1))) @ (cCOMB @ rel_s4 @ X1)) = $true)) )), 10.85/1.81 inference(combinator_demodulation,[],[f171])). 10.85/1.81 tff(f173,plain,( 10.85/1.81 ( ! [X2,X3,X1] : ((sCOMB @ (bCOMB @ vIMP @ (cCOMB @ (bCOMB @ vAND @ (cCOMB @ rel_s4 @ X2)) @ (rel_s4 @ X2 @ X1))) @ (cCOMB @ rel_s4 @ X1) @ X3 = $true)) )), 10.85/1.81 inference(pi_clausification,[],[f172])). 10.85/1.81 tff(f174,plain,( 10.85/1.81 ( ! [X2,X3,X1] : ((vIMP @ (vAND @ (rel_s4 @ X3 @ X2) @ (rel_s4 @ X2 @ X1)) @ (rel_s4 @ X3 @ X1) = $true)) )), 10.85/1.81 inference(combinator_demodulation,[],[f173])). 10.85/1.81 tff(f175,plain,( 10.85/1.81 ( ! [X2,X3,X1] : ((vAND @ (rel_s4 @ X3 @ X2) @ (rel_s4 @ X2 @ X1) = $false) | (rel_s4 @ X3 @ X1 = $true)) )), 10.85/1.81 inference(binary_proxy_clausification,[],[f174])). 10.85/1.81 tff(f176,plain,( 10.85/1.81 ( ! [X2,X3,X1] : ((rel_s4 @ X3 @ X2 = $false) | (rel_s4 @ X3 @ X1 = $true) | (rel_s4 @ X2 @ X1 = $false)) )), 10.85/1.81 inference(binary_proxy_clausification,[],[f175])). 11.45/1.83 tff(f177,plain,( 11.45/1.83 (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4)))) @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT) @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4)))) @ (bCOMB @ (bCOMB @ vPI(mu)) @ (bCOMB @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ exists_in_world)))) @ cCOMB) @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ vNOT)) @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4)))) @ p)) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ big_q))) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ vNOT)) @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4)))) @ (bCOMB @ vNOT @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4)))) @ p)))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ big_r))))) @ (bCOMB @ sCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4)))) @ (bCOMB @ (bCOMB @ vPI(mu)) @ (bCOMB @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ exists_in_world)))) @ cCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ big_q))) @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4)))) @ (bCOMB @ (bCOMB @ vPI(mu)) @ (bCOMB @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ exists_in_world)))) @ cCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ big_r))))) @ sK2 = $false)), 11.45/1.83 inference(sigma_clausification,[],[f162])). 11.45/1.83 tff(f178,plain,( 11.45/1.83 (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ sK2))) @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ (bCOMB @ vPI(mu) @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ exists_in_world))) @ (cCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT) @ (bCOMB @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ p))))) @ (bCOMB @ vNOT))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ big_q))) @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT) @ (bCOMB @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ (bCOMB @ vNOT @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ p)))))))) @ (bCOMB @ vNOT))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ big_r)))))))))) @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ (bCOMB @ vPI(mu) @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ exists_in_world))) @ (cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ big_q))))))) @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ (bCOMB @ vPI(mu) @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ exists_in_world))) @ (cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ big_r))))))))) = $false)), 11.45/1.83 inference(combinator_demodulation,[],[f177])). 11.45/1.83 tff(f179,plain,( 11.45/1.83 (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ sK2))) @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ (bCOMB @ vPI(mu) @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ exists_in_world))) @ (cCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT) @ (bCOMB @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ p))))) @ (bCOMB @ vNOT))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ big_q))) @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT) @ (bCOMB @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ (bCOMB @ vNOT @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ p)))))))) @ (bCOMB @ vNOT))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ big_r)))))))))) @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ (bCOMB @ vPI(mu) @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ exists_in_world))) @ (cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ big_q))))))) @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ (bCOMB @ vPI(mu) @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ exists_in_world))) @ (cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ big_r)))))))) @ sK3 = $false)), 11.45/1.83 inference(sigma_clausification,[],[f178])). 11.45/1.83 tff(f180,plain,( 11.45/1.83 (vOR @ (vNOT @ (rel_s4 @ sK2 @ sK3)) @ (vOR @ (vNOT @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ sK3))) @ (bCOMB @ vPI(mu) @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ exists_in_world))) @ (cCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT) @ (bCOMB @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ p))))) @ (bCOMB @ vNOT))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ big_q))) @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT) @ (bCOMB @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ (bCOMB @ vNOT @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ p)))))))) @ (bCOMB @ vNOT))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ big_r))))))))) @ (vOR @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ sK3))) @ (bCOMB @ vPI(mu) @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ exists_in_world))) @ (cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ big_q)))))) @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ sK3))) @ (bCOMB @ vPI(mu) @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ exists_in_world))) @ (cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ big_r)))))))) = $false)), 11.45/1.83 inference(combinator_demodulation,[],[f179])). 11.45/1.83 tff(f181,plain,( 11.45/1.83 (vNOT @ (rel_s4 @ sK2 @ sK3) = $false)), 11.45/1.83 inference(binary_proxy_clausification,[],[f180])). 11.45/1.83 tff(f182,plain,( 11.45/1.83 (vOR @ (vNOT @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ sK3))) @ (bCOMB @ vPI(mu) @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ exists_in_world))) @ (cCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT) @ (bCOMB @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ p))))) @ (bCOMB @ vNOT))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ big_q))) @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT) @ (bCOMB @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ (bCOMB @ vNOT @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ p)))))))) @ (bCOMB @ vNOT))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ big_r))))))))) @ (vOR @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ sK3))) @ (bCOMB @ vPI(mu) @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ exists_in_world))) @ (cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ big_q)))))) @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ sK3))) @ (bCOMB @ vPI(mu) @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ exists_in_world))) @ (cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ big_r))))))) = $false)), 11.45/1.83 inference(binary_proxy_clausification,[],[f180])). 