0.06/0.10 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.06/0.11 % Command : run_vampire %s %d 0.10/0.32 % Computer : n007.cluster.edu 0.10/0.32 % Model : x86_64 x86_64 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.10/0.32 % Memory : 8042.1875MB 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64 0.10/0.32 % CPULimit : 960 0.10/0.32 % WCLimit : 120 0.10/0.32 % DateTime : Thu Jul 2 09:14:39 EDT 2020 0.10/0.32 % CPUTime : 0.16/0.37 % (22632)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 0.16/0.37 % (22631)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 0.16/0.38 % (22649)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 0.16/0.38 % (22629)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 0.16/0.38 % (22628)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 0.16/0.38 % (22627)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 0.16/0.38 % (22636)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 0.16/0.38 % (22635)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 0.16/0.38 % (22637)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 0.16/0.38 % (22630)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 0.16/0.38 % (22634)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 0.16/0.38 % (22641)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 0.16/0.39 % (22640)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 0.16/0.39 % (22648)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 0.16/0.39 % (22633)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 0.16/0.39 % (22652)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 0.16/0.39 % (22653)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 0.16/0.39 % (22651)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 0.16/0.40 % (22644)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 0.16/0.40 % (22645)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 0.16/0.40 % (22643)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 0.16/0.40 % (22626)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 0.16/0.40 % (22646)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 0.16/0.40 % (22655)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 0.16/0.41 % (22647)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 0.16/0.41 % (22650)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 0.16/0.42 % (22638)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 0.16/0.42 % (22639)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 0.16/0.42 % (22642)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 0.16/0.42 % (22654)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 2.55/0.76 % (22640)Time limit reached! 2.55/0.76 % (22640)------------------------------ 2.55/0.76 % (22640)Version: Vampire 4.5.0 (commit 7ae30c7f on 2020-06-30 15:57:20 +0100) 3.35/0.77 % (22640)Termination reason: Time limit 3.35/0.77 3.35/0.77 % (22640)Memory used [KB]: 6524 3.35/0.77 % (22640)Time elapsed: 0.409 s 3.35/0.77 % (22640)------------------------------ 3.35/0.77 % (22640)------------------------------ 3.54/0.82 % (22656)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 3.83/0.85 % (22629)Time limit reached! 3.83/0.85 % (22629)------------------------------ 3.83/0.85 % (22629)Version: Vampire 4.5.0 (commit 7ae30c7f on 2020-06-30 15:57:20 +0100) 3.83/0.85 % (22629)Termination reason: Time limit 3.83/0.85 % (22629)Termination phase: Saturation 3.83/0.85 3.83/0.85 % (22629)Memory used [KB]: 11641 3.83/0.85 % (22629)Time elapsed: 0.500 s 3.83/0.85 % (22629)------------------------------ 3.83/0.85 % (22629)------------------------------ 3.83/0.86 % (22637)Time limit reached! 3.83/0.86 % (22637)------------------------------ 3.83/0.86 % (22637)Version: Vampire 4.5.0 (commit 7ae30c7f on 2020-06-30 15:57:20 +0100) 3.83/0.86 % (22637)Termination reason: Time limit 3.83/0.86 3.83/0.86 % (22637)Memory used [KB]: 11641 3.83/0.86 % (22637)Time elapsed: 0.507 s 3.83/0.86 % (22637)------------------------------ 3.83/0.86 % (22637)------------------------------ 3.83/0.88 % (22627)Time limit reached! 3.83/0.88 % (22627)------------------------------ 3.83/0.88 % (22627)Version: Vampire 4.5.0 (commit 7ae30c7f on 2020-06-30 15:57:20 +0100) 3.83/0.88 % (22627)Termination reason: Time limit 3.83/0.88 3.83/0.88 % (22627)Memory used [KB]: 12153 3.83/0.88 % (22627)Time elapsed: 0.507 s 3.83/0.88 % (22627)------------------------------ 3.83/0.88 % (22627)------------------------------ 3.83/0.88 % (22626)Time limit reached! 3.83/0.88 % (22626)------------------------------ 3.83/0.88 % (22626)Version: Vampire 4.5.0 (commit 7ae30c7f on 2020-06-30 15:57:20 +0100) 3.83/0.88 % (22626)Termination reason: Time limit 3.83/0.88 3.83/0.88 % (22626)Memory used [KB]: 2430 3.83/0.88 % (22626)Time elapsed: 0.526 s 3.83/0.88 % (22626)------------------------------ 3.83/0.88 % (22626)------------------------------ 3.83/0.89 % (22638)Time limit reached! 3.83/0.89 % (22638)------------------------------ 3.83/0.89 % (22638)Version: Vampire 4.5.0 (commit 7ae30c7f on 2020-06-30 15:57:20 +0100) 3.83/0.89 % (22638)Termination reason: Time limit 3.83/0.89 % (22638)Termination phase: Saturation 3.83/0.89 3.83/0.89 % (22638)Memory used [KB]: 6908 3.83/0.89 % (22638)Time elapsed: 0.500 s 3.83/0.89 % (22638)------------------------------ 3.83/0.89 % (22638)------------------------------ 4.37/0.91 % (22657)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 4.37/0.91 % (22658)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 4.37/0.94 % (22660)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 4.37/0.95 % (22661)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 4.37/0.96 % (22659)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 4.37/0.96 % (22628)Time limit reached! 4.37/0.96 % (22628)------------------------------ 4.37/0.96 % (22628)Version: Vampire 4.5.0 (commit 7ae30c7f on 2020-06-30 15:57:20 +0100) 4.37/0.96 % (22628)Termination reason: Time limit 4.37/0.96 4.37/0.96 % (22628)Memory used [KB]: 10618 4.37/0.96 % (22628)Time elapsed: 0.606 s 4.37/0.96 % (22628)------------------------------ 4.37/0.96 % (22628)------------------------------ 4.37/0.96 % (22632)Time limit reached! 4.37/0.96 % (22632)------------------------------ 4.37/0.96 % (22632)Version: Vampire 4.5.0 (commit 7ae30c7f on 2020-06-30 15:57:20 +0100) 4.37/0.96 % (22632)Termination reason: Time limit 4.37/0.96 4.37/0.96 % (22632)Memory used [KB]: 12792 4.37/0.96 % (22632)Time elapsed: 0.609 s 4.37/0.96 % (22632)------------------------------ 4.37/0.96 % (22632)------------------------------ 4.80/0.97 % (22635)Time limit reached! 4.80/0.97 % (22635)------------------------------ 4.80/0.97 % (22635)Version: Vampire 4.5.0 (commit 7ae30c7f on 2020-06-30 15:57:20 +0100) 4.80/0.97 % (22635)Termination reason: Time limit 4.80/0.97 % (22635)Termination phase: Saturation 4.80/0.97 4.80/0.97 % (22635)Memory used [KB]: 12281 4.80/0.97 % (22635)Time elapsed: 0.600 s 4.80/0.97 % (22635)------------------------------ 4.80/0.97 % (22635)------------------------------ 4.80/1.02 % (22663)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 4.80/1.04 % (22662)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 4.80/1.05 % (22664)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 7.26/1.29 % (22644)Time limit reached! 7.26/1.29 % (22644)------------------------------ 7.26/1.29 % (22644)Version: Vampire 4.5.0 (commit 7ae30c7f on 2020-06-30 15:57:20 +0100) 7.26/1.29 % (22644)Termination reason: Time limit 7.26/1.29 7.26/1.29 % (22644)Memory used [KB]: 8699 7.26/1.29 % (22644)Time elapsed: 0.938 s 7.26/1.29 % (22644)------------------------------ 7.26/1.29 % (22644)------------------------------ 7.90/1.37 % (22725)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 8.79/1.47 % (22639)Time limit reached! 8.79/1.47 % (22639)------------------------------ 8.79/1.47 % (22639)Version: Vampire 4.5.0 (commit 7ae30c7f on 2020-06-30 15:57:20 +0100) 8.79/1.47 % (22639)Termination reason: Time limit 8.79/1.47 % (22639)Termination phase: Saturation 8.79/1.47 8.79/1.47 % (22639)Memory used [KB]: 8571 8.79/1.47 % (22639)Time elapsed: 1.100 s 8.79/1.47 % (22639)------------------------------ 8.79/1.47 % (22639)------------------------------ 8.79/1.48 % (22641)Time limit reached! 8.79/1.48 % (22641)------------------------------ 8.79/1.48 % (22641)Version: Vampire 4.5.0 (commit 7ae30c7f on 2020-06-30 15:57:20 +0100) 8.79/1.48 % (22641)Termination reason: Time limit 8.79/1.48 % (22641)Termination phase: Saturation 8.79/1.48 8.79/1.48 % (22641)Memory used [KB]: 12665 8.79/1.48 % (22641)Time elapsed: 1.0000 s 8.79/1.48 % (22641)------------------------------ 8.79/1.48 % (22641)------------------------------ 8.79/1.50 % (22648)Time limit reached! 8.79/1.50 % (22648)------------------------------ 8.79/1.50 % (22648)Version: Vampire 4.5.0 (commit 7ae30c7f on 2020-06-30 15:57:20 +0100) 8.79/1.50 % (22648)Termination reason: Time limit 8.79/1.50 % (22648)Termination phase: Saturation 8.79/1.50 8.79/1.50 % (22648)Memory used [KB]: 5628 8.79/1.50 % (22648)Time elapsed: 1.100 s 8.79/1.50 % (22648)------------------------------ 8.79/1.50 % (22648)------------------------------ 8.79/1.51 % (22645)Time limit reached! 8.79/1.51 % (22645)------------------------------ 8.79/1.51 % (22645)Version: Vampire 4.5.0 (commit 7ae30c7f on 2020-06-30 15:57:20 +0100) 8.79/1.51 % (22645)Termination reason: Time limit 8.79/1.51 % (22645)Termination phase: Saturation 8.79/1.51 8.79/1.51 % (22645)Memory used [KB]: 8955 8.79/1.51 % (22645)Time elapsed: 1.100 s 8.79/1.51 % (22645)------------------------------ 8.79/1.51 % (22645)------------------------------ 9.30/1.54 % (22748)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 9.30/1.54 % (22750)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 9.30/1.56 % (22751)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 9.30/1.56 % (22749)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 11.70/1.89 % (22630)Time limit reached! 11.70/1.89 % (22630)------------------------------ 11.70/1.89 % (22630)Version: Vampire 4.5.0 (commit 7ae30c7f on 2020-06-30 15:57:20 +0100) 11.70/1.90 % (22630)Termination reason: Time limit 11.70/1.90 11.70/1.90 % (22630)Memory used [KB]: 10362 11.70/1.90 % (22630)Time elapsed: 1.538 s 11.70/1.90 % (22630)------------------------------ 11.70/1.90 % (22630)------------------------------ 11.70/1.90 % (22651)Time limit reached! 11.70/1.90 % (22651)------------------------------ 11.70/1.90 % (22651)Version: Vampire 4.5.0 (commit 7ae30c7f on 2020-06-30 15:57:20 +0100) 11.70/1.90 % (22651)Termination reason: Time limit 11.70/1.90 % (22651)Termination phase: Saturation 11.70/1.90 11.70/1.90 % (22651)Memory used [KB]: 10490 11.70/1.90 % (22651)Time elapsed: 1.500 s 11.70/1.90 % (22651)------------------------------ 11.70/1.90 % (22651)------------------------------ 12.52/1.97 % (22753)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 12.52/1.98 % (22752)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 13.06/2.02 % (22631)Time limit reached! 13.06/2.02 % (22631)------------------------------ 13.06/2.02 % (22631)Version: Vampire 4.5.0 (commit 7ae30c7f on 2020-06-30 15:57:20 +0100) 13.06/2.02 % (22631)Termination reason: Time limit 13.06/2.02 13.06/2.02 % (22631)Memory used [KB]: 18549 13.06/2.02 % (22631)Time elapsed: 1.656 s 13.06/2.02 % (22631)------------------------------ 13.06/2.02 % (22631)------------------------------ 13.60/2.09 % (22754)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 13.60/2.10 % (22655)Refutation found. Thanks to Tanya! 13.60/2.10 % SZS status Theorem for theBenchmark 13.60/2.10 % SZS output start Proof for theBenchmark 13.60/2.10 tff(func_def_0, type, u: '$tType'). 13.60/2.10 tff(func_def_2, type, d: '$tType'). 13.60/2.10 tff(func_def_3, type, du: '$tType'). 13.60/2.10 tff(func_def_6, type, tyop_2Emin_2Ebool: d). 13.60/2.10 tff(func_def_7, type, ->: ('$tType' * '$tType') > '$tType'). 13.60/2.10 tff(func_def_8, type, tyop_2Emin_2Efun: d -> d -> d). 13.60/2.10 tff(func_def_9, type, tyop_2Eoption_2Eoption: d -> d). 13.60/2.10 tff(func_def_10, type, s: d -> u -> du). 13.60/2.10 tff(func_def_11, type, app_2E2: du -> du -> u). 13.60/2.10 tff(func_def_12, type, combin_i_2E0: u). 13.60/2.10 tff(func_def_13, type, combin_k_2E0: u). 13.60/2.10 tff(func_def_14, type, combin_s_2E0: u). 13.60/2.10 tff(func_def_15, type, c_2Ebool_2E_21_2E0: u). 13.60/2.10 tff(func_def_16, type, c_2Ebool_2E_21_2E1: du -> u). 13.60/2.10 tff(func_def_17, type, c_2Ebool_2E_2F_5C_2E0: u). 13.60/2.10 tff(func_def_18, type, c_2Ebool_2E_2F_5C_2E2: du -> du -> u). 13.60/2.10 tff(func_def_19, type, c_2Emin_2E_3D_2E0: u). 13.60/2.10 tff(func_def_20, type, c_2Emin_2E_3D_2E2: du -> du -> u). 13.60/2.10 tff(func_def_21, type, c_2Emin_2E_3D_3D_3E_2E0: u). 13.60/2.10 tff(func_def_22, type, c_2Emin_2E_3D_3D_3E_2E2: du -> du -> u). 13.60/2.10 tff(func_def_23, type, c_2Ebool_2E_3F_2E0: u). 13.60/2.10 tff(func_def_24, type, c_2Ebool_2E_3F_2E1: du -> u). 13.60/2.10 tff(func_def_25, type, c_2Ebool_2EF_2E0: u). 13.60/2.10 tff(func_def_26, type, c_2Eoption_2EIS__NONE_2E0: u). 13.60/2.10 tff(func_def_27, type, c_2Eoption_2EIS__NONE_2E1: du -> u). 13.60/2.10 tff(func_def_28, type, c_2Eoption_2EIS__SOME_2E0: u). 13.60/2.10 tff(func_def_29, type, c_2Eoption_2EIS__SOME_2E1: du -> u). 13.60/2.10 tff(func_def_30, type, c_2Eoption_2ENONE_2E0: u). 13.60/2.10 tff(func_def_31, type, c_2Eoption_2EOPTION__JOIN_2E0: u). 13.60/2.10 tff(func_def_32, type, c_2Eoption_2EOPTION__JOIN_2E1: du -> u). 