0.13/0.13	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.13/0.14	% Command    : run_vampire %s %d
0.14/0.35	% Computer   : n017.cluster.edu
0.14/0.35	% Model      : x86_64 x86_64
0.14/0.35	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.14/0.35	% Memory     : 8042.1875MB
0.14/0.35	% OS         : Linux 3.10.0-693.el7.x86_64
0.14/0.35	% CPULimit   : 960
0.14/0.35	% WCLimit    : 120
0.14/0.35	% DateTime   : Thu Jul  2 08:24:51 EDT 2020
0.14/0.35	% CPUTime    : 
0.22/0.39	% (14278)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
0.22/0.40	% (14290)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
0.22/0.40	% (14270)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
0.22/0.40	% (14276)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
0.22/0.40	% (14275)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
0.22/0.40	% (14273)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
0.22/0.40	% (14277)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
0.22/0.40	% (14279)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
0.22/0.41	% (14294)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
0.22/0.41	% (14282)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
0.22/0.41	% (14286)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
0.22/0.41	% (14289)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
0.22/0.42	% (14269)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
0.22/0.42	% (14274)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
0.22/0.42	% (14272)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
0.22/0.42	% (14271)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
0.22/0.42	% (14295)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
0.22/0.43	% (14268)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
0.22/0.43	% (14281)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
0.22/0.43	% (14297)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
0.22/0.44	% (14292)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
0.22/0.44	% (14293)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
0.22/0.44	% (14296)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
0.22/0.44	% (14287)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
0.22/0.44	% (14291)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
0.22/0.45	% (14285)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
0.22/0.45	% (14283)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
0.22/0.45	% (14288)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
0.22/0.45	% (14280)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
0.22/0.45	% (14284)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
0.22/0.46	% (14278)Refutation not found, incomplete strategy
0.22/0.46	% (14278)------------------------------
0.22/0.46	% (14278)Version: Vampire 4.5.0 (commit 7ae30c7f on 2020-06-30 15:57:20 +0100)
0.22/0.46	% (14278)Termination reason: Refutation not found, incomplete strategy
0.22/0.46	
0.22/0.46	% (14278)Memory used [KB]: 10490
0.22/0.46	% (14278)Time elapsed: 0.090 s
0.22/0.46	% (14278)------------------------------
0.22/0.46	% (14278)------------------------------
0.22/0.47	% (14291)Refutation not found, incomplete strategy
0.22/0.47	% (14291)------------------------------
0.22/0.47	% (14291)Version: Vampire 4.5.0 (commit 7ae30c7f on 2020-06-30 15:57:20 +0100)
0.22/0.47	% (14291)Termination reason: Refutation not found, incomplete strategy
0.22/0.47	
0.22/0.47	% (14291)Memory used [KB]: 10234
0.22/0.47	% (14291)Time elapsed: 0.095 s
0.22/0.47	% (14291)------------------------------
0.22/0.47	% (14291)------------------------------
0.22/0.50	% (14298)dis+1011_10_add=large:csup=on:inj=on:chr=on:foolp=on:cnfonf=eager:afr=on:afp=4000:afq=1.0:amm=off:anc=none:lma=on:nm=64:nwc=4:sac=on:sp=occurrence_75 on theBenchmark
0.22/0.52	% (14299)dis+1010_3:2_av=off:csup=on:prag=on:chr=on:foolp=on:bet=on:cnfonf=lazy_not_be_gen:gsp=input_only:nm=2:nwc=1:sp=reverse_arity:urr=ec_only_29 on theBenchmark
1.47/0.57	% (14268)Refutation found. Thanks to Tanya!
1.47/0.57	% SZS status Theorem for theBenchmark
1.47/0.57	% SZS output start Proof for theBenchmark
1.47/0.57	tff(func_def_0, type, mu: '$tType').
1.47/0.57	tff(func_def_4, type, ->: ('$tType' * '$tType') > '$tType').
1.47/0.57	tff(func_def_5, type, meq_ind: mu -> mu -> '$i' -> '$o').
1.47/0.57	tff(func_def_6, type, mtrue: '$i' -> '$o').
1.47/0.57	tff(func_def_7, type, mfalse: '$i' -> '$o').
1.47/0.57	tff(func_def_8, type, mnot: ('$i' -> '$o') -> '$i' -> '$o').
1.47/0.57	tff(func_def_9, type, vAPP: !>[X0: $ttype, X1: $ttype]:(X0 -> X1 * X0) > X1).
1.47/0.57	tff(func_def_10, type, mor: ('$i' -> '$o') -> ('$i' -> '$o') -> '$i' -> '$o').
1.47/0.57	tff(func_def_11, type, mand: ('$i' -> '$o') -> ('$i' -> '$o') -> '$i' -> '$o').
1.47/0.57	tff(func_def_12, type, mimplies: ('$i' -> '$o') -> ('$i' -> '$o') -> '$i' -> '$o').
1.47/0.57	tff(func_def_13, type, mimplied: ('$i' -> '$o') -> ('$i' -> '$o') -> '$i' -> '$o').
1.47/0.57	tff(func_def_14, type, mequiv: ('$i' -> '$o') -> ('$i' -> '$o') -> '$i' -> '$o').
1.47/0.57	tff(func_def_15, type, mxor: ('$i' -> '$o') -> ('$i' -> '$o') -> '$i' -> '$o').
1.47/0.57	tff(func_def_16, type, mforall_ind: (mu -> '$i' -> '$o') -> '$i' -> '$o').
1.47/0.57	tff(func_def_17, type, mforall_indset: ((mu -> '$i' -> '$o') -> '$i' -> '$o') -> '$i' -> '$o').
1.47/0.57	tff(func_def_18, type, mforall_prop: (('$i' -> '$o') -> '$i' -> '$o') -> '$i' -> '$o').
1.47/0.57	tff(func_def_19, type, mexists_ind: (mu -> '$i' -> '$o') -> '$i' -> '$o').
1.47/0.57	tff(func_def_20, type, mexists_indset: ((mu -> '$i' -> '$o') -> '$i' -> '$o') -> '$i' -> '$o').
1.47/0.57	tff(func_def_21, type, mexists_prop: (('$i' -> '$o') -> '$i' -> '$o') -> '$i' -> '$o').
1.47/0.57	tff(func_def_22, type, mbox_generic: ('$i' -> '$i' -> '$o') -> ('$i' -> '$o') -> '$i' -> '$o').
1.47/0.57	tff(func_def_23, type, mdia_generic: ('$i' -> '$i' -> '$o') -> ('$i' -> '$o') -> '$i' -> '$o').
1.47/0.57	tff(func_def_24, type, rel: '$i' -> '$i' -> '$o').
1.47/0.57	tff(func_def_25, type, mbox: ('$i' -> '$o') -> '$i' -> '$o').
1.47/0.57	tff(func_def_26, type, mdia: ('$i' -> '$o') -> '$i' -> '$o').
1.47/0.57	tff(func_def_27, type, mvalid: ('$i' -> '$o') -> '$o').
1.47/0.57	tff(func_def_28, type, minvalid: ('$i' -> '$o') -> '$o').
1.47/0.57	tff(func_def_29, type, msymmetric: ('$i' -> '$i' -> '$o') -> '$o').
1.47/0.57	tff(func_def_30, type, positive: (mu -> '$i' -> '$o') -> '$i' -> '$o').
1.47/0.57	tff(func_def_31, type, god: mu -> '$i' -> '$o').
1.47/0.57	tff(func_def_32, type, essence: (mu -> '$i' -> '$o') -> mu -> '$i' -> '$o').
1.47/0.57	tff(func_def_33, type, necessary_existence: mu -> '$i' -> '$o').
1.47/0.57	tff(func_def_34, type, vEPSILON: !>[X0: $ttype]:(X0 -> '$o') -> X0).
1.47/0.57	tff(func_def_37, type, bCOMB: !>[X0: $ttype, X1: $ttype, X2: $ttype]:(X1 -> X2) -> (X0 -> X1) -> X0 -> X2).
1.47/0.57	tff(func_def_38, type, sCOMB: !>[X0: $ttype, X1: $ttype, X2: $ttype]:(X0 -> X1 -> X2) -> (X0 -> X1) -> X0 -> X2).
1.47/0.57	tff(func_def_39, type, vNOT: '$o' -> '$o').
1.47/0.57	tff(func_def_40, type, vPI: !>[X0: $ttype]:(X0 -> '$o') -> '$o').
1.47/0.57	tff(func_def_41, type, kCOMB: !>[X1: $ttype, X2: $ttype]:X1 -> X2 -> X1).
1.47/0.57	tff(func_def_42, type, cCOMB: !>[X0: $ttype, X1: $ttype, X2: $ttype]:(X0 -> X1 -> X2) -> X1 -> X0 -> X2).