11.45/1.83 tff(f183,plain,( 11.45/1.83 (vNOT @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ sK3))) @ (bCOMB @ vPI(mu) @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ exists_in_world))) @ (cCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT) @ (bCOMB @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ p))))) @ (bCOMB @ vNOT))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ big_q))) @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT) @ (bCOMB @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ (bCOMB @ vNOT @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ p)))))))) @ (bCOMB @ vNOT))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ big_r)))))))) = $false)), 11.45/1.83 inference(binary_proxy_clausification,[],[f182])). 11.45/1.83 tff(f184,plain,( 11.45/1.83 (vOR @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ sK3))) @ (bCOMB @ vPI(mu) @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ exists_in_world))) @ (cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ big_q)))))) @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ sK3))) @ (bCOMB @ vPI(mu) @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ exists_in_world))) @ (cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ big_r)))))) = $false)), 11.45/1.83 inference(binary_proxy_clausification,[],[f182])). 11.45/1.83 tff(f185,plain,( 11.45/1.83 (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ sK3))) @ (bCOMB @ vPI(mu) @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ exists_in_world))) @ (cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ big_q))))) = $false)), 11.45/1.83 inference(binary_proxy_clausification,[],[f184])). 11.45/1.83 tff(f186,plain,( 11.45/1.83 (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ sK3))) @ (bCOMB @ vPI(mu) @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ exists_in_world))) @ (cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ big_r))))) = $false)), 11.45/1.83 inference(binary_proxy_clausification,[],[f184])). 11.45/1.83 tff(f187,plain,( 11.45/1.83 (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ sK3))) @ (bCOMB @ vPI(mu) @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ exists_in_world))) @ (cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ big_r)))) @ sK4 = $false)), 11.45/1.83 inference(sigma_clausification,[],[f186])). 11.45/1.83 tff(f188,plain,( 11.45/1.83 (vOR @ (vNOT @ (rel_s4 @ sK3 @ sK4)) @ (vPI(mu) @ (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ exists_in_world @ sK4)) @ (cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ big_r) @ sK4))) = $false)), 11.45/1.83 inference(combinator_demodulation,[],[f187])). 11.45/1.83 tff(f189,plain,( 11.45/1.83 (vNOT @ (rel_s4 @ sK3 @ sK4) = $false)), 11.45/1.83 inference(binary_proxy_clausification,[],[f188])). 11.45/1.83 tff(f190,plain,( 11.45/1.83 (vPI(mu) @ (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ exists_in_world @ sK4)) @ (cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ big_r) @ sK4)) = $false)), 11.45/1.83 inference(binary_proxy_clausification,[],[f188])). 11.45/1.83 tff(f191,plain,( 11.45/1.83 (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ exists_in_world @ sK4)) @ (cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ big_r) @ sK4) @ sK5 = $false)), 11.45/1.83 inference(sigma_clausification,[],[f190])). 11.45/1.83 tff(f192,plain,( 11.45/1.83 (vIMP @ (exists_in_world @ sK5 @ sK4) @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ sK4))) @ (big_r @ sK5))) = $false)), 11.45/1.83 inference(combinator_demodulation,[],[f191])). 11.45/1.83 tff(f193,plain,( 11.45/1.83 (exists_in_world @ sK5 @ sK4 = $true)), 11.45/1.83 inference(binary_proxy_clausification,[],[f192])). 11.45/1.83 tff(f194,plain,( 11.45/1.83 (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ sK4))) @ (big_r @ sK5)) = $false)), 11.45/1.83 inference(binary_proxy_clausification,[],[f192])). 11.45/1.83 tff(f195,plain,( 11.45/1.83 (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ sK4))) @ (big_r @ sK5) @ sK6 = $false)), 11.45/1.83 inference(sigma_clausification,[],[f194])). 11.45/1.83 tff(f196,plain,( 11.45/1.83 (vOR @ (vNOT @ (rel_s4 @ sK4 @ sK6)) @ (big_r @ sK5 @ sK6) = $false)), 11.45/1.83 inference(combinator_demodulation,[],[f195])). 11.45/1.83 tff(f197,plain,( 11.45/1.83 (vNOT @ (rel_s4 @ sK4 @ sK6) = $false)), 11.45/1.83 inference(binary_proxy_clausification,[],[f196])). 11.45/1.83 tff(f198,plain,( 11.45/1.83 (big_r @ sK5 @ sK6 = $false)), 11.45/1.83 inference(binary_proxy_clausification,[],[f196])). 11.45/1.83 tff(f199,plain,( 11.45/1.83 (rel_s4 @ sK4 @ sK6 = $true)), 11.45/1.83 inference(not_proxy_clausification,[],[f197])). 11.45/1.83 tff(f200,plain,( 11.45/1.83 (rel_s4 @ sK3 @ sK4 = $true)), 11.45/1.83 inference(not_proxy_clausification,[],[f189])). 11.45/1.83 tff(f201,plain,( 11.45/1.83 (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ sK3))) @ (bCOMB @ vPI(mu) @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ exists_in_world))) @ (cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ big_q)))) @ sK7 = $false)), 11.45/1.83 inference(sigma_clausification,[],[f185])). 11.45/1.83 tff(f202,plain,( 11.45/1.83 (vOR @ (vNOT @ (rel_s4 @ sK3 @ sK7)) @ (vPI(mu) @ (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ exists_in_world @ sK7)) @ (cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ big_q) @ sK7))) = $false)), 11.45/1.83 inference(combinator_demodulation,[],[f201])). 11.45/1.83 tff(f203,plain,( 11.45/1.83 (vNOT @ (rel_s4 @ sK3 @ sK7) = $false)), 11.45/1.83 inference(binary_proxy_clausification,[],[f202])). 11.45/1.83 tff(f204,plain,( 11.45/1.83 (vPI(mu) @ (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ exists_in_world @ sK7)) @ (cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ big_q) @ sK7)) = $false)), 11.45/1.83 inference(binary_proxy_clausification,[],[f202])). 11.45/1.83 tff(f205,plain,( 11.45/1.83 (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ exists_in_world @ sK7)) @ (cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ big_q) @ sK7) @ sK8 = $false)), 11.45/1.83 inference(sigma_clausification,[],[f204])). 11.45/1.83 tff(f206,plain,( 11.45/1.83 (vIMP @ (exists_in_world @ sK8 @ sK7) @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ sK7))) @ (big_q @ sK8))) = $false)), 11.45/1.83 inference(combinator_demodulation,[],[f205])). 11.45/1.83 tff(f207,plain,( 11.45/1.83 (exists_in_world @ sK8 @ sK7 = $true)), 11.45/1.83 inference(binary_proxy_clausification,[],[f206])). 11.45/1.83 tff(f208,plain,( 11.45/1.83 (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ sK7))) @ (big_q @ sK8)) = $false)), 11.45/1.83 inference(binary_proxy_clausification,[],[f206])). 11.45/1.83 tff(f209,plain,( 11.45/1.83 (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ sK7))) @ (big_q @ sK8) @ sK9 = $false)), 11.45/1.83 inference(sigma_clausification,[],[f208])). 11.45/1.83 tff(f210,plain,( 11.45/1.83 (vOR @ (vNOT @ (rel_s4 @ sK7 @ sK9)) @ (big_q @ sK8 @ sK9) = $false)), 11.45/1.83 inference(combinator_demodulation,[],[f209])). 11.45/1.83 tff(f211,plain,( 11.45/1.83 (vNOT @ (rel_s4 @ sK7 @ sK9) = $false)), 11.45/1.83 inference(binary_proxy_clausification,[],[f210])). 