13.60/2.10 tff(func_def_33, type, c_2Eoption_2EOPTION__MAP_2E0: u). 13.60/2.10 tff(func_def_34, type, c_2Eoption_2EOPTION__MAP_2E2: du -> du -> u). 13.60/2.10 tff(func_def_35, type, c_2Eoption_2EOPTREL_2E0: u). 13.60/2.10 tff(func_def_36, type, c_2Eoption_2EOPTREL_2E3: du -> du -> du -> u). 13.60/2.10 tff(func_def_37, type, c_2Eoption_2ESOME_2E0: u). 13.60/2.10 tff(func_def_38, type, c_2Eoption_2ESOME_2E1: du -> u). 13.60/2.10 tff(func_def_39, type, c_2Ebool_2ET_2E0: u). 13.60/2.10 tff(func_def_40, type, c_2Eoption_2ETHE_2E0: u). 13.60/2.10 tff(func_def_41, type, c_2Eoption_2ETHE_2E1: du -> u). 13.60/2.10 tff(func_def_42, type, c_2Ebool_2E_5C_2F_2E0: u). 13.60/2.10 tff(func_def_43, type, c_2Ebool_2E_5C_2F_2E2: du -> du -> u). 13.60/2.10 tff(func_def_44, type, c_2Eoption_2Eoption__CASE_2E0: u). 13.60/2.10 tff(func_def_45, type, c_2Eoption_2Eoption__CASE_2E3: du -> du -> du -> u). 13.60/2.10 tff(func_def_46, type, c_2Ebool_2E_7E_2E0: u). 13.60/2.10 tff(func_def_47, type, c_2Ebool_2E_7E_2E1: du -> u). 13.60/2.10 tff(func_def_48, type, mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: ('$o' -> '$o') -> '$o' -> '$o'). 13.60/2.10 tff(func_def_49, type, mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ('$o' -> '$o' -> '$o') -> '$o' -> '$o' -> '$o'). 13.60/2.10 tff(func_def_50, type, mono_2Ec_2Ebool_2E_2F_5C: '$o' -> '$o' -> '$o'). 13.60/2.10 tff(func_def_51, type, mono_2Ec_2Emin_2E_3D_3D_3E: '$o' -> '$o' -> '$o'). 13.60/2.10 tff(func_def_54, type, mono_2Ec_2Ebool_2E_5C_2F: '$o' -> '$o' -> '$o'). 13.60/2.10 tff(func_def_55, type, mono_2Ec_2Ebool_2E_7E: '$o' -> '$o'). 13.60/2.10 tff(func_def_56, type, i_mono_2Etyop_2Emin_2Ebool: '$o' -> u). 13.60/2.10 tff(func_def_57, type, i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ('$o' -> '$o') -> u). 13.60/2.10 tff(func_def_58, type, i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: ('$o' -> '$o' -> '$o') -> u). 13.60/2.10 tff(func_def_59, type, j_mono_2Etyop_2Emin_2Ebool: du -> '$o'). 13.60/2.10 tff(func_def_60, type, j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: du -> '$o' -> '$o'). 13.60/2.10 tff(func_def_61, type, j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: du -> '$o' -> '$o' -> '$o'). 13.60/2.10 tff(func_def_62, type, vAPP: !>[X0: $ttype, X1: $ttype]:(X0 -> X1 * X0) > X1). 13.60/2.10 tff(func_def_63, type, vNOT: '$o' -> '$o'). 13.60/2.10 tff(func_def_64, type, vEPSILON: !>[X0: $ttype]:(X0 -> '$o') -> X0). 13.60/2.10 tff(func_def_67, type, vEQ: !>[X0: $ttype]:X0 -> X0 -> '$o'). 13.60/2.10 tff(func_def_68, type, sP0: u -> d -> u -> d -> u -> '$o'). 13.60/2.10 tff(func_def_69, type, sK1: d). 13.60/2.10 tff(func_def_70, type, sK2: u). 13.60/2.10 tff(func_def_71, type, sK3: u). 13.60/2.10 tff(func_def_72, type, sK4: u). 13.60/2.10 tff(func_def_73, type, sK5: u -> u -> d -> d -> u). 13.60/2.10 tff(func_def_74, type, sK6: u -> d -> u -> d -> u -> u). 13.60/2.10 tff(func_def_75, type, sK7: u -> d -> u -> d -> u -> u). 13.60/2.10 tff(func_def_77, type, kCOMB: !>[X1: $ttype, X2: $ttype]:X1 -> X2 -> X1). 13.60/2.10 tff(func_def_78, type, bCOMB: !>[X0: $ttype, X1: $ttype, X2: $ttype]:(X1 -> X2) -> (X0 -> X1) -> X0 -> X2). 13.60/2.10 tff(func_def_79, type, vAND: '$o' -> '$o' -> '$o'). 13.60/2.10 tff(func_def_80, type, vOR: '$o' -> '$o' -> '$o'). 13.60/2.10 tff(func_def_81, type, vIMP: '$o' -> '$o' -> '$o'). 13.60/2.10 tff(func_def_82, type, sCOMB: !>[X0: $ttype, X1: $ttype, X2: $ttype]:(X0 -> X1 -> X2) -> (X0 -> X1) -> X0 -> X2). 13.60/2.10 tff(func_def_83, type, cCOMB: !>[X0: $ttype, X1: $ttype, X2: $ttype]:(X0 -> X1 -> X2) -> X1 -> X0 -> X2). 13.60/2.10 tff(func_def_84, type, iCOMB: !>[X2: $ttype]:X2 -> X2). 13.60/2.10 tff(f9,axiom,( 13.60/2.10 ! [X2 : d,X8 : d,X9 : u,X7 : u,X10 : u] : (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X2 @ (tyop_2Emin_2Efun @ X8 @ tyop_2Emin_2Ebool)) @ X9) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X7) @ (s @ (tyop_2Eoption_2Eoption @ X8) @ X10))) <=> ((s @ (tyop_2Eoption_2Eoption @ X8) @ c_2Eoption_2ENONE_2E0 = s @ (tyop_2Eoption_2Eoption @ X8) @ X10 & s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0 = s @ (tyop_2Eoption_2Eoption @ X2) @ X7) | ? [X11 : u,X12 : u] : (s @ (tyop_2Eoption_2Eoption @ X8) @ X10 = s @ (tyop_2Eoption_2Eoption @ X8) @ (c_2Eoption_2ESOME_2E1 @ (s @ X8 @ X12)) & j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X8 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ (tyop_2Emin_2Efun @ X8 @ tyop_2Emin_2Ebool)) @ X9) @ (s @ X2 @ X11))) @ (s @ X8 @ X12))) & s @ (tyop_2Eoption_2Eoption @ X2) @ X7 = s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X11)))))), 13.60/2.10 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eoption_2EOPTREL__def)). 13.60/2.10 tff(f10,axiom,( 13.60/2.10 ! [X2 : d,X8 : d,X6 : u,X13 : u,X14 : u] : (! [X37 : u] : vNOT @ s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0 = s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X37)) & ! [X36 : u] : (mono_2Ec_2Ebool_2ET = j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X36)))))) & ! [X35 : u] : (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__NONE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X35))) <=> s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0 = s @ (tyop_2Eoption_2Eoption @ X2) @ X35) & ! [X34 : u] : (vNOT @ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X34)))) <=> s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0 = s @ (tyop_2Eoption_2Eoption @ X2) @ X34) & ! [X33 : u] : s @ (tyop_2Eoption_2Eoption @ X2) @ X33 = s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X33) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X33) @ (s @ (tyop_2Emin_2Efun @ X2 @ (tyop_2Eoption_2Eoption @ X2)) @ c_2Eoption_2ESOME_2E0)) & ! [X32 : u] : (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__NONE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X32))) => s @ X8 @ X14 = s @ X8 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X32) @ (s @ X8 @ X14) @ (s @ (tyop_2Emin_2Efun @ X2 @ X8) @ X6))) & ! [X30 : u,X31 : u] : s @ X8 @ X30 = s @ X8 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0) @ (s @ X8 @ X30) @ (s @ (tyop_2Emin_2Efun @ X2 @ X8) @ X31)) & ! [X29 : u] : s @ (tyop_2Eoption_2Eoption @ X8) @ c_2Eoption_2ENONE_2E0 = s @ (tyop_2Eoption_2Eoption @ X8) @ (c_2Eoption_2EOPTION__MAP_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ X8) @ X29) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0)) & ! [X28 : u] : s @ (tyop_2Eoption_2Eoption @ X2) @ X28 = s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2EOPTION__JOIN_2E1 @ (s @ (tyop_2Eoption_2Eoption @ (tyop_2Eoption_2Eoption @ X2)) @ (c_2Eoption_2ESOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X28)))) & s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0 = s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2EOPTION__JOIN_2E1 @ (s @ (tyop_2Eoption_2Eoption @ (tyop_2Eoption_2Eoption @ X2)) @ c_2Eoption_2ENONE_2E0)) & ! [X26 : u,X27 : u] : s @ (tyop_2Eoption_2Eoption @ X8) @ (c_2Eoption_2ESOME_2E1 @ (s @ X8 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ X8) @ X26) @ (s @ X2 @ X27)))) = s @ (tyop_2Eoption_2Eoption @ X8) @ (c_2Eoption_2EOPTION__MAP_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ X8) @ X26) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X27)))) & ! [X23 : u,X24 : u,X25 : u] : s @ X8 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ X8) @ X25) @ (s @ X2 @ X23)) = s @ X8 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X23))) @ (s @ X8 @ X24) @ (s @ (tyop_2Emin_2Efun @ X2 @ X8) @ X25)) & ! [X22 : u] : (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X22))) => s @ (tyop_2Eoption_2Eoption @ X2) @ X22 = s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X22) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X13) @ (s @ (tyop_2Emin_2Efun @ X2 @ (tyop_2Eoption_2Eoption @ X2)) @ c_2Eoption_2ESOME_2E0))) & ! [X21 : u] : (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X21))) => s @ X8 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ X8) @ X6) @ (s @ X2 @ (c_2Eoption_2ETHE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X21)))) = s @ X8 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X21) @ (s @ X8 @ X14) @ (s @ (tyop_2Emin_2Efun @ X2 @ X8) @ X6))) & ! [X20 : u] : s @ (tyop_2Eoption_2Eoption @ X2) @ X20 = s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X20) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Emin_2Efun @ X2 @ (tyop_2Eoption_2Eoption @ X2)) @ c_2Eoption_2ESOME_2E0)) & ! [X19 : u] : (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X19))) => s @ (tyop_2Eoption_2Eoption @ X2) @ X19 = s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ (c_2Eoption_2ETHE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ X19))))) & (mono_2Ec_2Ebool_2EF = j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0)))) & ! [X18 : u] : vNOT @ s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0 = s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X18)) & ! [X17 : u] : s @ X2 @ X17 = s @ X2 @ (c_2Eoption_2ETHE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X17)))) & ! [X15 : u,X16 : u] : (s @ X2 @ X15 = s @ X2 @ X16 <=> s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X15)) = s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X16))))), 13.60/2.10 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eoption_2Eoption__CLAUSES)). 13.60/2.10 tff(f13,axiom,( 13.60/2.10 ! [X38 : '$o'] : ((mono_2Ec_2Ebool_2ET <=> (X38 | mono_2Ec_2Ebool_2ET)) & ((X38 | mono_2Ec_2Ebool_2EF) <=> X38) & (X38 <=> (X38 | X38)) & ((mono_2Ec_2Ebool_2EF | X38) <=> X38) & (mono_2Ec_2Ebool_2ET <=> (mono_2Ec_2Ebool_2ET | X38)))), 13.60/2.10 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EOR__CLAUSES)). 13.60/2.10 tff(f26,axiom,( 13.60/2.10 (vNOT @ mono_2Ec_2Ebool_2EF <=> mono_2Ec_2Ebool_2ET) & (vNOT @ mono_2Ec_2Ebool_2ET <=> mono_2Ec_2Ebool_2EF) & ! [X38 : '$o'] : (X38 <=> vNOT @ (vNOT @ X38))), 13.60/2.10 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ENOT__CLAUSES)). 13.60/2.10 tff(f27,conjecture,( 13.60/2.10 ! [X2 : d,X42 : u,X7 : u,X43 : u] : ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool)) @ X43) @ (s @ X2 @ X7))) @ (s @ X2 @ X42))) = j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X2 @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool)) @ X43) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X7))) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X42)))))) & (mono_2Ec_2Ebool_2EF = j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X2 @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool)) @ X43) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X42)))))) & (mono_2Ec_2Ebool_2EF = j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X2 @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool)) @ X43) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X7))) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0)))) & (mono_2Ec_2Ebool_2ET = j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X2 @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool)) @ X43) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0)))))), 13.60/2.10 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Equotient__option_2EOPTION__REL__def)). 13.60/2.10 tff(f28,negated_conjecture,( 13.60/2.10 ~! [X2 : d,X42 : u,X7 : u,X43 : u] : ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X2 @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool)) @ X43) @ (s @ X2 @ X7))) @ (s @ X2 @ X42))) = j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X2 @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool)) @ X43) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X7))) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X42)))))) & (mono_2Ec_2Ebool_2EF = j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X2 @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool)) @ X43) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X42)))))) & (mono_2Ec_2Ebool_2EF = j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X2 @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool)) @ X43) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ (c_2Eoption_2ESOME_2E1 @ (s @ X2 @ X7))) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0)))) & (mono_2Ec_2Ebool_2ET = j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X2 @ (tyop_2Emin_2Efun @ X2 @ tyop_2Emin_2Ebool)) @ X43) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ X2) @ c_2Eoption_2ENONE_2E0)))))), 13.60/2.10 inference(negated_conjecture,[],[f27])). 13.60/2.10 tff(f50,plain,( 13.60/2.10 (vNOT @ mono_2Ec_2Ebool_2EF <=> mono_2Ec_2Ebool_2ET) & (vNOT @ mono_2Ec_2Ebool_2ET <=> mono_2Ec_2Ebool_2EF) & ! [X0 : '$o'] : (X0 <=> vNOT @ (vNOT @ X0))), 13.60/2.10 inference(rectify,[],[f26])). 13.60/2.10 tff(f51,plain,( 13.60/2.10 (mono_2Ec_2Ebool_2ET = vNOT @ mono_2Ec_2Ebool_2EF) & (mono_2Ec_2Ebool_2EF = vNOT @ mono_2Ec_2Ebool_2ET) & ! [X0 : '$o'] : (vNOT @ (vNOT @ X0) = X0)), 13.60/2.10 inference(fool_elimination,[],[f50])). 13.60/2.10 tff(f56,plain,( 13.60/2.10 ! [X0 : '$o'] : ((mono_2Ec_2Ebool_2ET <=> (X0 | mono_2Ec_2Ebool_2ET)) & ((X0 | mono_2Ec_2Ebool_2EF) <=> X0) & (X0 <=> (X0 | X0)) & ((mono_2Ec_2Ebool_2EF | X0) <=> X0) & (mono_2Ec_2Ebool_2ET <=> (mono_2Ec_2Ebool_2ET | X0)))), 13.60/2.10 inference(rectify,[],[f13])). 13.60/2.10 tff(f57,plain,( 13.60/2.10 ! [X0 : '$o'] : (((mono_2Ec_2Ebool_2ET = $true) <=> (($true = X0) | (mono_2Ec_2Ebool_2ET = $true))) & ((($true = X0) | (mono_2Ec_2Ebool_2EF = $true)) <=> ($true = X0)) & (($true = X0) <=> (($true = X0) | ($true = X0))) & (((mono_2Ec_2Ebool_2EF = $true) | ($true = X0)) <=> ($true = X0)) & ((mono_2Ec_2Ebool_2ET = $true) <=> ((mono_2Ec_2Ebool_2ET = $true) | ($true = X0))))), 13.60/2.10 inference(fool_elimination,[],[f56])). 