0.07/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.13 % Command : run_vampire %s %d 0.13/0.34 % Computer : n026.cluster.edu 0.13/0.34 % Model : x86_64 x86_64 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.34 % Memory : 8042.1875MB 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.34 % CPULimit : 960 0.13/0.34 % WCLimit : 120 0.13/0.34 % DateTime : Thu Jul 2 08:02:39 EDT 2020 0.13/0.35 % CPUTime : 0.13/0.39 % (32616)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 0.13/0.40 % (32619)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 0.13/0.40 % (32614)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 0.13/0.40 % (32617)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 0.13/0.40 % (32618)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 0.13/0.40 % (32615)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 0.13/0.41 % (32636)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 0.20/0.41 % (32628)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 0.20/0.41 % (32632)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 0.20/0.41 % (32626)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 0.20/0.42 % (32624)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 0.20/0.42 % (32637)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 0.20/0.42 % (32635)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 0.20/0.42 % (32621)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 0.20/0.42 % (32641)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 0.20/0.42 % (32620)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 0.20/0.42 % (32642)dis+1002_4_add=large:csup=on:inj=on:chr=on:foolp=on:cnfonf=eager:afp=40000:afq=1.0:anc=none:cond=fast:fde=none:gs=on:gsaa=full_model:lma=on:lwlo=on:nm=0:nwc=1.5:sp=reverse_arity:tha=off_300 on theBenchmark 0.20/0.42 % (32622)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 0.20/0.43 % (32640)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 0.20/0.43 % (32634)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 0.20/0.43 % (32643)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 0.20/0.43 % (32630)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 0.20/0.43 % (32629)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 0.20/0.43 % (32639)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 0.20/0.43 % (32631)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 0.20/0.44 % (32627)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 0.20/0.44 % (32638)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 0.20/0.44 % (32625)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 0.20/0.44 % (32633)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 0.20/0.44 % (32623)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 0.20/0.57 % (32637)Refutation not found, incomplete strategy 0.20/0.57 % (32637)------------------------------ 0.20/0.57 % (32637)Version: Vampire 4.5.0 (commit 7ae30c7f on 2020-06-30 15:57:20 +0100) 0.20/0.57 % (32637)Termination reason: Refutation not found, incomplete strategy 0.20/0.57 0.20/0.57 % (32637)Memory used [KB]: 12537 0.20/0.57 % (32637)Time elapsed: 0.184 s 0.20/0.57 % (32637)------------------------------ 0.20/0.57 % (32637)------------------------------ 0.20/0.58 % (32626)Refutation found. Thanks to Tanya! 0.20/0.58 % SZS status Theorem for theBenchmark 0.20/0.58 % SZS output start Proof for theBenchmark 0.20/0.58 tff(func_def_0, type, mu: '$tType'). 0.20/0.58 tff(func_def_4, type, ->: ('$tType' * '$tType') > '$tType'). 0.20/0.58 tff(func_def_5, type, qmltpeq: mu -> mu -> '$i' -> '$o'). 0.20/0.58 tff(func_def_6, type, meq_prop: ('$i' -> '$o') -> ('$i' -> '$o') -> '$i' -> '$o'). 0.20/0.58 tff(func_def_7, type, vAPP: !>[X0: $ttype, X1: $ttype]:(X0 -> X1 * X0) > X1). 0.20/0.58 tff(func_def_8, type, mnot: ('$i' -> '$o') -> '$i' -> '$o'). 0.20/0.58 tff(func_def_9, type, mor: ('$i' -> '$o') -> ('$i' -> '$o') -> '$i' -> '$o'). 0.20/0.58 tff(func_def_10, type, mbox: ('$i' -> '$i' -> '$o') -> ('$i' -> '$o') -> '$i' -> '$o'). 0.20/0.58 tff(func_def_11, type, mforall_prop: (('$i' -> '$o') -> '$i' -> '$o') -> '$i' -> '$o'). 0.20/0.58 tff(func_def_12, type, mtrue: '$i' -> '$o'). 0.20/0.58 tff(func_def_13, type, mfalse: '$i' -> '$o'). 0.20/0.58 tff(func_def_14, type, mand: ('$i' -> '$o') -> ('$i' -> '$o') -> '$i' -> '$o'). 0.20/0.58 tff(func_def_15, type, mimplies: ('$i' -> '$o') -> ('$i' -> '$o') -> '$i' -> '$o'). 0.20/0.58 tff(func_def_16, type, mimplied: ('$i' -> '$o') -> ('$i' -> '$o') -> '$i' -> '$o'). 0.20/0.58 tff(func_def_17, type, mequiv: ('$i' -> '$o') -> ('$i' -> '$o') -> '$i' -> '$o'). 0.20/0.58 tff(func_def_18, type, mxor: ('$i' -> '$o') -> ('$i' -> '$o') -> '$i' -> '$o'). 0.20/0.58 tff(func_def_19, type, mdia: ('$i' -> '$i' -> '$o') -> ('$i' -> '$o') -> '$i' -> '$o'). 0.20/0.58 tff(func_def_20, type, exists_in_world: mu -> '$i' -> '$o'). 0.20/0.58 tff(func_def_21, type, mforall_ind: (mu -> '$i' -> '$o') -> '$i' -> '$o'). 0.20/0.58 tff(func_def_22, type, mexists_ind: (mu -> '$i' -> '$o') -> '$i' -> '$o'). 0.20/0.58 tff(func_def_23, type, mexists_prop: (('$i' -> '$o') -> '$i' -> '$o') -> '$i' -> '$o'). 0.20/0.58 tff(func_def_24, type, mreflexive: ('$i' -> '$i' -> '$o') -> '$o'). 0.20/0.58 tff(func_def_25, type, msymmetric: ('$i' -> '$i' -> '$o') -> '$o'). 0.20/0.58 tff(func_def_26, type, mserial: ('$i' -> '$i' -> '$o') -> '$o'). 0.20/0.58 tff(func_def_27, type, mtransitive: ('$i' -> '$i' -> '$o') -> '$o'). 0.20/0.58 tff(func_def_28, type, meuclidean: ('$i' -> '$i' -> '$o') -> '$o'). 0.20/0.58 tff(func_def_29, type, mpartially_functional: ('$i' -> '$i' -> '$o') -> '$o'). 0.20/0.58 tff(func_def_30, type, mfunctional: ('$i' -> '$i' -> '$o') -> '$o'). 0.20/0.58 tff(func_def_31, type, mweakly_dense: ('$i' -> '$i' -> '$o') -> '$o'). 0.20/0.58 tff(func_def_32, type, mweakly_connected: ('$i' -> '$i' -> '$o') -> '$o'). 0.20/0.58 tff(func_def_33, type, mweakly_directed: ('$i' -> '$i' -> '$o') -> '$o'). 0.20/0.58 tff(func_def_34, type, mvalid: ('$i' -> '$o') -> '$o'). 0.20/0.58 tff(func_def_35, type, msatisfiable: ('$i' -> '$o') -> '$o'). 0.20/0.58 tff(func_def_36, type, mcountersatisfiable: ('$i' -> '$o') -> '$o'). 0.20/0.58 tff(func_def_37, type, minvalid: ('$i' -> '$o') -> '$o'). 0.20/0.58 tff(func_def_38, type, rel_s4: '$i' -> '$i' -> '$o'). 0.20/0.58 tff(func_def_39, type, mbox_s4: ('$i' -> '$o') -> '$i' -> '$o'). 0.20/0.58 tff(func_def_40, type, mdia_s4: ('$i' -> '$o') -> '$i' -> '$o'). 0.20/0.58 tff(func_def_41, type, closed: mu -> '$i' -> '$o'). 0.20/0.58 tff(func_def_42, type, open: mu -> '$i' -> '$o'). 0.20/0.58 tff(func_def_43, type, h: mu -> '$i' -> '$o'). 0.20/0.58 tff(func_def_44, type, combo: mu -> mu -> '$i' -> '$o'). 0.20/0.58 tff(func_def_45, type, o: mu). 0.20/0.58 tff(func_def_46, type, n: mu). 0.20/0.58 tff(func_def_47, type, d: mu). 0.20/0.58 tff(func_def_48, type, vEPSILON: !>[X0: $ttype]:(X0 -> '$o') -> X0). 0.20/0.58 tff(func_def_49, type, bCOMB: !>[X0: $ttype, X1: $ttype, X2: $ttype]:(X1 -> X2) -> (X0 -> X1) -> X0 -> X2). 0.20/0.58 tff(func_def_50, type, cCOMB: !>[X0: $ttype, X1: $ttype, X2: $ttype]:(X0 -> X1 -> X2) -> X1 -> X0 -> X2). 0.20/0.58 tff(func_def_53, type, vNOT: '$o' -> '$o'). 0.20/0.58 tff(func_def_54, type, vPI: !>[X0: $ttype]:(X0 -> '$o') -> '$o'). 0.20/0.58 tff(func_def_55, type, vAND: '$o' -> '$o' -> '$o'). 0.20/0.58 tff(func_def_56, type, vIMP: '$o' -> '$o' -> '$o'). 0.20/0.58 tff(func_def_57, type, vEQ: !>[X0: $ttype]:X0 -> X0 -> '$o'). 0.20/0.58 tff(func_def_58, type, sCOMB: !>[X0: $ttype, X1: $ttype, X2: $ttype]:(X0 -> X1 -> X2) -> (X0 -> X1) -> X0 -> X2). 0.20/0.58 tff(func_def_59, type, vSIGMA: !>[X0: $ttype]:(X0 -> '$o') -> '$o'). 0.20/0.58 tff(func_def_60, type, iCOMB: !>[X2: $ttype]:X2 -> X2). 0.20/0.58 tff(func_def_61, type, vOR: '$o' -> '$o' -> '$o'). 0.20/0.58 tff(func_def_62, type, kCOMB: !>[X1: $ttype, X2: $ttype]:X1 -> X2 -> X1). 0.20/0.58 tff(func_def_63, type, sK0: '$i' -> mu). 0.20/0.58 tff(func_def_65, type, sK2: '$i' -> mu). 0.20/0.58 tff(func_def_66, type, sK3: mu -> mu -> '$i' -> mu). 0.20/0.58 tff(f2,axiom,( 0.20/0.58 mnot = (^[X3 : '$i' -> '$o', X2 : '$i'] : ~X3 @ X2)), 0.20/0.58 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot)). 0.20/0.58 tff(f3,axiom,( 0.20/0.58 mor = (^[X3 : '$i' -> '$o', X4 : '$i' -> '$o', X2 : '$i'] : X4 @ X2 | X3 @ X2)), 0.20/0.58 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor)). 0.20/0.58 tff(f8,axiom,( 0.20/0.58 mand = (^[X3 : '$i' -> '$o', X4 : '$i' -> '$o'] : mnot @ (mor @ (mnot @ X3) @ (mnot @ X4)))), 0.20/0.58 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mand)). 0.20/0.59 tff(f9,axiom,( 0.20/0.59 mimplies = (^[X3 : '$i' -> '$o', X4 : '$i' -> '$o'] : mor @ (mnot @ X3) @ X4)), 0.20/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies)). 0.20/0.59 tff(f14,axiom,( 0.20/0.59 mforall_ind = (^[X3 : mu -> '$i' -> '$o', X2 : '$i'] : ! [X0 : mu] : (exists_in_world @ X0 @ X2 => X3 @ X0 @ X2))), 0.20/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_ind)). 0.20/0.59 tff(f15,axiom,( 0.20/0.59 mexists_ind = (^[X3 : mu -> '$i' -> '$o'] : mnot @ (mforall_ind @ (^[X0 : mu] : mnot @ (X3 @ X0))))), 0.20/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mexists_ind)). 0.20/0.59 tff(f17,axiom,( 0.20/0.59 mreflexive = (^[X5 : '$i' -> '$i' -> '$o'] : ! [X8] : X5 @ X8 @ X8)), 0.20/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mreflexive)). 0.20/0.59 tff(f27,axiom,( 0.20/0.59 mvalid = (^[X3 : '$i' -> '$o'] : ! [X2] : X3 @ X2)), 0.20/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mvalid)). 0.20/0.59 tff(f32,axiom,( 0.20/0.59 mbox_s4 = (^[X3 : '$i' -> '$o', X2 : '$i'] : ! [X6] : (X3 @ X6 | ~rel_s4 @ X2 @ X6))), 0.20/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_s4)). 0.20/0.59 tff(f35,axiom,( 0.20/0.59 mreflexive @ rel_s4), 0.20/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a1)). 0.20/0.59 tff(f37,conjecture,( 0.20/0.59 mvalid @ (mbox_s4 @ (mexists_ind @ (^[X6 : mu] : mexists_ind @ (^[X11 : mu] : mimplies @ (mbox_s4 @ (mand @ (combo @ d @ X6) @ (h @ X11))) @ (mbox_s4 @ (open @ d))))))), 0.20/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con)). 0.20/0.59 tff(f38,negated_conjecture,( 0.20/0.59 ~mvalid @ (mbox_s4 @ (mexists_ind @ (^[X6 : mu] : mexists_ind @ (^[X11 : mu] : mimplies @ (mbox_s4 @ (mand @ (combo @ d @ X6) @ (h @ X11))) @ (mbox_s4 @ (open @ d))))))), 0.20/0.59 inference(negated_conjecture,[],[f37])). 0.20/0.59 tff(f40,axiom,( 0.20/0.59 ! [X6] : exists_in_world @ d @ X6), 0.20/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_d_ax)). 