11.45/1.83 tff(f212,plain,( 11.45/1.83 (big_q @ sK8 @ sK9 = $false)), 11.45/1.83 inference(binary_proxy_clausification,[],[f210])). 11.45/1.83 tff(f213,plain,( 11.45/1.83 (rel_s4 @ sK7 @ sK9 = $true)), 11.45/1.83 inference(not_proxy_clausification,[],[f211])). 11.45/1.83 tff(f214,plain,( 11.45/1.83 (rel_s4 @ sK3 @ sK7 = $true)), 11.45/1.83 inference(not_proxy_clausification,[],[f203])). 11.45/1.83 tff(f215,plain,( 11.45/1.83 (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ sK3))) @ (bCOMB @ vPI(mu) @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ exists_in_world))) @ (cCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT) @ (bCOMB @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ p))))) @ (bCOMB @ vNOT))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ big_q))) @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT) @ (bCOMB @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ (bCOMB @ vNOT @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ p)))))))) @ (bCOMB @ vNOT))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ big_r))))))) = $true)), 11.45/1.83 inference(not_proxy_clausification,[],[f183])). 11.45/1.83 tff(f216,plain,( 11.45/1.83 ( ! [X1] : ((sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ sK3))) @ (bCOMB @ vPI(mu) @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ exists_in_world))) @ (cCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT) @ (bCOMB @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ p))))) @ (bCOMB @ vNOT))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ big_q))) @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT) @ (bCOMB @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ (bCOMB @ vNOT @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ p)))))))) @ (bCOMB @ vNOT))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ big_r)))))) @ X1 = $true)) )), 11.45/1.83 inference(pi_clausification,[],[f215])). 11.45/1.83 tff(f217,plain,( 11.45/1.83 ( ! [X1] : ((vOR @ (vNOT @ (rel_s4 @ sK3 @ X1)) @ (vPI(mu) @ (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ exists_in_world @ X1)) @ (cCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT) @ (bCOMB @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ p))))) @ (bCOMB @ vNOT))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ big_q))) @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT) @ (bCOMB @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ (bCOMB @ vNOT @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ p)))))))) @ (bCOMB @ vNOT))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ big_r))) @ X1))) = $true)) )), 11.45/1.83 inference(combinator_demodulation,[],[f216])). 11.45/1.84 tff(f218,plain,( 11.45/1.84 ( ! [X1] : ((vNOT @ (rel_s4 @ sK3 @ X1) = $true) | (vPI(mu) @ (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ exists_in_world @ X1)) @ (cCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT) @ (bCOMB @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ p))))) @ (bCOMB @ vNOT))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ big_q))) @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT) @ (bCOMB @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ (bCOMB @ vNOT @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ p)))))))) @ (bCOMB @ vNOT))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ big_r))) @ X1)) = $true)) )), 11.45/1.84 inference(binary_proxy_clausification,[],[f217])). 11.45/1.84 tff(f219,plain,( 11.45/1.84 ( ! [X2:mu,X1] : ((vNOT @ (rel_s4 @ sK3 @ X1) = $true) | (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ exists_in_world @ X1)) @ (cCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT) @ (bCOMB @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ p))))) @ (bCOMB @ vNOT))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ big_q))) @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT) @ (bCOMB @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ (bCOMB @ vNOT @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ p)))))))) @ (bCOMB @ vNOT))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ big_r))) @ X1) @ X2 = $true)) )), 11.45/1.84 inference(pi_clausification,[],[f218])). 11.45/1.84 tff(f220,plain,( 11.45/1.84 ( ! [X2:mu,X1] : ((rel_s4 @ sK3 @ X1 = $false) | (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ exists_in_world @ X1)) @ (cCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT) @ (bCOMB @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ p))))) @ (bCOMB @ vNOT))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ big_q))) @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT) @ (bCOMB @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ (bCOMB @ vNOT @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ p)))))))) @ (bCOMB @ vNOT))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ big_r))) @ X1) @ X2 = $true)) )), 11.45/1.84 inference(not_proxy_clausification,[],[f219])). 11.45/1.84 tff(f221,plain,( 11.45/1.84 ( ! [X2:mu,X1] : ((rel_s4 @ sK3 @ X1 = $false) | (vIMP @ (exists_in_world @ X2 @ X1) @ (vOR @ (vNOT @ (vOR @ (vNOT @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X1))) @ p))) @ (vNOT @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X1))) @ (big_q @ X2)))))) @ (vNOT @ (vOR @ (vNOT @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X1))) @ (bCOMB @ vNOT @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ p)))))) @ (vNOT @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X1))) @ (big_r @ X2))))))) = $true)) )), 11.45/1.84 inference(combinator_demodulation,[],[f220])). 11.45/1.84 tff(f222,plain,( 11.45/1.84 ( ! [X2:mu,X1] : ((rel_s4 @ sK3 @ X1 = $false) | (exists_in_world @ X2 @ X1 = $false) | (vOR @ (vNOT @ (vOR @ (vNOT @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X1))) @ p))) @ (vNOT @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X1))) @ (big_q @ X2)))))) @ (vNOT @ (vOR @ (vNOT @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X1))) @ (bCOMB @ vNOT @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ p)))))) @ (vNOT @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X1))) @ (big_r @ X2)))))) = $true)) )), 11.45/1.84 inference(binary_proxy_clausification,[],[f221])). 11.45/1.84 tff(f223,plain,( 11.45/1.84 ( ! [X2:mu,X1] : ((rel_s4 @ sK3 @ X1 = $false) | (exists_in_world @ X2 @ X1 = $false) | (vNOT @ (vOR @ (vNOT @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X1))) @ p))) @ (vNOT @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X1))) @ (big_q @ X2))))) = $true) | (vNOT @ (vOR @ (vNOT @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X1))) @ (bCOMB @ vNOT @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ p)))))) @ (vNOT @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X1))) @ (big_r @ X2))))) = $true)) )), 11.45/1.84 inference(binary_proxy_clausification,[],[f222])). 11.45/1.84 tff(f224,plain,( 11.45/1.84 ( ! [X2:mu,X1] : ((rel_s4 @ sK3 @ X1 = $false) | (exists_in_world @ X2 @ X1 = $false) | (vNOT @ (vOR @ (vNOT @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X1))) @ p))) @ (vNOT @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X1))) @ (big_q @ X2))))) = $true) | (vOR @ (vNOT @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X1))) @ (bCOMB @ vNOT @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ p)))))) @ (vNOT @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X1))) @ (big_r @ X2)))) = $false)) )), 11.45/1.84 inference(not_proxy_clausification,[],[f223])). 