13.60/2.13 tff(f82,plain,( 13.60/2.13 ! [X0 : d,X1 : d,X2 : u,X3 : u,X4 : u] : (! [X5 : u] : vNOT @ s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0 = s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X5)) & ! [X6 : u] : (mono_2Ec_2Ebool_2ET = j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X6)))))) & ! [X7 : u] : (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__NONE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X7))) <=> s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0 = s @ (tyop_2Eoption_2Eoption @ X0) @ X7) & ! [X8 : u] : (vNOT @ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X8)))) <=> s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0 = s @ (tyop_2Eoption_2Eoption @ X0) @ X8) & ! [X9 : u] : s @ (tyop_2Eoption_2Eoption @ X0) @ X9 = s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X9) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X9) @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Eoption_2Eoption @ X0)) @ c_2Eoption_2ESOME_2E0)) & ! [X10 : u] : (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__NONE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X10))) => s @ X1 @ X4 = s @ X1 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X10) @ (s @ X1 @ X4) @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X2))) & ! [X11 : u,X12 : u] : s @ X1 @ X11 = s @ X1 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0) @ (s @ X1 @ X11) @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X12)) & ! [X13 : u] : s @ (tyop_2Eoption_2Eoption @ X1) @ c_2Eoption_2ENONE_2E0 = s @ (tyop_2Eoption_2Eoption @ X1) @ (c_2Eoption_2EOPTION__MAP_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X13) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0)) & ! [X14 : u] : s @ (tyop_2Eoption_2Eoption @ X0) @ X14 = s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2EOPTION__JOIN_2E1 @ (s @ (tyop_2Eoption_2Eoption @ (tyop_2Eoption_2Eoption @ X0)) @ (c_2Eoption_2ESOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X14)))) & s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0 = s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2EOPTION__JOIN_2E1 @ (s @ (tyop_2Eoption_2Eoption @ (tyop_2Eoption_2Eoption @ X0)) @ c_2Eoption_2ENONE_2E0)) & ! [X15 : u,X16 : u] : s @ (tyop_2Eoption_2Eoption @ X1) @ (c_2Eoption_2ESOME_2E1 @ (s @ X1 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X15) @ (s @ X0 @ X16)))) = s @ (tyop_2Eoption_2Eoption @ X1) @ (c_2Eoption_2EOPTION__MAP_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X15) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X16)))) & ! [X17 : u,X18 : u,X19 : u] : s @ X1 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X19) @ (s @ X0 @ X17)) = s @ X1 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X17))) @ (s @ X1 @ X18) @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X19)) & ! [X20 : u] : (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X20))) => s @ (tyop_2Eoption_2Eoption @ X0) @ X20 = s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X20) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X3) @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Eoption_2Eoption @ X0)) @ c_2Eoption_2ESOME_2E0))) & ! [X21 : u] : (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X21))) => s @ X1 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X2) @ (s @ X0 @ (c_2Eoption_2ETHE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X21)))) = s @ X1 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X21) @ (s @ X1 @ X4) @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X2))) & ! [X22 : u] : s @ (tyop_2Eoption_2Eoption @ X0) @ X22 = s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X22) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Eoption_2Eoption @ X0)) @ c_2Eoption_2ESOME_2E0)) & ! [X23 : u] : (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X23))) => s @ (tyop_2Eoption_2Eoption @ X0) @ X23 = s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ (c_2Eoption_2ETHE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X23))))) & (mono_2Ec_2Ebool_2EF = j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0)))) & ! [X24 : u] : vNOT @ s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0 = s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X24)) & ! [X25 : u] : s @ X0 @ X25 = s @ X0 @ (c_2Eoption_2ETHE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X25)))) & ! [X26 : u,X27 : u] : (s @ X0 @ X26 = s @ X0 @ X27 <=> s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X26)) = s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X27))))), 13.60/2.13 inference(rectify,[],[f10])). 13.60/2.13 tff(f83,plain,( 13.60/2.13 ! [X0 : d,X1 : d,X2 : u,X3 : u,X4 : u] : (! [X5 : u] : (vNOT @ (vEQ(du) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X5)))) = $true) & ! [X6 : u] : ((mono_2Ec_2Ebool_2ET = $true) <=> (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X6))))) = $true)) & ! [X7 : u] : ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__NONE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X7))) = $true) <=> s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0 = s @ (tyop_2Eoption_2Eoption @ X0) @ X7) & ! [X8 : u] : ((vNOT @ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X8)))) = $true) <=> s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0 = s @ (tyop_2Eoption_2Eoption @ X0) @ X8) & ! [X9 : u] : s @ (tyop_2Eoption_2Eoption @ X0) @ X9 = s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X9) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X9) @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Eoption_2Eoption @ X0)) @ c_2Eoption_2ESOME_2E0)) & ! [X10 : u] : ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__NONE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X10))) = $true) => s @ X1 @ X4 = s @ X1 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X10) @ (s @ X1 @ X4) @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X2))) & ! [X11 : u,X12 : u] : s @ X1 @ X11 = s @ X1 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0) @ (s @ X1 @ X11) @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X12)) & ! [X13 : u] : s @ (tyop_2Eoption_2Eoption @ X1) @ c_2Eoption_2ENONE_2E0 = s @ (tyop_2Eoption_2Eoption @ X1) @ (c_2Eoption_2EOPTION__MAP_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X13) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0)) & ! [X14 : u] : s @ (tyop_2Eoption_2Eoption @ X0) @ X14 = s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2EOPTION__JOIN_2E1 @ (s @ (tyop_2Eoption_2Eoption @ (tyop_2Eoption_2Eoption @ X0)) @ (c_2Eoption_2ESOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X14)))) & s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0 = s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2EOPTION__JOIN_2E1 @ (s @ (tyop_2Eoption_2Eoption @ (tyop_2Eoption_2Eoption @ X0)) @ c_2Eoption_2ENONE_2E0)) & ! [X15 : u,X16 : u] : s @ (tyop_2Eoption_2Eoption @ X1) @ (c_2Eoption_2ESOME_2E1 @ (s @ X1 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X15) @ (s @ X0 @ X16)))) = s @ (tyop_2Eoption_2Eoption @ X1) @ (c_2Eoption_2EOPTION__MAP_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X15) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X16)))) & ! [X17 : u,X18 : u,X19 : u] : s @ X1 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X19) @ (s @ X0 @ X17)) = s @ X1 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X17))) @ (s @ X1 @ X18) @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X19)) & ! [X20 : u] : ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X20))) = $true) => s @ (tyop_2Eoption_2Eoption @ X0) @ X20 = s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X20) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X3) @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Eoption_2Eoption @ X0)) @ c_2Eoption_2ESOME_2E0))) & ! [X21 : u] : ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X21))) = $true) => s @ X1 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X2) @ (s @ X0 @ (c_2Eoption_2ETHE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X21)))) = s @ X1 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X21) @ (s @ X1 @ X4) @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X2))) & ! [X22 : u] : s @ (tyop_2Eoption_2Eoption @ X0) @ X22 = s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X22) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Eoption_2Eoption @ X0)) @ c_2Eoption_2ESOME_2E0)) & ! [X23 : u] : ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X23))) = $true) => s @ (tyop_2Eoption_2Eoption @ X0) @ X23 = s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ (c_2Eoption_2ETHE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X23))))) & ((mono_2Ec_2Ebool_2EF = $true) <=> (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0))) = $true)) & ! [X24 : u] : (vNOT @ (vEQ(du) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X24)))) = $true) & ! [X25 : u] : s @ X0 @ X25 = s @ X0 @ (c_2Eoption_2ETHE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X25)))) & ! [X26 : u,X27 : u] : (s @ X0 @ X26 = s @ X0 @ X27 <=> s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X26)) = s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X27))))), 13.60/2.13 inference(fool_elimination,[],[f82])). 13.60/2.13 tff(f84,plain,( 13.60/2.13 ! [X0 : d,X1 : d,X2 : u,X3 : u,X4 : u] : (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool)) @ X2) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X3) @ (s @ (tyop_2Eoption_2Eoption @ X1) @ X4))) <=> ((s @ (tyop_2Eoption_2Eoption @ X1) @ c_2Eoption_2ENONE_2E0 = s @ (tyop_2Eoption_2Eoption @ X1) @ X4 & s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0 = s @ (tyop_2Eoption_2Eoption @ X0) @ X3) | ? [X5 : u,X6 : u] : (s @ (tyop_2Eoption_2Eoption @ X1) @ X4 = s @ (tyop_2Eoption_2Eoption @ X1) @ (c_2Eoption_2ESOME_2E1 @ (s @ X1 @ X6)) & j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool)) @ X2) @ (s @ X0 @ X5))) @ (s @ X1 @ X6))) & s @ (tyop_2Eoption_2Eoption @ X0) @ X3 = s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X5)))))), 13.60/2.13 inference(rectify,[],[f9])). 13.60/2.13 tff(f85,plain,( 13.60/2.13 ! [X0 : d,X1 : d,X2 : u,X3 : u,X4 : u] : ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool)) @ X2) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X3) @ (s @ (tyop_2Eoption_2Eoption @ X1) @ X4))) = $true) <=> ((s @ (tyop_2Eoption_2Eoption @ X1) @ c_2Eoption_2ENONE_2E0 = s @ (tyop_2Eoption_2Eoption @ X1) @ X4 & s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0 = s @ (tyop_2Eoption_2Eoption @ X0) @ X3) | ? [X5 : u,X6 : u] : (s @ (tyop_2Eoption_2Eoption @ X1) @ X4 = s @ (tyop_2Eoption_2Eoption @ X1) @ (c_2Eoption_2ESOME_2E1 @ (s @ X1 @ X6)) & (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool)) @ X2) @ (s @ X0 @ X5))) @ (s @ X1 @ X6))) = $true) & s @ (tyop_2Eoption_2Eoption @ X0) @ X3 = s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X5)))))), 13.60/2.13 inference(fool_elimination,[],[f84])). 13.60/2.13 tff(f88,plain,( 13.60/2.13 ~! [X0 : d,X1 : u,X2 : u,X3 : u] : ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool)) @ X3) @ (s @ X0 @ X2))) @ (s @ X0 @ X1))) = j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool)) @ X3) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X2))) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X1)))))) & (mono_2Ec_2Ebool_2EF = j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool)) @ X3) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X1)))))) & (mono_2Ec_2Ebool_2EF = j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool)) @ X3) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X2))) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0)))) & (mono_2Ec_2Ebool_2ET = j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool)) @ X3) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0)))))), 13.60/2.13 inference(rectify,[],[f28])). 13.60/2.13 tff(f103,plain,( 13.60/2.13 ? [X0 : d,X1 : u,X2 : u,X3 : u] : ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool)) @ X3) @ (s @ X0 @ X2))) @ (s @ X0 @ X1))) != j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool)) @ X3) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X2))) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X1)))))) | (mono_2Ec_2Ebool_2EF != j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool)) @ X3) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X1)))))) | (mono_2Ec_2Ebool_2EF != j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool)) @ X3) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X2))) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0)))) | (mono_2Ec_2Ebool_2ET != j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool)) @ X3) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0)))))), 13.60/2.13 inference(ennf_transformation,[],[f88])). 