0.20/0.59 tff(f41,axiom,( 0.20/0.59 ! [X6] : exists_in_world @ n @ X6), 0.20/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_n_ax)). 0.20/0.59 tff(f42,axiom,( 0.20/0.59 mvalid @ (mbox_s4 @ (mforall_ind @ (^[X8 : mu] : mforall_ind @ (^[X6 : mu] : mexists_ind @ (^[X11 : mu] : mand @ (mbox_s4 @ (mimplies @ (mand @ (closed @ X8) @ (mand @ (combo @ X8 @ X6) @ (h @ X11))) @ (mbox_s4 @ (open @ X8)))) @ (mbox_s4 @ (mimplies @ (mand @ (closed @ X8) @ (mand @ (mnot @ (combo @ X8 @ X6)) @ (h @ o))) @ (mbox_s4 @ (closed @ X8)))))))))), 0.20/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1)). 0.20/0.59 tff(f44,axiom,( 0.20/0.59 mvalid @ (mbox_s4 @ (closed @ d))), 0.20/0.59 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2)). 0.20/0.59 tff(f47,plain,( 0.20/0.59 ~mvalid @ (mbox_s4 @ (mexists_ind @ (^[X0 : mu] : mexists_ind @ (^[X1 : mu] : mimplies @ (mbox_s4 @ (mand @ (combo @ d @ X0) @ (h @ X1))) @ (mbox_s4 @ (open @ d))))))), 0.20/0.59 inference(rectify,[],[f38])). 0.20/0.59 tff(f48,plain,( 0.20/0.59 ~(mvalid @ (mbox_s4 @ (mexists_ind @ (bCOMB @ mexists_ind @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ mimplies) @ (bCOMB @ (bCOMB @ mbox_s4) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ mand @ (combo @ d))) @ h)))) @ (mbox_s4 @ (open @ d)))))) = $true)), 0.20/0.59 inference(fool_elimination,[],[f47])). 0.20/0.59 tff(f82,plain,( 0.20/0.59 mreflexive = (^[X0 : '$i' -> '$i' -> '$o'] : ! [X1] : X0 @ X1 @ X1)), 0.20/0.59 inference(rectify,[],[f17])). 0.20/0.59 tff(f83,plain,( 0.20/0.59 bCOMB @ vPI('$i') @ (cCOMB @ sCOMB @ iCOMB) = mreflexive), 0.20/0.59 inference(fool_elimination,[],[f82])). 0.20/0.59 tff(f94,plain,( 0.20/0.59 mor = (^[X0 : '$i' -> '$o', X1 : '$i' -> '$o', X2 : '$i'] : X1 @ X2 | X0 @ X2)), 0.20/0.59 inference(rectify,[],[f3])). 0.20/0.59 tff(f95,plain,( 0.20/0.59 bCOMB @ sCOMB @ (bCOMB @ vOR) = mor), 0.20/0.59 inference(fool_elimination,[],[f94])). 0.20/0.59 tff(f96,plain,( 0.20/0.59 mvalid = (^[X0 : '$i' -> '$o'] : ! [X1] : X0 @ X1)), 0.20/0.59 inference(rectify,[],[f27])). 0.20/0.59 tff(f97,plain,( 0.20/0.59 mvalid = vPI('$i')), 0.20/0.59 inference(fool_elimination,[],[f96])). 0.20/0.59 tff(f98,plain,( 0.20/0.59 mexists_ind = (^[X0 : mu -> '$i' -> '$o'] : mnot @ (mforall_ind @ (^[X1 : mu] : mnot @ (X0 @ X1))))), 0.20/0.59 inference(rectify,[],[f15])). 0.20/0.59 tff(f99,plain,( 0.20/0.59 bCOMB @ mnot @ (bCOMB @ mforall_ind @ (bCOMB @ mnot)) = mexists_ind), 0.20/0.59 inference(fool_elimination,[],[f98])). 0.20/0.59 tff(f100,plain,( 0.20/0.59 mimplies = (^[X0 : '$i' -> '$o', X1 : '$i' -> '$o'] : mor @ (mnot @ X0) @ X1)), 0.20/0.59 inference(rectify,[],[f9])). 0.20/0.59 tff(f101,plain,( 0.20/0.59 bCOMB @ mor @ mnot = mimplies), 0.20/0.59 inference(fool_elimination,[],[f100])). 0.20/0.59 tff(f102,plain,( 0.20/0.59 mforall_ind = (^[X0 : mu -> '$i' -> '$o', X1 : '$i'] : ! [X2 : mu] : (exists_in_world @ X2 @ X1 => X0 @ X2 @ X1))), 0.20/0.59 inference(rectify,[],[f14])). 0.20/0.59 tff(f103,plain,( 0.20/0.59 bCOMB @ (bCOMB @ vPI(mu)) @ (bCOMB @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ exists_in_world)))) @ cCOMB) = mforall_ind), 0.20/0.59 inference(fool_elimination,[],[f102])). 0.20/0.59 tff(f104,plain,( 0.20/0.59 mnot = (^[X0 : '$i' -> '$o', X1 : '$i'] : ~X0 @ X1)), 0.20/0.59 inference(rectify,[],[f2])). 0.20/0.59 tff(f105,plain,( 0.20/0.59 bCOMB @ vNOT = mnot), 0.20/0.59 inference(fool_elimination,[],[f104])). 0.20/0.59 tff(f106,plain,( 0.20/0.59 mand = (^[X0 : '$i' -> '$o', X1 : '$i' -> '$o'] : mnot @ (mor @ (mnot @ X0) @ (mnot @ X1)))), 0.20/0.59 inference(rectify,[],[f8])). 0.20/0.59 tff(f107,plain,( 0.20/0.59 bCOMB @ (bCOMB @ mnot) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ mor @ mnot)) @ mnot) = mand), 0.20/0.59 inference(fool_elimination,[],[f106])). 0.20/0.59 tff(f108,plain,( 0.20/0.59 mbox_s4 = (^[X0 : '$i' -> '$o', X1 : '$i'] : ! [X2] : (X0 @ X2 | ~rel_s4 @ X1 @ X2))), 0.20/0.59 inference(rectify,[],[f32])). 0.20/0.59 tff(f109,plain,( 0.20/0.59 bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4)))) = mbox_s4), 0.20/0.59 inference(fool_elimination,[],[f108])). 0.20/0.59 tff(f112,plain,( 0.20/0.59 ! [X0] : exists_in_world @ n @ X0), 0.20/0.59 inference(rectify,[],[f41])). 0.20/0.59 tff(f113,plain,( 0.20/0.59 ! [X0] : (exists_in_world @ n @ X0 = $true)), 0.20/0.59 inference(fool_elimination,[],[f112])). 0.20/0.59 tff(f116,plain,( 0.20/0.59 ! [X0] : exists_in_world @ d @ X0), 0.20/0.59 inference(rectify,[],[f40])). 0.20/0.59 tff(f117,plain,( 0.20/0.59 ! [X0] : (exists_in_world @ d @ X0 = $true)), 0.20/0.59 inference(fool_elimination,[],[f116])). 0.20/0.59 tff(f122,plain,( 0.20/0.59 mreflexive @ rel_s4), 0.20/0.59 inference(rectify,[],[f35])). 0.20/0.59 tff(f123,plain,( 0.20/0.59 (mreflexive @ rel_s4 = $true)), 0.20/0.59 inference(fool_elimination,[],[f122])). 0.20/0.59 tff(f124,plain,( 0.20/0.59 mvalid @ (mbox_s4 @ (closed @ d))), 0.20/0.59 inference(rectify,[],[f44])). 0.20/0.59 tff(f125,plain,( 0.20/0.59 (mvalid @ (mbox_s4 @ (closed @ d)) = $true)), 0.20/0.59 inference(fool_elimination,[],[f124])). 0.20/0.59 tff(f130,plain,( 0.20/0.59 mvalid @ (mbox_s4 @ (mforall_ind @ (^[X0 : mu] : mforall_ind @ (^[X1 : mu] : mexists_ind @ (^[X2 : mu] : mand @ (mbox_s4 @ (mimplies @ (mand @ (closed @ X0) @ (mand @ (combo @ X0 @ X1) @ (h @ X2))) @ (mbox_s4 @ (open @ X0)))) @ (mbox_s4 @ (mimplies @ (mand @ (closed @ X0) @ (mand @ (mnot @ (combo @ X0 @ X1)) @ (h @ o))) @ (mbox_s4 @ (closed @ X0)))))))))), 0.20/0.59 inference(rectify,[],[f42])). 0.20/0.59 tff(f131,plain,( 0.20/0.59 (mvalid @ (mbox_s4 @ (mforall_ind @ (bCOMB @ mforall_ind @ (bCOMB @ (bCOMB @ mexists_ind) @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ cCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ mand)) @ (bCOMB @ (bCOMB @ (bCOMB @ mbox_s4)) @ (sCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ cCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ mimplies)) @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ (bCOMB @ mand @ closed))) @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ bCOMB) @ (bCOMB @ (bCOMB @ mand) @ combo))) @ h))))) @ (bCOMB @ mbox_s4 @ open)))))) @ (bCOMB @ (bCOMB @ mbox_s4) @ (sCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ mimplies) @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ mand @ closed)) @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ mand) @ (bCOMB @ (bCOMB @ mnot) @ combo))) @ (h @ o))))) @ (bCOMB @ mbox_s4 @ closed)))))))) = $true)), 0.20/0.59 inference(fool_elimination,[],[f130])). 0.20/0.59 tff(f134,plain,( 0.20/0.59 (mvalid @ (mbox_s4 @ (mexists_ind @ (bCOMB @ mexists_ind @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ mimplies) @ (bCOMB @ (bCOMB @ mbox_s4) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ mand @ (combo @ d))) @ h)))) @ (mbox_s4 @ (open @ d)))))) != $true)), 0.20/0.59 inference(flattening,[],[f48])). 0.20/0.59 tff(f139,plain,( 0.20/0.59 (mvalid @ (mbox_s4 @ (mexists_ind @ (bCOMB @ mexists_ind @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ mimplies) @ (bCOMB @ (bCOMB @ mbox_s4) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ mand @ (combo @ d))) @ h)))) @ (mbox_s4 @ (open @ d)))))) != $true)), 0.20/0.59 inference(cnf_transformation,[],[f134])). 0.20/0.59 tff(f158,plain,( 0.20/0.59 bCOMB @ vPI('$i') @ (cCOMB @ sCOMB @ iCOMB) = mreflexive), 0.20/0.59 inference(cnf_transformation,[],[f83])). 0.20/0.59 tff(f164,plain,( 0.20/0.59 bCOMB @ sCOMB @ (bCOMB @ vOR) = mor), 0.20/0.59 inference(cnf_transformation,[],[f95])). 0.20/0.59 tff(f165,plain,( 0.20/0.59 mvalid = vPI('$i')), 0.20/0.59 inference(cnf_transformation,[],[f97])). 0.20/0.59 tff(f166,plain,( 0.20/0.59 bCOMB @ mnot @ (bCOMB @ mforall_ind @ (bCOMB @ mnot)) = mexists_ind), 0.20/0.59 inference(cnf_transformation,[],[f99])). 0.20/0.59 tff(f167,plain,( 0.20/0.59 bCOMB @ mor @ mnot = mimplies), 0.20/0.59 inference(cnf_transformation,[],[f101])). 0.20/0.59 tff(f168,plain,( 0.20/0.59 bCOMB @ (bCOMB @ vPI(mu)) @ (bCOMB @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ exists_in_world)))) @ cCOMB) = mforall_ind), 0.20/0.59 inference(cnf_transformation,[],[f103])). 0.20/0.59 tff(f169,plain,( 0.20/0.59 bCOMB @ vNOT = mnot), 0.20/0.59 inference(cnf_transformation,[],[f105])). 0.20/0.59 tff(f170,plain,( 0.20/0.59 bCOMB @ (bCOMB @ mnot) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ mor @ mnot)) @ mnot) = mand), 0.20/0.59 inference(cnf_transformation,[],[f107])). 0.20/0.59 tff(f171,plain,( 0.20/0.59 bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4)))) = mbox_s4), 0.20/0.59 inference(cnf_transformation,[],[f109])). 0.20/0.59 tff(f173,plain,( 0.20/0.59 ( ! [X0] : ((exists_in_world @ n @ X0 = $true)) )), 0.20/0.59 inference(cnf_transformation,[],[f113])). 0.20/0.59 tff(f175,plain,( 0.20/0.59 ( ! [X0] : ((exists_in_world @ d @ X0 = $true)) )), 0.20/0.59 inference(cnf_transformation,[],[f117])). 0.20/0.59 tff(f178,plain,( 0.20/0.59 (mreflexive @ rel_s4 = $true)), 0.20/0.59 inference(cnf_transformation,[],[f123])). 0.20/0.59 tff(f179,plain,( 0.20/0.59 (mvalid @ (mbox_s4 @ (closed @ d)) = $true)), 0.20/0.59 inference(cnf_transformation,[],[f125])). 0.20/0.59 tff(f182,plain,( 0.20/0.59 (mvalid @ (mbox_s4 @ (mforall_ind @ (bCOMB @ mforall_ind @ (bCOMB @ (bCOMB @ mexists_ind) @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ cCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ mand)) @ (bCOMB @ (bCOMB @ (bCOMB @ mbox_s4)) @ (sCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ cCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ mimplies)) @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ (bCOMB @ mand @ closed))) @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ bCOMB) @ (bCOMB @ (bCOMB @ mand) @ combo))) @ h))))) @ (bCOMB @ mbox_s4 @ open)))))) @ (bCOMB @ (bCOMB @ mbox_s4) @ (sCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ mimplies) @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ mand @ closed)) @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ mand) @ (bCOMB @ (bCOMB @ mnot) @ combo))) @ (h @ o))))) @ (bCOMB @ mbox_s4 @ closed)))))))) = $true)), 0.20/0.59 inference(cnf_transformation,[],[f131])). 0.20/0.59 tff(f185,plain,( 0.20/0.59 bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ vNOT)) = mand), 0.20/0.59 inference(definition_unfolding,[],[f170,f169,f164,f169,f169])). 0.20/0.59 tff(f186,plain,( 0.20/0.59 bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT) = mimplies), 0.20/0.59 inference(definition_unfolding,[],[f167,f164,f169])). 