11.45/1.84 tff(f225,plain,( 11.45/1.84 ( ! [X2:mu,X1] : ((rel_s4 @ sK3 @ X1 = $false) | (exists_in_world @ X2 @ X1 = $false) | (vOR @ (vNOT @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X1))) @ p))) @ (vNOT @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X1))) @ (big_q @ X2)))) = $false) | (vOR @ (vNOT @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X1))) @ (bCOMB @ vNOT @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ p)))))) @ (vNOT @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X1))) @ (big_r @ X2)))) = $false)) )), 11.45/1.84 inference(not_proxy_clausification,[],[f224])). 11.45/1.84 tff(f226,plain,( 11.45/1.84 ( ! [X2:mu,X1] : ((rel_s4 @ sK3 @ X1 = $false) | (exists_in_world @ X2 @ X1 = $false) | (vNOT @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X1))) @ p)) = $false) | (vOR @ (vNOT @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X1))) @ (bCOMB @ vNOT @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ p)))))) @ (vNOT @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X1))) @ (big_r @ X2)))) = $false)) )), 11.45/1.84 inference(binary_proxy_clausification,[],[f225])). 11.45/1.84 tff(f227,plain,( 11.45/1.84 ( ! [X2:mu,X1] : ((rel_s4 @ sK3 @ X1 = $false) | (exists_in_world @ X2 @ X1 = $false) | (vNOT @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X1))) @ (big_q @ X2))) = $false) | (vOR @ (vNOT @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X1))) @ (bCOMB @ vNOT @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ p)))))) @ (vNOT @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X1))) @ (big_r @ X2)))) = $false)) )), 11.45/1.84 inference(binary_proxy_clausification,[],[f225])). 11.45/1.84 tff(f228,plain,( 11.45/1.84 ( ! [X2:mu,X1] : ((rel_s4 @ sK3 @ X1 = $false) | (exists_in_world @ X2 @ X1 = $false) | (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X1))) @ (big_q @ X2)) = $true) | (vOR @ (vNOT @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X1))) @ (bCOMB @ vNOT @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ p)))))) @ (vNOT @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X1))) @ (big_r @ X2)))) = $false)) )), 11.45/1.84 inference(not_proxy_clausification,[],[f227])). 11.45/1.84 tff(f229,plain,( 11.45/1.84 ( ! [X2:mu,X3,X1] : ((rel_s4 @ sK3 @ X1 = $false) | (exists_in_world @ X2 @ X1 = $false) | (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X1))) @ (big_q @ X2) @ X3 = $true) | (vOR @ (vNOT @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X1))) @ (bCOMB @ vNOT @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ p)))))) @ (vNOT @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X1))) @ (big_r @ X2)))) = $false)) )), 11.45/1.84 inference(pi_clausification,[],[f228])). 11.45/1.84 tff(f230,plain,( 11.45/1.84 ( ! [X2:mu,X3,X1] : ((rel_s4 @ sK3 @ X1 = $false) | (exists_in_world @ X2 @ X1 = $false) | (vOR @ (vNOT @ (rel_s4 @ X1 @ X3)) @ (big_q @ X2 @ X3) = $true) | (vOR @ (vNOT @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X1))) @ (bCOMB @ vNOT @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ p)))))) @ (vNOT @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X1))) @ (big_r @ X2)))) = $false)) )), 11.45/1.84 inference(combinator_demodulation,[],[f229])). 11.45/1.86 % (18703)Time limit reached! 11.45/1.86 % (18703)------------------------------ 11.45/1.86 % (18703)Version: Vampire 4.5.0 (commit 7ae30c7f on 2020-06-30 15:57:20 +0100) 11.45/1.86 % (18703)Termination reason: Time limit 11.45/1.86 11.45/1.86 % (18703)Memory used [KB]: 10746 11.45/1.86 % (18703)Time elapsed: 1.514 s 11.45/1.86 % (18703)------------------------------ 11.45/1.86 % (18703)------------------------------ 11.45/1.86 % (18724)Time limit reached! 11.45/1.86 % (18724)------------------------------ 11.45/1.86 % (18724)Version: Vampire 4.5.0 (commit 7ae30c7f on 2020-06-30 15:57:20 +0100) 11.45/1.86 % (18724)Termination reason: Time limit 11.45/1.86 11.45/1.86 % (18724)Memory used [KB]: 10746 11.45/1.86 % (18724)Time elapsed: 1.518 s 11.45/1.86 % (18724)------------------------------ 11.45/1.86 % (18724)------------------------------ 11.45/1.86 tff(f231,plain,( 11.45/1.86 ( ! [X2:mu,X3,X1] : ((rel_s4 @ sK3 @ X1 = $false) | (exists_in_world @ X2 @ X1 = $false) | (vNOT @ (rel_s4 @ X1 @ X3) = $true) | (vOR @ (vNOT @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X1))) @ (bCOMB @ vNOT @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ p)))))) @ (vNOT @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X1))) @ (big_r @ X2)))) = $false) | (big_q @ X2 @ X3 = $true)) )), 11.45/1.86 inference(binary_proxy_clausification,[],[f230])). 11.45/1.86 tff(f232,plain,( 11.45/1.86 ( ! [X2:mu,X3,X1] : ((rel_s4 @ sK3 @ X1 = $false) | (exists_in_world @ X2 @ X1 = $false) | (rel_s4 @ X1 @ X3 = $false) | (vOR @ (vNOT @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X1))) @ (bCOMB @ vNOT @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ p)))))) @ (vNOT @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X1))) @ (big_r @ X2)))) = $false) | (big_q @ X2 @ X3 = $true)) )), 11.45/1.86 inference(not_proxy_clausification,[],[f231])). 11.45/1.86 tff(f233,plain,( 11.45/1.86 ( ! [X2:mu,X3,X1] : ((rel_s4 @ sK3 @ X1 = $false) | (exists_in_world @ X2 @ X1 = $false) | (rel_s4 @ X1 @ X3 = $false) | (vNOT @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X1))) @ (bCOMB @ vNOT @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ p))))) = $false) | (big_q @ X2 @ X3 = $true)) )), 11.45/1.86 inference(binary_proxy_clausification,[],[f232])). 11.45/1.86 tff(f240,plain,( 11.45/1.86 ( ! [X2:mu,X3,X1] : ((rel_s4 @ sK3 @ X1 = $false) | (exists_in_world @ X2 @ X1 = $false) | (rel_s4 @ X1 @ X3 = $false) | (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X1))) @ (bCOMB @ vNOT @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ p)))) = $true) | (big_q @ X2 @ X3 = $true)) )), 11.45/1.86 inference(not_proxy_clausification,[],[f233])). 11.45/1.86 tff(f241,plain,( 11.45/1.86 ( ! [X4,X2:mu,X3,X1] : ((rel_s4 @ sK3 @ X1 = $false) | (exists_in_world @ X2 @ X1 = $false) | (rel_s4 @ X1 @ X3 = $false) | (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X1))) @ (bCOMB @ vNOT @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ p))) @ X4 = $true) | (big_q @ X2 @ X3 = $true)) )), 11.45/1.86 inference(pi_clausification,[],[f240])). 11.45/1.86 tff(f242,plain,( 11.45/1.86 ( ! [X4,X2:mu,X3,X1] : ((rel_s4 @ sK3 @ X1 = $false) | (exists_in_world @ X2 @ X1 = $false) | (rel_s4 @ X1 @ X3 = $false) | (vOR @ (vNOT @ (rel_s4 @ X1 @ X4)) @ (vNOT @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X4))) @ p))) = $true) | (big_q @ X2 @ X3 = $true)) )), 11.45/1.86 inference(combinator_demodulation,[],[f241])). 11.45/1.86 tff(f243,plain,( 11.45/1.86 ( ! [X4,X2:mu,X3,X1] : ((rel_s4 @ sK3 @ X1 = $false) | (exists_in_world @ X2 @ X1 = $false) | (rel_s4 @ X1 @ X3 = $false) | (vNOT @ (rel_s4 @ X1 @ X4) = $true) | (big_q @ X2 @ X3 = $true) | (vNOT @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X4))) @ p)) = $true)) )), 11.45/1.86 inference(binary_proxy_clausification,[],[f242])). 