13.60/2.13 tff(f108,plain,( 13.60/2.13 ! [X0 : d,X1 : d,X2 : u,X3 : u,X4 : u] : (! [X5 : u] : (vNOT @ (vEQ(du) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X5)))) = $true) & ! [X6 : u] : ((mono_2Ec_2Ebool_2ET = $true) <=> (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X6))))) = $true)) & ! [X7 : u] : ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__NONE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X7))) = $true) <=> s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0 = s @ (tyop_2Eoption_2Eoption @ X0) @ X7) & ! [X8 : u] : ((vNOT @ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X8)))) = $true) <=> s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0 = s @ (tyop_2Eoption_2Eoption @ X0) @ X8) & ! [X9 : u] : s @ (tyop_2Eoption_2Eoption @ X0) @ X9 = s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X9) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X9) @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Eoption_2Eoption @ X0)) @ c_2Eoption_2ESOME_2E0)) & ! [X10 : u] : (s @ X1 @ X4 = s @ X1 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X10) @ (s @ X1 @ X4) @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X2)) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__NONE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X10))) != $true)) & ! [X11 : u,X12 : u] : s @ X1 @ X11 = s @ X1 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0) @ (s @ X1 @ X11) @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X12)) & ! [X13 : u] : s @ (tyop_2Eoption_2Eoption @ X1) @ c_2Eoption_2ENONE_2E0 = s @ (tyop_2Eoption_2Eoption @ X1) @ (c_2Eoption_2EOPTION__MAP_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X13) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0)) & ! [X14 : u] : s @ (tyop_2Eoption_2Eoption @ X0) @ X14 = s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2EOPTION__JOIN_2E1 @ (s @ (tyop_2Eoption_2Eoption @ (tyop_2Eoption_2Eoption @ X0)) @ (c_2Eoption_2ESOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X14)))) & s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0 = s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2EOPTION__JOIN_2E1 @ (s @ (tyop_2Eoption_2Eoption @ (tyop_2Eoption_2Eoption @ X0)) @ c_2Eoption_2ENONE_2E0)) & ! [X15 : u,X16 : u] : s @ (tyop_2Eoption_2Eoption @ X1) @ (c_2Eoption_2ESOME_2E1 @ (s @ X1 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X15) @ (s @ X0 @ X16)))) = s @ (tyop_2Eoption_2Eoption @ X1) @ (c_2Eoption_2EOPTION__MAP_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X15) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X16)))) & ! [X17 : u,X18 : u,X19 : u] : s @ X1 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X19) @ (s @ X0 @ X17)) = s @ X1 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X17))) @ (s @ X1 @ X18) @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X19)) & ! [X20 : u] : (s @ (tyop_2Eoption_2Eoption @ X0) @ X20 = s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X20) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X3) @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Eoption_2Eoption @ X0)) @ c_2Eoption_2ESOME_2E0)) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X20))) != $true)) & ! [X21 : u] : (s @ X1 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X2) @ (s @ X0 @ (c_2Eoption_2ETHE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X21)))) = s @ X1 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X21) @ (s @ X1 @ X4) @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X2)) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X21))) != $true)) & ! [X22 : u] : s @ (tyop_2Eoption_2Eoption @ X0) @ X22 = s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X22) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Eoption_2Eoption @ X0)) @ c_2Eoption_2ESOME_2E0)) & ! [X23 : u] : (s @ (tyop_2Eoption_2Eoption @ X0) @ X23 = s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ (c_2Eoption_2ETHE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X23)))) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X23))) != $true)) & ((mono_2Ec_2Ebool_2EF = $true) <=> (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0))) = $true)) & ! [X24 : u] : (vNOT @ (vEQ(du) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X24)))) = $true) & ! [X25 : u] : s @ X0 @ X25 = s @ X0 @ (c_2Eoption_2ETHE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X25)))) & ! [X26 : u,X27 : u] : (s @ X0 @ X26 = s @ X0 @ X27 <=> s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X26)) = s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X27))))), 13.60/2.13 inference(ennf_transformation,[],[f83])). 13.60/2.13 tff(f109,plain,( 13.60/2.13 ! [X4 : u,X1 : d,X3 : u,X0 : d,X2 : u] : ((sP0 @ X2 @ X0 @ X3 @ X1 @ X4 = $true) <=> ((s @ (tyop_2Eoption_2Eoption @ X1) @ c_2Eoption_2ENONE_2E0 = s @ (tyop_2Eoption_2Eoption @ X1) @ X4 & s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0 = s @ (tyop_2Eoption_2Eoption @ X0) @ X3) | ? [X5 : u,X6 : u] : (s @ (tyop_2Eoption_2Eoption @ X1) @ X4 = s @ (tyop_2Eoption_2Eoption @ X1) @ (c_2Eoption_2ESOME_2E1 @ (s @ X1 @ X6)) & (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool)) @ X2) @ (s @ X0 @ X5))) @ (s @ X1 @ X6))) = $true) & s @ (tyop_2Eoption_2Eoption @ X0) @ X3 = s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X5)))))), 13.60/2.13 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])). 13.60/2.13 tff(f110,plain,( 13.60/2.13 ! [X0 : d,X1 : d,X2 : u,X3 : u,X4 : u] : ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool)) @ X2) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X3) @ (s @ (tyop_2Eoption_2Eoption @ X1) @ X4))) = $true) <=> (sP0 @ X2 @ X0 @ X3 @ X1 @ X4 = $true))), 13.60/2.13 inference(definition_folding,[],[f85,f109])). 13.60/2.13 tff(f111,plain,( 13.60/2.13 ? [X0 : d,X1 : u,X2 : u,X3 : u] : ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool)) @ X3) @ (s @ X0 @ X2))) @ (s @ X0 @ X1))) != j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool)) @ X3) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X2))) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X1)))))) | (mono_2Ec_2Ebool_2EF != j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool)) @ X3) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X1)))))) | (mono_2Ec_2Ebool_2EF != j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool)) @ X3) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X2))) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0)))) | (mono_2Ec_2Ebool_2ET != j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X0 @ tyop_2Emin_2Ebool)) @ X3) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0))))) => ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ sK1 @ sK3))) @ (s @ sK1 @ sK2))) != j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3))) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2)))))) | (mono_2Ec_2Ebool_2EF != j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2)))))) | (mono_2Ec_2Ebool_2EF != j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3))) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0)))) | (mono_2Ec_2Ebool_2ET != j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0)))))), 13.60/2.13 introduced(choice_axiom,[])). 13.60/2.13 tff(f112,plain,( 13.60/2.13 (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ sK1 @ sK3))) @ (s @ sK1 @ sK2))) != j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3))) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2)))))) | (mono_2Ec_2Ebool_2EF != j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2)))))) | (mono_2Ec_2Ebool_2EF != j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3))) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0)))) | (mono_2Ec_2Ebool_2ET != j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0))))), 13.60/2.13 inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4])],[f103,f111])). 13.60/2.13 tff(f115,plain,( 13.60/2.13 ! [X4 : u,X1 : d,X3 : u,X0 : d,X2 : u] : (((sP0 @ X2 @ X0 @ X3 @ X1 @ X4 = $true) | ((s @ (tyop_2Eoption_2Eoption @ X1) @ c_2Eoption_2ENONE_2E0 != s @ (tyop_2Eoption_2Eoption @ X1) @ X4 | s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0 != s @ (tyop_2Eoption_2Eoption @ X0) @ X3) & ! [X5 : u,X6 : u] : (s @ (tyop_2Eoption_2Eoption @ X1) @ X4 != s @ (tyop_2Eoption_2Eoption @ X1) @ (c_2Eoption_2ESOME_2E1 @ (s @ X1 @ X6)) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool)) @ X2) @ (s @ X0 @ X5))) @ (s @ X1 @ X6))) != $true) | s @ (tyop_2Eoption_2Eoption @ X0) @ X3 != s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X5))))) & (((s @ (tyop_2Eoption_2Eoption @ X1) @ c_2Eoption_2ENONE_2E0 = s @ (tyop_2Eoption_2Eoption @ X1) @ X4 & s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0 = s @ (tyop_2Eoption_2Eoption @ X0) @ X3) | ? [X5 : u,X6 : u] : (s @ (tyop_2Eoption_2Eoption @ X1) @ X4 = s @ (tyop_2Eoption_2Eoption @ X1) @ (c_2Eoption_2ESOME_2E1 @ (s @ X1 @ X6)) & (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool)) @ X2) @ (s @ X0 @ X5))) @ (s @ X1 @ X6))) = $true) & s @ (tyop_2Eoption_2Eoption @ X0) @ X3 = s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X5)))) | (sP0 @ X2 @ X0 @ X3 @ X1 @ X4 != $true)))), 13.60/2.13 inference(nnf_transformation,[],[f109])). 13.60/2.13 tff(f116,plain,( 13.60/2.13 ! [X4 : u,X1 : d,X3 : u,X0 : d,X2 : u] : (((sP0 @ X2 @ X0 @ X3 @ X1 @ X4 = $true) | ((s @ (tyop_2Eoption_2Eoption @ X1) @ c_2Eoption_2ENONE_2E0 != s @ (tyop_2Eoption_2Eoption @ X1) @ X4 | s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0 != s @ (tyop_2Eoption_2Eoption @ X0) @ X3) & ! [X5 : u,X6 : u] : (s @ (tyop_2Eoption_2Eoption @ X1) @ X4 != s @ (tyop_2Eoption_2Eoption @ X1) @ (c_2Eoption_2ESOME_2E1 @ (s @ X1 @ X6)) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool)) @ X2) @ (s @ X0 @ X5))) @ (s @ X1 @ X6))) != $true) | s @ (tyop_2Eoption_2Eoption @ X0) @ X3 != s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X5))))) & ((s @ (tyop_2Eoption_2Eoption @ X1) @ c_2Eoption_2ENONE_2E0 = s @ (tyop_2Eoption_2Eoption @ X1) @ X4 & s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0 = s @ (tyop_2Eoption_2Eoption @ X0) @ X3) | ? [X5 : u,X6 : u] : (s @ (tyop_2Eoption_2Eoption @ X1) @ X4 = s @ (tyop_2Eoption_2Eoption @ X1) @ (c_2Eoption_2ESOME_2E1 @ (s @ X1 @ X6)) & (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool)) @ X2) @ (s @ X0 @ X5))) @ (s @ X1 @ X6))) = $true) & s @ (tyop_2Eoption_2Eoption @ X0) @ X3 = s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X5))) | (sP0 @ X2 @ X0 @ X3 @ X1 @ X4 != $true)))), 13.60/2.13 inference(flattening,[],[f115])). 13.60/2.13 tff(f117,plain,( 13.60/2.13 ! [X0 : u,X1 : d,X2 : u,X3 : d,X4 : u] : (((sP0 @ X4 @ X3 @ X2 @ X1 @ X0 = $true) | ((s @ (tyop_2Eoption_2Eoption @ X1) @ c_2Eoption_2ENONE_2E0 != s @ (tyop_2Eoption_2Eoption @ X1) @ X0 | s @ (tyop_2Eoption_2Eoption @ X3) @ c_2Eoption_2ENONE_2E0 != s @ (tyop_2Eoption_2Eoption @ X3) @ X2) & ! [X5 : u,X6 : u] : (s @ (tyop_2Eoption_2Eoption @ X1) @ X0 != s @ (tyop_2Eoption_2Eoption @ X1) @ (c_2Eoption_2ESOME_2E1 @ (s @ X1 @ X6)) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool)) @ X4) @ (s @ X3 @ X5))) @ (s @ X1 @ X6))) != $true) | s @ (tyop_2Eoption_2Eoption @ X3) @ X2 != s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2ESOME_2E1 @ (s @ X3 @ X5))))) & ((s @ (tyop_2Eoption_2Eoption @ X1) @ c_2Eoption_2ENONE_2E0 = s @ (tyop_2Eoption_2Eoption @ X1) @ X0 & s @ (tyop_2Eoption_2Eoption @ X3) @ c_2Eoption_2ENONE_2E0 = s @ (tyop_2Eoption_2Eoption @ X3) @ X2) | ? [X7 : u,X8 : u] : (s @ (tyop_2Eoption_2Eoption @ X1) @ X0 = s @ (tyop_2Eoption_2Eoption @ X1) @ (c_2Eoption_2ESOME_2E1 @ (s @ X1 @ X8)) & (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool)) @ X4) @ (s @ X3 @ X7))) @ (s @ X1 @ X8))) = $true) & s @ (tyop_2Eoption_2Eoption @ X3) @ X2 = s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2ESOME_2E1 @ (s @ X3 @ X7))) | (sP0 @ X4 @ X3 @ X2 @ X1 @ X0 != $true)))), 13.60/2.13 inference(rectify,[],[f116])). 13.60/2.13 tff(f118,plain,( 13.60/2.13 ! [X4 : u,X3 : d,X2 : u,X1 : d,X0 : u] : (? [X7 : u,X8 : u] : (s @ (tyop_2Eoption_2Eoption @ X1) @ X0 = s @ (tyop_2Eoption_2Eoption @ X1) @ (c_2Eoption_2ESOME_2E1 @ (s @ X1 @ X8)) & (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool)) @ X4) @ (s @ X3 @ X7))) @ (s @ X1 @ X8))) = $true) & s @ (tyop_2Eoption_2Eoption @ X3) @ X2 = s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2ESOME_2E1 @ (s @ X3 @ X7))) => (s @ (tyop_2Eoption_2Eoption @ X1) @ X0 = s @ (tyop_2Eoption_2Eoption @ X1) @ (c_2Eoption_2ESOME_2E1 @ (s @ X1 @ (sK7 @ X4 @ X3 @ X2 @ X1 @ X0))) & (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool)) @ X4) @ (s @ X3 @ (sK6 @ X4 @ X3 @ X2 @ X1 @ X0)))) @ (s @ X1 @ (sK7 @ X4 @ X3 @ X2 @ X1 @ X0)))) = $true) & s @ (tyop_2Eoption_2Eoption @ X3) @ X2 = s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2ESOME_2E1 @ (s @ X3 @ (sK6 @ X4 @ X3 @ X2 @ X1 @ X0)))))), 13.60/2.13 introduced(choice_axiom,[])). 13.60/2.13 tff(f119,plain,( 13.60/2.13 ! [X0 : u,X1 : d,X2 : u,X3 : d,X4 : u] : (((sP0 @ X4 @ X3 @ X2 @ X1 @ X0 = $true) | ((s @ (tyop_2Eoption_2Eoption @ X1) @ c_2Eoption_2ENONE_2E0 != s @ (tyop_2Eoption_2Eoption @ X1) @ X0 | s @ (tyop_2Eoption_2Eoption @ X3) @ c_2Eoption_2ENONE_2E0 != s @ (tyop_2Eoption_2Eoption @ X3) @ X2) & ! [X5 : u,X6 : u] : (s @ (tyop_2Eoption_2Eoption @ X1) @ X0 != s @ (tyop_2Eoption_2Eoption @ X1) @ (c_2Eoption_2ESOME_2E1 @ (s @ X1 @ X6)) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool)) @ X4) @ (s @ X3 @ X5))) @ (s @ X1 @ X6))) != $true) | s @ (tyop_2Eoption_2Eoption @ X3) @ X2 != s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2ESOME_2E1 @ (s @ X3 @ X5))))) & ((s @ (tyop_2Eoption_2Eoption @ X1) @ c_2Eoption_2ENONE_2E0 = s @ (tyop_2Eoption_2Eoption @ X1) @ X0 & s @ (tyop_2Eoption_2Eoption @ X3) @ c_2Eoption_2ENONE_2E0 = s @ (tyop_2Eoption_2Eoption @ X3) @ X2) | (s @ (tyop_2Eoption_2Eoption @ X1) @ X0 = s @ (tyop_2Eoption_2Eoption @ X1) @ (c_2Eoption_2ESOME_2E1 @ (s @ X1 @ (sK7 @ X4 @ X3 @ X2 @ X1 @ X0))) & (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool)) @ X4) @ (s @ X3 @ (sK6 @ X4 @ X3 @ X2 @ X1 @ X0)))) @ (s @ X1 @ (sK7 @ X4 @ X3 @ X2 @ X1 @ X0)))) = $true) & s @ (tyop_2Eoption_2Eoption @ X3) @ X2 = s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2ESOME_2E1 @ (s @ X3 @ (sK6 @ X4 @ X3 @ X2 @ X1 @ X0)))) | (sP0 @ X4 @ X3 @ X2 @ X1 @ X0 != $true)))), 13.60/2.13 inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7])],[f117,f118])). 