0.20/0.59 tff(f191,plain,( 0.20/0.59 bCOMB @ (bCOMB @ vNOT) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu)) @ (bCOMB @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ exists_in_world)))) @ cCOMB)) @ (bCOMB @ (bCOMB @ vNOT))) = mexists_ind), 0.20/0.59 inference(definition_unfolding,[],[f166,f169,f168,f169])). 0.20/0.59 tff(f194,plain,( 0.20/0.59 (vPI('$i') @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4)))) @ (bCOMB @ (bCOMB @ vNOT) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu)) @ (bCOMB @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ exists_in_world)))) @ cCOMB)) @ (bCOMB @ (bCOMB @ vNOT))) @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu)) @ (bCOMB @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ exists_in_world)))) @ cCOMB)) @ (bCOMB @ (bCOMB @ vNOT)))) @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4)))))) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ vNOT))) @ (combo @ d))) @ h)))) @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4)))) @ (open @ d)))))) != $true)), 0.20/0.59 inference(definition_unfolding,[],[f139,f165,f171,f191,f191,f186,f171,f185,f171])). 0.20/0.59 tff(f196,plain,( 0.20/0.59 (bCOMB @ vPI('$i') @ (cCOMB @ sCOMB @ iCOMB) @ rel_s4 = $true)), 0.20/0.59 inference(definition_unfolding,[],[f178,f158])). 0.20/0.59 tff(f197,plain,( 0.20/0.59 (vPI('$i') @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4)))) @ (closed @ d)) = $true)), 0.20/0.59 inference(definition_unfolding,[],[f179,f165,f171])). 0.20/0.59 tff(f200,plain,( 0.20/0.59 (vPI('$i') @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4)))) @ (bCOMB @ (bCOMB @ vPI(mu)) @ (bCOMB @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ exists_in_world)))) @ cCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu)) @ (bCOMB @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ exists_in_world)))) @ cCOMB)) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu)) @ (bCOMB @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ exists_in_world)))) @ cCOMB)) @ (bCOMB @ (bCOMB @ vNOT))))) @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ cCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ vNOT))))) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))))) @ (sCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ cCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT)))) @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ vNOT))) @ closed))) @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ bCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ vNOT)))) @ combo))) @ h))))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ open)))))) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4)))))) @ (sCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ vNOT))) @ closed)) @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ vNOT)))) @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ combo))) @ (h @ o))))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ closed)))))))) = $true)), 0.20/0.59 inference(definition_unfolding,[],[f182,f165,f171,f168,f168,f191,f185,f171,f186,f185,f185,f171,f171,f186,f185,f185,f169,f171])). 0.20/0.60 tff(f214,plain,( 0.20/0.60 ( ! [X1] : ((bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4)))) @ (bCOMB @ (bCOMB @ vPI(mu)) @ (bCOMB @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ exists_in_world)))) @ cCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu)) @ (bCOMB @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ exists_in_world)))) @ cCOMB)) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu)) @ (bCOMB @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ exists_in_world)))) @ cCOMB)) @ (bCOMB @ (bCOMB @ vNOT))))) @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ cCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ vNOT))))) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))))) @ (sCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ cCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT)))) @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ vNOT))) @ closed))) @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ bCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ vNOT)))) @ combo))) @ h))))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ open)))))) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4)))))) @ (sCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ vNOT))) @ closed)) @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ vNOT)))) @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ combo))) @ (h @ o))))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ closed))))))) @ X1 = $true)) )), 0.20/0.60 inference(pi_clausification,[],[f200])). 1.85/0.61 tff(f215,plain,( 1.85/0.61 ( ! [X1] : ((vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X1))) @ (bCOMB @ vPI(mu) @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ exists_in_world))) @ (cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu)) @ (bCOMB @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ exists_in_world)))) @ cCOMB)) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu)) @ (bCOMB @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ exists_in_world)))) @ cCOMB)) @ (bCOMB @ (bCOMB @ vNOT))))) @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ cCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ vNOT))))) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))))) @ (sCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ cCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT)))) @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ vNOT))) @ closed))) @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ bCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ vNOT)))) @ combo))) @ h))))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ open)))))) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4)))))) @ (sCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ vNOT))) @ closed)) @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ vNOT)))) @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ combo))) @ (h @ o))))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ closed)))))))))) = $true)) )), 1.85/0.61 inference(combinator_demodulation,[],[f214])). 1.85/0.61 tff(f216,plain,( 1.85/0.61 ( ! [X2,X1] : ((sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X1))) @ (bCOMB @ vPI(mu) @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ exists_in_world))) @ (cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu)) @ (bCOMB @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ exists_in_world)))) @ cCOMB)) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu)) @ (bCOMB @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ exists_in_world)))) @ cCOMB)) @ (bCOMB @ (bCOMB @ vNOT))))) @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ cCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ vNOT))))) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))))) @ (sCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ cCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT)))) @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ vNOT))) @ closed))) @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ bCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ vNOT)))) @ combo))) @ h))))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ open)))))) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4)))))) @ (sCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ vNOT))) @ closed)) @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ vNOT)))) @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ combo))) @ (h @ o))))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ closed))))))))) @ X2 = $true)) )), 1.85/0.61 inference(pi_clausification,[],[f215])). 1.85/0.61 tff(f217,plain,( 1.85/0.61 ( ! [X2,X1] : ((vOR @ (vNOT @ (rel_s4 @ X1 @ X2)) @ (vPI(mu) @ (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ exists_in_world @ X2)) @ (cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu)) @ (bCOMB @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ exists_in_world)))) @ cCOMB)) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu)) @ (bCOMB @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ exists_in_world)))) @ cCOMB)) @ (bCOMB @ (bCOMB @ vNOT))))) @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ cCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ vNOT))))) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))))) @ (sCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ cCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT)))) @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ vNOT))) @ closed))) @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ bCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ vNOT)))) @ combo))) @ h))))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ open)))))) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4)))))) @ (sCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ vNOT))) @ closed)) @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ vNOT)))) @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ combo))) @ (h @ o))))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ closed)))))) @ X2))) = $true)) )), 1.85/0.61 inference(combinator_demodulation,[],[f216])). 1.85/0.61 tff(f218,plain,( 1.85/0.61 ( ! [X2,X1] : ((vNOT @ (rel_s4 @ X1 @ X2) = $true) | (vPI(mu) @ (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ exists_in_world @ X2)) @ (cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu)) @ (bCOMB @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ exists_in_world)))) @ cCOMB)) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu)) @ (bCOMB @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ exists_in_world)))) @ cCOMB)) @ (bCOMB @ (bCOMB @ vNOT))))) @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ cCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ vNOT))))) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))))) @ (sCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ cCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT)))) @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ vNOT))) @ closed))) @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ bCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ vNOT)))) @ combo))) @ h))))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ open)))))) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4)))))) @ (sCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ vNOT))) @ closed)) @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ vNOT)))) @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ combo))) @ (h @ o))))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ closed)))))) @ X2)) = $true)) )), 1.85/0.62 inference(binary_proxy_clausification,[],[f217])). 