1.47/0.57	tff(func_def_43, type, vSIGMA: !>[X0: $ttype]:(X0 -> '$o') -> '$o').
1.47/0.57	tff(func_def_44, type, vEQ: !>[X0: $ttype]:X0 -> X0 -> '$o').
1.47/0.57	tff(func_def_45, type, vAND: '$o' -> '$o' -> '$o').
1.47/0.57	tff(func_def_46, type, vOR: '$o' -> '$o' -> '$o').
1.47/0.57	tff(func_def_47, type, vIMP: '$o' -> '$o' -> '$o').
1.47/0.57	tff(func_def_48, type, vIFF: '$o' -> '$o' -> '$o').
1.47/0.57	tff(func_def_49, type, iCOMB: !>[X2: $ttype]:X2 -> X2).
1.47/0.57	tff(func_def_50, type, sK0: mu -> '$i' -> mu -> '$i' -> '$o').
1.47/0.57	tff(func_def_51, type, sK1: '$i' -> '$i').
1.47/0.57	tff(func_def_52, type, sK2: '$i' -> mu).
1.47/0.57	tff(func_def_55, type, sK5: mu -> mu -> '$i' -> '$o').
1.47/0.57	tff(func_def_56, type, sK6: '$i' -> (mu -> '$i' -> '$o') -> mu).
1.47/0.57	tff(func_def_57, type, sK7: '$i' -> (mu -> '$i' -> '$o') -> mu).
1.47/0.57	tff(func_def_58, type, sK8: mu -> mu).
1.47/0.57	tff(func_def_59, type, sK9: mu -> mu).
1.47/0.57	tff(f7,axiom,(
1.47/0.57	  mimplies = (^[X3 : '$i' -> '$o', X4 : '$i' -> '$o', X2 : '$i'] : X3 @ X2 => X4 @ X2)),
1.47/0.57	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies)).
1.47/0.57	tff(f11,axiom,(
1.47/0.57	  mforall_ind = (^[X3 : mu -> '$i' -> '$o', X2 : '$i'] : ! [X0 : mu] : X3 @ X0 @ X2)),
1.47/0.57	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_ind)).
1.47/0.57	tff(f12,axiom,(
1.47/0.57	  mforall_indset = (^[X3 : (mu -> '$i' -> '$o') -> '$i' -> '$o', X2 : '$i'] : ! [X0 : mu -> '$i' -> '$o'] : X3 @ X0 @ X2)),
1.47/0.57	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_indset)).
1.47/0.57	tff(f14,axiom,(
1.47/0.57	  mexists_ind = (^[X3 : mu -> '$i' -> '$o', X2 : '$i'] : ? [X0 : mu] : X3 @ X0 @ X2)),
1.47/0.57	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mexists_ind)).
1.47/0.57	tff(f17,axiom,(
1.47/0.57	  mbox_generic = (^[X6 : '$i' -> '$i' -> '$o', X3 : '$i' -> '$o', X2 : '$i'] : ! [X7] : (X3 @ X7 | ~X6 @ X2 @ X7))),
1.47/0.57	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_generic)).
1.47/0.57	tff(f18,axiom,(
1.47/0.57	  mdia_generic = (^[X6 : '$i' -> '$i' -> '$o', X3 : '$i' -> '$o', X2 : '$i'] : ? [X7] : (X3 @ X7 & X6 @ X2 @ X7))),
1.47/0.57	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia_generic)).
1.47/0.57	tff(f19,axiom,(
1.47/0.57	  mbox_generic @ rel = mbox),
1.47/0.57	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox)).
1.47/0.57	tff(f20,axiom,(
1.47/0.57	  mdia_generic @ rel = mdia),
1.47/0.57	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia)).
1.47/0.57	tff(f21,axiom,(
1.47/0.57	  mvalid = (^[X3 : '$i' -> '$o'] : ! [X2] : X3 @ X2)),
1.47/0.57	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mvalid)).
1.47/0.57	tff(f23,axiom,(
1.47/0.57	  msymmetric = (^[X6 : '$i' -> '$i' -> '$o'] : ! [X8,X9] : (X6 @ X8 @ X9 => X6 @ X9 @ X8))),
1.47/0.57	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',msymmetric)).
1.47/0.57	tff(f24,axiom,(
1.47/0.57	  msymmetric @ rel),
1.47/0.57	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sym)).
1.47/0.57	tff(f25,axiom,(
1.47/0.57	  god = (^[X0 : mu] : mforall_indset @ (^[X3 : mu -> '$i' -> '$o'] : mimplies @ (positive @ X3) @ (X3 @ X0)))),
1.47/0.57	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',defD1)).
1.47/0.57	tff(f26,axiom,(
1.47/0.57	  necessary_existence = (^[X0 : mu] : mforall_indset @ (^[X3 : mu -> '$i' -> '$o'] : mimplies @ (essence @ X3 @ X0) @ (mbox @ (mexists_ind @ (^[X1 : mu] : X3 @ X1)))))),
1.47/0.57	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',defD3)).
1.47/0.57	tff(f27,conjecture,(
1.47/0.57	  mvalid @ (mbox @ (mexists_ind @ (^[X0 : mu] : god @ X0)))),
1.47/0.57	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thmT3)).
1.47/0.57	tff(f28,negated_conjecture,(
1.47/0.57	  ~mvalid @ (mbox @ (mexists_ind @ (^[X0 : mu] : god @ X0)))),
1.47/0.57	  inference(negated_conjecture,[],[f27])).
1.47/0.57	tff(f29,axiom,(
1.47/0.57	  mvalid @ (positive @ necessary_existence)),
1.47/0.57	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axA5)).
1.47/0.57	tff(f30,axiom,(
1.47/0.57	  mvalid @ (mdia @ (mexists_ind @ (^[X0 : mu] : god @ X0)))),
1.47/0.57	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corC)).
1.47/0.57	tff(f31,axiom,(
1.47/0.57	  mvalid @ (mforall_ind @ (^[X0 : mu] : mimplies @ (god @ X0) @ (essence @ god @ X0)))),
1.47/0.57	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thmT2)).
1.47/0.57	tff(f32,plain,(
1.47/0.57	  ~mvalid @ (mbox @ (mexists_ind @ (^[X0 : mu] : god @ X0)))),
1.47/0.57	  inference(rectify,[],[f28])).
1.47/0.57	tff(f33,plain,(
1.47/0.57	  ~(mvalid @ (mbox @ (mexists_ind @ god)) = $true)),
1.47/0.57	  inference(fool_elimination,[],[f32])).
1.47/0.57	tff(f34,plain,(
1.47/0.57	  mvalid @ (mdia @ (mexists_ind @ (^[X0 : mu] : god @ X0)))),
1.47/0.57	  inference(rectify,[],[f30])).
1.47/0.57	tff(f35,plain,(
1.47/0.57	  (mvalid @ (mdia @ (mexists_ind @ god)) = $true)),
1.47/0.57	  inference(fool_elimination,[],[f34])).
1.47/0.57	tff(f36,plain,(
1.47/0.57	  mvalid @ (mforall_ind @ (^[X0 : mu] : mimplies @ (god @ X0) @ (essence @ god @ X0)))),
1.47/0.57	  inference(rectify,[],[f31])).
1.47/0.57	tff(f37,plain,(
1.47/0.57	  (mvalid @ (mforall_ind @ (sCOMB @ (bCOMB @ mimplies @ god) @ (essence @ god))) = $true)),
1.47/0.57	  inference(fool_elimination,[],[f36])).
1.47/0.57	tff(f63,plain,(
1.47/0.57	  msymmetric = (^[X0 : '$i' -> '$i' -> '$o'] : ! [X1,X2] : (X0 @ X1 @ X2 => X0 @ X2 @ X1))),
1.47/0.57	  inference(rectify,[],[f23])).
1.47/0.57	tff(f64,plain,(
1.47/0.57	  bCOMB @ vPI('$i') @ (bCOMB @ (bCOMB @ vPI('$i')) @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ sCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vIMP)) @ cCOMB))) @ iCOMB)) = msymmetric),
1.47/0.57	  inference(fool_elimination,[],[f63])).
1.47/0.57	tff(f65,plain,(
1.47/0.57	  necessary_existence = (^[X0 : mu] : mforall_indset @ (^[X1 : mu -> '$i' -> '$o'] : mimplies @ (essence @ X1 @ X0) @ (mbox @ (mexists_ind @ (^[X2 : mu] : X1 @ X2)))))),
1.47/0.57	  inference(rectify,[],[f26])).
1.47/0.57	tff(f66,plain,(
1.47/0.57	  bCOMB @ mforall_indset @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ mimplies) @ (cCOMB @ essence))) @ (bCOMB @ mbox @ (bCOMB @ mexists_ind @ iCOMB))) = necessary_existence),
1.47/0.57	  inference(fool_elimination,[],[f65])).