13.60/2.13 tff(f120,plain,( 13.60/2.13 ! [X0 : d,X1 : d,X2 : u,X3 : u,X4 : u] : (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool)) @ X2) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X3) @ (s @ (tyop_2Eoption_2Eoption @ X1) @ X4))) = $true) | (sP0 @ X2 @ X0 @ X3 @ X1 @ X4 != $true)) & ((sP0 @ X2 @ X0 @ X3 @ X1 @ X4 = $true) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool)) @ X2) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X3) @ (s @ (tyop_2Eoption_2Eoption @ X1) @ X4))) != $true)))), 13.60/2.13 inference(nnf_transformation,[],[f110])). 13.60/2.13 tff(f121,plain,( 13.60/2.13 ! [X0 : '$o'] : ((((mono_2Ec_2Ebool_2ET = $true) | (($true != X0) & (mono_2Ec_2Ebool_2ET != $true))) & ((($true = X0) | (mono_2Ec_2Ebool_2ET = $true)) | (mono_2Ec_2Ebool_2ET != $true))) & (((($true = X0) | (mono_2Ec_2Ebool_2EF = $true)) | ($true != X0)) & (($true = X0) | (($true != X0) & (mono_2Ec_2Ebool_2EF != $true)))) & ((($true = X0) | (($true != X0) & ($true != X0))) & ((($true = X0) | ($true = X0)) | ($true != X0))) & ((((mono_2Ec_2Ebool_2EF = $true) | ($true = X0)) | ($true != X0)) & (($true = X0) | ((mono_2Ec_2Ebool_2EF != $true) & ($true != X0)))) & (((mono_2Ec_2Ebool_2ET = $true) | ((mono_2Ec_2Ebool_2ET != $true) & ($true != X0))) & (((mono_2Ec_2Ebool_2ET = $true) | ($true = X0)) | (mono_2Ec_2Ebool_2ET != $true))))), 13.60/2.13 inference(nnf_transformation,[],[f57])). 13.60/2.13 tff(f122,plain,( 13.60/2.13 ! [X0 : '$o'] : (((mono_2Ec_2Ebool_2ET = $true) | (($true != X0) & (mono_2Ec_2Ebool_2ET != $true))) & (($true = X0) | (mono_2Ec_2Ebool_2ET = $true) | (mono_2Ec_2Ebool_2ET != $true)) & (($true = X0) | (mono_2Ec_2Ebool_2EF = $true) | ($true != X0)) & (($true = X0) | (($true != X0) & (mono_2Ec_2Ebool_2EF != $true))) & (($true = X0) | (($true != X0) & ($true != X0))) & (($true = X0) | ($true = X0) | ($true != X0)) & ((mono_2Ec_2Ebool_2EF = $true) | ($true = X0) | ($true != X0)) & (($true = X0) | ((mono_2Ec_2Ebool_2EF != $true) & ($true != X0))) & ((mono_2Ec_2Ebool_2ET = $true) | ((mono_2Ec_2Ebool_2ET != $true) & ($true != X0))) & ((mono_2Ec_2Ebool_2ET = $true) | ($true = X0) | (mono_2Ec_2Ebool_2ET != $true)))), 13.60/2.13 inference(flattening,[],[f121])). 13.60/2.13 tff(f127,plain,( 13.60/2.13 ! [X0 : d,X1 : d,X2 : u,X3 : u,X4 : u] : (! [X5 : u] : (vNOT @ (vEQ(du) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X5)))) = $true) & ! [X6 : u] : (((mono_2Ec_2Ebool_2ET = $true) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X6))))) != $true)) & ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X6))))) = $true) | (mono_2Ec_2Ebool_2ET != $true))) & ! [X7 : u] : (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__NONE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X7))) = $true) | s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0 != s @ (tyop_2Eoption_2Eoption @ X0) @ X7) & (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0 = s @ (tyop_2Eoption_2Eoption @ X0) @ X7 | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__NONE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X7))) != $true))) & ! [X8 : u] : (((vNOT @ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X8)))) = $true) | s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0 != s @ (tyop_2Eoption_2Eoption @ X0) @ X8) & (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0 = s @ (tyop_2Eoption_2Eoption @ X0) @ X8 | (vNOT @ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X8)))) != $true))) & ! [X9 : u] : s @ (tyop_2Eoption_2Eoption @ X0) @ X9 = s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X9) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X9) @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Eoption_2Eoption @ X0)) @ c_2Eoption_2ESOME_2E0)) & ! [X10 : u] : (s @ X1 @ X4 = s @ X1 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X10) @ (s @ X1 @ X4) @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X2)) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__NONE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X10))) != $true)) & ! [X11 : u,X12 : u] : s @ X1 @ X11 = s @ X1 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0) @ (s @ X1 @ X11) @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X12)) & ! [X13 : u] : s @ (tyop_2Eoption_2Eoption @ X1) @ c_2Eoption_2ENONE_2E0 = s @ (tyop_2Eoption_2Eoption @ X1) @ (c_2Eoption_2EOPTION__MAP_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X13) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0)) & ! [X14 : u] : s @ (tyop_2Eoption_2Eoption @ X0) @ X14 = s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2EOPTION__JOIN_2E1 @ (s @ (tyop_2Eoption_2Eoption @ (tyop_2Eoption_2Eoption @ X0)) @ (c_2Eoption_2ESOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X14)))) & s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0 = s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2EOPTION__JOIN_2E1 @ (s @ (tyop_2Eoption_2Eoption @ (tyop_2Eoption_2Eoption @ X0)) @ c_2Eoption_2ENONE_2E0)) & ! [X15 : u,X16 : u] : s @ (tyop_2Eoption_2Eoption @ X1) @ (c_2Eoption_2ESOME_2E1 @ (s @ X1 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X15) @ (s @ X0 @ X16)))) = s @ (tyop_2Eoption_2Eoption @ X1) @ (c_2Eoption_2EOPTION__MAP_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X15) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X16)))) & ! [X17 : u,X18 : u,X19 : u] : s @ X1 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X19) @ (s @ X0 @ X17)) = s @ X1 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X17))) @ (s @ X1 @ X18) @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X19)) & ! [X20 : u] : (s @ (tyop_2Eoption_2Eoption @ X0) @ X20 = s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X20) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X3) @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Eoption_2Eoption @ X0)) @ c_2Eoption_2ESOME_2E0)) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X20))) != $true)) & ! [X21 : u] : (s @ X1 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X2) @ (s @ X0 @ (c_2Eoption_2ETHE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X21)))) = s @ X1 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X21) @ (s @ X1 @ X4) @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X2)) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X21))) != $true)) & ! [X22 : u] : s @ (tyop_2Eoption_2Eoption @ X0) @ X22 = s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X22) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Eoption_2Eoption @ X0)) @ c_2Eoption_2ESOME_2E0)) & ! [X23 : u] : (s @ (tyop_2Eoption_2Eoption @ X0) @ X23 = s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ (c_2Eoption_2ETHE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X23)))) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X23))) != $true)) & (((mono_2Ec_2Ebool_2EF = $true) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0))) != $true)) & ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0))) = $true) | (mono_2Ec_2Ebool_2EF != $true))) & ! [X24 : u] : (vNOT @ (vEQ(du) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X24)))) = $true) & ! [X25 : u] : s @ X0 @ X25 = s @ X0 @ (c_2Eoption_2ETHE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X25)))) & ! [X26 : u,X27 : u] : ((s @ X0 @ X26 = s @ X0 @ X27 | s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X26)) != s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X27))) & (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X26)) = s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X27)) | s @ X0 @ X26 != s @ X0 @ X27)))), 13.60/2.13 inference(nnf_transformation,[],[f108])). 13.60/2.13 tff(f128,plain,( 13.60/2.13 ! [X0 : d,X1 : d,X2 : u,X3 : u,X4 : u] : (! [X5 : u] : (vNOT @ (vEQ(du) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X5)))) = $true) & ! [X6 : u] : (((mono_2Ec_2Ebool_2ET = $true) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X6))))) != $true)) & ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X6))))) = $true) | (mono_2Ec_2Ebool_2ET != $true))) & ! [X7 : u] : (((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__NONE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X7))) = $true) | s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0 != s @ (tyop_2Eoption_2Eoption @ X0) @ X7) & (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0 = s @ (tyop_2Eoption_2Eoption @ X0) @ X7 | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__NONE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X7))) != $true))) & ! [X8 : u] : (((vNOT @ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X8)))) = $true) | s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0 != s @ (tyop_2Eoption_2Eoption @ X0) @ X8) & (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0 = s @ (tyop_2Eoption_2Eoption @ X0) @ X8 | (vNOT @ (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X8)))) != $true))) & ! [X9 : u] : s @ (tyop_2Eoption_2Eoption @ X0) @ X9 = s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X9) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X9) @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Eoption_2Eoption @ X0)) @ c_2Eoption_2ESOME_2E0)) & ! [X10 : u] : (s @ X1 @ X4 = s @ X1 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X10) @ (s @ X1 @ X4) @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X2)) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__NONE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X10))) != $true)) & ! [X11 : u,X12 : u] : s @ X1 @ X11 = s @ X1 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0) @ (s @ X1 @ X11) @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X12)) & ! [X13 : u] : s @ (tyop_2Eoption_2Eoption @ X1) @ c_2Eoption_2ENONE_2E0 = s @ (tyop_2Eoption_2Eoption @ X1) @ (c_2Eoption_2EOPTION__MAP_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X13) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0)) & ! [X14 : u] : s @ (tyop_2Eoption_2Eoption @ X0) @ X14 = s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2EOPTION__JOIN_2E1 @ (s @ (tyop_2Eoption_2Eoption @ (tyop_2Eoption_2Eoption @ X0)) @ (c_2Eoption_2ESOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X14)))) & s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0 = s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2EOPTION__JOIN_2E1 @ (s @ (tyop_2Eoption_2Eoption @ (tyop_2Eoption_2Eoption @ X0)) @ c_2Eoption_2ENONE_2E0)) & ! [X15 : u,X16 : u] : s @ (tyop_2Eoption_2Eoption @ X1) @ (c_2Eoption_2ESOME_2E1 @ (s @ X1 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X15) @ (s @ X0 @ X16)))) = s @ (tyop_2Eoption_2Eoption @ X1) @ (c_2Eoption_2EOPTION__MAP_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X15) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X16)))) & ! [X17 : u,X18 : u,X19 : u] : s @ X1 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X19) @ (s @ X0 @ X17)) = s @ X1 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X17))) @ (s @ X1 @ X18) @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X19)) & ! [X20 : u] : (s @ (tyop_2Eoption_2Eoption @ X0) @ X20 = s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X20) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X3) @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Eoption_2Eoption @ X0)) @ c_2Eoption_2ESOME_2E0)) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X20))) != $true)) & ! [X21 : u] : (s @ X1 @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X2) @ (s @ X0 @ (c_2Eoption_2ETHE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X21)))) = s @ X1 @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X21) @ (s @ X1 @ X4) @ (s @ (tyop_2Emin_2Efun @ X0 @ X1) @ X2)) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X21))) != $true)) & ! [X22 : u] : s @ (tyop_2Eoption_2Eoption @ X0) @ X22 = s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2Eoption__CASE_2E3 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X22) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Eoption_2Eoption @ X0)) @ c_2Eoption_2ESOME_2E0)) & ! [X23 : u] : (s @ (tyop_2Eoption_2Eoption @ X0) @ X23 = s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ (c_2Eoption_2ETHE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X23)))) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X23))) != $true)) & ((mono_2Ec_2Ebool_2EF = $true) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0))) != $true)) & ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EIS__SOME_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0))) = $true) | (mono_2Ec_2Ebool_2EF != $true)) & ! [X24 : u] : (vNOT @ (vEQ(du) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X24)))) = $true) & ! [X25 : u] : s @ X0 @ X25 = s @ X0 @ (c_2Eoption_2ETHE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X25)))) & ! [X26 : u,X27 : u] : ((s @ X0 @ X26 = s @ X0 @ X27 | s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X26)) != s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X27))) & (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X26)) = s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X27)) | s @ X0 @ X26 != s @ X0 @ X27)))), 13.60/2.13 inference(flattening,[],[f127])). 