1.85/0.62 tff(f219,plain,( 1.85/0.62 ( ! [X2,X3:mu,X1] : ((vNOT @ (rel_s4 @ X1 @ X2) = $true) | (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ exists_in_world @ X2)) @ (cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu)) @ (bCOMB @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ exists_in_world)))) @ cCOMB)) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu)) @ (bCOMB @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ exists_in_world)))) @ cCOMB)) @ (bCOMB @ (bCOMB @ vNOT))))) @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ cCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ vNOT))))) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))))) @ (sCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ cCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT)))) @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ vNOT))) @ closed))) @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ bCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ vNOT)))) @ combo))) @ h))))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ open)))))) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4)))))) @ (sCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ vNOT))) @ closed)) @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ vNOT)))) @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ combo))) @ (h @ o))))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ closed)))))) @ X2) @ X3 = $true)) )), 1.85/0.62 inference(pi_clausification,[],[f218])). 1.85/0.62 % (32644)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 1.85/0.62 tff(f220,plain,( 1.85/0.62 ( ! [X2,X3:mu,X1] : ((rel_s4 @ X1 @ X2 = $false) | (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ exists_in_world @ X2)) @ (cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu)) @ (bCOMB @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ exists_in_world)))) @ cCOMB)) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu)) @ (bCOMB @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ exists_in_world)))) @ cCOMB)) @ (bCOMB @ (bCOMB @ vNOT))))) @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ cCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ vNOT))))) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))))) @ (sCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ cCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT)))) @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ vNOT))) @ closed))) @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ bCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ vNOT)))) @ combo))) @ h))))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ open)))))) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4)))))) @ (sCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ vNOT))) @ closed)) @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ vNOT)))) @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ combo))) @ (h @ o))))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ closed)))))) @ X2) @ X3 = $true)) )), 1.85/0.62 inference(not_proxy_clausification,[],[f219])). 2.02/0.62 tff(f221,plain,( 2.02/0.62 ( ! [X2,X3:mu,X1] : ((rel_s4 @ X1 @ X2 = $false) | (vIMP @ (exists_in_world @ X3 @ X2) @ (vPI(mu) @ (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ exists_in_world @ X2)) @ (cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu)) @ (bCOMB @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ exists_in_world)))) @ cCOMB)) @ (bCOMB @ (bCOMB @ vNOT)))) @ (sCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ vNOT)))) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4)))))) @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT) @ (bCOMB @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (closed @ X3)))) @ (bCOMB @ vNOT)))) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ vNOT))) @ (combo @ X3))) @ h)))) @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ (open @ X3))))))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ (cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT)) @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT) @ (bCOMB @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (closed @ X3)))) @ (bCOMB @ vNOT))) @ (cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ vNOT))) @ (bCOMB @ (bCOMB @ vNOT) @ (combo @ X3))) @ (h @ o)))) @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ (closed @ X3))))))) @ X2))) = $true)) )), 2.02/0.62 inference(combinator_demodulation,[],[f220])). 2.12/0.63 tff(f222,plain,( 2.12/0.63 ( ! [X2,X3:mu,X1] : ((rel_s4 @ X1 @ X2 = $false) | (exists_in_world @ X3 @ X2 = $false) | (vPI(mu) @ (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ exists_in_world @ X2)) @ (cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu)) @ (bCOMB @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ exists_in_world)))) @ cCOMB)) @ (bCOMB @ (bCOMB @ vNOT)))) @ (sCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ vNOT)))) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4)))))) @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT) @ (bCOMB @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (closed @ X3)))) @ (bCOMB @ vNOT)))) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ vNOT))) @ (combo @ X3))) @ h)))) @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ (open @ X3))))))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ (cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT)) @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT) @ (bCOMB @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (closed @ X3)))) @ (bCOMB @ vNOT))) @ (cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ vNOT))) @ (bCOMB @ (bCOMB @ vNOT) @ (combo @ X3))) @ (h @ o)))) @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ (closed @ X3))))))) @ X2)) = $true)) )), 2.12/0.63 inference(binary_proxy_clausification,[],[f221])). 2.12/0.63 tff(f223,plain,( 2.12/0.63 ( ! [X4:mu,X2,X3:mu,X1] : ((rel_s4 @ X1 @ X2 = $false) | (exists_in_world @ X3 @ X2 = $false) | (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ exists_in_world @ X2)) @ (cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu)) @ (bCOMB @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ exists_in_world)))) @ cCOMB)) @ (bCOMB @ (bCOMB @ vNOT)))) @ (sCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ vNOT)))) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4)))))) @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT) @ (bCOMB @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (closed @ X3)))) @ (bCOMB @ vNOT)))) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ vNOT))) @ (combo @ X3))) @ h)))) @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ (open @ X3))))))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ (cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT)) @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT) @ (bCOMB @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (closed @ X3)))) @ (bCOMB @ vNOT))) @ (cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ vNOT))) @ (bCOMB @ (bCOMB @ vNOT) @ (combo @ X3))) @ (h @ o)))) @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ (closed @ X3))))))) @ X2) @ X4 = $true)) )), 2.12/0.64 inference(pi_clausification,[],[f222])). 2.12/0.64 tff(f224,plain,( 2.12/0.64 ( ! [X4:mu,X2,X3:mu,X1] : ((rel_s4 @ X1 @ X2 = $false) | (exists_in_world @ X3 @ X2 = $false) | (vIMP @ (exists_in_world @ X4 @ X2) @ (vNOT @ (vPI(mu) @ (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ exists_in_world @ X2)) @ (cCOMB @ (bCOMB @ (bCOMB @ vNOT) @ (cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ vNOT))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ (cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT)) @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT) @ (bCOMB @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (closed @ X3)))) @ (bCOMB @ vNOT))) @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT) @ (bCOMB @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (combo @ X3 @ X4)))) @ (bCOMB @ vNOT))) @ h))) @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ (open @ X3)))))) @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (bCOMB @ vNOT @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (closed @ X3))) @ (bCOMB @ vNOT @ (bCOMB @ vNOT @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (bCOMB @ vNOT @ (combo @ X3 @ X4)))) @ (bCOMB @ vNOT @ (h @ o))))))))) @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ (closed @ X3)))))))) @ X2)))) = $true)) )), 2.12/0.64 inference(combinator_demodulation,[],[f223])). 2.12/0.64 tff(f225,plain,( 2.12/0.64 ( ! [X4:mu,X2,X3:mu,X1] : ((rel_s4 @ X1 @ X2 = $false) | (exists_in_world @ X3 @ X2 = $false) | (exists_in_world @ X4 @ X2 = $false) | (vNOT @ (vPI(mu) @ (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ exists_in_world @ X2)) @ (cCOMB @ (bCOMB @ (bCOMB @ vNOT) @ (cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ vNOT))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ (cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT)) @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT) @ (bCOMB @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (closed @ X3)))) @ (bCOMB @ vNOT))) @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT) @ (bCOMB @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (combo @ X3 @ X4)))) @ (bCOMB @ vNOT))) @ h))) @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ (open @ X3)))))) @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (bCOMB @ vNOT @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (closed @ X3))) @ (bCOMB @ vNOT @ (bCOMB @ vNOT @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (bCOMB @ vNOT @ (combo @ X3 @ X4)))) @ (bCOMB @ vNOT @ (h @ o))))))))) @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ (closed @ X3)))))))) @ X2))) = $true)) )), 2.12/0.64 inference(binary_proxy_clausification,[],[f224])). 