1.47/0.57	tff(f67,plain,(
1.47/0.57	  mbox_generic = (^[X0 : '$i' -> '$i' -> '$o', X1 : '$i' -> '$o', X2 : '$i'] : ! [X3] : (X1 @ X3 | ~X0 @ X2 @ X3))),
1.47/0.57	  inference(rectify,[],[f17])).
1.47/0.57	tff(f68,plain,(
1.47/0.57	  bCOMB @ (bCOMB @ (bCOMB @ vPI('$i'))) @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ sCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vOR)) @ (bCOMB @ (bCOMB @ vNOT))))) = mbox_generic),
1.47/0.57	  inference(fool_elimination,[],[f67])).
1.47/0.57	tff(f69,plain,(
1.47/0.57	  mdia_generic = (^[X0 : '$i' -> '$i' -> '$o', X1 : '$i' -> '$o', X2 : '$i'] : ? [X3] : (X1 @ X3 & X0 @ X2 @ X3))),
1.47/0.57	  inference(rectify,[],[f18])).
1.47/0.57	tff(f70,plain,(
1.47/0.57	  bCOMB @ (bCOMB @ (bCOMB @ vSIGMA('$i'))) @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ sCOMB) @ (bCOMB @ (bCOMB @ vAND)))) = mdia_generic),
1.47/0.57	  inference(fool_elimination,[],[f69])).
1.47/0.57	tff(f71,plain,(
1.47/0.57	  mforall_ind = (^[X0 : mu -> '$i' -> '$o', X1 : '$i'] : ! [X2 : mu] : X0 @ X2 @ X1)),
1.47/0.57	  inference(rectify,[],[f11])).
1.47/0.57	tff(f72,plain,(
1.47/0.57	  bCOMB @ (bCOMB @ vPI(mu)) @ cCOMB = mforall_ind),
1.47/0.57	  inference(fool_elimination,[],[f71])).
1.47/0.57	tff(f73,plain,(
1.47/0.57	  mforall_indset = (^[X0 : (mu -> '$i' -> '$o') -> '$i' -> '$o', X1 : '$i'] : ! [X2 : mu -> '$i' -> '$o'] : X0 @ X2 @ X1)),
1.47/0.57	  inference(rectify,[],[f12])).
1.47/0.57	tff(f74,plain,(
1.47/0.57	  bCOMB @ (bCOMB @ vPI(mu -> '$i' -> '$o')) @ cCOMB = mforall_indset),
1.47/0.57	  inference(fool_elimination,[],[f73])).
1.47/0.57	tff(f75,plain,(
1.47/0.57	  mvalid = (^[X0 : '$i' -> '$o'] : ! [X1] : X0 @ X1)),
1.47/0.57	  inference(rectify,[],[f21])).
1.47/0.57	tff(f76,plain,(
1.47/0.57	  mvalid = vPI('$i')),
1.47/0.57	  inference(fool_elimination,[],[f75])).
1.47/0.57	tff(f77,plain,(
1.47/0.57	  mimplies = (^[X0 : '$i' -> '$o', X1 : '$i' -> '$o', X2 : '$i'] : X0 @ X2 => X1 @ X2)),
1.47/0.57	  inference(rectify,[],[f7])).
1.47/0.57	tff(f78,plain,(
1.47/0.57	  bCOMB @ sCOMB @ (bCOMB @ vIMP) = mimplies),
1.47/0.57	  inference(fool_elimination,[],[f77])).
1.47/0.57	tff(f79,plain,(
1.47/0.57	  god = (^[X0 : mu] : mforall_indset @ (^[X1 : mu -> '$i' -> '$o'] : mimplies @ (positive @ X1) @ (X1 @ X0)))),
1.47/0.57	  inference(rectify,[],[f25])).
1.47/0.57	tff(f80,plain,(
1.47/0.57	  bCOMB @ mforall_indset @ (bCOMB @ (sCOMB @ (bCOMB @ mimplies @ positive)) @ (cCOMB @ iCOMB)) = god),
1.47/0.57	  inference(fool_elimination,[],[f79])).
1.47/0.57	tff(f81,plain,(
1.47/0.57	  mexists_ind = (^[X0 : mu -> '$i' -> '$o', X1 : '$i'] : ? [X2 : mu] : X0 @ X2 @ X1)),
1.47/0.57	  inference(rectify,[],[f14])).
1.47/0.57	tff(f82,plain,(
1.47/0.57	  bCOMB @ (bCOMB @ vSIGMA(mu)) @ cCOMB = mexists_ind),
1.47/0.57	  inference(fool_elimination,[],[f81])).
1.47/0.57	tff(f83,plain,(
1.47/0.57	  msymmetric @ rel),
1.47/0.57	  inference(rectify,[],[f24])).
1.47/0.57	tff(f84,plain,(
1.47/0.57	  (msymmetric @ rel = $true)),
1.47/0.57	  inference(fool_elimination,[],[f83])).
1.47/0.57	tff(f85,plain,(
1.47/0.57	  mvalid @ (positive @ necessary_existence)),
1.47/0.57	  inference(rectify,[],[f29])).
1.47/0.57	tff(f86,plain,(
1.47/0.57	  (mvalid @ (positive @ necessary_existence) = $true)),
1.47/0.57	  inference(fool_elimination,[],[f85])).
1.47/0.57	tff(f87,plain,(
1.47/0.57	  (mvalid @ (mbox @ (mexists_ind @ god)) != $true)),
1.47/0.57	  inference(flattening,[],[f33])).
1.47/0.57	tff(f88,plain,(
1.47/0.57	  (mvalid @ (mbox @ (mexists_ind @ god)) != $true)),
1.47/0.57	  inference(cnf_transformation,[],[f87])).
1.47/0.57	tff(f89,plain,(
1.47/0.57	  (mvalid @ (mdia @ (mexists_ind @ god)) = $true)),
1.47/0.57	  inference(cnf_transformation,[],[f35])).
1.47/0.57	tff(f90,plain,(
1.47/0.57	  (mvalid @ (mforall_ind @ (sCOMB @ (bCOMB @ mimplies @ god) @ (essence @ god))) = $true)),
1.47/0.57	  inference(cnf_transformation,[],[f37])).
1.47/0.57	tff(f91,plain,(
1.47/0.57	  mdia_generic @ rel = mdia),
1.47/0.57	  inference(cnf_transformation,[],[f20])).
1.47/0.57	tff(f92,plain,(
1.47/0.57	  mbox_generic @ rel = mbox),
1.47/0.57	  inference(cnf_transformation,[],[f19])).
1.47/0.57	tff(f106,plain,(
1.47/0.57	  bCOMB @ vPI('$i') @ (bCOMB @ (bCOMB @ vPI('$i')) @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ sCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vIMP)) @ cCOMB))) @ iCOMB)) = msymmetric),
1.47/0.57	  inference(cnf_transformation,[],[f64])).
1.47/0.57	tff(f107,plain,(
1.47/0.57	  bCOMB @ mforall_indset @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ mimplies) @ (cCOMB @ essence))) @ (bCOMB @ mbox @ (bCOMB @ mexists_ind @ iCOMB))) = necessary_existence),
1.47/0.57	  inference(cnf_transformation,[],[f66])).
1.47/0.57	tff(f108,plain,(
1.47/0.57	  bCOMB @ (bCOMB @ (bCOMB @ vPI('$i'))) @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ sCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vOR)) @ (bCOMB @ (bCOMB @ vNOT))))) = mbox_generic),
1.47/0.57	  inference(cnf_transformation,[],[f68])).
1.47/0.57	tff(f109,plain,(
1.47/0.57	  bCOMB @ (bCOMB @ (bCOMB @ vSIGMA('$i'))) @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ sCOMB) @ (bCOMB @ (bCOMB @ vAND)))) = mdia_generic),
1.47/0.57	  inference(cnf_transformation,[],[f70])).
1.47/0.57	tff(f110,plain,(
1.47/0.57	  bCOMB @ (bCOMB @ vPI(mu)) @ cCOMB = mforall_ind),
1.47/0.57	  inference(cnf_transformation,[],[f72])).
1.47/0.57	tff(f111,plain,(
1.47/0.57	  bCOMB @ (bCOMB @ vPI(mu -> '$i' -> '$o')) @ cCOMB = mforall_indset),
1.47/0.57	  inference(cnf_transformation,[],[f74])).
1.47/0.57	tff(f112,plain,(
1.47/0.57	  mvalid = vPI('$i')),
1.47/0.57	  inference(cnf_transformation,[],[f76])).
1.47/0.57	tff(f113,plain,(
1.47/0.57	  bCOMB @ sCOMB @ (bCOMB @ vIMP) = mimplies),
1.47/0.57	  inference(cnf_transformation,[],[f78])).