13.60/2.13 tff(f130,plain,( 13.60/2.13 (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ sK1 @ sK3))) @ (s @ sK1 @ sK2))) != j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3))) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2)))))) | (mono_2Ec_2Ebool_2EF != j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2)))))) | (mono_2Ec_2Ebool_2EF != j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3))) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0)))) | (mono_2Ec_2Ebool_2ET != j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0))))), 13.60/2.13 inference(cnf_transformation,[],[f112])). 13.60/2.15 tff(f132,plain,( 13.60/2.15 ( ! [X4:u,X2:u,X0:u,X3:d,X1:d] : ((sP0 @ X4 @ X3 @ X2 @ X1 @ X0 != $true) | s @ (tyop_2Eoption_2Eoption @ X3) @ X2 = s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2ESOME_2E1 @ (s @ X3 @ (sK6 @ X4 @ X3 @ X2 @ X1 @ X0))) | s @ (tyop_2Eoption_2Eoption @ X3) @ c_2Eoption_2ENONE_2E0 = s @ (tyop_2Eoption_2Eoption @ X3) @ X2) )), 13.60/2.15 inference(cnf_transformation,[],[f119])). 13.60/2.15 tff(f133,plain,( 13.60/2.15 ( ! [X4:u,X2:u,X0:u,X3:d,X1:d] : ((sP0 @ X4 @ X3 @ X2 @ X1 @ X0 != $true) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool)) @ X4) @ (s @ X3 @ (sK6 @ X4 @ X3 @ X2 @ X1 @ X0)))) @ (s @ X1 @ (sK7 @ X4 @ X3 @ X2 @ X1 @ X0)))) = $true) | s @ (tyop_2Eoption_2Eoption @ X3) @ c_2Eoption_2ENONE_2E0 = s @ (tyop_2Eoption_2Eoption @ X3) @ X2) )), 13.60/2.15 inference(cnf_transformation,[],[f119])). 13.60/2.15 tff(f134,plain,( 13.60/2.15 ( ! [X4:u,X2:u,X0:u,X3:d,X1:d] : ((sP0 @ X4 @ X3 @ X2 @ X1 @ X0 != $true) | s @ (tyop_2Eoption_2Eoption @ X1) @ X0 = s @ (tyop_2Eoption_2Eoption @ X1) @ (c_2Eoption_2ESOME_2E1 @ (s @ X1 @ (sK7 @ X4 @ X3 @ X2 @ X1 @ X0))) | s @ (tyop_2Eoption_2Eoption @ X3) @ c_2Eoption_2ENONE_2E0 = s @ (tyop_2Eoption_2Eoption @ X3) @ X2) )), 13.60/2.15 inference(cnf_transformation,[],[f119])). 13.60/2.15 tff(f135,plain,( 13.60/2.15 ( ! [X4:u,X2:u,X0:u,X3:d,X1:d] : ((sP0 @ X4 @ X3 @ X2 @ X1 @ X0 != $true) | s @ (tyop_2Eoption_2Eoption @ X3) @ X2 = s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2ESOME_2E1 @ (s @ X3 @ (sK6 @ X4 @ X3 @ X2 @ X1 @ X0))) | s @ (tyop_2Eoption_2Eoption @ X1) @ c_2Eoption_2ENONE_2E0 = s @ (tyop_2Eoption_2Eoption @ X1) @ X0) )), 13.60/2.15 inference(cnf_transformation,[],[f119])). 13.60/2.15 tff(f138,plain,( 13.60/2.15 ( ! [X6:u,X4:u,X2:u,X0:u,X5:u,X3:d,X1:d] : ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ X3 @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool)) @ X4) @ (s @ X3 @ X5))) @ (s @ X1 @ X6))) != $true) | s @ (tyop_2Eoption_2Eoption @ X1) @ X0 != s @ (tyop_2Eoption_2Eoption @ X1) @ (c_2Eoption_2ESOME_2E1 @ (s @ X1 @ X6)) | (sP0 @ X4 @ X3 @ X2 @ X1 @ X0 = $true) | s @ (tyop_2Eoption_2Eoption @ X3) @ X2 != s @ (tyop_2Eoption_2Eoption @ X3) @ (c_2Eoption_2ESOME_2E1 @ (s @ X3 @ X5))) )), 13.60/2.15 inference(cnf_transformation,[],[f119])). 13.60/2.15 tff(f139,plain,( 13.60/2.15 ( ! [X4:u,X2:u,X0:u,X3:d,X1:d] : ((sP0 @ X4 @ X3 @ X2 @ X1 @ X0 = $true) | s @ (tyop_2Eoption_2Eoption @ X1) @ c_2Eoption_2ENONE_2E0 != s @ (tyop_2Eoption_2Eoption @ X1) @ X0 | s @ (tyop_2Eoption_2Eoption @ X3) @ c_2Eoption_2ENONE_2E0 != s @ (tyop_2Eoption_2Eoption @ X3) @ X2) )), 13.60/2.15 inference(cnf_transformation,[],[f119])). 13.60/2.15 tff(f140,plain,( 13.60/2.15 ( ! [X4:u,X2:u,X0:d,X3:u,X1:d] : ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool)) @ X2) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X3) @ (s @ (tyop_2Eoption_2Eoption @ X1) @ X4))) != $true) | (sP0 @ X2 @ X0 @ X3 @ X1 @ X4 = $true)) )), 13.60/2.15 inference(cnf_transformation,[],[f120])). 13.60/2.15 tff(f141,plain,( 13.60/2.15 ( ! [X4:u,X2:u,X0:d,X3:u,X1:d] : ((j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ X0 @ (tyop_2Emin_2Efun @ X1 @ tyop_2Emin_2Ebool)) @ X2) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ X3) @ (s @ (tyop_2Eoption_2Eoption @ X1) @ X4))) = $true) | (sP0 @ X2 @ X0 @ X3 @ X1 @ X4 != $true)) )), 13.60/2.15 inference(cnf_transformation,[],[f120])). 13.60/2.15 tff(f160,plain,( 13.60/2.15 ( ! [X0:'$o'] : ((mono_2Ec_2Ebool_2ET = $true) | ($true != X0)) )), 13.60/2.15 inference(cnf_transformation,[],[f122])). 13.60/2.15 tff(f193,plain,( 13.60/2.15 (mono_2Ec_2Ebool_2EF = vNOT @ mono_2Ec_2Ebool_2ET)), 13.60/2.15 inference(cnf_transformation,[],[f51])). 13.60/2.15 tff(f204,plain,( 13.60/2.15 ( ! [X0:d,X25:u] : (s @ X0 @ X25 = s @ X0 @ (c_2Eoption_2ETHE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X25))))) )), 13.60/2.15 inference(cnf_transformation,[],[f128])). 13.60/2.15 tff(f205,plain,( 13.60/2.15 ( ! [X24:u,X0:d] : ((vNOT @ (vEQ(du) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X24)))) = $true)) )), 13.60/2.15 inference(cnf_transformation,[],[f128])). 13.60/2.15 tff(f240,plain,( 13.60/2.15 (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ sK1 @ sK3))) @ (s @ sK1 @ sK2))) != j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3))) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2)))))) | (vNOT @ mono_2Ec_2Ebool_2ET != j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2)))))) | (vNOT @ mono_2Ec_2Ebool_2ET != j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3))) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0)))) | (mono_2Ec_2Ebool_2ET != j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0))))), 13.60/2.15 inference(definition_unfolding,[],[f130,f193,f193])). 13.60/2.15 tff(f262,plain,( 13.60/2.15 (mono_2Ec_2Ebool_2ET = $true)), 13.60/2.15 inference(equality_resolution,[],[f160])). 13.60/2.15 tff(f334,plain,( 13.60/2.15 ( ! [X24:u,X0:d] : ((vEQ(du) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X24))) = $false)) )), 13.60/2.15 inference(not_proxy_clausification,[],[f205])). 13.60/2.15 tff(f335,plain,( 13.60/2.15 ( ! [X24:u,X0:d] : (s @ (tyop_2Eoption_2Eoption @ X0) @ c_2Eoption_2ENONE_2E0 != s @ (tyop_2Eoption_2Eoption @ X0) @ (c_2Eoption_2ESOME_2E1 @ (s @ X0 @ X24))) )), 13.60/2.15 inference(equality_proxy_clausification,[],[f334])). 13.60/2.15 tff(f337,plain,( 13.60/2.15 (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ sK1 @ sK3))) @ (s @ sK1 @ sK2))) = $true) | (vNOT @ mono_2Ec_2Ebool_2ET != j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2)))))) | (vNOT @ mono_2Ec_2Ebool_2ET != j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3))) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0)))) | (mono_2Ec_2Ebool_2ET != j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0)))) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3))) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2))))) = $true)), 13.60/2.15 inference(binary_proxy_clausification,[],[f240])). 13.60/2.15 tff(f338,plain,( 13.60/2.15 (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ sK1 @ sK3))) @ (s @ sK1 @ sK2))) = $false) | (vNOT @ mono_2Ec_2Ebool_2ET != j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2)))))) | (vNOT @ mono_2Ec_2Ebool_2ET != j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3))) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0)))) | (mono_2Ec_2Ebool_2ET != j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0)))) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3))) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2))))) = $false)), 13.60/2.15 inference(binary_proxy_clausification,[],[f240])). 13.60/2.15 tff(f339,plain,( 13.60/2.15 (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ sK1 @ sK3))) @ (s @ sK1 @ sK2))) = $false) | (vNOT @ mono_2Ec_2Ebool_2ET = $true) | (vNOT @ mono_2Ec_2Ebool_2ET != j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3))) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0)))) | (mono_2Ec_2Ebool_2ET != j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0)))) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3))) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2))))) = $false) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2))))) = $true)), 13.60/2.15 inference(binary_proxy_clausification,[],[f338])). 13.60/2.16 tff(f354,plain,( 13.60/2.16 (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ sK1 @ sK3))) @ (s @ sK1 @ sK2))) = $false) | (mono_2Ec_2Ebool_2ET = $false) | (vNOT @ mono_2Ec_2Ebool_2ET != j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3))) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0)))) | (mono_2Ec_2Ebool_2ET != j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0)))) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3))) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2))))) = $false) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2))))) = $true)), 13.60/2.16 inference(not_proxy_clausification,[],[f339])). 13.60/2.16 tff(f355,plain,( 13.60/2.16 (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ sK1 @ sK3))) @ (s @ sK1 @ sK2))) = $false) | (mono_2Ec_2Ebool_2ET = $false) | (vNOT @ mono_2Ec_2Ebool_2ET = $true) | (mono_2Ec_2Ebool_2ET != j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0)))) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3))) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2))))) = $false) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2))))) = $true) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3))) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0))) = $true)), 13.60/2.16 inference(binary_proxy_clausification,[],[f354])). 13.60/2.16 tff(f362,plain,( 13.60/2.16 (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ sK1 @ sK3))) @ (s @ sK1 @ sK2))) = $false) | (mono_2Ec_2Ebool_2ET = $false) | (mono_2Ec_2Ebool_2ET = $false) | (mono_2Ec_2Ebool_2ET != j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0)))) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3))) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2))))) = $false) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2))))) = $true) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3))) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0))) = $true)), 13.60/2.16 inference(not_proxy_clausification,[],[f355])). 13.60/2.16 tff(f363,plain,( 13.60/2.16 (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ sK1 @ sK3))) @ (s @ sK1 @ sK2))) = $false) | (mono_2Ec_2Ebool_2ET = $false) | (mono_2Ec_2Ebool_2ET != j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0)))) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3))) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2))))) = $false) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2))))) = $true) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3))) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0))) = $true)), 13.60/2.16 inference(duplicate_literal_removal,[],[f362])). 13.60/2.16 tff(f365,plain,( 13.60/2.16 (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ sK1 @ sK3))) @ (s @ sK1 @ sK2))) = $false) | (mono_2Ec_2Ebool_2ET = $false) | (mono_2Ec_2Ebool_2ET = $false) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3))) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2))))) = $false) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2))))) = $true) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3))) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0))) = $true) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0))) = $false)), 13.60/2.16 inference(binary_proxy_clausification,[],[f363])). 13.60/2.16 tff(f366,plain,( 13.60/2.16 (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ sK1 @ sK3))) @ (s @ sK1 @ sK2))) = $false) | (mono_2Ec_2Ebool_2ET = $false) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3))) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2))))) = $false) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2))))) = $true) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3))) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0))) = $true) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0))) = $false)), 13.60/2.16 inference(duplicate_literal_removal,[],[f365])). 13.60/2.16 tff(f367,plain,( 13.60/2.16 (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ sK1 @ sK3))) @ (s @ sK1 @ sK2))) = $true) | (vNOT @ mono_2Ec_2Ebool_2ET = $true) | (vNOT @ mono_2Ec_2Ebool_2ET != j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3))) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0)))) | (mono_2Ec_2Ebool_2ET != j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0)))) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3))) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2))))) = $true) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2))))) = $true)), 13.60/2.16 inference(binary_proxy_clausification,[],[f337])). 13.60/2.16 tff(f382,plain,( 13.60/2.16 (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ sK1 @ sK3))) @ (s @ sK1 @ sK2))) = $true) | (mono_2Ec_2Ebool_2ET = $false) | (vNOT @ mono_2Ec_2Ebool_2ET != j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3))) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0)))) | (mono_2Ec_2Ebool_2ET != j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0)))) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3))) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2))))) = $true) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2))))) = $true)), 13.60/2.16 inference(not_proxy_clausification,[],[f367])). 