2.12/0.64 tff(f226,plain,( 2.12/0.64 ( ! [X4:mu,X2,X3:mu,X1] : ((rel_s4 @ X1 @ X2 = $false) | (exists_in_world @ X3 @ X2 = $false) | (exists_in_world @ X4 @ X2 = $false) | (vPI(mu) @ (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ exists_in_world @ X2)) @ (cCOMB @ (bCOMB @ (bCOMB @ vNOT) @ (cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ vNOT))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ (cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT)) @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT) @ (bCOMB @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (closed @ X3)))) @ (bCOMB @ vNOT))) @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT) @ (bCOMB @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (combo @ X3 @ X4)))) @ (bCOMB @ vNOT))) @ h))) @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ (open @ X3)))))) @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (bCOMB @ vNOT @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (closed @ X3))) @ (bCOMB @ vNOT @ (bCOMB @ vNOT @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (bCOMB @ vNOT @ (combo @ X3 @ X4)))) @ (bCOMB @ vNOT @ (h @ o))))))))) @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ (closed @ X3)))))))) @ X2)) = $false)) )), 2.12/0.64 inference(not_proxy_clausification,[],[f225])). 2.12/0.64 tff(f227,plain,( 2.12/0.64 ( ! [X4:mu,X2,X3:mu,X1] : ((rel_s4 @ X1 @ X2 = $false) | (exists_in_world @ X3 @ X2 = $false) | (exists_in_world @ X4 @ X2 = $false) | (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ exists_in_world @ X2)) @ (cCOMB @ (bCOMB @ (bCOMB @ vNOT) @ (cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ vNOT))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ (cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT)) @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT) @ (bCOMB @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (closed @ X3)))) @ (bCOMB @ vNOT))) @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT) @ (bCOMB @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (combo @ X3 @ X4)))) @ (bCOMB @ vNOT))) @ h))) @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ (open @ X3)))))) @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (bCOMB @ vNOT @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (closed @ X3))) @ (bCOMB @ vNOT @ (bCOMB @ vNOT @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (bCOMB @ vNOT @ (combo @ X3 @ X4)))) @ (bCOMB @ vNOT @ (h @ o))))))))) @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ (closed @ X3)))))))) @ X2) @ (sK3 @ X4 @ X3 @ X2) = $false)) )), 2.12/0.64 inference(sigma_clausification,[],[f226])). 2.12/0.64 tff(f228,plain,( 2.12/0.64 ( ! [X4:mu,X2,X3:mu,X1] : ((rel_s4 @ X1 @ X2 = $false) | (exists_in_world @ X3 @ X2 = $false) | (exists_in_world @ X4 @ X2 = $false) | (vIMP @ (exists_in_world @ (sK3 @ X4 @ X3 @ X2) @ X2) @ (vNOT @ (vNOT @ (vOR @ (vNOT @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X2))) @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (bCOMB @ vNOT @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (closed @ X3))) @ (bCOMB @ vNOT @ (bCOMB @ vNOT @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (combo @ X3 @ X4))) @ (bCOMB @ vNOT @ (h @ (sK3 @ X4 @ X3 @ X2)))))))))) @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ (open @ X3))))))) @ (vNOT @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X2))) @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (bCOMB @ vNOT @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (closed @ X3))) @ (bCOMB @ vNOT @ (bCOMB @ vNOT @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (bCOMB @ vNOT @ (combo @ X3 @ X4)))) @ (bCOMB @ vNOT @ (h @ o))))))))) @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ (closed @ X3)))))))))) = $false)) )), 2.12/0.64 inference(combinator_demodulation,[],[f227])). 2.12/0.64 tff(f229,plain,( 2.12/0.64 ( ! [X4:mu,X2,X3:mu,X1] : ((rel_s4 @ X1 @ X2 = $false) | (exists_in_world @ X3 @ X2 = $false) | (exists_in_world @ X4 @ X2 = $false) | (vIMP @ (exists_in_world @ (sK3 @ X4 @ X3 @ X2) @ X2) @ (vOR @ (vNOT @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X2))) @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (bCOMB @ vNOT @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (closed @ X3))) @ (bCOMB @ vNOT @ (bCOMB @ vNOT @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (combo @ X3 @ X4))) @ (bCOMB @ vNOT @ (h @ (sK3 @ X4 @ X3 @ X2)))))))))) @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ (open @ X3))))))) @ (vNOT @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X2))) @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (bCOMB @ vNOT @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (closed @ X3))) @ (bCOMB @ vNOT @ (bCOMB @ vNOT @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (bCOMB @ vNOT @ (combo @ X3 @ X4)))) @ (bCOMB @ vNOT @ (h @ o))))))))) @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ (closed @ X3)))))))) = $false)) )), 2.12/0.64 inference(boolean_simplification,[],[f228])). 2.12/0.64 tff(f230,plain,( 2.12/0.64 ( ! [X4:mu,X2,X3:mu,X1] : ((exists_in_world @ (sK3 @ X4 @ X3 @ X2) @ X2 = $true) | (exists_in_world @ X3 @ X2 = $false) | (exists_in_world @ X4 @ X2 = $false) | (rel_s4 @ X1 @ X2 = $false)) )), 2.12/0.64 inference(binary_proxy_clausification,[],[f229])). 2.12/0.64 tff(f231,plain,( 2.12/0.64 ( ! [X4:mu,X2,X3:mu,X1] : ((rel_s4 @ X1 @ X2 = $false) | (exists_in_world @ X3 @ X2 = $false) | (exists_in_world @ X4 @ X2 = $false) | (vOR @ (vNOT @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X2))) @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (bCOMB @ vNOT @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (closed @ X3))) @ (bCOMB @ vNOT @ (bCOMB @ vNOT @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (combo @ X3 @ X4))) @ (bCOMB @ vNOT @ (h @ (sK3 @ X4 @ X3 @ X2)))))))))) @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ (open @ X3))))))) @ (vNOT @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X2))) @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (bCOMB @ vNOT @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (closed @ X3))) @ (bCOMB @ vNOT @ (bCOMB @ vNOT @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (bCOMB @ vNOT @ (combo @ X3 @ X4)))) @ (bCOMB @ vNOT @ (h @ o))))))))) @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ (closed @ X3))))))) = $false)) )), 2.12/0.64 inference(binary_proxy_clausification,[],[f229])). 2.12/0.64 tff(f232,plain,( 2.12/0.64 ( ! [X4:mu,X2,X3:mu,X1] : ((rel_s4 @ X1 @ X2 = $false) | (exists_in_world @ X3 @ X2 = $false) | (exists_in_world @ X4 @ X2 = $false) | (vNOT @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X2))) @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (bCOMB @ vNOT @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (closed @ X3))) @ (bCOMB @ vNOT @ (bCOMB @ vNOT @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (combo @ X3 @ X4))) @ (bCOMB @ vNOT @ (h @ (sK3 @ X4 @ X3 @ X2)))))))))) @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ (open @ X3)))))) = $false)) )), 2.12/0.64 inference(binary_proxy_clausification,[],[f231])). 2.12/0.64 tff(f251,plain,( 2.12/0.64 ( ! [X4:mu,X2,X3:mu,X1] : ((rel_s4 @ X1 @ X2 = $false) | (exists_in_world @ X3 @ X2 = $false) | (exists_in_world @ X4 @ X2 = $false) | (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X2))) @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (bCOMB @ vNOT @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (closed @ X3))) @ (bCOMB @ vNOT @ (bCOMB @ vNOT @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (combo @ X3 @ X4))) @ (bCOMB @ vNOT @ (h @ (sK3 @ X4 @ X3 @ X2)))))))))) @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ (open @ X3))))) = $true)) )), 2.12/0.64 inference(not_proxy_clausification,[],[f232])). 2.12/0.64 tff(f252,plain,( 2.12/0.64 ( ! [X4:mu,X2,X5,X3:mu,X1] : ((rel_s4 @ X1 @ X2 = $false) | (exists_in_world @ X3 @ X2 = $false) | (exists_in_world @ X4 @ X2 = $false) | (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X2))) @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (bCOMB @ vNOT @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (closed @ X3))) @ (bCOMB @ vNOT @ (bCOMB @ vNOT @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (combo @ X3 @ X4))) @ (bCOMB @ vNOT @ (h @ (sK3 @ X4 @ X3 @ X2)))))))))) @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ (open @ X3)))) @ X5 = $true)) )), 2.12/0.64 inference(pi_clausification,[],[f251])). 2.12/0.64 tff(f253,plain,( 2.12/0.64 ( ! [X4:mu,X2,X5,X3:mu,X1] : ((rel_s4 @ X1 @ X2 = $false) | (exists_in_world @ X3 @ X2 = $false) | (exists_in_world @ X4 @ X2 = $false) | (vOR @ (vNOT @ (rel_s4 @ X2 @ X5)) @ (vOR @ (vNOT @ (vNOT @ (vOR @ (vNOT @ (closed @ X3 @ X5)) @ (vNOT @ (vNOT @ (vOR @ (vNOT @ (combo @ X3 @ X4 @ X5)) @ (vNOT @ (h @ (sK3 @ X4 @ X3 @ X2) @ X5)))))))) @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X5))) @ (open @ X3)))) = $true)) )), 2.12/0.64 inference(combinator_demodulation,[],[f252])). 2.12/0.64 tff(f254,plain,( 2.12/0.64 ( ! [X4:mu,X2,X5,X3:mu,X1] : ((rel_s4 @ X1 @ X2 = $false) | (exists_in_world @ X3 @ X2 = $false) | (exists_in_world @ X4 @ X2 = $false) | (vOR @ (vNOT @ (rel_s4 @ X2 @ X5)) @ (vOR @ (vOR @ (vNOT @ (closed @ X3 @ X5)) @ (vNOT @ (vNOT @ (vOR @ (vNOT @ (combo @ X3 @ X4 @ X5)) @ (vNOT @ (h @ (sK3 @ X4 @ X3 @ X2) @ X5)))))) @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X5))) @ (open @ X3)))) = $true)) )), 2.12/0.64 inference(boolean_simplification,[],[f253])). 2.12/0.64 tff(f255,plain,( 2.12/0.64 ( ! [X4:mu,X2,X5,X3:mu,X1] : ((rel_s4 @ X1 @ X2 = $false) | (exists_in_world @ X3 @ X2 = $false) | (exists_in_world @ X4 @ X2 = $false) | (vOR @ (vNOT @ (rel_s4 @ X2 @ X5)) @ (vOR @ (vOR @ (vNOT @ (closed @ X3 @ X5)) @ (vOR @ (vNOT @ (combo @ X3 @ X4 @ X5)) @ (vNOT @ (h @ (sK3 @ X4 @ X3 @ X2) @ X5)))) @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X5))) @ (open @ X3)))) = $true)) )), 2.12/0.64 inference(boolean_simplification,[],[f254])). 2.12/0.64 tff(f256,plain,( 2.12/0.64 ( ! [X4:mu,X2,X5,X3:mu,X1] : ((rel_s4 @ X1 @ X2 = $false) | (exists_in_world @ X3 @ X2 = $false) | (exists_in_world @ X4 @ X2 = $false) | (vNOT @ (rel_s4 @ X2 @ X5) = $true) | (vOR @ (vOR @ (vNOT @ (closed @ X3 @ X5)) @ (vOR @ (vNOT @ (combo @ X3 @ X4 @ X5)) @ (vNOT @ (h @ (sK3 @ X4 @ X3 @ X2) @ X5)))) @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X5))) @ (open @ X3))) = $true)) )), 2.12/0.64 inference(binary_proxy_clausification,[],[f255])). 