11.45/1.86 tff(f244,plain,( 11.45/1.86 ( ! [X4,X2:mu,X3,X1] : ((rel_s4 @ sK3 @ X1 = $false) | (exists_in_world @ X2 @ X1 = $false) | (rel_s4 @ X1 @ X3 = $false) | (vNOT @ (rel_s4 @ X1 @ X4) = $true) | (big_q @ X2 @ X3 = $true) | (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X4))) @ p) = $false)) )), 11.45/1.86 inference(not_proxy_clausification,[],[f243])). 11.45/1.86 tff(f245,plain,( 11.45/1.86 ( ! [X4,X2:mu,X3,X1] : ((rel_s4 @ sK3 @ X1 = $false) | (exists_in_world @ X2 @ X1 = $false) | (rel_s4 @ X1 @ X3 = $false) | (vNOT @ (rel_s4 @ X1 @ X4) = $true) | (big_q @ X2 @ X3 = $true) | (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X4))) @ p @ (sK10 @ X4) = $false)) )), 11.45/1.86 inference(sigma_clausification,[],[f244])). 11.45/1.86 tff(f246,plain,( 11.45/1.86 ( ! [X4,X2:mu,X3,X1] : ((rel_s4 @ sK3 @ X1 = $false) | (exists_in_world @ X2 @ X1 = $false) | (rel_s4 @ X1 @ X3 = $false) | (rel_s4 @ X1 @ X4 = $false) | (big_q @ X2 @ X3 = $true) | (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X4))) @ p @ (sK10 @ X4) = $false)) )), 11.45/1.86 inference(not_proxy_clausification,[],[f245])). 11.45/1.86 tff(f247,plain,( 11.45/1.86 ( ! [X4,X2:mu,X3,X1] : ((rel_s4 @ sK3 @ X1 = $false) | (exists_in_world @ X2 @ X1 = $false) | (rel_s4 @ X1 @ X3 = $false) | (rel_s4 @ X1 @ X4 = $false) | (big_q @ X2 @ X3 = $true) | (vOR @ (vNOT @ (rel_s4 @ X4 @ (sK10 @ X4))) @ (p @ (sK10 @ X4)) = $false)) )), 11.45/1.86 inference(combinator_demodulation,[],[f246])). 11.45/1.86 tff(f248,plain,( 11.45/1.86 ( ! [X4,X2:mu,X3,X1] : ((rel_s4 @ sK3 @ X1 = $false) | (exists_in_world @ X2 @ X1 = $false) | (rel_s4 @ X1 @ X3 = $false) | (rel_s4 @ X1 @ X4 = $false) | (big_q @ X2 @ X3 = $true) | (vNOT @ (rel_s4 @ X4 @ (sK10 @ X4)) = $false)) )), 11.45/1.86 inference(binary_proxy_clausification,[],[f247])). 11.45/1.86 tff(f249,plain,( 11.45/1.86 ( ! [X4,X2:mu,X3,X1] : ((rel_s4 @ sK3 @ X1 = $false) | (exists_in_world @ X2 @ X1 = $false) | (rel_s4 @ X1 @ X3 = $false) | (rel_s4 @ X1 @ X4 = $false) | (big_q @ X2 @ X3 = $true) | (p @ (sK10 @ X4) = $false)) )), 11.45/1.86 inference(binary_proxy_clausification,[],[f247])). 11.45/1.86 tff(f250,plain,( 11.45/1.86 ( ! [X4,X2:mu,X3,X1] : ((rel_s4 @ X4 @ (sK10 @ X4) = $true) | (exists_in_world @ X2 @ X1 = $false) | (rel_s4 @ X1 @ X3 = $false) | (rel_s4 @ X1 @ X4 = $false) | (big_q @ X2 @ X3 = $true) | (rel_s4 @ sK3 @ X1 = $false)) )), 11.45/1.86 inference(not_proxy_clausification,[],[f248])). 11.45/1.86 tff(f251,plain,( 11.45/1.86 ( ! [X2:mu,X1] : ((rel_s4 @ sK3 @ X1 = $false) | (exists_in_world @ X2 @ X1 = $false) | (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X1))) @ p) = $true) | (vOR @ (vNOT @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X1))) @ (bCOMB @ vNOT @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ p)))))) @ (vNOT @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X1))) @ (big_r @ X2)))) = $false)) )), 11.45/1.86 inference(not_proxy_clausification,[],[f226])). 11.45/1.86 tff(f252,plain,( 11.45/1.86 ( ! [X2:mu,X3,X1] : ((rel_s4 @ sK3 @ X1 = $false) | (exists_in_world @ X2 @ X1 = $false) | (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X1))) @ p @ X3 = $true) | (vOR @ (vNOT @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X1))) @ (bCOMB @ vNOT @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ p)))))) @ (vNOT @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X1))) @ (big_r @ X2)))) = $false)) )), 11.45/1.86 inference(pi_clausification,[],[f251])). 11.45/1.86 tff(f253,plain,( 11.45/1.86 ( ! [X2:mu,X3,X1] : ((rel_s4 @ sK3 @ X1 = $false) | (exists_in_world @ X2 @ X1 = $false) | (vOR @ (vNOT @ (rel_s4 @ X1 @ X3)) @ (p @ X3) = $true) | (vOR @ (vNOT @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X1))) @ (bCOMB @ vNOT @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ p)))))) @ (vNOT @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X1))) @ (big_r @ X2)))) = $false)) )), 11.45/1.86 inference(combinator_demodulation,[],[f252])). 11.45/1.86 tff(f254,plain,( 11.45/1.86 ( ! [X2:mu,X3,X1] : ((rel_s4 @ sK3 @ X1 = $false) | (exists_in_world @ X2 @ X1 = $false) | (vNOT @ (rel_s4 @ X1 @ X3) = $true) | (vOR @ (vNOT @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X1))) @ (bCOMB @ vNOT @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ p)))))) @ (vNOT @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X1))) @ (big_r @ X2)))) = $false) | (p @ X3 = $true)) )), 11.45/1.86 inference(binary_proxy_clausification,[],[f253])). 11.45/1.86 tff(f255,plain,( 11.45/1.86 ( ! [X2:mu,X3,X1] : ((rel_s4 @ sK3 @ X1 = $false) | (exists_in_world @ X2 @ X1 = $false) | (rel_s4 @ X1 @ X3 = $false) | (vOR @ (vNOT @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X1))) @ (bCOMB @ vNOT @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ p)))))) @ (vNOT @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X1))) @ (big_r @ X2)))) = $false) | (p @ X3 = $true)) )), 11.45/1.86 inference(not_proxy_clausification,[],[f254])). 11.45/1.86 tff(f256,plain,( 11.45/1.86 ( ! [X2:mu,X3,X1] : ((rel_s4 @ sK3 @ X1 = $false) | (exists_in_world @ X2 @ X1 = $false) | (rel_s4 @ X1 @ X3 = $false) | (vNOT @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X1))) @ (bCOMB @ vNOT @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ p))))) = $false) | (p @ X3 = $true)) )), 11.45/1.86 inference(binary_proxy_clausification,[],[f255])). 11.45/1.86 tff(f257,plain,( 11.45/1.86 ( ! [X2:mu,X3,X1] : ((rel_s4 @ sK3 @ X1 = $false) | (exists_in_world @ X2 @ X1 = $false) | (rel_s4 @ X1 @ X3 = $false) | (vNOT @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X1))) @ (big_r @ X2))) = $false) | (p @ X3 = $true)) )), 11.45/1.86 inference(binary_proxy_clausification,[],[f255])). 11.45/1.86 tff(f258,plain,( 11.45/1.86 ( ! [X2:mu,X3,X1] : ((rel_s4 @ sK3 @ X1 = $false) | (exists_in_world @ X2 @ X1 = $false) | (rel_s4 @ X1 @ X3 = $false) | (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X1))) @ (big_r @ X2)) = $true) | (p @ X3 = $true)) )), 11.45/1.86 inference(not_proxy_clausification,[],[f257])). 11.45/1.86 tff(f259,plain,( 11.45/1.86 ( ! [X4,X2:mu,X3,X1] : ((rel_s4 @ sK3 @ X1 = $false) | (exists_in_world @ X2 @ X1 = $false) | (rel_s4 @ X1 @ X3 = $false) | (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X1))) @ (big_r @ X2) @ X4 = $true) | (p @ X3 = $true)) )), 11.45/1.86 inference(pi_clausification,[],[f258])). 11.45/1.86 tff(f260,plain,( 11.45/1.86 ( ! [X4,X2:mu,X3,X1] : ((rel_s4 @ sK3 @ X1 = $false) | (exists_in_world @ X2 @ X1 = $false) | (rel_s4 @ X1 @ X3 = $false) | (vOR @ (vNOT @ (rel_s4 @ X1 @ X4)) @ (big_r @ X2 @ X4) = $true) | (p @ X3 = $true)) )), 11.45/1.86 inference(combinator_demodulation,[],[f259])). 11.45/1.86 tff(f261,plain,( 11.45/1.86 ( ! [X4,X2:mu,X3,X1] : ((rel_s4 @ sK3 @ X1 = $false) | (exists_in_world @ X2 @ X1 = $false) | (rel_s4 @ X1 @ X3 = $false) | (vNOT @ (rel_s4 @ X1 @ X4) = $true) | (p @ X3 = $true) | (big_r @ X2 @ X4 = $true)) )), 11.45/1.86 inference(binary_proxy_clausification,[],[f260])). 11.45/1.86 tff(f262,plain,( 11.45/1.86 ( ! [X4,X2:mu,X3,X1] : ((rel_s4 @ sK3 @ X1 = $false) | (exists_in_world @ X2 @ X1 = $false) | (rel_s4 @ X1 @ X3 = $false) | (rel_s4 @ X1 @ X4 = $false) | (p @ X3 = $true) | (big_r @ X2 @ X4 = $true)) )), 11.45/1.86 inference(not_proxy_clausification,[],[f261])). 