13.60/2.16 tff(f383,plain,( 13.60/2.16 (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ sK1 @ sK3))) @ (s @ sK1 @ sK2))) = $true) | (mono_2Ec_2Ebool_2ET = $false) | (vNOT @ mono_2Ec_2Ebool_2ET = $true) | (mono_2Ec_2Ebool_2ET != j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0)))) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3))) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2))))) = $true) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2))))) = $true) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3))) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0))) = $true)), 13.60/2.16 inference(binary_proxy_clausification,[],[f382])). 13.60/2.16 tff(f390,plain,( 13.60/2.16 (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ sK1 @ sK3))) @ (s @ sK1 @ sK2))) = $true) | (mono_2Ec_2Ebool_2ET = $false) | (mono_2Ec_2Ebool_2ET = $false) | (mono_2Ec_2Ebool_2ET != j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0)))) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3))) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2))))) = $true) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2))))) = $true) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3))) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0))) = $true)), 13.60/2.16 inference(not_proxy_clausification,[],[f383])). 13.60/2.16 tff(f391,plain,( 13.60/2.16 (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ sK1 @ sK3))) @ (s @ sK1 @ sK2))) = $true) | (mono_2Ec_2Ebool_2ET = $false) | (mono_2Ec_2Ebool_2ET != j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0)))) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3))) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2))))) = $true) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2))))) = $true) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3))) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0))) = $true)), 13.60/2.16 inference(duplicate_literal_removal,[],[f390])). 13.60/2.16 tff(f393,plain,( 13.60/2.16 (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ sK1 @ sK3))) @ (s @ sK1 @ sK2))) = $true) | (mono_2Ec_2Ebool_2ET = $false) | (mono_2Ec_2Ebool_2ET = $false) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3))) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2))))) = $true) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2))))) = $true) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3))) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0))) = $true) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0))) = $false)), 13.60/2.16 inference(binary_proxy_clausification,[],[f391])). 13.60/2.16 tff(f394,plain,( 13.60/2.16 (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ sK1 @ sK3))) @ (s @ sK1 @ sK2))) = $true) | (mono_2Ec_2Ebool_2ET = $false) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3))) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2))))) = $true) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2))))) = $true) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3))) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0))) = $true) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0))) = $false)), 13.60/2.16 inference(duplicate_literal_removal,[],[f393])). 13.60/2.16 tff(f395,plain,( 13.60/2.16 ($false = $true) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ sK1 @ sK3))) @ (s @ sK1 @ sK2))) = $true) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3))) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2))))) = $true) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2))))) = $true) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3))) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0))) = $true) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0))) = $false)), 13.60/2.16 inference(forward_demodulation,[],[f394,f262])). 13.60/2.16 tff(f396,plain,( 13.60/2.16 (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ sK1 @ sK3))) @ (s @ sK1 @ sK2))) = $true) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3))) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2))))) = $true) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2))))) = $true) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3))) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0))) = $true) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0))) = $false)), 13.60/2.16 inference(trivial_inequality_removal,[],[f395])). 13.60/2.16 tff(f397,plain,( 13.60/2.16 ($false = $true) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ sK1 @ sK3))) @ (s @ sK1 @ sK2))) = $false) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3))) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2))))) = $false) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2))))) = $true) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3))) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0))) = $true) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0))) = $false)), 13.60/2.16 inference(forward_demodulation,[],[f366,f262])). 13.60/2.16 tff(f398,plain,( 13.60/2.16 (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ sK1 @ sK3))) @ (s @ sK1 @ sK2))) = $false) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3))) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2))))) = $false) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2))))) = $true) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3))) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0))) = $true) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0))) = $false)), 13.60/2.16 inference(trivial_inequality_removal,[],[f397])). 13.60/2.16 tff(f403,plain,( 13.60/2.16 spl8_0 <=> (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0))) = $false)), 13.60/2.16 introduced(avatar_definition,[new_symbols(naming,[spl8_0])])). 13.60/2.16 tff(f404,plain,( 13.60/2.16 (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0))) = $false) | ~spl8_0), 13.60/2.16 inference(avatar_component_clause,[],[f403])). 13.60/2.16 tff(f406,plain,( 13.60/2.16 spl8_3 <=> (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3))) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0))) != $true)), 13.60/2.16 introduced(avatar_definition,[new_symbols(naming,[spl8_3])])). 13.60/2.16 tff(f407,plain,( 13.60/2.16 (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3))) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0))) != $true) | ~spl8_3), 13.60/2.16 inference(avatar_component_clause,[],[f406])). 13.60/2.16 tff(f409,plain,( 13.60/2.16 spl8_2 <=> (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3))) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0))) = $true)), 13.60/2.16 introduced(avatar_definition,[new_symbols(naming,[spl8_2])])). 13.60/2.16 tff(f410,plain,( 13.60/2.16 (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3))) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0))) = $true) | ~spl8_2), 13.60/2.16 inference(avatar_component_clause,[],[f409])). 13.60/2.16 tff(f412,plain,( 13.60/2.16 spl8_5 <=> (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2))))) != $true)), 13.60/2.16 introduced(avatar_definition,[new_symbols(naming,[spl8_5])])). 13.60/2.16 tff(f413,plain,( 13.60/2.16 (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2))))) != $true) | ~spl8_5), 13.60/2.16 inference(avatar_component_clause,[],[f412])). 13.60/2.16 tff(f415,plain,( 13.60/2.16 spl8_4 <=> (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2))))) = $true)), 13.60/2.16 introduced(avatar_definition,[new_symbols(naming,[spl8_4])])). 13.60/2.16 tff(f416,plain,( 13.60/2.16 (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2))))) = $true) | ~spl8_4), 13.60/2.16 inference(avatar_component_clause,[],[f415])). 13.60/2.16 tff(f421,plain,( 13.60/2.16 spl8_6 <=> (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3))) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2))))) = $true)), 13.60/2.16 introduced(avatar_definition,[new_symbols(naming,[spl8_6])])). 13.60/2.16 tff(f422,plain,( 13.60/2.16 (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3))) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2))))) = $true) | ~spl8_6), 13.60/2.16 inference(avatar_component_clause,[],[f421])). 13.60/2.16 tff(f427,plain,( 13.60/2.16 spl8_8 <=> (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ sK1 @ sK3))) @ (s @ sK1 @ sK2))) = $true)), 13.60/2.16 introduced(avatar_definition,[new_symbols(naming,[spl8_8])])). 13.60/2.16 tff(f428,plain,( 13.60/2.16 (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ sK1 @ sK3))) @ (s @ sK1 @ sK2))) = $true) | ~spl8_8), 13.60/2.16 inference(avatar_component_clause,[],[f427])). 13.60/2.16 tff(f429,plain,( 13.60/2.16 spl8_0 | spl8_2 | spl8_4 | spl8_6 | spl8_8), 13.60/2.16 inference(avatar_split_clause,[],[f396,f427,f421,f415,f409,f403])). 13.60/2.16 tff(f433,plain,( 13.60/2.16 ($true != $true) | (sP0 @ sK4 @ sK1 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3)) @ sK1 @ c_2Eoption_2ENONE_2E0 = $true) | ~spl8_2), 13.60/2.16 inference(superposition,[],[f140,f410])). 13.60/2.16 tff(f434,plain,( 13.60/2.16 (sP0 @ sK4 @ sK1 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3)) @ sK1 @ c_2Eoption_2ENONE_2E0 = $true) | ~spl8_2), 13.60/2.16 inference(trivial_inequality_removal,[],[f433])). 13.60/2.16 tff(f442,plain,( 13.60/2.16 ($true != $true) | s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0 = s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ (sK7 @ sK4 @ sK1 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3)) @ sK1 @ c_2Eoption_2ENONE_2E0))) | s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0 = s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3)) | ~spl8_2), 13.60/2.16 inference(superposition,[],[f134,f434])). 13.60/2.16 tff(f446,plain,( 13.60/2.16 s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0 = s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ (sK7 @ sK4 @ sK1 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3)) @ sK1 @ c_2Eoption_2ENONE_2E0))) | s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0 = s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3)) | ~spl8_2), 13.60/2.16 inference(trivial_inequality_removal,[],[f442])). 13.60/2.16 tff(f453,plain,( 13.60/2.16 s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0 = s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3)) | ~spl8_2), 13.60/2.16 inference(subsumption_resolution,[],[f446,f335])). 13.60/2.16 tff(f454,plain,( 13.60/2.16 $false | ~spl8_2), 13.60/2.16 inference(subsumption_resolution,[],[f453,f335])). 13.60/2.16 tff(f455,plain,( 13.60/2.16 ~spl8_2), 13.60/2.16 inference(avatar_contradiction_clause,[],[f454])). 13.60/2.16 tff(f717,plain,( 13.60/2.16 ($true != $true) | (sP0 @ sK4 @ sK1 @ c_2Eoption_2ENONE_2E0 @ sK1 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2)) = $true) | ~spl8_4), 13.60/2.16 inference(superposition,[],[f140,f416])). 13.60/2.16 tff(f718,plain,( 13.60/2.16 (sP0 @ sK4 @ sK1 @ c_2Eoption_2ENONE_2E0 @ sK1 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2)) = $true) | ~spl8_4), 13.60/2.16 inference(trivial_inequality_removal,[],[f717])). 13.60/2.16 tff(f880,plain,( 13.60/2.16 ($true != $true) | s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0 = s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ (sK6 @ sK4 @ sK1 @ c_2Eoption_2ENONE_2E0 @ sK1 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2))))) | s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0 = s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2)) | ~spl8_4), 13.60/2.16 inference(superposition,[],[f135,f718])). 13.60/2.16 tff(f885,plain,( 13.60/2.16 s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0 = s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ (sK6 @ sK4 @ sK1 @ c_2Eoption_2ENONE_2E0 @ sK1 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2))))) | s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0 = s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2)) | ~spl8_4), 13.60/2.16 inference(trivial_inequality_removal,[],[f880])). 13.60/2.16 tff(f888,plain,( 13.60/2.16 s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0 = s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2)) | ~spl8_4), 13.60/2.16 inference(subsumption_resolution,[],[f885,f335])). 13.60/2.16 tff(f889,plain,( 13.60/2.16 $false | ~spl8_4), 13.60/2.16 inference(subsumption_resolution,[],[f888,f335])). 13.60/2.16 tff(f890,plain,( 13.60/2.16 ~spl8_4), 13.60/2.16 inference(avatar_contradiction_clause,[],[f889])). 13.60/2.16 tff(f893,plain,( 13.60/2.16 (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ sK1 @ sK3))) @ (s @ sK1 @ sK2))) = $false) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3))) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2))))) = $false) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2))))) = $true) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0))) = $false) | ~spl8_3), 13.60/2.16 inference(subsumption_resolution,[],[f398,f407])). 13.60/2.16 tff(f1079,plain,( 13.60/2.16 ($true != $true) | (sP0 @ sK4 @ sK1 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3)) @ sK1 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2)) = $true) | ~spl8_6), 13.60/2.16 inference(superposition,[],[f140,f422])). 13.60/2.16 tff(f1080,plain,( 13.60/2.16 (sP0 @ sK4 @ sK1 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3)) @ sK1 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2)) = $true) | ~spl8_6), 13.60/2.16 inference(trivial_inequality_removal,[],[f1079])). 13.60/2.16 tff(f1083,plain,( 13.60/2.16 (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ sK1 @ sK3))) @ (s @ sK1 @ sK2))) = $false) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3))) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2))))) = $false) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0))) = $false) | (~spl8_3 | ~spl8_5)), 13.60/2.16 inference(subsumption_resolution,[],[f893,f413])). 