2.12/0.64 tff(f257,plain,( 2.12/0.64 ( ! [X4:mu,X2,X5,X3:mu,X1] : ((rel_s4 @ X1 @ X2 = $false) | (exists_in_world @ X3 @ X2 = $false) | (exists_in_world @ X4 @ X2 = $false) | (rel_s4 @ X2 @ X5 = $false) | (vOR @ (vOR @ (vNOT @ (closed @ X3 @ X5)) @ (vOR @ (vNOT @ (combo @ X3 @ X4 @ X5)) @ (vNOT @ (h @ (sK3 @ X4 @ X3 @ X2) @ X5)))) @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X5))) @ (open @ X3))) = $true)) )), 2.12/0.64 inference(not_proxy_clausification,[],[f256])). 2.12/0.64 tff(f258,plain,( 2.12/0.64 ( ! [X4:mu,X2,X5,X3:mu,X1] : ((rel_s4 @ X1 @ X2 = $false) | (exists_in_world @ X3 @ X2 = $false) | (exists_in_world @ X4 @ X2 = $false) | (rel_s4 @ X2 @ X5 = $false) | (vOR @ (vNOT @ (closed @ X3 @ X5)) @ (vOR @ (vNOT @ (combo @ X3 @ X4 @ X5)) @ (vNOT @ (h @ (sK3 @ X4 @ X3 @ X2) @ X5))) = $true) | (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X5))) @ (open @ X3)) = $true)) )), 2.12/0.64 inference(binary_proxy_clausification,[],[f257])). 2.12/0.64 tff(f259,plain,( 2.12/0.64 ( ! [X6,X4:mu,X2,X5,X3:mu,X1] : ((rel_s4 @ X1 @ X2 = $false) | (exists_in_world @ X3 @ X2 = $false) | (exists_in_world @ X4 @ X2 = $false) | (rel_s4 @ X2 @ X5 = $false) | (vOR @ (vNOT @ (closed @ X3 @ X5)) @ (vOR @ (vNOT @ (combo @ X3 @ X4 @ X5)) @ (vNOT @ (h @ (sK3 @ X4 @ X3 @ X2) @ X5))) = $true) | (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X5))) @ (open @ X3) @ X6 = $true)) )), 2.12/0.64 inference(pi_clausification,[],[f258])). 2.12/0.64 tff(f260,plain,( 2.12/0.64 ( ! [X6,X4:mu,X2,X5,X3:mu,X1] : ((rel_s4 @ X1 @ X2 = $false) | (exists_in_world @ X3 @ X2 = $false) | (exists_in_world @ X4 @ X2 = $false) | (rel_s4 @ X2 @ X5 = $false) | (vNOT @ (closed @ X3 @ X5) = $true) | (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X5))) @ (open @ X3) @ X6 = $true) | (vOR @ (vNOT @ (combo @ X3 @ X4 @ X5)) @ (vNOT @ (h @ (sK3 @ X4 @ X3 @ X2) @ X5)) = $true)) )), 2.12/0.64 inference(binary_proxy_clausification,[],[f259])). 2.12/0.64 tff(f261,plain,( 2.12/0.64 ( ! [X6,X4:mu,X2,X5,X3:mu,X1] : ((rel_s4 @ X1 @ X2 = $false) | (exists_in_world @ X3 @ X2 = $false) | (exists_in_world @ X4 @ X2 = $false) | (rel_s4 @ X2 @ X5 = $false) | (closed @ X3 @ X5 = $false) | (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X5))) @ (open @ X3) @ X6 = $true) | (vOR @ (vNOT @ (combo @ X3 @ X4 @ X5)) @ (vNOT @ (h @ (sK3 @ X4 @ X3 @ X2) @ X5)) = $true)) )), 2.12/0.64 inference(not_proxy_clausification,[],[f260])). 2.12/0.64 tff(f262,plain,( 2.12/0.64 ( ! [X6,X4:mu,X2,X5,X3:mu,X1] : ((rel_s4 @ X1 @ X2 = $false) | (exists_in_world @ X3 @ X2 = $false) | (exists_in_world @ X4 @ X2 = $false) | (rel_s4 @ X2 @ X5 = $false) | (closed @ X3 @ X5 = $false) | (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X5))) @ (open @ X3) @ X6 = $true) | (vNOT @ (combo @ X3 @ X4 @ X5) = $true) | (vNOT @ (h @ (sK3 @ X4 @ X3 @ X2) @ X5) = $true)) )), 2.12/0.64 inference(binary_proxy_clausification,[],[f261])). 2.12/0.64 tff(f263,plain,( 2.12/0.64 ( ! [X6,X4:mu,X2,X5,X3:mu,X1] : ((rel_s4 @ X1 @ X2 = $false) | (exists_in_world @ X3 @ X2 = $false) | (exists_in_world @ X4 @ X2 = $false) | (rel_s4 @ X2 @ X5 = $false) | (closed @ X3 @ X5 = $false) | (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X5))) @ (open @ X3) @ X6 = $true) | (vNOT @ (combo @ X3 @ X4 @ X5) = $true) | (h @ (sK3 @ X4 @ X3 @ X2) @ X5 = $false)) )), 2.12/0.64 inference(not_proxy_clausification,[],[f262])). 2.12/0.64 tff(f264,plain,( 2.12/0.64 ( ! [X6,X4:mu,X2,X5,X3:mu,X1] : ((rel_s4 @ X1 @ X2 = $false) | (exists_in_world @ X3 @ X2 = $false) | (exists_in_world @ X4 @ X2 = $false) | (rel_s4 @ X2 @ X5 = $false) | (closed @ X3 @ X5 = $false) | (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X5))) @ (open @ X3) @ X6 = $true) | (combo @ X3 @ X4 @ X5 = $false) | (h @ (sK3 @ X4 @ X3 @ X2) @ X5 = $false)) )), 2.12/0.64 inference(not_proxy_clausification,[],[f263])). 2.12/0.64 tff(f265,plain,( 2.12/0.64 ( ! [X6,X4:mu,X2,X5,X3:mu,X1] : ((rel_s4 @ X1 @ X2 = $false) | (exists_in_world @ X3 @ X2 = $false) | (exists_in_world @ X4 @ X2 = $false) | (rel_s4 @ X2 @ X5 = $false) | (closed @ X3 @ X5 = $false) | (vOR @ (vNOT @ (rel_s4 @ X5 @ X6)) @ (open @ X3 @ X6) = $true) | (combo @ X3 @ X4 @ X5 = $false) | (h @ (sK3 @ X4 @ X3 @ X2) @ X5 = $false)) )), 2.12/0.64 inference(combinator_demodulation,[],[f264])). 2.12/0.64 tff(f266,plain,( 2.12/0.64 ( ! [X6,X4:mu,X2,X5,X3:mu,X1] : ((rel_s4 @ X1 @ X2 = $false) | (exists_in_world @ X3 @ X2 = $false) | (exists_in_world @ X4 @ X2 = $false) | (rel_s4 @ X2 @ X5 = $false) | (closed @ X3 @ X5 = $false) | (vNOT @ (rel_s4 @ X5 @ X6) = $true) | (combo @ X3 @ X4 @ X5 = $false) | (h @ (sK3 @ X4 @ X3 @ X2) @ X5 = $false) | (open @ X3 @ X6 = $true)) )), 2.12/0.64 inference(binary_proxy_clausification,[],[f265])). 2.12/0.64 tff(f267,plain,( 2.12/0.64 ( ! [X6,X4:mu,X2,X5,X3:mu,X1] : ((h @ (sK3 @ X4 @ X3 @ X2) @ X5 = $false) | (exists_in_world @ X3 @ X2 = $false) | (exists_in_world @ X4 @ X2 = $false) | (rel_s4 @ X2 @ X5 = $false) | (closed @ X3 @ X5 = $false) | (rel_s4 @ X5 @ X6 = $false) | (combo @ X3 @ X4 @ X5 = $false) | (rel_s4 @ X1 @ X2 = $false) | (open @ X3 @ X6 = $true)) )), 2.12/0.64 inference(not_proxy_clausification,[],[f266])). 2.12/0.64 tff(f287,plain,( 2.12/0.64 ( ! [X1] : ((bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4)))) @ (closed @ d) @ X1 = $true)) )), 2.12/0.64 inference(pi_clausification,[],[f197])). 2.12/0.64 tff(f288,plain,( 2.12/0.64 ( ! [X1] : ((vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X1))) @ (closed @ d)) = $true)) )), 2.12/0.64 inference(combinator_demodulation,[],[f287])). 2.12/0.64 tff(f289,plain,( 2.12/0.64 ( ! [X2,X1] : ((sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ X1))) @ (closed @ d) @ X2 = $true)) )), 2.12/0.64 inference(pi_clausification,[],[f288])). 2.12/0.64 tff(f290,plain,( 2.12/0.64 ( ! [X2,X1] : ((vOR @ (vNOT @ (rel_s4 @ X1 @ X2)) @ (closed @ d @ X2) = $true)) )), 2.12/0.64 inference(combinator_demodulation,[],[f289])). 2.12/0.64 tff(f291,plain,( 2.12/0.64 ( ! [X2,X1] : ((vNOT @ (rel_s4 @ X1 @ X2) = $true) | (closed @ d @ X2 = $true)) )), 2.12/0.64 inference(binary_proxy_clausification,[],[f290])). 2.12/0.64 tff(f292,plain,( 2.12/0.64 ( ! [X2,X1] : ((rel_s4 @ X1 @ X2 = $false) | (closed @ d @ X2 = $true)) )), 2.12/0.64 inference(not_proxy_clausification,[],[f291])). 2.12/0.64 tff(f293,plain,( 2.12/0.64 (vPI('$i') @ (sCOMB @ rel_s4 @ iCOMB) = $true)), 2.12/0.64 inference(combinator_demodulation,[],[f196])). 2.12/0.64 tff(f294,plain,( 2.12/0.64 ( ! [X1] : ((sCOMB @ rel_s4 @ iCOMB @ X1 = $true)) )), 2.12/0.64 inference(pi_clausification,[],[f293])). 2.12/0.64 tff(f295,plain,( 2.12/0.64 ( ! [X1] : ((rel_s4 @ X1 @ X1 = $true)) )), 2.12/0.64 inference(combinator_demodulation,[],[f294])). 2.12/0.64 tff(f305,plain,( 2.12/0.64 (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4)))) @ (bCOMB @ (bCOMB @ vNOT) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu)) @ (bCOMB @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ exists_in_world)))) @ cCOMB)) @ (bCOMB @ (bCOMB @ vNOT))) @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu)) @ (bCOMB @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ exists_in_world)))) @ cCOMB)) @ (bCOMB @ (bCOMB @ vNOT)))) @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4)))))) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ vNOT))) @ (combo @ d))) @ h)))) @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4)))) @ (open @ d))))) @ sK4 = $false)), 2.12/0.64 inference(sigma_clausification,[],[f194])). 2.12/0.64 tff(f306,plain,( 2.12/0.64 (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ sK4))) @ (bCOMB @ vNOT @ (bCOMB @ vPI(mu) @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ exists_in_world))) @ (cCOMB @ (bCOMB @ (bCOMB @ vNOT) @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu)) @ (bCOMB @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ exists_in_world)))) @ cCOMB)) @ (bCOMB @ (bCOMB @ vNOT)))) @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4)))))) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ vNOT))) @ (combo @ d))) @ h)))) @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ (open @ d))))))))))) = $false)), 2.12/0.64 inference(combinator_demodulation,[],[f305])). 2.12/0.64 tff(f307,plain,( 2.12/0.64 (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ sK4))) @ (bCOMB @ vNOT @ (bCOMB @ vPI(mu) @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ exists_in_world))) @ (cCOMB @ (bCOMB @ (bCOMB @ vNOT) @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu)) @ (bCOMB @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ exists_in_world)))) @ cCOMB)) @ (bCOMB @ (bCOMB @ vNOT)))) @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4)))))) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ vNOT))) @ (combo @ d))) @ h)))) @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ (open @ d)))))))))) @ sK5 = $false)), 2.12/0.64 inference(sigma_clausification,[],[f306])). 2.12/0.64 tff(f308,plain,( 2.12/0.64 (vOR @ (vNOT @ (rel_s4 @ sK4 @ sK5)) @ (vNOT @ (vPI(mu) @ (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ exists_in_world @ sK5)) @ (cCOMB @ (bCOMB @ (bCOMB @ vNOT) @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu)) @ (bCOMB @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ exists_in_world)))) @ cCOMB)) @ (bCOMB @ (bCOMB @ vNOT)))) @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4)))))) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ vNOT))) @ (combo @ d))) @ h)))) @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ (open @ d)))))) @ sK5)))) = $false)), 2.12/0.64 inference(combinator_demodulation,[],[f307])). 2.12/0.66 tff(f309,plain,( 2.12/0.66 (vNOT @ (rel_s4 @ sK4 @ sK5) = $false)), 2.12/0.66 inference(binary_proxy_clausification,[],[f308])). 2.12/0.66 tff(f310,plain,( 2.12/0.66 (vNOT @ (vPI(mu) @ (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ exists_in_world @ sK5)) @ (cCOMB @ (bCOMB @ (bCOMB @ vNOT) @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu)) @ (bCOMB @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ exists_in_world)))) @ cCOMB)) @ (bCOMB @ (bCOMB @ vNOT)))) @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4)))))) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ vNOT))) @ (combo @ d))) @ h)))) @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ (open @ d)))))) @ sK5))) = $false)), 2.12/0.66 inference(binary_proxy_clausification,[],[f308])). 