11.45/1.86 tff(f263,plain,( 11.45/1.86 ( ! [X2:mu,X3,X1] : ((rel_s4 @ sK3 @ X1 = $false) | (exists_in_world @ X2 @ X1 = $false) | (rel_s4 @ X1 @ X3 = $false) | (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X1))) @ (bCOMB @ vNOT @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ p)))) = $true) | (p @ X3 = $true)) )), 11.45/1.86 inference(not_proxy_clausification,[],[f256])). 11.45/1.86 tff(f264,plain,( 11.45/1.86 ( ! [X4,X2:mu,X3,X1] : ((rel_s4 @ sK3 @ X1 = $false) | (exists_in_world @ X2 @ X1 = $false) | (rel_s4 @ X1 @ X3 = $false) | (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X1))) @ (bCOMB @ vNOT @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ p))) @ X4 = $true) | (p @ X3 = $true)) )), 11.45/1.86 inference(pi_clausification,[],[f263])). 11.45/1.86 tff(f265,plain,( 11.45/1.86 ( ! [X4,X2:mu,X3,X1] : ((rel_s4 @ sK3 @ X1 = $false) | (exists_in_world @ X2 @ X1 = $false) | (rel_s4 @ X1 @ X3 = $false) | (vOR @ (vNOT @ (rel_s4 @ X1 @ X4)) @ (vNOT @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X4))) @ p))) = $true) | (p @ X3 = $true)) )), 11.45/1.86 inference(combinator_demodulation,[],[f264])). 11.45/1.86 tff(f266,plain,( 11.45/1.86 ( ! [X4,X2:mu,X3,X1] : ((rel_s4 @ sK3 @ X1 = $false) | (exists_in_world @ X2 @ X1 = $false) | (rel_s4 @ X1 @ X3 = $false) | (vNOT @ (rel_s4 @ X1 @ X4) = $true) | (p @ X3 = $true) | (vNOT @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X4))) @ p)) = $true)) )), 11.45/1.86 inference(binary_proxy_clausification,[],[f265])). 11.45/1.86 tff(f267,plain,( 11.45/1.86 ( ! [X4,X2:mu,X3,X1] : ((rel_s4 @ sK3 @ X1 = $false) | (exists_in_world @ X2 @ X1 = $false) | (rel_s4 @ X1 @ X3 = $false) | (vNOT @ (rel_s4 @ X1 @ X4) = $true) | (p @ X3 = $true) | (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X4))) @ p) = $false)) )), 11.45/1.86 inference(not_proxy_clausification,[],[f266])). 11.45/1.86 tff(f268,plain,( 11.45/1.86 ( ! [X4,X2:mu,X3,X1] : ((rel_s4 @ sK3 @ X1 = $false) | (exists_in_world @ X2 @ X1 = $false) | (rel_s4 @ X1 @ X3 = $false) | (vNOT @ (rel_s4 @ X1 @ X4) = $true) | (p @ X3 = $true) | (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X4))) @ p @ (sK11 @ X4) = $false)) )), 11.45/1.86 inference(sigma_clausification,[],[f267])). 11.45/1.86 tff(f269,plain,( 11.45/1.86 ( ! [X4,X2:mu,X3,X1] : ((rel_s4 @ sK3 @ X1 = $false) | (exists_in_world @ X2 @ X1 = $false) | (rel_s4 @ X1 @ X3 = $false) | (rel_s4 @ X1 @ X4 = $false) | (p @ X3 = $true) | (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X4))) @ p @ (sK11 @ X4) = $false)) )), 11.45/1.86 inference(not_proxy_clausification,[],[f268])). 11.45/1.86 tff(f270,plain,( 11.45/1.86 ( ! [X4,X2:mu,X3,X1] : ((rel_s4 @ sK3 @ X1 = $false) | (exists_in_world @ X2 @ X1 = $false) | (rel_s4 @ X1 @ X3 = $false) | (rel_s4 @ X1 @ X4 = $false) | (p @ X3 = $true) | (vOR @ (vNOT @ (rel_s4 @ X4 @ (sK11 @ X4))) @ (p @ (sK11 @ X4)) = $false)) )), 11.45/1.86 inference(combinator_demodulation,[],[f269])). 11.45/1.86 tff(f271,plain,( 11.45/1.86 ( ! [X4,X2:mu,X3,X1] : ((rel_s4 @ sK3 @ X1 = $false) | (exists_in_world @ X2 @ X1 = $false) | (rel_s4 @ X1 @ X3 = $false) | (rel_s4 @ X1 @ X4 = $false) | (p @ X3 = $true) | (vNOT @ (rel_s4 @ X4 @ (sK11 @ X4)) = $false)) )), 11.45/1.86 inference(binary_proxy_clausification,[],[f270])). 11.45/1.86 tff(f272,plain,( 11.45/1.86 ( ! [X4,X2:mu,X3,X1] : ((rel_s4 @ sK3 @ X1 = $false) | (exists_in_world @ X2 @ X1 = $false) | (rel_s4 @ X1 @ X3 = $false) | (rel_s4 @ X1 @ X4 = $false) | (p @ X3 = $true) | (p @ (sK11 @ X4) = $false)) )), 11.45/1.86 inference(binary_proxy_clausification,[],[f270])). 11.45/1.86 tff(f273,plain,( 11.45/1.86 ( ! [X4,X2:mu,X3,X1] : ((rel_s4 @ X4 @ (sK11 @ X4) = $true) | (exists_in_world @ X2 @ X1 = $false) | (rel_s4 @ X1 @ X3 = $false) | (rel_s4 @ X1 @ X4 = $false) | (p @ X3 = $true) | (rel_s4 @ sK3 @ X1 = $false)) )), 11.45/1.86 inference(not_proxy_clausification,[],[f271])). 11.45/1.86 tff(f274,plain,( 11.45/1.86 (rel_s4 @ sK2 @ sK3 = $true)), 11.45/1.86 inference(not_proxy_clausification,[],[f181])). 11.45/1.86 tff(f281,plain,( 11.45/1.86 ( ! [X2:mu] : (($true != $true) | (exists_in_world @ X2 @ sK2 != $true) | (exists_in_world @ X2 @ sK3 = $true)) )), 11.45/1.86 inference(superposition,[],[f149,f274])). 11.45/1.86 tff(f284,plain,( 11.45/1.86 ( ! [X2:mu] : ((exists_in_world @ X2 @ sK2 != $true) | (exists_in_world @ X2 @ sK3 = $true)) )), 11.45/1.86 inference(trivial_inequality_removal,[],[f281])). 11.45/1.86 tff(f305,plain,( 11.45/1.86 ( ! [X0] : (($false = $true) | (rel_s4 @ sK3 @ X0 = $true) | (rel_s4 @ sK7 @ X0 = $false)) )), 11.45/1.86 inference(superposition,[],[f214,f176])). 11.45/1.86 tff(f310,plain,( 11.45/1.86 ( ! [X0] : ((rel_s4 @ sK7 @ X0 = $false) | (rel_s4 @ sK3 @ X0 = $true)) )), 11.45/1.86 inference(trivial_inequality_removal,[],[f305])). 11.45/1.86 tff(f345,plain,( 11.45/1.86 ($true != $true) | (exists_in_world @ (sK0 @ sK2) @ sK3 = $true)), 11.45/1.86 inference(superposition,[],[f284,f148])). 11.45/1.86 tff(f346,plain,( 11.45/1.86 (exists_in_world @ (sK0 @ sK2) @ sK3 = $true)), 11.45/1.86 inference(trivial_inequality_removal,[],[f345])). 11.45/1.86 tff(f513,plain,( 11.45/1.86 ( ! [X14,X12:mu,X13] : (($false = $true) | (exists_in_world @ X12 @ sK4 = $false) | (rel_s4 @ sK4 @ X13 = $false) | (rel_s4 @ sK4 @ X14 = $false) | (p @ X13 = $true) | (big_r @ X12 @ X14 = $true)) )), 11.45/1.86 inference(superposition,[],[f262,f200])). 11.45/1.86 tff(f529,plain,( 11.45/1.86 ( ! [X14,X12:mu,X13] : ((exists_in_world @ X12 @ sK4 = $false) | (rel_s4 @ sK4 @ X13 = $false) | (rel_s4 @ sK4 @ X14 = $false) | (p @ X13 = $true) | (big_r @ X12 @ X14 = $true)) )), 11.45/1.86 inference(trivial_inequality_removal,[],[f513])). 11.45/1.86 tff(f757,plain,( 11.45/1.86 spl1_10 <=> ! [X13] : ((rel_s4 @ sK4 @ X13 = $false) | (p @ X13 = $true))), 11.45/1.86 introduced(avatar_definition,[new_symbols(naming,[spl1_10])])). 11.45/1.86 tff(f758,plain,( 11.45/1.86 ( ! [X13] : ((rel_s4 @ sK4 @ X13 = $false) | (p @ X13 = $true)) ) | ~spl1_10), 11.45/1.86 inference(avatar_component_clause,[],[f757])). 11.45/1.86 tff(f760,plain,( 11.45/1.86 spl1_12 <=> ! [X12 : mu,X14] : ((exists_in_world @ X12 @ sK4 = $false) | (big_r @ X12 @ X14 = $true) | (rel_s4 @ sK4 @ X14 = $false))), 11.45/1.86 introduced(avatar_definition,[new_symbols(naming,[spl1_12])])). 11.45/1.86 tff(f761,plain,( 11.45/1.86 ( ! [X14,X12:mu] : ((rel_s4 @ sK4 @ X14 = $false) | (big_r @ X12 @ X14 = $true) | (exists_in_world @ X12 @ sK4 = $false)) ) | ~spl1_12), 11.45/1.86 inference(avatar_component_clause,[],[f760])). 11.45/1.86 tff(f762,plain,( 11.45/1.86 spl1_10 | spl1_12), 11.45/1.86 inference(avatar_split_clause,[],[f529,f760,f757])). 11.45/1.86 tff(f778,plain,( 11.45/1.86 spl1_14 <=> ! [X4] : ((rel_s4 @ sK3 @ X4 = $false) | (p @ X4 = $true))), 11.45/1.86 introduced(avatar_definition,[new_symbols(naming,[spl1_14])])). 11.45/1.86 tff(f779,plain,( 11.45/1.86 ( ! [X4] : ((rel_s4 @ sK3 @ X4 = $false) | (p @ X4 = $true)) ) | ~spl1_14), 11.45/1.86 inference(avatar_component_clause,[],[f778])). 11.45/1.86 tff(f888,plain,( 11.45/1.86 ( ! [X6:mu,X8,X7] : (($false = $true) | (exists_in_world @ X6 @ sK3 = $false) | (rel_s4 @ sK3 @ X7 = $false) | (rel_s4 @ sK3 @ X8 = $false) | (p @ X7 = $true) | (p @ (sK11 @ X8) = $false)) )), 11.45/1.86 inference(superposition,[],[f167,f272])). 