1.47/0.57	tff(f114,plain,(
1.47/0.57	  bCOMB @ mforall_indset @ (bCOMB @ (sCOMB @ (bCOMB @ mimplies @ positive)) @ (cCOMB @ iCOMB)) = god),
1.47/0.57	  inference(cnf_transformation,[],[f80])).
1.47/0.57	tff(f115,plain,(
1.47/0.57	  bCOMB @ (bCOMB @ vSIGMA(mu)) @ cCOMB = mexists_ind),
1.47/0.57	  inference(cnf_transformation,[],[f82])).
1.47/0.57	tff(f116,plain,(
1.47/0.57	  (msymmetric @ rel = $true)),
1.47/0.57	  inference(cnf_transformation,[],[f84])).
1.47/0.57	tff(f117,plain,(
1.47/0.57	  (mvalid @ (positive @ necessary_existence) = $true)),
1.47/0.57	  inference(cnf_transformation,[],[f86])).
1.47/0.57	tff(f118,plain,(
1.47/0.57	  bCOMB @ (bCOMB @ (bCOMB @ vPI('$i'))) @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ sCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vOR)) @ (bCOMB @ (bCOMB @ vNOT))))) @ rel = mbox),
1.47/0.57	  inference(definition_unfolding,[],[f92,f108])).
1.47/0.57	tff(f119,plain,(
1.47/0.57	  bCOMB @ (bCOMB @ (bCOMB @ vSIGMA('$i'))) @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ sCOMB) @ (bCOMB @ (bCOMB @ vAND)))) @ rel = mdia),
1.47/0.57	  inference(definition_unfolding,[],[f91,f109])).
1.47/0.57	tff(f120,plain,(
1.47/0.57	  bCOMB @ (bCOMB @ (bCOMB @ vPI(mu -> '$i' -> '$o')) @ cCOMB) @ (bCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) @ positive)) @ (cCOMB @ iCOMB)) = god),
1.47/0.57	  inference(definition_unfolding,[],[f114,f111,f113])).
1.47/0.57	tff(f121,plain,(
1.47/0.57	  bCOMB @ (bCOMB @ (bCOMB @ vPI(mu -> '$i' -> '$o')) @ cCOMB) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP))) @ (cCOMB @ essence))) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i'))) @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ sCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vOR)) @ (bCOMB @ (bCOMB @ vNOT))))) @ rel) @ (bCOMB @ (bCOMB @ (bCOMB @ vSIGMA(mu)) @ cCOMB) @ iCOMB))) = necessary_existence),
1.47/0.57	  inference(definition_unfolding,[],[f107,f111,f113,f118,f115])).
1.47/0.57	tff(f122,plain,(
1.47/0.57	  (vPI('$i') @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i'))) @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ sCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vOR)) @ (bCOMB @ (bCOMB @ vNOT))))) @ rel @ (bCOMB @ (bCOMB @ vSIGMA(mu)) @ cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu -> '$i' -> '$o')) @ cCOMB) @ (bCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) @ positive)) @ (cCOMB @ iCOMB))))) != $true)),
1.47/0.57	  inference(definition_unfolding,[],[f88,f112,f118,f115,f120])).
1.47/0.57	tff(f123,plain,(
1.47/0.57	  (vPI('$i') @ (bCOMB @ (bCOMB @ (bCOMB @ vSIGMA('$i'))) @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ sCOMB) @ (bCOMB @ (bCOMB @ vAND)))) @ rel @ (bCOMB @ (bCOMB @ vSIGMA(mu)) @ cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu -> '$i' -> '$o')) @ cCOMB) @ (bCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) @ positive)) @ (cCOMB @ iCOMB))))) = $true)),
1.47/0.57	  inference(definition_unfolding,[],[f89,f112,f119,f115,f120])).
1.47/0.57	tff(f124,plain,(
1.47/0.57	  (vPI('$i') @ (bCOMB @ (bCOMB @ vPI(mu)) @ cCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu -> '$i' -> '$o')) @ cCOMB) @ (bCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) @ positive)) @ (cCOMB @ iCOMB)))) @ (essence @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu -> '$i' -> '$o')) @ cCOMB) @ (bCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) @ positive)) @ (cCOMB @ iCOMB)))))) = $true)),
1.47/0.57	  inference(definition_unfolding,[],[f90,f112,f110,f113,f120,f120])).
1.47/0.57	tff(f125,plain,(
1.47/0.57	  (bCOMB @ vPI('$i') @ (bCOMB @ (bCOMB @ vPI('$i')) @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ sCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vIMP)) @ cCOMB))) @ iCOMB)) @ rel = $true)),
1.47/0.57	  inference(definition_unfolding,[],[f116,f106])).
1.47/0.57	tff(f126,plain,(
1.47/0.57	  (vPI('$i') @ (positive @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu -> '$i' -> '$o')) @ cCOMB) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP))) @ (cCOMB @ essence))) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i'))) @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ sCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vOR)) @ (bCOMB @ (bCOMB @ vNOT))))) @ rel) @ (bCOMB @ (bCOMB @ (bCOMB @ vSIGMA(mu)) @ cCOMB) @ iCOMB))))) = $true)),
1.47/0.57	  inference(definition_unfolding,[],[f117,f112,f121])).
1.47/0.57	tff(f127,plain,(
1.47/0.57	  ( ! [X1] : ((positive @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu -> '$i' -> '$o')) @ cCOMB) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP))) @ (cCOMB @ essence))) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i'))) @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ sCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vOR)) @ (bCOMB @ (bCOMB @ vNOT))))) @ rel) @ (bCOMB @ (bCOMB @ (bCOMB @ vSIGMA(mu)) @ cCOMB) @ iCOMB)))) @ X1 = $true)) )),
1.47/0.57	  inference(pi_clausification,[],[f126])).
1.47/0.57	tff(f128,plain,(
1.47/0.57	  ( ! [X1] : ((positive @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu -> '$i' -> '$o')) @ cCOMB) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP))) @ (cCOMB @ essence))) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i'))) @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ sCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vOR)) @ (bCOMB @ (bCOMB @ vNOT))))) @ rel) @ (bCOMB @ (bCOMB @ vSIGMA(mu)) @ cCOMB)))) @ X1 = $true)) )),
1.47/0.57	  inference(combinator_normalisation,[],[f127])).
1.47/0.57	tff(f129,plain,(
1.47/0.57	  ( ! [X1] : ((positive @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu -> '$i' -> '$o')) @ cCOMB) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP))) @ (cCOMB @ essence))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel))))) @ (bCOMB @ (bCOMB @ vSIGMA(mu)) @ cCOMB)))) @ X1 = $true)) )),
1.47/0.57	  inference(combinator_demodulation,[],[f128])).
1.47/0.57	tff(f130,plain,(
1.47/0.57	  (vPI('$i') @ (bCOMB @ vPI('$i') @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ rel))) @ rel)) = $true)),
1.47/0.57	  inference(combinator_demodulation,[],[f125])).
1.47/0.57	tff(f131,plain,(
1.47/0.57	  ( ! [X1] : ((bCOMB @ vPI('$i') @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ rel))) @ rel) @ X1 = $true)) )),
1.47/0.57	  inference(pi_clausification,[],[f130])).
1.47/0.57	tff(f132,plain,(
1.47/0.57	  ( ! [X1] : ((vPI('$i') @ (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ rel @ X1)) @ (rel @ X1)) = $true)) )),
1.47/0.57	  inference(combinator_demodulation,[],[f131])).
1.74/0.59	tff(f133,plain,(
1.74/0.59	  ( ! [X2,X1] : ((sCOMB @ (bCOMB @ vIMP @ (cCOMB @ rel @ X1)) @ (rel @ X1) @ X2 = $true)) )),
1.74/0.59	  inference(pi_clausification,[],[f132])).
1.74/0.59	tff(f134,plain,(
1.74/0.59	  ( ! [X2,X1] : ((vIMP @ (rel @ X2 @ X1) @ (rel @ X1 @ X2) = $true)) )),
1.74/0.59	  inference(combinator_demodulation,[],[f133])).
1.74/0.59	tff(f135,plain,(
1.74/0.59	  ( ! [X2,X1] : ((rel @ X2 @ X1 = $false) | (rel @ X1 @ X2 = $true)) )),
1.74/0.59	  inference(binary_proxy_clausification,[],[f134])).
1.74/0.59	tff(f136,plain,(
1.74/0.59	  ( ! [X1] : ((bCOMB @ (bCOMB @ vPI(mu)) @ cCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu -> '$i' -> '$o')) @ cCOMB) @ (bCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) @ positive)) @ (cCOMB @ iCOMB)))) @ (essence @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu -> '$i' -> '$o')) @ cCOMB) @ (bCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) @ positive)) @ (cCOMB @ iCOMB))))) @ X1 = $true)) )),
1.74/0.59	  inference(pi_clausification,[],[f124])).