2.12/0.66 tff(f311,plain,( 2.12/0.66 (vPI(mu) @ (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ exists_in_world @ sK5)) @ (cCOMB @ (bCOMB @ (bCOMB @ vNOT) @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu)) @ (bCOMB @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ exists_in_world)))) @ cCOMB)) @ (bCOMB @ (bCOMB @ vNOT)))) @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4)))))) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ vNOT))) @ (combo @ d))) @ h)))) @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ (open @ d)))))) @ sK5)) = $true)), 2.12/0.66 inference(not_proxy_clausification,[],[f310])). 2.12/0.66 tff(f312,plain,( 2.12/0.66 ( ! [X1:mu] : ((sCOMB @ (bCOMB @ vIMP @ (cCOMB @ exists_in_world @ sK5)) @ (cCOMB @ (bCOMB @ (bCOMB @ vNOT) @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu)) @ (bCOMB @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ exists_in_world)))) @ cCOMB)) @ (bCOMB @ (bCOMB @ vNOT)))) @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4)))))) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT))) @ (bCOMB @ vNOT))) @ (combo @ d))) @ h)))) @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ (open @ d)))))) @ sK5) @ X1 = $true)) )), 2.12/0.66 inference(pi_clausification,[],[f311])). 2.12/0.66 tff(f313,plain,( 2.12/0.66 ( ! [X1:mu] : ((vIMP @ (exists_in_world @ X1 @ sK5) @ (vNOT @ (vNOT @ (vPI(mu) @ (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ exists_in_world @ sK5)) @ (cCOMB @ (bCOMB @ (bCOMB @ vNOT) @ (cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT)) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT) @ (bCOMB @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (combo @ d @ X1)))) @ (bCOMB @ vNOT))) @ h))) @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ (open @ d))))) @ sK5))))) = $true)) )), 2.12/0.66 inference(combinator_demodulation,[],[f312])). 2.12/0.66 tff(f314,plain,( 2.12/0.66 ( ! [X1:mu] : ((vIMP @ (exists_in_world @ X1 @ sK5) @ (vPI(mu) @ (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ exists_in_world @ sK5)) @ (cCOMB @ (bCOMB @ (bCOMB @ vNOT) @ (cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT)) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT) @ (bCOMB @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (combo @ d @ X1)))) @ (bCOMB @ vNOT))) @ h))) @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ (open @ d))))) @ sK5))) = $true)) )), 2.12/0.66 inference(boolean_simplification,[],[f313])). 2.12/0.66 tff(f315,plain,( 2.12/0.66 ( ! [X1:mu] : ((exists_in_world @ X1 @ sK5 = $false) | (vPI(mu) @ (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ exists_in_world @ sK5)) @ (cCOMB @ (bCOMB @ (bCOMB @ vNOT) @ (cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT)) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT) @ (bCOMB @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (combo @ d @ X1)))) @ (bCOMB @ vNOT))) @ h))) @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ (open @ d))))) @ sK5)) = $true)) )), 2.12/0.66 inference(binary_proxy_clausification,[],[f314])). 2.12/0.66 tff(f316,plain,( 2.12/0.66 ( ! [X2:mu,X1:mu] : ((exists_in_world @ X1 @ sK5 = $false) | (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ exists_in_world @ sK5)) @ (cCOMB @ (bCOMB @ (bCOMB @ vNOT) @ (cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT)) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))))) @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT) @ (bCOMB @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (combo @ d @ X1)))) @ (bCOMB @ vNOT))) @ h))) @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel_s4))) @ (open @ d))))) @ sK5) @ X2 = $true)) )), 2.12/0.66 inference(pi_clausification,[],[f315])). 2.12/0.66 tff(f317,plain,( 2.12/0.66 ( ! [X2:mu,X1:mu] : ((exists_in_world @ X1 @ sK5 = $false) | (vIMP @ (exists_in_world @ X2 @ sK5) @ (vNOT @ (vOR @ (vNOT @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ sK5))) @ (bCOMB @ vNOT @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (combo @ d @ X1))) @ (bCOMB @ vNOT @ (h @ X2))))))) @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ sK5))) @ (open @ d))))) = $true)) )), 2.12/0.66 inference(combinator_demodulation,[],[f316])). 2.12/0.66 tff(f318,plain,( 2.12/0.66 ( ! [X2:mu,X1:mu] : ((exists_in_world @ X1 @ sK5 = $false) | (exists_in_world @ X2 @ sK5 = $false) | (vNOT @ (vOR @ (vNOT @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ sK5))) @ (bCOMB @ vNOT @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (combo @ d @ X1))) @ (bCOMB @ vNOT @ (h @ X2))))))) @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ sK5))) @ (open @ d)))) = $true)) )), 2.12/0.66 inference(binary_proxy_clausification,[],[f317])). 2.12/0.66 tff(f319,plain,( 2.12/0.66 ( ! [X2:mu,X1:mu] : ((exists_in_world @ X1 @ sK5 = $false) | (exists_in_world @ X2 @ sK5 = $false) | (vOR @ (vNOT @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ sK5))) @ (bCOMB @ vNOT @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (combo @ d @ X1))) @ (bCOMB @ vNOT @ (h @ X2))))))) @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ sK5))) @ (open @ d))) = $false)) )), 2.12/0.66 inference(not_proxy_clausification,[],[f318])). 2.12/0.66 tff(f320,plain,( 2.12/0.66 ( ! [X2:mu,X1:mu] : ((exists_in_world @ X1 @ sK5 = $false) | (exists_in_world @ X2 @ sK5 = $false) | (vNOT @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ sK5))) @ (bCOMB @ vNOT @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (combo @ d @ X1))) @ (bCOMB @ vNOT @ (h @ X2)))))) = $false)) )), 2.12/0.66 inference(binary_proxy_clausification,[],[f319])). 2.12/0.66 tff(f321,plain,( 2.12/0.66 ( ! [X2:mu,X1:mu] : ((exists_in_world @ X1 @ sK5 = $false) | (exists_in_world @ X2 @ sK5 = $false) | (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ sK5))) @ (open @ d)) = $false)) )), 2.12/0.66 inference(binary_proxy_clausification,[],[f319])). 2.12/0.66 tff(f322,plain,( 2.12/0.66 ( ! [X2:mu,X1:mu] : ((exists_in_world @ X1 @ sK5 = $false) | (exists_in_world @ X2 @ sK5 = $false) | (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ sK5))) @ (open @ d) @ sK6 = $false)) )), 2.12/0.66 inference(sigma_clausification,[],[f321])). 2.12/0.66 tff(f323,plain,( 2.12/0.66 ( ! [X2:mu,X1:mu] : ((exists_in_world @ X1 @ sK5 = $false) | (exists_in_world @ X2 @ sK5 = $false) | (vOR @ (vNOT @ (rel_s4 @ sK5 @ sK6)) @ (open @ d @ sK6) = $false)) )), 2.12/0.66 inference(combinator_demodulation,[],[f322])). 2.12/0.66 tff(f324,plain,( 2.12/0.66 ( ! [X0:mu] : ((exists_in_world @ X0 @ sK5 = $false) | (vOR @ (vNOT @ (rel_s4 @ sK5 @ sK6)) @ (open @ d @ sK6) = $false)) )), 2.12/0.66 inference(condensation,[],[f323])). 2.12/0.66 tff(f325,plain,( 2.12/0.66 ( ! [X0:mu] : ((exists_in_world @ X0 @ sK5 = $false) | (vNOT @ (rel_s4 @ sK5 @ sK6) = $false)) )), 2.12/0.66 inference(binary_proxy_clausification,[],[f324])). 2.12/0.66 tff(f326,plain,( 2.12/0.66 ( ! [X0:mu] : ((exists_in_world @ X0 @ sK5 = $false) | (open @ d @ sK6 = $false)) )), 2.12/0.66 inference(binary_proxy_clausification,[],[f324])). 2.12/0.66 tff(f327,plain,( 2.12/0.66 ( ! [X0:mu] : ((exists_in_world @ X0 @ sK5 = $false) | (rel_s4 @ sK5 @ sK6 = $true)) )), 2.12/0.66 inference(not_proxy_clausification,[],[f325])). 2.12/0.66 tff(f328,plain,( 2.12/0.66 ( ! [X2:mu,X1:mu] : ((exists_in_world @ X1 @ sK5 = $false) | (exists_in_world @ X2 @ sK5 = $false) | (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ sK5))) @ (bCOMB @ vNOT @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (combo @ d @ X1))) @ (bCOMB @ vNOT @ (h @ X2))))) = $true)) )), 2.12/0.66 inference(not_proxy_clausification,[],[f320])). 2.12/0.66 tff(f329,plain,( 2.12/0.66 ( ! [X2:mu,X3,X1:mu] : ((exists_in_world @ X1 @ sK5 = $false) | (exists_in_world @ X2 @ sK5 = $false) | (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel_s4 @ sK5))) @ (bCOMB @ vNOT @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (combo @ d @ X1))) @ (bCOMB @ vNOT @ (h @ X2)))) @ X3 = $true)) )), 2.12/0.66 inference(pi_clausification,[],[f328])). 2.12/0.66 tff(f330,plain,( 2.12/0.66 ( ! [X2:mu,X3,X1:mu] : ((exists_in_world @ X1 @ sK5 = $false) | (exists_in_world @ X2 @ sK5 = $false) | (vOR @ (vNOT @ (rel_s4 @ sK5 @ X3)) @ (vNOT @ (vOR @ (vNOT @ (combo @ d @ X1 @ X3)) @ (vNOT @ (h @ X2 @ X3)))) = $true)) )), 2.12/0.66 inference(combinator_demodulation,[],[f329])). 2.12/0.66 tff(f331,plain,( 2.12/0.66 ( ! [X2:mu,X3,X1:mu] : ((exists_in_world @ X1 @ sK5 = $false) | (exists_in_world @ X2 @ sK5 = $false) | (vNOT @ (rel_s4 @ sK5 @ X3) = $true) | (vNOT @ (vOR @ (vNOT @ (combo @ d @ X1 @ X3)) @ (vNOT @ (h @ X2 @ X3))) = $true)) )), 2.12/0.66 inference(binary_proxy_clausification,[],[f330])). 2.12/0.66 tff(f332,plain,( 2.12/0.66 ( ! [X2:mu,X3,X1:mu] : ((exists_in_world @ X1 @ sK5 = $false) | (exists_in_world @ X2 @ sK5 = $false) | (vNOT @ (rel_s4 @ sK5 @ X3) = $true) | (vOR @ (vNOT @ (combo @ d @ X1 @ X3)) @ (vNOT @ (h @ X2 @ X3)) = $false)) )), 2.12/0.66 inference(not_proxy_clausification,[],[f331])). 2.12/0.66 tff(f333,plain,( 2.12/0.66 ( ! [X2:mu,X3,X1:mu] : ((exists_in_world @ X1 @ sK5 = $false) | (exists_in_world @ X2 @ sK5 = $false) | (rel_s4 @ sK5 @ X3 = $false) | (vOR @ (vNOT @ (combo @ d @ X1 @ X3)) @ (vNOT @ (h @ X2 @ X3)) = $false)) )), 2.12/0.66 inference(not_proxy_clausification,[],[f332])). 2.12/0.66 tff(f334,plain,( 2.12/0.66 ( ! [X2:mu,X3,X1:mu] : ((exists_in_world @ X1 @ sK5 = $false) | (exists_in_world @ X2 @ sK5 = $false) | (rel_s4 @ sK5 @ X3 = $false) | (vNOT @ (combo @ d @ X1 @ X3) = $false)) )), 2.12/0.66 inference(binary_proxy_clausification,[],[f333])). 2.12/0.66 tff(f335,plain,( 2.12/0.66 ( ! [X2:mu,X3,X1:mu] : ((exists_in_world @ X1 @ sK5 = $false) | (exists_in_world @ X2 @ sK5 = $false) | (rel_s4 @ sK5 @ X3 = $false) | (vNOT @ (h @ X2 @ X3) = $false)) )), 2.12/0.66 inference(binary_proxy_clausification,[],[f333])). 2.12/0.66 tff(f336,plain,( 2.12/0.66 ( ! [X2:mu,X3,X1:mu] : ((exists_in_world @ X1 @ sK5 = $false) | (exists_in_world @ X2 @ sK5 = $false) | (rel_s4 @ sK5 @ X3 = $false) | (h @ X2 @ X3 = $true)) )), 2.12/0.66 inference(not_proxy_clausification,[],[f335])). 2.12/0.66 tff(f337,plain,( 2.12/0.66 ( ! [X0:mu,X1] : ((rel_s4 @ sK5 @ X1 = $false) | (exists_in_world @ X0 @ sK5 = $false) | (h @ X0 @ X1 = $true)) )), 2.12/0.66 inference(condensation,[],[f336])). 2.12/0.66 tff(f338,plain,( 2.12/0.66 ( ! [X2:mu,X3,X1:mu] : ((exists_in_world @ X1 @ sK5 = $false) | (exists_in_world @ X2 @ sK5 = $false) | (rel_s4 @ sK5 @ X3 = $false) | (combo @ d @ X1 @ X3 = $true)) )), 2.12/0.66 inference(not_proxy_clausification,[],[f334])). 