13.60/2.16 tff(f1088,plain,( 13.60/2.16 spl8_14 <=> (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3))) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2))))) = $false)), 13.60/2.16 introduced(avatar_definition,[new_symbols(naming,[spl8_14])])). 13.60/2.16 tff(f1089,plain,( 13.60/2.16 (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (c_2Eoption_2EOPTREL_2E3 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3))) @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2))))) = $false) | ~spl8_14), 13.60/2.16 inference(avatar_component_clause,[],[f1088])). 13.60/2.16 tff(f1094,plain,( 13.60/2.16 spl8_16 <=> (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ sK1 @ sK3))) @ (s @ sK1 @ sK2))) = $false)), 13.60/2.16 introduced(avatar_definition,[new_symbols(naming,[spl8_16])])). 13.60/2.16 tff(f1095,plain,( 13.60/2.16 (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ sK1 @ sK3))) @ (s @ sK1 @ sK2))) = $false) | ~spl8_16), 13.60/2.16 inference(avatar_component_clause,[],[f1094])). 13.60/2.16 tff(f1096,plain,( 13.60/2.16 spl8_0 | spl8_14 | spl8_16 | spl8_3 | spl8_5), 13.60/2.16 inference(avatar_split_clause,[],[f1083,f412,f406,f1094,f1088,f403])). 13.60/2.16 tff(f1158,plain,( 13.60/2.16 ($true != $true) | s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3)) = s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ (sK6 @ sK4 @ sK1 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3)) @ sK1 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2))))) | s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0 = s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3)) | ~spl8_6), 13.60/2.16 inference(superposition,[],[f132,f1080])). 13.60/2.16 tff(f1159,plain,( 13.60/2.16 ($true != $true) | (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ sK1 @ (sK6 @ sK4 @ sK1 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3)) @ sK1 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2)))))) @ (s @ sK1 @ (sK7 @ sK4 @ sK1 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3)) @ sK1 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2)))))) = $true) | s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0 = s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3)) | ~spl8_6), 13.60/2.16 inference(superposition,[],[f133,f1080])). 13.60/2.16 tff(f1160,plain,( 13.60/2.16 ($true != $true) | s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2)) = s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ (sK7 @ sK4 @ sK1 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3)) @ sK1 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2))))) | s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0 = s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3)) | ~spl8_6), 13.60/2.16 inference(superposition,[],[f134,f1080])). 13.60/2.16 tff(f1167,plain,( 13.60/2.16 s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2)) = s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ (sK7 @ sK4 @ sK1 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3)) @ sK1 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2))))) | s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0 = s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3)) | ~spl8_6), 13.60/2.16 inference(trivial_inequality_removal,[],[f1160])). 13.60/2.16 tff(f1168,plain,( 13.60/2.16 (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ sK1 @ (sK6 @ sK4 @ sK1 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3)) @ sK1 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2)))))) @ (s @ sK1 @ (sK7 @ sK4 @ sK1 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3)) @ sK1 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2)))))) = $true) | s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0 = s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3)) | ~spl8_6), 13.60/2.16 inference(trivial_inequality_removal,[],[f1159])). 13.60/2.16 tff(f1169,plain,( 13.60/2.16 s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3)) = s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ (sK6 @ sK4 @ sK1 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3)) @ sK1 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2))))) | s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0 = s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3)) | ~spl8_6), 13.60/2.16 inference(trivial_inequality_removal,[],[f1158])). 13.60/2.16 tff(f1172,plain,( 13.60/2.16 s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3)) = s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ (sK6 @ sK4 @ sK1 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3)) @ sK1 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2))))) | ~spl8_6), 13.60/2.16 inference(subsumption_resolution,[],[f1169,f335])). 13.60/2.16 tff(f1173,plain,( 13.60/2.16 (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ sK1 @ (sK6 @ sK4 @ sK1 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3)) @ sK1 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2)))))) @ (s @ sK1 @ (sK7 @ sK4 @ sK1 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3)) @ sK1 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2)))))) = $true) | ~spl8_6), 13.60/2.16 inference(subsumption_resolution,[],[f1168,f335])). 13.60/2.16 tff(f1174,plain,( 13.60/2.16 s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2)) = s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ (sK7 @ sK4 @ sK1 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3)) @ sK1 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2))))) | ~spl8_6), 13.60/2.16 inference(subsumption_resolution,[],[f1167,f335])). 13.60/2.16 tff(f1196,plain,( 13.60/2.16 ($false = $true) | (sP0 @ sK4 @ sK1 @ c_2Eoption_2ENONE_2E0 @ sK1 @ c_2Eoption_2ENONE_2E0 != $true) | ~spl8_0), 13.60/2.16 inference(superposition,[],[f141,f404])). 13.60/2.16 tff(f1197,plain,( 13.60/2.16 (sP0 @ sK4 @ sK1 @ c_2Eoption_2ENONE_2E0 @ sK1 @ c_2Eoption_2ENONE_2E0 != $true) | ~spl8_0), 13.60/2.16 inference(trivial_inequality_removal,[],[f1196])). 13.60/2.16 tff(f1236,plain,( 13.60/2.16 ($true != $true) | s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0 != s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0 | s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0 != s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0 | ~spl8_0), 13.60/2.16 inference(superposition,[],[f1197,f139])). 13.60/2.16 tff(f1237,plain,( 13.60/2.16 ($true != $true) | s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0 != s @ (tyop_2Eoption_2Eoption @ sK1) @ c_2Eoption_2ENONE_2E0 | ~spl8_0), 13.60/2.16 inference(duplicate_literal_removal,[],[f1236])). 13.60/2.16 tff(f1238,plain,( 13.60/2.16 $false | ~spl8_0), 13.60/2.16 inference(trivial_inequality_removal,[],[f1237])). 13.60/2.16 tff(f1239,plain,( 13.60/2.16 ~spl8_0), 13.60/2.16 inference(avatar_contradiction_clause,[],[f1238])). 13.60/2.16 tff(f1346,plain,( 13.60/2.16 ($false = $true) | (sP0 @ sK4 @ sK1 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3)) @ sK1 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2)) != $true) | ~spl8_14), 13.60/2.16 inference(superposition,[],[f141,f1089])). 13.60/2.16 tff(f1347,plain,( 13.60/2.16 (sP0 @ sK4 @ sK1 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3)) @ sK1 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2)) != $true) | ~spl8_14), 13.60/2.16 inference(trivial_inequality_removal,[],[f1346])). 13.60/2.16 tff(f1373,plain,( 13.60/2.16 $false | (~spl8_6 | ~spl8_14)), 13.60/2.16 inference(subsumption_resolution,[],[f1347,f1080])). 13.60/2.16 tff(f1374,plain,( 13.60/2.16 ~spl8_6 | ~spl8_14), 13.60/2.16 inference(avatar_contradiction_clause,[],[f1373])). 13.60/2.16 tff(f2860,plain,( 13.60/2.16 s @ sK1 @ (c_2Eoption_2ETHE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3)))) = s @ sK1 @ (sK6 @ sK4 @ sK1 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3)) @ sK1 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2))) | ~spl8_6), 13.60/2.16 inference(superposition,[],[f204,f1172])). 13.60/2.16 tff(f2941,plain,( 13.60/2.16 s @ sK1 @ sK3 = s @ sK1 @ (sK6 @ sK4 @ sK1 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3)) @ sK1 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2))) | ~spl8_6), 13.60/2.16 inference(forward_demodulation,[],[f2860,f204])). 13.60/2.16 tff(f3157,plain,( 13.60/2.16 s @ sK1 @ (c_2Eoption_2ETHE_2E1 @ (s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2)))) = s @ sK1 @ (sK7 @ sK4 @ sK1 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3)) @ sK1 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2))) | ~spl8_6), 13.60/2.16 inference(superposition,[],[f204,f1174])). 13.60/2.16 tff(f3240,plain,( 13.60/2.16 s @ sK1 @ sK2 = s @ sK1 @ (sK7 @ sK4 @ sK1 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3)) @ sK1 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2))) | ~spl8_6), 13.60/2.16 inference(forward_demodulation,[],[f3157,f204])). 13.60/2.16 tff(f3644,plain,( 13.60/2.16 (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ sK1 @ sK3))) @ (s @ sK1 @ (sK7 @ sK4 @ sK1 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3)) @ sK1 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2)))))) = $true) | ~spl8_6), 13.60/2.16 inference(forward_demodulation,[],[f1173,f2941])). 13.60/2.16 tff(f3645,plain,( 13.60/2.16 (j_mono_2Etyop_2Emin_2Ebool @ (s @ tyop_2Emin_2Ebool @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool) @ (app_2E2 @ (s @ (tyop_2Emin_2Efun @ sK1 @ (tyop_2Emin_2Efun @ sK1 @ tyop_2Emin_2Ebool)) @ sK4) @ (s @ sK1 @ sK3))) @ (s @ sK1 @ sK2))) = $true) | ~spl8_6), 13.60/2.16 inference(forward_demodulation,[],[f3644,f3240])). 13.60/2.16 tff(f3646,plain,( 13.60/2.16 ($false = $true) | (~spl8_6 | ~spl8_16)), 13.60/2.16 inference(forward_demodulation,[],[f3645,f1095])). 13.60/2.16 tff(f3647,plain,( 13.60/2.16 $false | (~spl8_6 | ~spl8_16)), 13.60/2.16 inference(trivial_inequality_removal,[],[f3646])). 13.60/2.16 tff(f3648,plain,( 13.60/2.16 ~spl8_6 | ~spl8_16), 13.60/2.16 inference(avatar_contradiction_clause,[],[f3647])). 13.60/2.16 tff(f3649,plain,( 13.60/2.16 ($false = $true) | (~spl8_8 | ~spl8_16)), 13.60/2.16 inference(forward_demodulation,[],[f428,f1095])). 13.60/2.16 tff(f3650,plain,( 13.60/2.16 $false | (~spl8_8 | ~spl8_16)), 13.60/2.16 inference(trivial_inequality_removal,[],[f3649])). 13.60/2.16 tff(f3651,plain,( 13.60/2.16 ~spl8_8 | ~spl8_16), 13.60/2.16 inference(avatar_contradiction_clause,[],[f3650])). 13.60/2.16 tff(f3686,plain,( 13.60/2.16 ($true != $true) | (sP0 @ sK4 @ sK1 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3)) @ sK1 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2)) = $false) | ~spl8_14), 13.60/2.16 inference(fool_paramodulation,[],[f1347])). 13.60/2.16 tff(f3725,plain,( 13.60/2.16 (sP0 @ sK4 @ sK1 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3)) @ sK1 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2)) = $false) | ~spl8_14), 13.60/2.16 inference(trivial_inequality_removal,[],[f3686])). 13.60/2.16 tff(f3733,plain,( 13.60/2.16 ( ! [X0:u,X1:u] : (($true != $true) | s @ (tyop_2Eoption_2Eoption @ sK1) @ X0 != s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2)) | (sP0 @ sK4 @ sK1 @ X1 @ sK1 @ X0 = $true) | s @ (tyop_2Eoption_2Eoption @ sK1) @ X1 != s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3))) ) | ~spl8_8), 13.60/2.16 inference(superposition,[],[f138,f428])). 13.60/2.16 tff(f3734,plain,( 13.60/2.16 ( ! [X0:u,X1:u] : (s @ (tyop_2Eoption_2Eoption @ sK1) @ X1 != s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3)) | (sP0 @ sK4 @ sK1 @ X1 @ sK1 @ X0 = $true) | s @ (tyop_2Eoption_2Eoption @ sK1) @ X0 != s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2))) ) | ~spl8_8), 13.60/2.16 inference(trivial_inequality_removal,[],[f3733])). 13.60/2.16 tff(f4408,plain,( 13.60/2.16 ( ! [X0:u] : (s @ (tyop_2Eoption_2Eoption @ sK1) @ X0 != s @ (tyop_2Eoption_2Eoption @ sK1) @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2)) | (sP0 @ sK4 @ sK1 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3)) @ sK1 @ X0 = $true)) ) | ~spl8_8), 13.60/2.16 inference(equality_resolution,[],[f3734])). 13.60/2.16 tff(f4431,plain,( 13.60/2.16 (sP0 @ sK4 @ sK1 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK3)) @ sK1 @ (c_2Eoption_2ESOME_2E1 @ (s @ sK1 @ sK2)) = $true) | ~spl8_8), 13.60/2.16 inference(equality_resolution,[],[f4408])). 13.60/2.16 tff(f4432,plain,( 13.60/2.16 ($false = $true) | (~spl8_8 | ~spl8_14)), 13.60/2.16 inference(forward_demodulation,[],[f4431,f3725])). 13.60/2.16 tff(f4433,plain,( 13.60/2.16 $false | (~spl8_8 | ~spl8_14)), 13.60/2.16 inference(trivial_inequality_removal,[],[f4432])). 13.60/2.16 tff(f4434,plain,( 13.60/2.16 ~spl8_8 | ~spl8_14), 13.60/2.16 inference(avatar_contradiction_clause,[],[f4433])). 13.60/2.16 tff(f4435,plain,( 13.60/2.16 $false), 13.60/2.16 inference(avatar_sat_refutation,[],[f429,f455,f890,f1096,f1239,f1374,f3648,f3651,f4434])). 13.60/2.16 % SZS output end Proof for theBenchmark 13.60/2.16 % (22655)------------------------------ 13.60/2.16 % (22655)Version: Vampire 4.5.0 (commit 7ae30c7f on 2020-06-30 15:57:20 +0100) 13.60/2.16 % (22655)Termination reason: Refutation 13.60/2.16 13.60/2.16 % (22655)Memory used [KB]: 16502 13.60/2.16 % (22655)Time elapsed: 1.768 s 13.60/2.16 % (22655)------------------------------ 13.60/2.16 % (22655)------------------------------ 14.27/2.18 % (22625)Success in time 1.853 s 14.27/2.19 EOF