1.74/0.59	tff(f137,plain,(
1.74/0.59	  ( ! [X1] : ((vPI(mu) @ (cCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu -> '$i' -> '$o')) @ cCOMB) @ (bCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) @ positive)) @ (cCOMB @ iCOMB)))) @ (essence @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu -> '$i' -> '$o')) @ cCOMB) @ (bCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) @ positive)) @ (cCOMB @ iCOMB))))) @ X1) = $true)) )),
1.74/0.59	  inference(combinator_demodulation,[],[f136])).
1.74/0.59	tff(f138,plain,(
1.74/0.59	  ( ! [X2:mu,X1] : ((cCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu -> '$i' -> '$o')) @ cCOMB) @ (bCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) @ positive)) @ (cCOMB @ iCOMB)))) @ (essence @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu -> '$i' -> '$o')) @ cCOMB) @ (bCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) @ positive)) @ (cCOMB @ iCOMB))))) @ X1 @ X2 = $true)) )),
1.74/0.59	  inference(pi_clausification,[],[f137])).
1.74/0.59	tff(f139,plain,(
1.74/0.59	  ( ! [X2:mu,X1] : ((vIMP @ (vPI(mu -> '$i' -> '$o') @ (cCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) @ positive) @ (cCOMB @ iCOMB @ X2)) @ X1)) @ (essence @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu -> '$i' -> '$o')) @ cCOMB) @ (bCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) @ positive)) @ (cCOMB @ iCOMB))) @ X2 @ X1) = $true)) )),
1.74/0.59	  inference(combinator_demodulation,[],[f138])).
1.74/0.59	tff(f140,plain,(
1.74/0.59	  ( ! [X2:mu,X1] : ((vPI(mu -> '$i' -> '$o') @ (cCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) @ positive) @ (cCOMB @ iCOMB @ X2)) @ X1) = $false) | (essence @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu -> '$i' -> '$o')) @ cCOMB) @ (bCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) @ positive)) @ (cCOMB @ iCOMB))) @ X2 @ X1 = $true)) )),
1.74/0.59	  inference(binary_proxy_clausification,[],[f139])).
1.74/0.59	tff(f141,plain,(
1.74/0.59	  ( ! [X2:mu,X1] : ((cCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) @ positive) @ (cCOMB @ iCOMB @ X2)) @ X1 @ (sK0 @ X2 @ X1) = $false) | (essence @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu -> '$i' -> '$o')) @ cCOMB) @ (bCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) @ positive)) @ (cCOMB @ iCOMB))) @ X2 @ X1 = $true)) )),
1.74/0.59	  inference(sigma_clausification,[],[f140])).
1.74/0.59	tff(f142,plain,(
1.74/0.59	  ( ! [X2:mu,X1] : ((vIMP @ (positive @ (sK0 @ X2 @ X1) @ X1) @ (sK0 @ X2 @ X1 @ X2 @ X1) = $false) | (essence @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu -> '$i' -> '$o')) @ cCOMB) @ (bCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) @ positive)) @ (cCOMB @ iCOMB))) @ X2 @ X1 = $true)) )),
1.74/0.59	  inference(combinator_demodulation,[],[f141])).
1.74/0.59	tff(f143,plain,(
1.74/0.59	  ( ! [X2:mu,X1] : ((essence @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu -> '$i' -> '$o')) @ cCOMB) @ (bCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) @ positive)) @ (cCOMB @ iCOMB))) @ X2 @ X1 = $true) | (positive @ (sK0 @ X2 @ X1) @ X1 = $true)) )),
1.74/0.59	  inference(binary_proxy_clausification,[],[f142])).
1.74/0.59	tff(f144,plain,(
1.74/0.59	  ( ! [X2:mu,X1] : ((essence @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu -> '$i' -> '$o')) @ cCOMB) @ (bCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) @ positive)) @ (cCOMB @ iCOMB))) @ X2 @ X1 = $true) | (sK0 @ X2 @ X1 @ X2 @ X1 = $false)) )),
1.74/0.59	  inference(binary_proxy_clausification,[],[f142])).
1.74/0.59	tff(f145,plain,(
1.74/0.59	  ( ! [X1] : ((bCOMB @ (bCOMB @ (bCOMB @ vSIGMA('$i'))) @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ sCOMB) @ (bCOMB @ (bCOMB @ vAND)))) @ rel @ (bCOMB @ (bCOMB @ vSIGMA(mu)) @ cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu -> '$i' -> '$o')) @ cCOMB) @ (bCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) @ positive)) @ (cCOMB @ iCOMB)))) @ X1 = $true)) )),
1.74/0.59	  inference(pi_clausification,[],[f123])).
1.74/0.59	tff(f146,plain,(
1.74/0.59	  ( ! [X1] : ((vSIGMA('$i') @ (sCOMB @ (bCOMB @ vAND @ (rel @ X1)) @ (bCOMB @ vSIGMA(mu) @ (cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu -> '$i' -> '$o')) @ cCOMB) @ (bCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) @ positive)) @ (cCOMB @ iCOMB)))))) = $true)) )),
1.74/0.59	  inference(combinator_demodulation,[],[f145])).
1.74/0.59	tff(f147,plain,(
1.74/0.59	  ( ! [X1] : ((sCOMB @ (bCOMB @ vAND @ (rel @ X1)) @ (bCOMB @ vSIGMA(mu) @ (cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu -> '$i' -> '$o')) @ cCOMB) @ (bCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) @ positive)) @ (cCOMB @ iCOMB))))) @ (sK1 @ X1) = $true)) )),
1.74/0.59	  inference(sigma_clausification,[],[f146])).
1.74/0.59	tff(f148,plain,(
1.74/0.59	  ( ! [X1] : ((vAND @ (rel @ X1 @ (sK1 @ X1)) @ (vSIGMA(mu) @ (cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu -> '$i' -> '$o')) @ cCOMB) @ (bCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) @ positive)) @ (cCOMB @ iCOMB))) @ (sK1 @ X1))) = $true)) )),
1.74/0.59	  inference(combinator_demodulation,[],[f147])).
1.74/0.59	tff(f149,plain,(
1.74/0.59	  ( ! [X1] : ((rel @ X1 @ (sK1 @ X1) = $true)) )),
1.74/0.59	  inference(binary_proxy_clausification,[],[f148])).
1.74/0.59	tff(f150,plain,(
1.74/0.59	  ( ! [X1] : ((vSIGMA(mu) @ (cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu -> '$i' -> '$o')) @ cCOMB) @ (bCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) @ positive)) @ (cCOMB @ iCOMB))) @ (sK1 @ X1)) = $true)) )),
1.74/0.59	  inference(binary_proxy_clausification,[],[f148])).
1.74/0.59	tff(f151,plain,(
1.74/0.59	  ( ! [X1] : ((cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu -> '$i' -> '$o')) @ cCOMB) @ (bCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) @ positive)) @ (cCOMB @ iCOMB))) @ (sK1 @ X1) @ (sK2 @ X1) = $true)) )),
1.74/0.59	  inference(sigma_clausification,[],[f150])).
1.74/0.59	tff(f152,plain,(
1.74/0.59	  ( ! [X1] : ((vPI(mu -> '$i' -> '$o') @ (cCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) @ positive) @ (cCOMB @ iCOMB @ (sK2 @ X1))) @ (sK1 @ X1)) = $true)) )),
1.74/0.59	  inference(combinator_demodulation,[],[f151])).
1.74/0.59	tff(f153,plain,(
1.74/0.59	  ( ! [X2:mu -> '$i' -> '$o',X1] : ((cCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) @ positive) @ (cCOMB @ iCOMB @ (sK2 @ X1))) @ (sK1 @ X1) @ X2 = $true)) )),
1.74/0.59	  inference(pi_clausification,[],[f152])).
1.74/0.59	tff(f154,plain,(
1.74/0.59	  ( ! [X2:mu -> '$i' -> '$o',X1] : ((vIMP @ (positive @ X2 @ (sK1 @ X1)) @ (X2 @ (sK2 @ X1) @ (sK1 @ X1)) = $true)) )),
1.74/0.59	  inference(combinator_demodulation,[],[f153])).
1.74/0.59	tff(f155,plain,(
1.74/0.59	  ( ! [X2:mu -> '$i' -> '$o',X1] : ((positive @ X2 @ (sK1 @ X1) = $false) | (X2 @ (sK2 @ X1) @ (sK1 @ X1) = $true)) )),
1.74/0.59	  inference(binary_proxy_clausification,[],[f154])).