2.12/0.66 tff(f339,plain,( 2.12/0.66 ( ! [X0:mu,X1] : ((combo @ d @ X0 @ X1 = $true) | (rel_s4 @ sK5 @ X1 = $false) | (exists_in_world @ X0 @ sK5 = $false)) )), 2.12/0.66 inference(condensation,[],[f338])). 2.12/0.66 tff(f340,plain,( 2.12/0.66 (rel_s4 @ sK4 @ sK5 = $true)), 2.12/0.66 inference(not_proxy_clausification,[],[f309])). 2.12/0.66 tff(f345,plain,( 2.12/0.66 spl1_0 <=> (rel_s4 @ sK5 @ sK6 = $true)), 2.12/0.66 introduced(avatar_definition,[new_symbols(naming,[spl1_0])])). 2.12/0.66 tff(f346,plain,( 2.12/0.66 (rel_s4 @ sK5 @ sK6 = $true) | ~spl1_0), 2.12/0.66 inference(avatar_component_clause,[],[f345])). 2.12/0.66 tff(f348,plain,( 2.12/0.66 spl1_2 <=> ! [X0 : mu] : (exists_in_world @ X0 @ sK5 = $false)), 2.12/0.66 introduced(avatar_definition,[new_symbols(naming,[spl1_2])])). 2.12/0.66 tff(f349,plain,( 2.12/0.66 ( ! [X0:mu] : ((exists_in_world @ X0 @ sK5 = $false)) ) | ~spl1_2), 2.12/0.66 inference(avatar_component_clause,[],[f348])). 2.12/0.66 tff(f350,plain,( 2.12/0.66 spl1_0 | spl1_2), 2.12/0.66 inference(avatar_split_clause,[],[f327,f348,f345])). 2.12/0.66 tff(f355,plain,( 2.12/0.66 spl1_4 <=> (open @ d @ sK6 = $false)), 2.12/0.66 introduced(avatar_definition,[new_symbols(naming,[spl1_4])])). 2.12/0.66 tff(f356,plain,( 2.12/0.66 (open @ d @ sK6 = $false) | ~spl1_4), 2.12/0.66 inference(avatar_component_clause,[],[f355])). 2.12/0.66 tff(f357,plain,( 2.12/0.66 spl1_4 | spl1_2), 2.12/0.66 inference(avatar_split_clause,[],[f326,f348,f355])). 2.12/0.66 tff(f360,plain,( 2.12/0.66 ($false = $true) | ~spl1_2), 2.12/0.66 inference(superposition,[],[f349,f173])). 2.12/0.66 tff(f364,plain,( 2.12/0.66 $false | ~spl1_2), 2.12/0.66 inference(trivial_inequality_removal,[],[f360])). 2.12/0.66 tff(f365,plain,( 2.12/0.66 ~spl1_2), 2.12/0.66 inference(avatar_contradiction_clause,[],[f364])). 2.12/0.66 tff(f373,plain,( 2.12/0.66 ( ! [X0:mu] : (($false = $true) | (exists_in_world @ X0 @ sK5 = $false) | (h @ X0 @ sK5 = $true)) )), 2.12/0.66 inference(superposition,[],[f295,f337])). 2.12/0.66 tff(f376,plain,( 2.12/0.66 ( ! [X0:mu] : ((h @ X0 @ sK5 = $true) | (exists_in_world @ X0 @ sK5 = $false)) )), 2.12/0.66 inference(trivial_inequality_removal,[],[f373])). 2.12/0.66 tff(f386,plain,( 2.12/0.66 ($false = $true) | (closed @ d @ sK5 = $true)), 2.12/0.66 inference(superposition,[],[f340,f292])). 2.12/0.66 tff(f389,plain,( 2.12/0.66 (closed @ d @ sK5 = $true)), 2.12/0.66 inference(trivial_inequality_removal,[],[f386])). 2.12/0.66 tff(f503,plain,( 2.12/0.66 ( ! [X4,X2,X0:mu,X3,X1:mu] : (($false = $true) | (exists_in_world @ (sK3 @ X0 @ X1 @ X2) @ sK5 = $false) | (exists_in_world @ X1 @ X2 = $false) | (exists_in_world @ X0 @ X2 = $false) | (rel_s4 @ X2 @ sK5 = $false) | (closed @ X1 @ sK5 = $false) | (rel_s4 @ sK5 @ X3 = $false) | (combo @ X1 @ X0 @ sK5 = $false) | (rel_s4 @ X4 @ X2 = $false) | (open @ X1 @ X3 = $true)) )), 2.12/0.66 inference(superposition,[],[f376,f267])). 2.12/0.66 tff(f506,plain,( 2.12/0.66 ( ! [X4,X2,X0:mu,X3,X1:mu] : ((exists_in_world @ (sK3 @ X0 @ X1 @ X2) @ sK5 = $false) | (exists_in_world @ X1 @ X2 = $false) | (exists_in_world @ X0 @ X2 = $false) | (rel_s4 @ X2 @ sK5 = $false) | (closed @ X1 @ sK5 = $false) | (rel_s4 @ sK5 @ X3 = $false) | (combo @ X1 @ X0 @ sK5 = $false) | (rel_s4 @ X4 @ X2 = $false) | (open @ X1 @ X3 = $true)) )), 2.12/0.66 inference(trivial_inequality_removal,[],[f503])). 2.12/0.66 tff(f510,plain,( 2.12/0.66 ( ! [X12,X10:mu,X13,X11,X9:mu] : (($false = $true) | (exists_in_world @ X10 @ sK5 = $false) | (exists_in_world @ X9 @ sK5 = $false) | (rel_s4 @ sK5 @ sK5 = $false) | (closed @ X10 @ sK5 = $false) | (rel_s4 @ sK5 @ X11 = $false) | (combo @ X10 @ X9 @ sK5 = $false) | (rel_s4 @ X12 @ sK5 = $false) | (open @ X10 @ X11 = $true) | (exists_in_world @ X10 @ sK5 = $false) | (exists_in_world @ X9 @ sK5 = $false) | (rel_s4 @ X13 @ sK5 = $false)) )), 2.12/0.66 inference(superposition,[],[f506,f230])). 2.12/0.66 tff(f518,plain,( 2.12/0.66 ( ! [X12,X10:mu,X13,X11,X9:mu] : (($false = $true) | (exists_in_world @ X10 @ sK5 = $false) | (exists_in_world @ X9 @ sK5 = $false) | (rel_s4 @ sK5 @ sK5 = $false) | (closed @ X10 @ sK5 = $false) | (rel_s4 @ sK5 @ X11 = $false) | (combo @ X10 @ X9 @ sK5 = $false) | (rel_s4 @ X12 @ sK5 = $false) | (open @ X10 @ X11 = $true) | (rel_s4 @ X13 @ sK5 = $false)) )), 2.12/0.66 inference(duplicate_literal_removal,[],[f510])). 2.12/0.66 tff(f519,plain,( 2.12/0.66 ( ! [X12,X10:mu,X13,X11,X9:mu] : ((exists_in_world @ X10 @ sK5 = $false) | (exists_in_world @ X9 @ sK5 = $false) | (rel_s4 @ sK5 @ sK5 = $false) | (closed @ X10 @ sK5 = $false) | (rel_s4 @ sK5 @ X11 = $false) | (combo @ X10 @ X9 @ sK5 = $false) | (rel_s4 @ X12 @ sK5 = $false) | (open @ X10 @ X11 = $true) | (rel_s4 @ X13 @ sK5 = $false)) )), 2.12/0.66 inference(trivial_inequality_removal,[],[f518])). 2.12/0.66 tff(f520,plain,( 2.12/0.66 ( ! [X2,X0:mu,X3,X1:mu] : ((rel_s4 @ sK5 @ sK5 = $false) | (exists_in_world @ X0 @ sK5 = $false) | (exists_in_world @ X1 @ sK5 = $false) | (closed @ X0 @ sK5 = $false) | (rel_s4 @ sK5 @ X2 = $false) | (combo @ X0 @ X1 @ sK5 = $false) | (open @ X0 @ X2 = $true) | (rel_s4 @ X3 @ sK5 = $false)) )), 2.12/0.66 inference(condensation,[],[f519])). 2.12/0.66 tff(f521,plain,( 2.12/0.66 ( ! [X2,X0:mu,X1:mu] : ((rel_s4 @ sK5 @ sK5 = $false) | (exists_in_world @ X0 @ sK5 = $false) | (exists_in_world @ X1 @ sK5 = $false) | (closed @ X0 @ sK5 = $false) | (rel_s4 @ sK5 @ X2 = $false) | (combo @ X0 @ X1 @ sK5 = $false) | (open @ X0 @ X2 = $true)) )), 2.12/0.66 inference(condensation,[],[f520])). 2.12/0.66 tff(f523,plain,( 2.12/0.66 ( ! [X2,X0:mu,X1:mu] : (($false = $true) | (exists_in_world @ X0 @ sK5 = $false) | (exists_in_world @ X1 @ sK5 = $false) | (closed @ X0 @ sK5 = $false) | (rel_s4 @ sK5 @ X2 = $false) | (combo @ X0 @ X1 @ sK5 = $false) | (open @ X0 @ X2 = $true)) )), 2.12/0.66 inference(forward_demodulation,[],[f521,f295])). 2.12/0.66 tff(f524,plain,( 2.12/0.66 ( ! [X2,X0:mu,X1:mu] : ((combo @ X0 @ X1 @ sK5 = $false) | (exists_in_world @ X1 @ sK5 = $false) | (closed @ X0 @ sK5 = $false) | (rel_s4 @ sK5 @ X2 = $false) | (exists_in_world @ X0 @ sK5 = $false) | (open @ X0 @ X2 = $true)) )), 2.12/0.66 inference(trivial_inequality_removal,[],[f523])). 2.12/0.66 tff(f527,plain,( 2.12/0.66 ( ! [X2:mu,X3] : (($false = $true) | (exists_in_world @ X2 @ sK5 = $false) | (closed @ d @ sK5 = $false) | (rel_s4 @ sK5 @ X3 = $false) | (exists_in_world @ d @ sK5 = $false) | (open @ d @ X3 = $true) | (rel_s4 @ sK5 @ sK5 = $false) | (exists_in_world @ X2 @ sK5 = $false)) )), 2.12/0.66 inference(superposition,[],[f524,f339])). 2.12/0.66 tff(f546,plain,( 2.12/0.66 ( ! [X2:mu,X3] : (($false = $true) | (exists_in_world @ X2 @ sK5 = $false) | (closed @ d @ sK5 = $false) | (rel_s4 @ sK5 @ X3 = $false) | (exists_in_world @ d @ sK5 = $false) | (open @ d @ X3 = $true) | (rel_s4 @ sK5 @ sK5 = $false)) )), 2.12/0.66 inference(duplicate_literal_removal,[],[f527])). 2.12/0.66 tff(f547,plain,( 2.12/0.66 ( ! [X2:mu,X3] : ((exists_in_world @ X2 @ sK5 = $false) | (closed @ d @ sK5 = $false) | (rel_s4 @ sK5 @ X3 = $false) | (exists_in_world @ d @ sK5 = $false) | (open @ d @ X3 = $true) | (rel_s4 @ sK5 @ sK5 = $false)) )), 2.12/0.66 inference(trivial_inequality_removal,[],[f546])). 2.12/0.66 tff(f548,plain,( 2.12/0.66 ( ! [X0] : ((exists_in_world @ d @ sK5 = $false) | (closed @ d @ sK5 = $false) | (rel_s4 @ sK5 @ X0 = $false) | (open @ d @ X0 = $true) | (rel_s4 @ sK5 @ sK5 = $false)) )), 2.12/0.66 inference(condensation,[],[f547])). 2.12/0.66 tff(f549,plain,( 2.12/0.66 ( ! [X0] : (($false = $true) | (closed @ d @ sK5 = $false) | (rel_s4 @ sK5 @ X0 = $false) | (open @ d @ X0 = $true) | (rel_s4 @ sK5 @ sK5 = $false)) )), 2.12/0.66 inference(forward_demodulation,[],[f548,f175])). 2.12/0.66 tff(f550,plain,( 2.12/0.66 ( ! [X0] : ((closed @ d @ sK5 = $false) | (rel_s4 @ sK5 @ X0 = $false) | (open @ d @ X0 = $true) | (rel_s4 @ sK5 @ sK5 = $false)) )), 2.12/0.66 inference(trivial_inequality_removal,[],[f549])). 2.12/0.66 tff(f551,plain,( 2.12/0.66 ( ! [X0] : (($false = $true) | (rel_s4 @ sK5 @ X0 = $false) | (open @ d @ X0 = $true) | (rel_s4 @ sK5 @ sK5 = $false)) )), 2.12/0.66 inference(forward_demodulation,[],[f550,f389])). 2.12/0.66 tff(f552,plain,( 2.12/0.66 ( ! [X0] : ((rel_s4 @ sK5 @ X0 = $false) | (open @ d @ X0 = $true) | (rel_s4 @ sK5 @ sK5 = $false)) )), 2.12/0.66 inference(trivial_inequality_removal,[],[f551])). 2.12/0.66 tff(f553,plain,( 2.12/0.66 ( ! [X0] : (($false = $true) | (rel_s4 @ sK5 @ X0 = $false) | (open @ d @ X0 = $true)) )), 2.12/0.66 inference(forward_demodulation,[],[f552,f295])). 2.12/0.66 tff(f554,plain,( 2.12/0.66 ( ! [X0] : ((rel_s4 @ sK5 @ X0 = $false) | (open @ d @ X0 = $true)) )), 2.12/0.66 inference(trivial_inequality_removal,[],[f553])). 2.12/0.66 tff(f560,plain,( 2.12/0.66 spl1_10 <=> ! [X5] : ((rel_s4 @ sK5 @ X5 = $false) | (open @ d @ X5 = $true))), 2.12/0.66 introduced(avatar_definition,[new_symbols(naming,[spl1_10])])). 2.12/0.66 tff(f561,plain,( 2.12/0.66 ( ! [X5] : ((rel_s4 @ sK5 @ X5 = $false) | (open @ d @ X5 = $true)) ) | ~spl1_10), 2.12/0.66 inference(avatar_component_clause,[],[f560])). 2.12/0.66 tff(f607,plain,( 2.12/0.66 spl1_10), 2.12/0.66 inference(avatar_split_clause,[],[f554,f560])). 2.12/0.66 tff(f613,plain,( 2.12/0.66 ($false = $true) | (open @ d @ sK6 = $true) | (~spl1_0 | ~spl1_10)), 2.12/0.66 inference(superposition,[],[f346,f561])). 2.12/0.66 tff(f614,plain,( 2.12/0.66 (open @ d @ sK6 = $true) | (~spl1_0 | ~spl1_10)), 2.12/0.66 inference(trivial_inequality_removal,[],[f613])). 2.12/0.66 tff(f623,plain,( 2.12/0.66 ($false = $true) | (~spl1_0 | ~spl1_4 | ~spl1_10)), 2.12/0.66 inference(forward_demodulation,[],[f614,f356])). 2.12/0.66 tff(f624,plain,( 2.12/0.66 $false | (~spl1_0 | ~spl1_4 | ~spl1_10)), 2.12/0.66 inference(trivial_inequality_removal,[],[f623])). 2.12/0.66 tff(f625,plain,( 2.12/0.66 ~spl1_0 | ~spl1_4 | ~spl1_10), 2.12/0.66 inference(avatar_contradiction_clause,[],[f624])). 2.12/0.66 tff(f626,plain,( 2.12/0.66 $false), 2.12/0.66 inference(avatar_sat_refutation,[],[f350,f357,f365,f607,f625])). 2.12/0.66 % SZS output end Proof for theBenchmark 2.12/0.66 % (32626)------------------------------ 2.12/0.66 % (32626)Version: Vampire 4.5.0 (commit 7ae30c7f on 2020-06-30 15:57:20 +0100) 2.12/0.66 % (32626)Termination reason: Refutation 2.12/0.66 2.12/0.66 % (32626)Memory used [KB]: 6524 2.12/0.66 % (32626)Time elapsed: 0.254 s 2.12/0.66 % (32626)------------------------------ 2.12/0.66 % (32626)------------------------------ 2.12/0.67 % (32613)Success in time 0.307 s 2.12/0.67 EOF