11.45/1.86 tff(f904,plain,( 11.45/1.86 ( ! [X6:mu,X8,X7] : ((exists_in_world @ X6 @ sK3 = $false) | (rel_s4 @ sK3 @ X7 = $false) | (rel_s4 @ sK3 @ X8 = $false) | (p @ X7 = $true) | (p @ (sK11 @ X8) = $false)) )), 11.45/1.86 inference(trivial_inequality_removal,[],[f888])). 11.45/1.86 tff(f915,plain,( 11.45/1.86 ( ! [X24,X23:mu,X25] : (($false = $true) | (exists_in_world @ X23 @ sK7 = $false) | (rel_s4 @ sK7 @ X24 = $false) | (rel_s4 @ sK7 @ X25 = $false) | (big_q @ X23 @ X24 = $true) | (p @ (sK10 @ X25) = $false)) )), 11.45/1.86 inference(superposition,[],[f249,f214])). 11.45/1.86 tff(f935,plain,( 11.45/1.86 ( ! [X24,X23:mu,X25] : ((exists_in_world @ X23 @ sK7 = $false) | (rel_s4 @ sK7 @ X24 = $false) | (rel_s4 @ sK7 @ X25 = $false) | (big_q @ X23 @ X24 = $true) | (p @ (sK10 @ X25) = $false)) )), 11.45/1.86 inference(trivial_inequality_removal,[],[f915])). 11.45/1.86 tff(f954,plain,( 11.45/1.86 ( ! [X50,X48:mu,X49] : (($false = $true) | (exists_in_world @ X48 @ X49 = $false) | (rel_s4 @ X49 @ X50 = $false) | (rel_s4 @ X49 @ sK4 = $false) | (p @ X50 = $true) | (rel_s4 @ sK3 @ X49 = $false) | (p @ (sK11 @ sK4) = $true)) ) | ~spl1_10), 11.45/1.86 inference(superposition,[],[f273,f758])). 11.45/1.86 tff(f1005,plain,( 11.45/1.86 ( ! [X50,X48:mu,X49] : ((exists_in_world @ X48 @ X49 = $false) | (rel_s4 @ X49 @ X50 = $false) | (rel_s4 @ X49 @ sK4 = $false) | (p @ X50 = $true) | (rel_s4 @ sK3 @ X49 = $false) | (p @ (sK11 @ sK4) = $true)) ) | ~spl1_10), 11.45/1.86 inference(trivial_inequality_removal,[],[f954])). 11.45/1.86 tff(f1049,plain,( 11.45/1.86 ( ! [X66,X67,X65:mu] : (($false = $true) | (exists_in_world @ X65 @ X66 = $false) | (rel_s4 @ X66 @ X67 = $false) | (rel_s4 @ X66 @ sK7 = $false) | (big_q @ X65 @ X67 = $true) | (rel_s4 @ sK3 @ X66 = $false) | (rel_s4 @ sK3 @ (sK10 @ sK7) = $true)) )), 11.45/1.86 inference(superposition,[],[f250,f310])). 11.45/1.86 tff(f1094,plain,( 11.45/1.86 ( ! [X66,X67,X65:mu] : ((exists_in_world @ X65 @ X66 = $false) | (rel_s4 @ X66 @ X67 = $false) | (rel_s4 @ X66 @ sK7 = $false) | (big_q @ X65 @ X67 = $true) | (rel_s4 @ sK3 @ X66 = $false) | (rel_s4 @ sK3 @ (sK10 @ sK7) = $true)) )), 11.45/1.86 inference(trivial_inequality_removal,[],[f1049])). 11.45/1.86 tff(f1745,plain,( 11.45/1.86 spl1_18 <=> ! [X25] : ((rel_s4 @ sK7 @ X25 = $false) | (p @ (sK10 @ X25) = $false))), 11.45/1.86 introduced(avatar_definition,[new_symbols(naming,[spl1_18])])). 11.45/1.86 tff(f1746,plain,( 11.45/1.86 ( ! [X25] : ((rel_s4 @ sK7 @ X25 = $false) | (p @ (sK10 @ X25) = $false)) ) | ~spl1_18), 11.45/1.86 inference(avatar_component_clause,[],[f1745])). 11.45/1.86 tff(f1748,plain,( 11.45/1.86 spl1_20 <=> ! [X23 : mu,X24] : ((exists_in_world @ X23 @ sK7 = $false) | (big_q @ X23 @ X24 = $true) | (rel_s4 @ sK7 @ X24 = $false))), 11.45/1.86 introduced(avatar_definition,[new_symbols(naming,[spl1_20])])). 11.45/1.86 tff(f1749,plain,( 11.45/1.86 ( ! [X24,X23:mu] : ((rel_s4 @ sK7 @ X24 = $false) | (big_q @ X23 @ X24 = $true) | (exists_in_world @ X23 @ sK7 = $false)) ) | ~spl1_20), 11.45/1.86 inference(avatar_component_clause,[],[f1748])). 11.45/1.86 tff(f1750,plain,( 11.45/1.86 spl1_18 | spl1_20), 11.45/1.86 inference(avatar_split_clause,[],[f935,f1748,f1745])). 11.45/1.86 tff(f1751,plain,( 11.45/1.86 ($false = $true) | (p @ (sK10 @ sK7) = $false) | ~spl1_18), 11.45/1.86 inference(superposition,[],[f1746,f167])). 11.45/1.86 tff(f1771,plain,( 11.45/1.86 (p @ (sK10 @ sK7) = $false) | ~spl1_18), 11.45/1.86 inference(trivial_inequality_removal,[],[f1751])). 11.45/1.86 tff(f2209,plain,( 11.45/1.86 spl1_38 <=> (p @ (sK11 @ sK4) = $true)), 11.45/1.86 introduced(avatar_definition,[new_symbols(naming,[spl1_38])])). 11.45/1.86 tff(f2210,plain,( 11.45/1.86 (p @ (sK11 @ sK4) = $true) | ~spl1_38), 11.45/1.86 inference(avatar_component_clause,[],[f2209])). 11.45/1.86 tff(f2212,plain,( 11.45/1.86 spl1_40 <=> ! [X49,X48 : mu,X50] : ((exists_in_world @ X48 @ X49 = $false) | (rel_s4 @ sK3 @ X49 = $false) | (p @ X50 = $true) | (rel_s4 @ X49 @ sK4 = $false) | (rel_s4 @ X49 @ X50 = $false))), 11.45/1.86 introduced(avatar_definition,[new_symbols(naming,[spl1_40])])). 11.45/1.86 tff(f2213,plain,( 11.45/1.86 ( ! [X50,X48:mu,X49] : ((rel_s4 @ sK3 @ X49 = $false) | (exists_in_world @ X48 @ X49 = $false) | (p @ X50 = $true) | (rel_s4 @ X49 @ sK4 = $false) | (rel_s4 @ X49 @ X50 = $false)) ) | ~spl1_40), 11.45/1.86 inference(avatar_component_clause,[],[f2212])). 11.45/1.86 tff(f2214,plain,( 11.45/1.86 spl1_38 | spl1_40 | ~spl1_10), 11.45/1.86 inference(avatar_split_clause,[],[f1005,f757,f2212,f2209])). 11.45/1.86 tff(f2220,plain,( 11.45/1.86 ( ! [X22:mu] : (($false = $true) | (big_r @ X22 @ sK6 = $true) | (exists_in_world @ X22 @ sK4 = $false)) ) | ~spl1_12), 11.45/1.86 inference(superposition,[],[f761,f199])). 11.45/1.86 tff(f2232,plain,( 11.45/1.86 ( ! [X22:mu] : ((big_r @ X22 @ sK6 = $true) | (exists_in_world @ X22 @ sK4 = $false)) ) | ~spl1_12), 11.45/1.86 inference(trivial_inequality_removal,[],[f2220])). 11.45/1.86 tff(f2271,plain,( 11.45/1.86 ($false = $true) | (exists_in_world @ sK5 @ sK4 = $false) | ~spl1_12), 11.45/1.86 inference(superposition,[],[f2232,f198])). 11.45/1.86 tff(f2274,plain,( 11.45/1.86 (exists_in_world @ sK5 @ sK4 = $false) | ~spl1_12), 11.45/1.86 inference(trivial_inequality_removal,[],[f2271])). 11.45/1.86 tff(f2275,plain,( 11.45/1.86 ($false = $true) | ~spl1_12), 11.45/1.86 inference(backward_demodulation,[],[f2274,f193])). 11.45/1.86 tff(f2276,plain,( 11.45/1.86 $false | ~spl1_12), 11.45/1.86 inference(trivial_inequality_removal,[],[f2275])). 11.45/1.86 tff(f2277,plain,( 11.45/1.86 ~spl1_12), 11.45/1.86 inference(avatar_contradiction_clause,[],[f2276])). 11.45/1.86 tff(f2391,plain,( 11.45/1.86 spl1_52 <=> ! [X0 : mu] : (exists_in_world @ X0 @ sK3 = $false)), 11.45/1.86 introduced(avatar_definition,[new_symbols(naming,[spl1_52])])). 11.45/1.86 tff(f2392,plain,( 11.45/1.86 ( ! [X0:mu] : ((exists_in_world @ X0 @ sK3 = $false)) ) | ~spl1_52), 11.45/1.86 inference(avatar_component_clause,[],[f2391])). 11.45/1.86 tff(f2449,plain,( 11.45/1.86 spl1_54 <=> ! [X8] : ((rel_s4 @ sK3 @ X8 = $false) | (p @ (sK11 @ X8) = $false))), 11.45/1.86 introduced(avatar_definition,[new_symbols(naming,[spl1_54])])). 11.45/1.86 tff(f2450,plain,( 11.45/1.86 ( ! [X8] : ((rel_s4 @ sK3 @ X8 = $false) | (p @ (sK11 @ X8) = $false)) ) | ~spl1_54), 11.45/1.86 inference(avatar_component_clause,[],[f2449])). 11.45/1.86 tff(f2451,plain,( 11.45/1.86 spl1_54 | spl1_14 | spl1_52), 11.45/1.86 inference(avatar_split_clause,[],[f904,f2391,f778,f2449])). 11.45/1.86 tff(f2570,plain,( 11.45/1.86 ( ! [X19,X18:mu] : (($false = $true) | (exists_in_world @ X18 @ sK3 = $false) | (p @ X19 = $true) | (rel_s4 @ sK3 @ sK4 = $false) | (rel_s4 @ sK3 @ X19 = $false)) ) | ~spl1_40), 11.45/1.86 inference(superposition,[],[f167,f2213])). 11.45/1.86 tff(f2588,plain,( 11.45/1.86 ( ! [X19,X18:mu] : ((exists_in_world @ X18 @ sK3 = $false) | (p @ X19 = $true) | (rel_s4 @ sK3 @ sK4 = $false) | (rel_s4 @ sK3 @ X19 = $false)) ) | ~spl1_40), 11.45/1.86 inference(trivial_inequality_removal,[],[f2570])). 11.45/1.86 tff(f2667,plain,( 11.45/1.86 spl1_62 <=> (rel_s4 @ sK3 @ (sK10 @ sK7) = $true)), 11.45/1.86 introduced(avatar_definition,[new_symbols(naming,[spl1_62])])). 11.45/1.86 tff(f2668,plain,( 11.45/1.86 (rel_s4 @ sK3 @ (sK10 @ sK7) = $true) | ~spl1_62), 11.45/1.86 inference(avatar_component_clause,[],[f2667])). 