1.74/0.59	tff(f156,plain,(
1.74/0.59	  (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i'))) @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ sCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vOR)) @ (bCOMB @ (bCOMB @ vNOT))))) @ rel @ (bCOMB @ (bCOMB @ vSIGMA(mu)) @ cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu -> '$i' -> '$o')) @ cCOMB) @ (bCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) @ positive)) @ (cCOMB @ iCOMB)))) @ sK3 = $false)),
1.74/0.59	  inference(sigma_clausification,[],[f122])).
1.74/0.59	tff(f157,plain,(
1.74/0.59	  (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel @ sK3))) @ (bCOMB @ vSIGMA(mu) @ (cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu -> '$i' -> '$o')) @ cCOMB) @ (bCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) @ positive)) @ (cCOMB @ iCOMB)))))) = $false)),
1.74/0.59	  inference(combinator_demodulation,[],[f156])).
1.74/0.59	tff(f158,plain,(
1.74/0.59	  (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel @ sK3))) @ (bCOMB @ vSIGMA(mu) @ (cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu -> '$i' -> '$o')) @ cCOMB) @ (bCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) @ positive)) @ (cCOMB @ iCOMB))))) @ sK4 = $false)),
1.74/0.59	  inference(sigma_clausification,[],[f157])).
1.74/0.59	tff(f159,plain,(
1.74/0.59	  (vOR @ (vNOT @ (rel @ sK3 @ sK4)) @ (vSIGMA(mu) @ (cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu -> '$i' -> '$o')) @ cCOMB) @ (bCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) @ positive)) @ (cCOMB @ iCOMB))) @ sK4)) = $false)),
1.74/0.59	  inference(combinator_demodulation,[],[f158])).
1.74/0.59	tff(f161,plain,(
1.74/0.59	  (vSIGMA(mu) @ (cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu -> '$i' -> '$o')) @ cCOMB) @ (bCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) @ positive)) @ (cCOMB @ iCOMB))) @ sK4) = $false)),
1.74/0.59	  inference(binary_proxy_clausification,[],[f159])).
1.74/0.59	tff(f162,plain,(
1.74/0.59	  ( ! [X1:mu] : ((cCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu -> '$i' -> '$o')) @ cCOMB) @ (bCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) @ positive)) @ (cCOMB @ iCOMB))) @ sK4 @ X1 = $false)) )),
1.74/0.59	  inference(pi_clausification,[],[f161])).
1.74/0.59	tff(f163,plain,(
1.74/0.59	  ( ! [X1:mu] : ((vPI(mu -> '$i' -> '$o') @ (cCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) @ positive) @ (cCOMB @ iCOMB @ X1)) @ sK4) = $false)) )),
1.74/0.59	  inference(combinator_demodulation,[],[f162])).
1.74/0.59	tff(f164,plain,(
1.74/0.59	  ( ! [X1:mu] : ((cCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) @ positive) @ (cCOMB @ iCOMB @ X1)) @ sK4 @ (sK5 @ X1) = $false)) )),
1.74/0.59	  inference(sigma_clausification,[],[f163])).
1.74/0.59	tff(f165,plain,(
1.74/0.59	  ( ! [X1:mu] : ((vIMP @ (positive @ (sK5 @ X1) @ sK4) @ (sK5 @ X1 @ X1 @ sK4) = $false)) )),
1.74/0.59	  inference(combinator_demodulation,[],[f164])).
1.74/0.59	tff(f166,plain,(
1.74/0.59	  ( ! [X1:mu] : ((positive @ (sK5 @ X1) @ sK4 = $true)) )),
1.74/0.59	  inference(binary_proxy_clausification,[],[f165])).
1.74/0.59	tff(f167,plain,(
1.74/0.59	  ( ! [X1:mu] : ((sK5 @ X1 @ X1 @ sK4 = $false)) )),
1.74/0.59	  inference(binary_proxy_clausification,[],[f165])).
1.74/0.59	tff(f183,plain,(
1.74/0.59	  ( ! [X1] : (($false = $true) | (rel @ (sK1 @ X1) @ X1 = $true)) )),
1.74/0.59	  inference(superposition,[],[f149,f135])).
1.74/0.59	tff(f186,plain,(
1.74/0.59	  ( ! [X1] : ((rel @ (sK1 @ X1) @ X1 = $true)) )),
1.74/0.59	  inference(trivial_inequality_removal,[],[f183])).
1.74/0.59	tff(f194,plain,(
1.74/0.59	  ( ! [X0] : (($false = $true) | (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu -> '$i' -> '$o')) @ cCOMB) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP))) @ (cCOMB @ essence))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel))))) @ (bCOMB @ (bCOMB @ vSIGMA(mu)) @ cCOMB))) @ (sK2 @ X0) @ (sK1 @ X0) = $true)) )),
1.74/0.59	  inference(superposition,[],[f129,f155])).
1.74/0.59	tff(f195,plain,(
1.74/0.59	  ( ! [X0] : ((bCOMB @ (bCOMB @ (bCOMB @ vPI(mu -> '$i' -> '$o')) @ cCOMB) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP))) @ (cCOMB @ essence))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel))))) @ (bCOMB @ (bCOMB @ vSIGMA(mu)) @ cCOMB))) @ (sK2 @ X0) @ (sK1 @ X0) = $true)) )),
1.74/0.59	  inference(trivial_inequality_removal,[],[f194])).
1.74/0.59	tff(f196,plain,(
1.74/0.59	  ( ! [X0] : ((vPI(mu -> '$i' -> '$o') @ (cCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) @ (cCOMB @ essence @ (sK2 @ X0))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel))))) @ (bCOMB @ (bCOMB @ vSIGMA(mu)) @ cCOMB))) @ (sK1 @ X0)) = $true)) )),
1.74/0.59	  inference(combinator_demodulation,[],[f195])).
1.74/0.59	tff(f197,plain,(
1.74/0.59	  ( ! [X0,X1:mu -> '$i' -> '$o'] : ((cCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) @ (cCOMB @ essence @ (sK2 @ X0))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ rel))))) @ (bCOMB @ (bCOMB @ vSIGMA(mu)) @ cCOMB))) @ (sK1 @ X0) @ X1 = $true)) )),
1.74/0.59	  inference(pi_clausification,[],[f196])).
1.74/0.59	tff(f198,plain,(
1.74/0.59	  ( ! [X0,X1:mu -> '$i' -> '$o'] : ((vIMP @ (essence @ X1 @ (sK2 @ X0) @ (sK1 @ X0)) @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel @ (sK1 @ X0)))) @ (bCOMB @ vSIGMA(mu) @ (cCOMB @ X1)))) = $true)) )),
1.74/0.59	  inference(combinator_demodulation,[],[f197])).
1.74/0.59	tff(f199,plain,(
1.74/0.59	  ( ! [X0,X1:mu -> '$i' -> '$o'] : ((essence @ X1 @ (sK2 @ X0) @ (sK1 @ X0) = $false) | (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel @ (sK1 @ X0)))) @ (bCOMB @ vSIGMA(mu) @ (cCOMB @ X1))) = $true)) )),
1.74/0.59	  inference(binary_proxy_clausification,[],[f198])).
1.74/0.59	tff(f200,plain,(
1.74/0.59	  ( ! [X2,X0,X1:mu -> '$i' -> '$o'] : ((essence @ X1 @ (sK2 @ X0) @ (sK1 @ X0) = $false) | (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (rel @ (sK1 @ X0)))) @ (bCOMB @ vSIGMA(mu) @ (cCOMB @ X1)) @ X2 = $true)) )),
1.74/0.59	  inference(pi_clausification,[],[f199])).
1.74/0.59	tff(f201,plain,(
1.74/0.59	  ( ! [X2,X0,X1:mu -> '$i' -> '$o'] : ((essence @ X1 @ (sK2 @ X0) @ (sK1 @ X0) = $false) | (vOR @ (vNOT @ (rel @ (sK1 @ X0) @ X2)) @ (vSIGMA(mu) @ (cCOMB @ X1 @ X2)) = $true)) )),
1.74/0.59	  inference(combinator_demodulation,[],[f200])).
1.74/0.59	tff(f202,plain,(
1.74/0.59	  ( ! [X2,X0,X1:mu -> '$i' -> '$o'] : ((essence @ X1 @ (sK2 @ X0) @ (sK1 @ X0) = $false) | (vNOT @ (rel @ (sK1 @ X0) @ X2) = $true) | (vSIGMA(mu) @ (cCOMB @ X1 @ X2) = $true)) )),
1.74/0.59	  inference(binary_proxy_clausification,[],[f201])).
1.74/0.59	tff(f203,plain,(
1.74/0.59	  ( ! [X2,X0,X1:mu -> '$i' -> '$o'] : ((essence @ X1 @ (sK2 @ X0) @ (sK1 @ X0) = $false) | (vNOT @ (rel @ (sK1 @ X0) @ X2) = $true) | (cCOMB @ X1 @ X2 @ (sK6 @ X2 @ X1) = $true)) )),
1.74/0.59	  inference(sigma_clausification,[],[f202])).
1.74/0.59	tff(f204,plain,(
1.74/0.59	  ( ! [X2,X0,X1:mu -> '$i' -> '$o'] : ((essence @ X1 @ (sK2 @ X0) @ (sK1 @ X0) = $false) | (rel @ (sK1 @ X0) @ X2 = $false) | (cCOMB @ X1 @ X2 @ (sK6 @ X2 @ X1) = $true)) )),
1.74/0.59	  inference(not_proxy_clausification,[],[f203])).
1.74/0.59	tff(f205,plain,(
1.74/0.59	  ( ! [X2,X0,X1:mu -> '$i' -> '$o'] : ((essence @ X1 @ (sK2 @ X0) @ (sK1 @ X0) = $false) | (rel @ (sK1 @ X0) @ X2 = $false) | (X1 @ (sK6 @ X2 @ X1) @ X2 = $true)) )),
1.74/0.59	  inference(combinator_demodulation,[],[f204])).
1.74/0.59	tff(f218,plain,(
1.74/0.59	  ( ! [X2,X3] : (($false = $true) | (rel @ (sK1 @ X2) @ X3 = $false) | (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu -> '$i' -> '$o')) @ cCOMB) @ (bCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) @ positive)) @ (cCOMB @ iCOMB)) @ (sK6 @ X3 @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu -> '$i' -> '$o')) @ cCOMB) @ (bCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) @ positive)) @ (cCOMB @ iCOMB)))) @ X3 = $true) | (sK0 @ (sK2 @ X2) @ (sK1 @ X2) @ (sK2 @ X2) @ (sK1 @ X2) = $false)) )),
1.74/0.59	  inference(superposition,[],[f205,f144])).
1.74/0.59	tff(f225,plain,(
1.74/0.59	  ( ! [X2,X3] : ((rel @ (sK1 @ X2) @ X3 = $false) | (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu -> '$i' -> '$o')) @ cCOMB) @ (bCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) @ positive)) @ (cCOMB @ iCOMB)) @ (sK6 @ X3 @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu -> '$i' -> '$o')) @ cCOMB) @ (bCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) @ positive)) @ (cCOMB @ iCOMB)))) @ X3 = $true) | (sK0 @ (sK2 @ X2) @ (sK1 @ X2) @ (sK2 @ X2) @ (sK1 @ X2) = $false)) )),
1.74/0.59	  inference(trivial_inequality_removal,[],[f218])).
1.74/0.59	tff(f226,plain,(
1.74/0.59	  ( ! [X2,X3] : ((rel @ (sK1 @ X2) @ X3 = $false) | (vPI(mu -> '$i' -> '$o') @ (cCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) @ positive) @ (cCOMB @ iCOMB @ (sK6 @ X3 @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu -> '$i' -> '$o')) @ cCOMB) @ (bCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) @ positive)) @ (cCOMB @ iCOMB)))))) @ X3) = $true) | (sK0 @ (sK2 @ X2) @ (sK1 @ X2) @ (sK2 @ X2) @ (sK1 @ X2) = $false)) )),
1.74/0.59	  inference(combinator_demodulation,[],[f225])).
1.74/0.59	tff(f227,plain,(
1.74/0.59	  ( ! [X4:mu -> '$i' -> '$o',X2,X3] : ((rel @ (sK1 @ X2) @ X3 = $false) | (cCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) @ positive) @ (cCOMB @ iCOMB @ (sK6 @ X3 @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu -> '$i' -> '$o')) @ cCOMB) @ (bCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) @ positive)) @ (cCOMB @ iCOMB)))))) @ X3 @ X4 = $true) | (sK0 @ (sK2 @ X2) @ (sK1 @ X2) @ (sK2 @ X2) @ (sK1 @ X2) = $false)) )),
1.74/0.59	  inference(pi_clausification,[],[f226])).
1.74/0.59	tff(f228,plain,(
1.74/0.59	  ( ! [X4:mu -> '$i' -> '$o',X2,X3] : ((rel @ (sK1 @ X2) @ X3 = $false) | (vIMP @ (positive @ X4 @ X3) @ (X4 @ (sK6 @ X3 @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu -> '$i' -> '$o')) @ cCOMB) @ (bCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) @ positive)) @ (cCOMB @ iCOMB)))) @ X3) = $true) | (sK0 @ (sK2 @ X2) @ (sK1 @ X2) @ (sK2 @ X2) @ (sK1 @ X2) = $false)) )),
1.74/0.59	  inference(combinator_demodulation,[],[f227])).
1.74/0.59	tff(f229,plain,(
1.74/0.59	  ( ! [X4:mu -> '$i' -> '$o',X2,X3] : ((X4 @ (sK6 @ X3 @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu -> '$i' -> '$o')) @ cCOMB) @ (bCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) @ positive)) @ (cCOMB @ iCOMB)))) @ X3 = $true) | (positive @ X4 @ X3 = $false) | (sK0 @ (sK2 @ X2) @ (sK1 @ X2) @ (sK2 @ X2) @ (sK1 @ X2) = $false) | (rel @ (sK1 @ X2) @ X3 = $false)) )),
1.74/0.59	  inference(binary_proxy_clausification,[],[f228])).
1.74/0.59	tff(f244,plain,(
1.74/0.59	  ( ! [X6,X7] : (($false = $true) | (positive @ (sK0 @ (sK2 @ X6) @ (sK1 @ X6)) @ (sK1 @ X6) = $true) | (rel @ (sK1 @ X6) @ X7 = $false) | (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu -> '$i' -> '$o')) @ cCOMB) @ (bCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) @ positive)) @ (cCOMB @ iCOMB)) @ (sK6 @ X7 @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu -> '$i' -> '$o')) @ cCOMB) @ (bCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) @ positive)) @ (cCOMB @ iCOMB)))) @ X7 = $true)) )),
1.74/0.59	  inference(superposition,[],[f143,f205])).
1.74/0.59	tff(f257,plain,(
1.74/0.59	  ( ! [X6,X7] : ((positive @ (sK0 @ (sK2 @ X6) @ (sK1 @ X6)) @ (sK1 @ X6) = $true) | (rel @ (sK1 @ X6) @ X7 = $false) | (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu -> '$i' -> '$o')) @ cCOMB) @ (bCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) @ positive)) @ (cCOMB @ iCOMB)) @ (sK6 @ X7 @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu -> '$i' -> '$o')) @ cCOMB) @ (bCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) @ positive)) @ (cCOMB @ iCOMB)))) @ X7 = $true)) )),
1.74/0.59	  inference(trivial_inequality_removal,[],[f244])).
1.74/0.60	tff(f258,plain,(
1.74/0.60	  ( ! [X6,X7] : ((positive @ (sK0 @ (sK2 @ X6) @ (sK1 @ X6)) @ (sK1 @ X6) = $true) | (rel @ (sK1 @ X6) @ X7 = $false) | (vPI(mu -> '$i' -> '$o') @ (cCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) @ positive) @ (cCOMB @ iCOMB @ (sK6 @ X7 @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu -> '$i' -> '$o')) @ cCOMB) @ (bCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) @ positive)) @ (cCOMB @ iCOMB)))))) @ X7) = $true)) )),
1.74/0.60	  inference(combinator_demodulation,[],[f257])).
1.74/0.60	tff(f259,plain,(
1.74/0.60	  ( ! [X6,X8:mu -> '$i' -> '$o',X7] : ((positive @ (sK0 @ (sK2 @ X6) @ (sK1 @ X6)) @ (sK1 @ X6) = $true) | (rel @ (sK1 @ X6) @ X7 = $false) | (cCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) @ positive) @ (cCOMB @ iCOMB @ (sK6 @ X7 @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu -> '$i' -> '$o')) @ cCOMB) @ (bCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) @ positive)) @ (cCOMB @ iCOMB)))))) @ X7 @ X8 = $true)) )),
1.74/0.60	  inference(pi_clausification,[],[f258])).
1.74/0.60	tff(f260,plain,(
1.74/0.60	  ( ! [X6,X8:mu -> '$i' -> '$o',X7] : ((positive @ (sK0 @ (sK2 @ X6) @ (sK1 @ X6)) @ (sK1 @ X6) = $true) | (rel @ (sK1 @ X6) @ X7 = $false) | (vIMP @ (positive @ X8 @ X7) @ (X8 @ (sK6 @ X7 @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu -> '$i' -> '$o')) @ cCOMB) @ (bCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) @ positive)) @ (cCOMB @ iCOMB)))) @ X7) = $true)) )),
1.74/0.60	  inference(combinator_demodulation,[],[f259])).