11.45/1.86 tff(f2670,plain,( 11.45/1.86 spl1_64 <=> ! [X65 : mu,X67,X66] : ((exists_in_world @ X65 @ X66 = $false) | (rel_s4 @ sK3 @ X66 = $false) | (big_q @ X65 @ X67 = $true) | (rel_s4 @ X66 @ sK7 = $false) | (rel_s4 @ X66 @ X67 = $false))), 11.45/1.86 introduced(avatar_definition,[new_symbols(naming,[spl1_64])])). 11.45/1.86 tff(f2671,plain,( 11.45/1.86 ( ! [X66,X67,X65:mu] : ((rel_s4 @ sK3 @ X66 = $false) | (exists_in_world @ X65 @ X66 = $false) | (big_q @ X65 @ X67 = $true) | (rel_s4 @ X66 @ sK7 = $false) | (rel_s4 @ X66 @ X67 = $false)) ) | ~spl1_64), 11.45/1.86 inference(avatar_component_clause,[],[f2670])). 11.45/1.86 tff(f2672,plain,( 11.45/1.86 spl1_62 | spl1_64), 11.45/1.86 inference(avatar_split_clause,[],[f1094,f2670,f2667])). 11.45/1.86 tff(f2703,plain,( 11.45/1.86 ($false = $true) | (p @ (sK10 @ sK7) = $true) | (~spl1_14 | ~spl1_62)), 11.45/1.86 inference(superposition,[],[f779,f2668])). 11.45/1.86 tff(f2734,plain,( 11.45/1.86 (p @ (sK10 @ sK7) = $true) | (~spl1_14 | ~spl1_62)), 11.45/1.86 inference(trivial_inequality_removal,[],[f2703])). 11.45/1.86 tff(f2767,plain,( 11.45/1.86 ($false = $true) | (~spl1_14 | ~spl1_18 | ~spl1_62)), 11.45/1.86 inference(forward_demodulation,[],[f2734,f1771])). 11.45/1.86 tff(f2768,plain,( 11.45/1.86 $false | (~spl1_14 | ~spl1_18 | ~spl1_62)), 11.45/1.86 inference(trivial_inequality_removal,[],[f2767])). 11.45/1.86 tff(f2769,plain,( 11.45/1.86 ~spl1_14 | ~spl1_18 | ~spl1_62), 11.45/1.86 inference(avatar_contradiction_clause,[],[f2768])). 11.45/1.86 tff(f2777,plain,( 11.45/1.86 ($false = $true) | ~spl1_52), 11.45/1.86 inference(backward_demodulation,[],[f2392,f346])). 11.45/1.86 tff(f2786,plain,( 11.45/1.86 $false | ~spl1_52), 11.45/1.86 inference(trivial_inequality_removal,[],[f2777])). 11.45/1.86 tff(f2787,plain,( 11.45/1.86 ~spl1_52), 11.45/1.86 inference(avatar_contradiction_clause,[],[f2786])). 11.45/1.86 tff(f3138,plain,( 11.45/1.86 ( ! [X23:mu] : (($false = $true) | (big_q @ X23 @ sK9 = $true) | (exists_in_world @ X23 @ sK7 = $false)) ) | ~spl1_20), 11.45/1.86 inference(superposition,[],[f1749,f213])). 11.45/1.86 tff(f3150,plain,( 11.45/1.86 ( ! [X23:mu] : ((big_q @ X23 @ sK9 = $true) | (exists_in_world @ X23 @ sK7 = $false)) ) | ~spl1_20), 11.45/1.86 inference(trivial_inequality_removal,[],[f3138])). 11.45/1.86 tff(f3156,plain,( 11.45/1.86 ($false = $true) | (exists_in_world @ sK8 @ sK7 = $false) | ~spl1_20), 11.45/1.86 inference(superposition,[],[f3150,f212])). 11.45/1.86 tff(f3159,plain,( 11.45/1.86 (exists_in_world @ sK8 @ sK7 = $false) | ~spl1_20), 11.45/1.86 inference(trivial_inequality_removal,[],[f3156])). 11.45/1.86 tff(f3160,plain,( 11.45/1.86 ($false = $true) | ~spl1_20), 11.45/1.86 inference(backward_demodulation,[],[f3159,f207])). 11.45/1.86 tff(f3161,plain,( 11.45/1.86 $false | ~spl1_20), 11.45/1.86 inference(trivial_inequality_removal,[],[f3160])). 11.45/1.86 tff(f3162,plain,( 11.45/1.86 ~spl1_20), 11.45/1.86 inference(avatar_contradiction_clause,[],[f3161])). 11.45/1.86 tff(f3200,plain,( 11.45/1.86 ($false = $true) | (p @ (sK11 @ sK4) = $false) | ~spl1_54), 11.45/1.86 inference(superposition,[],[f2450,f200])). 11.45/1.86 tff(f3226,plain,( 11.45/1.86 (p @ (sK11 @ sK4) = $false) | ~spl1_54), 11.45/1.86 inference(trivial_inequality_removal,[],[f3200])). 11.45/1.86 tff(f3232,plain,( 11.45/1.86 ($false = $true) | (~spl1_38 | ~spl1_54)), 11.45/1.86 inference(backward_demodulation,[],[f3226,f2210])). 11.45/1.86 tff(f3233,plain,( 11.45/1.86 $false | (~spl1_38 | ~spl1_54)), 11.45/1.86 inference(trivial_inequality_removal,[],[f3232])). 11.45/1.86 tff(f3234,plain,( 11.45/1.86 ~spl1_38 | ~spl1_54), 11.45/1.86 inference(avatar_contradiction_clause,[],[f3233])). 11.45/1.86 tff(f5007,plain,( 11.45/1.86 ( ! [X41:mu,X42] : (($false = $true) | (exists_in_world @ X41 @ sK7 = $false) | (big_q @ X41 @ X42 = $true) | (rel_s4 @ sK7 @ sK7 = $false) | (rel_s4 @ sK7 @ X42 = $false)) ) | ~spl1_64), 11.45/1.86 inference(superposition,[],[f2671,f214])). 11.45/1.86 tff(f5035,plain,( 11.45/1.86 ( ! [X41:mu,X42] : ((exists_in_world @ X41 @ sK7 = $false) | (big_q @ X41 @ X42 = $true) | (rel_s4 @ sK7 @ sK7 = $false) | (rel_s4 @ sK7 @ X42 = $false)) ) | ~spl1_64), 11.45/1.86 inference(trivial_inequality_removal,[],[f5007])). 11.45/1.86 tff(f5045,plain,( 11.45/1.86 ( ! [X41:mu,X42] : (($false = $true) | (exists_in_world @ X41 @ sK7 = $false) | (big_q @ X41 @ X42 = $true) | (rel_s4 @ sK7 @ X42 = $false)) ) | ~spl1_64), 11.45/1.86 inference(forward_demodulation,[],[f5035,f167])). 11.45/1.86 tff(f5046,plain,( 11.45/1.86 ( ! [X41:mu,X42] : ((rel_s4 @ sK7 @ X42 = $false) | (big_q @ X41 @ X42 = $true) | (exists_in_world @ X41 @ sK7 = $false)) ) | ~spl1_64), 11.45/1.86 inference(trivial_inequality_removal,[],[f5045])). 11.45/1.86 tff(f5163,plain,( 11.45/1.86 ( ! [X25:mu] : (($false = $true) | (big_q @ X25 @ sK9 = $true) | (exists_in_world @ X25 @ sK7 = $false)) ) | ~spl1_64), 11.45/1.86 inference(superposition,[],[f5046,f213])). 11.45/1.86 tff(f5175,plain,( 11.45/1.86 ( ! [X25:mu] : ((big_q @ X25 @ sK9 = $true) | (exists_in_world @ X25 @ sK7 = $false)) ) | ~spl1_64), 11.45/1.86 inference(trivial_inequality_removal,[],[f5163])). 11.45/1.86 tff(f6395,plain,( 11.45/1.86 spl1_126 <=> (rel_s4 @ sK3 @ sK4 = $false)), 11.45/1.86 introduced(avatar_definition,[new_symbols(naming,[spl1_126])])). 11.45/1.86 tff(f6396,plain,( 11.45/1.86 (rel_s4 @ sK3 @ sK4 = $false) | ~spl1_126), 11.45/1.86 inference(avatar_component_clause,[],[f6395])). 11.45/1.86 tff(f6397,plain,( 11.45/1.86 spl1_126 | spl1_14 | spl1_52 | ~spl1_40), 11.45/1.86 inference(avatar_split_clause,[],[f2588,f2212,f2391,f778,f6395])). 11.45/1.86 tff(f6430,plain,( 11.45/1.86 ($false = $true) | (exists_in_world @ sK8 @ sK7 = $false) | ~spl1_64), 11.45/1.86 inference(superposition,[],[f5175,f212])). 11.45/1.86 tff(f6433,plain,( 11.45/1.86 (exists_in_world @ sK8 @ sK7 = $false) | ~spl1_64), 11.45/1.86 inference(trivial_inequality_removal,[],[f6430])). 11.45/1.86 tff(f6434,plain,( 11.45/1.86 ($false = $true) | ~spl1_64), 11.45/1.86 inference(backward_demodulation,[],[f6433,f207])). 11.45/1.86 tff(f6435,plain,( 11.45/1.86 $false | ~spl1_64), 11.45/1.86 inference(trivial_inequality_removal,[],[f6434])). 11.45/1.86 tff(f6436,plain,( 11.45/1.86 ~spl1_64), 11.45/1.86 inference(avatar_contradiction_clause,[],[f6435])). 11.45/1.86 tff(f6443,plain,( 11.45/1.86 ($false = $true) | ~spl1_126), 11.45/1.86 inference(backward_demodulation,[],[f6396,f200])). 11.45/1.86 tff(f6444,plain,( 11.45/1.86 $false | ~spl1_126), 11.45/1.86 inference(trivial_inequality_removal,[],[f6443])). 11.45/1.86 tff(f6445,plain,( 11.45/1.86 ~spl1_126), 11.45/1.86 inference(avatar_contradiction_clause,[],[f6444])). 11.45/1.86 tff(f6449,plain,( 11.45/1.86 $false), 11.45/1.86 inference(avatar_sat_refutation,[],[f762,f1750,f2214,f2277,f2451,f2672,f2769,f2787,f3162,f3234,f6397,f6436,f6445])). 11.45/1.86 % SZS output end Proof for theBenchmark 11.45/1.86 % (18715)------------------------------ 11.45/1.86 % (18715)Version: Vampire 4.5.0 (commit 7ae30c7f on 2020-06-30 15:57:20 +0100) 11.45/1.86 % (18715)Termination reason: Refutation 11.45/1.86 11.45/1.86 % (18715)Memory used [KB]: 9850 11.45/1.86 % (18715)Time elapsed: 1.439 s 11.45/1.86 % (18715)------------------------------ 11.45/1.86 % (18715)------------------------------ 11.45/1.86 % (18698)Success in time 1.518 s 11.45/1.87 EOF