1.74/0.60	tff(f261,plain,(
1.74/0.60	  ( ! [X6,X8:mu -> '$i' -> '$o',X7] : ((X8 @ (sK6 @ X7 @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu -> '$i' -> '$o')) @ cCOMB) @ (bCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) @ positive)) @ (cCOMB @ iCOMB)))) @ X7 = $true) | (rel @ (sK1 @ X6) @ X7 = $false) | (positive @ X8 @ X7 = $false) | (positive @ (sK0 @ (sK2 @ X6) @ (sK1 @ X6)) @ (sK1 @ X6) = $true)) )),
1.74/0.60	  inference(binary_proxy_clausification,[],[f260])).
1.74/0.60	tff(f273,plain,(
1.74/0.60	  ( ! [X0] : (($false = $true) | (positive @ (sK5 @ (sK6 @ sK4 @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu -> '$i' -> '$o')) @ cCOMB) @ (bCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) @ positive)) @ (cCOMB @ iCOMB))))) @ sK4 = $false) | (sK0 @ (sK2 @ X0) @ (sK1 @ X0) @ (sK2 @ X0) @ (sK1 @ X0) = $false) | (rel @ (sK1 @ X0) @ sK4 = $false)) )),
1.74/0.60	  inference(superposition,[],[f229,f167])).
1.74/0.60	tff(f276,plain,(
1.74/0.60	  ( ! [X0] : ((positive @ (sK5 @ (sK6 @ sK4 @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu -> '$i' -> '$o')) @ cCOMB) @ (bCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) @ positive)) @ (cCOMB @ iCOMB))))) @ sK4 = $false) | (sK0 @ (sK2 @ X0) @ (sK1 @ X0) @ (sK2 @ X0) @ (sK1 @ X0) = $false) | (rel @ (sK1 @ X0) @ sK4 = $false)) )),
1.74/0.60	  inference(trivial_inequality_removal,[],[f273])).
1.74/0.60	tff(f277,plain,(
1.74/0.60	  ( ! [X0:mu,X1] : (($false = $true) | (sK0 @ (sK2 @ X1) @ (sK1 @ X1) @ (sK2 @ X1) @ (sK1 @ X1) = $false) | (rel @ (sK1 @ X1) @ sK4 = $false) | sK5 @ X0 != sK5 @ (sK6 @ sK4 @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu -> '$i' -> '$o')) @ cCOMB) @ (bCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) @ positive)) @ (cCOMB @ iCOMB))))) )),
1.74/0.60	  inference(superposition,[],[f276,f166])).
1.74/0.60	tff(f284,plain,(
1.74/0.60	  ( ! [X0:mu,X1] : (sK5 @ X0 != sK5 @ (sK6 @ sK4 @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu -> '$i' -> '$o')) @ cCOMB) @ (bCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) @ positive)) @ (cCOMB @ iCOMB)))) | (rel @ (sK1 @ X1) @ sK4 = $false) | (sK0 @ (sK2 @ X1) @ (sK1 @ X1) @ (sK2 @ X1) @ (sK1 @ X1) = $false)) )),
1.74/0.60	  inference(trivial_inequality_removal,[],[f277])).
1.74/0.60	tff(f296,plain,(
1.74/0.60	  ( ! [X0] : ((sK0 @ (sK2 @ X0) @ (sK1 @ X0) @ (sK2 @ X0) @ (sK1 @ X0) = $false) | (rel @ (sK1 @ X0) @ sK4 = $false)) )),
1.74/0.60	  inference(equality_resolution,[],[f284])).
1.74/0.60	tff(f303,plain,(
1.74/0.60	  ( ! [X0] : (($false = $true) | (rel @ (sK1 @ X0) @ sK4 = $false) | (positive @ (sK5 @ (sK6 @ sK4 @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu -> '$i' -> '$o')) @ cCOMB) @ (bCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) @ positive)) @ (cCOMB @ iCOMB))))) @ sK4 = $false) | (positive @ (sK0 @ (sK2 @ X0) @ (sK1 @ X0)) @ (sK1 @ X0) = $true)) )),
1.74/0.60	  inference(superposition,[],[f261,f167])).
1.74/0.60	tff(f306,plain,(
1.74/0.60	  ( ! [X0] : ((positive @ (sK5 @ (sK6 @ sK4 @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu -> '$i' -> '$o')) @ cCOMB) @ (bCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) @ positive)) @ (cCOMB @ iCOMB))))) @ sK4 = $false) | (rel @ (sK1 @ X0) @ sK4 = $false) | (positive @ (sK0 @ (sK2 @ X0) @ (sK1 @ X0)) @ (sK1 @ X0) = $true)) )),
1.74/0.60	  inference(trivial_inequality_removal,[],[f303])).
1.74/0.60	tff(f315,plain,(
1.74/0.60	  ( ! [X0:mu,X1] : (($false = $true) | (rel @ (sK1 @ X1) @ sK4 = $false) | (positive @ (sK0 @ (sK2 @ X1) @ (sK1 @ X1)) @ (sK1 @ X1) = $true) | sK5 @ X0 != sK5 @ (sK6 @ sK4 @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu -> '$i' -> '$o')) @ cCOMB) @ (bCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) @ positive)) @ (cCOMB @ iCOMB))))) )),
1.74/0.60	  inference(superposition,[],[f306,f166])).
1.74/0.60	tff(f322,plain,(
1.74/0.60	  ( ! [X0:mu,X1] : (sK5 @ X0 != sK5 @ (sK6 @ sK4 @ (bCOMB @ (bCOMB @ (bCOMB @ vPI(mu -> '$i' -> '$o')) @ cCOMB) @ (bCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vIMP)) @ positive)) @ (cCOMB @ iCOMB)))) | (positive @ (sK0 @ (sK2 @ X1) @ (sK1 @ X1)) @ (sK1 @ X1) = $true) | (rel @ (sK1 @ X1) @ sK4 = $false)) )),
1.74/0.60	  inference(trivial_inequality_removal,[],[f315])).
1.74/0.60	tff(f334,plain,(
1.74/0.60	  ( ! [X0] : ((positive @ (sK0 @ (sK2 @ X0) @ (sK1 @ X0)) @ (sK1 @ X0) = $true) | (rel @ (sK1 @ X0) @ sK4 = $false)) )),
1.74/0.60	  inference(equality_resolution,[],[f322])).
1.74/0.60	tff(f336,plain,(
1.74/0.60	  ( ! [X0] : (($false = $true) | (rel @ (sK1 @ X0) @ sK4 = $false) | (sK0 @ (sK2 @ X0) @ (sK1 @ X0) @ (sK2 @ X0) @ (sK1 @ X0) = $true)) )),
1.74/0.60	  inference(superposition,[],[f334,f155])).
1.74/0.60	tff(f339,plain,(
1.74/0.60	  ( ! [X0] : ((sK0 @ (sK2 @ X0) @ (sK1 @ X0) @ (sK2 @ X0) @ (sK1 @ X0) = $true) | (rel @ (sK1 @ X0) @ sK4 = $false)) )),
1.74/0.60	  inference(trivial_inequality_removal,[],[f336])).
1.74/0.60	tff(f349,plain,(
1.74/0.60	  ( ! [X1] : (($false = $true) | (rel @ (sK1 @ X1) @ sK4 = $false) | (rel @ (sK1 @ X1) @ sK4 = $false)) )),
1.74/0.60	  inference(superposition,[],[f339,f296])).
1.74/0.60	tff(f353,plain,(
1.74/0.60	  ( ! [X1] : (($false = $true) | (rel @ (sK1 @ X1) @ sK4 = $false)) )),
1.74/0.60	  inference(duplicate_literal_removal,[],[f349])).
1.74/0.60	tff(f354,plain,(
1.74/0.60	  ( ! [X1] : ((rel @ (sK1 @ X1) @ sK4 = $false)) )),
1.74/0.60	  inference(trivial_inequality_removal,[],[f353])).
1.74/0.60	tff(f356,plain,(
1.74/0.60	  ($false = $true)),
1.74/0.60	  inference(superposition,[],[f186,f354])).
1.74/0.60	tff(f357,plain,(
1.74/0.60	  $false),
1.74/0.60	  inference(trivial_inequality_removal,[],[f356])).
1.74/0.60	% SZS output end Proof for theBenchmark
1.74/0.60	% (14268)------------------------------
1.74/0.60	% (14268)Version: Vampire 4.5.0 (commit 7ae30c7f on 2020-06-30 15:57:20 +0100)
1.74/0.60	% (14268)Termination reason: Refutation
1.74/0.60	
1.74/0.60	% (14268)Memory used [KB]: 1918
1.74/0.60	% (14268)Time elapsed: 0.204 s
1.74/0.60	% (14268)------------------------------
1.74/0.60	% (14268)------------------------------
1.74/0.60	% (14267)Success in time 0.234 s
1.74/0.60	EOF