0.11/0.17	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.13/0.18	% Command    : run_vampire %s %d
0.13/0.39	% Computer   : n004.cluster.edu
0.13/0.39	% Model      : x86_64 x86_64
0.13/0.39	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.39	% Memory     : 8042.1875MB
0.13/0.39	% OS         : Linux 3.10.0-693.el7.x86_64
0.13/0.39	% CPULimit   : 960
0.13/0.39	% WCLimit    : 120
0.13/0.39	% DateTime   : Thu Jul  2 07:52:14 EDT 2020
0.13/0.40	% CPUTime    : 
0.13/0.42	% (26651)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
0.13/0.42	% (26653)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
0.13/0.44	% (26659)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
0.20/0.44	% (26645)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
0.20/0.44	% (26649)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
0.20/0.44	% (26650)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
0.20/0.44	% (26658)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
0.20/0.45	% (26647)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
0.20/0.45	% (26668)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
0.20/0.45	% (26646)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
0.20/0.45	% (26657)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
0.20/0.45	% (26656)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
0.20/0.45	% (26660)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
0.20/0.46	% (26669)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
0.20/0.46	% (26652)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
0.20/0.46	% (26661)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
0.20/0.46	% (26655)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
0.20/0.46	% (26654)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
0.20/0.47	% (26648)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
0.20/0.47	% (26663)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
0.20/0.47	% (26674)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
0.20/0.47	% (26662)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
0.20/0.47	% (26671)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
0.20/0.48	% (26672)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
0.20/0.48	% (26664)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
0.20/0.48	% (26670)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
0.20/0.49	% (26665)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
0.20/0.49	% (26667)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
0.20/0.49	% (26673)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
0.20/0.50	% (26666)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
0.20/0.52	% (26668)Refutation not found, incomplete strategy
0.20/0.52	% (26668)------------------------------
0.20/0.52	% (26668)Version: Vampire 4.5.0 (commit 7ae30c7f on 2020-06-30 15:57:20 +0100)
0.20/0.53	% (26668)Termination reason: Refutation not found, incomplete strategy
0.20/0.53	
0.20/0.53	% (26668)Memory used [KB]: 9978
0.20/0.53	% (26668)Time elapsed: 0.102 s
0.20/0.53	% (26668)------------------------------
0.20/0.53	% (26668)------------------------------
1.09/0.56	% (26657)Refutation found. Thanks to Tanya!
1.09/0.56	% SZS status Theorem for theBenchmark
1.22/0.58	% (26675)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
1.22/0.58	% SZS output start Proof for theBenchmark
1.22/0.58	tff(func_def_0, type, mu: '$tType').
1.22/0.58	tff(func_def_4, type, ->: ('$tType' * '$tType') > '$tType').
1.22/0.58	tff(func_def_5, type, meq_ind: mu -> mu -> '$i' -> '$o').
1.22/0.58	tff(func_def_6, type, meq_prop: ('$i' -> '$o') -> ('$i' -> '$o') -> '$i' -> '$o').
1.22/0.58	tff(func_def_7, type, vAPP: !>[X0: $ttype, X1: $ttype]:(X0 -> X1 * X0) > X1).
1.22/0.58	tff(func_def_8, type, mnot: ('$i' -> '$o') -> '$i' -> '$o').
1.22/0.58	tff(func_def_9, type, mor: ('$i' -> '$o') -> ('$i' -> '$o') -> '$i' -> '$o').
1.22/0.58	tff(func_def_10, type, mand: ('$i' -> '$o') -> ('$i' -> '$o') -> '$i' -> '$o').
1.22/0.58	tff(func_def_11, type, mimplies: ('$i' -> '$o') -> ('$i' -> '$o') -> '$i' -> '$o').
1.22/0.59	tff(func_def_12, type, mimplied: ('$i' -> '$o') -> ('$i' -> '$o') -> '$i' -> '$o').
1.22/0.59	tff(func_def_13, type, mequiv: ('$i' -> '$o') -> ('$i' -> '$o') -> '$i' -> '$o').
1.22/0.59	tff(func_def_14, type, mxor: ('$i' -> '$o') -> ('$i' -> '$o') -> '$i' -> '$o').
1.22/0.59	tff(func_def_15, type, mforall_ind: (mu -> '$i' -> '$o') -> '$i' -> '$o').
1.22/0.59	tff(func_def_16, type, mforall_prop: (('$i' -> '$o') -> '$i' -> '$o') -> '$i' -> '$o').
1.22/0.59	tff(func_def_17, type, mexists_ind: (mu -> '$i' -> '$o') -> '$i' -> '$o').
1.22/0.59	tff(func_def_18, type, mexists_prop: (('$i' -> '$o') -> '$i' -> '$o') -> '$i' -> '$o').
1.22/0.59	tff(func_def_19, type, mtrue: '$i' -> '$o').
1.22/0.59	tff(func_def_20, type, mfalse: '$i' -> '$o').
1.22/0.59	tff(func_def_21, type, mbox: ('$i' -> '$i' -> '$o') -> ('$i' -> '$o') -> '$i' -> '$o').
1.22/0.59	tff(func_def_22, type, mdia: ('$i' -> '$i' -> '$o') -> ('$i' -> '$o') -> '$i' -> '$o').
1.22/0.59	tff(func_def_23, type, mreflexive: ('$i' -> '$i' -> '$o') -> '$o').
1.22/0.59	tff(func_def_24, type, msymmetric: ('$i' -> '$i' -> '$o') -> '$o').
1.22/0.59	tff(func_def_25, type, mserial: ('$i' -> '$i' -> '$o') -> '$o').
1.22/0.59	tff(func_def_26, type, mtransitive: ('$i' -> '$i' -> '$o') -> '$o').
1.22/0.59	tff(func_def_27, type, meuclidean: ('$i' -> '$i' -> '$o') -> '$o').
1.22/0.59	tff(func_def_28, type, mpartially_functional: ('$i' -> '$i' -> '$o') -> '$o').
1.22/0.59	tff(func_def_29, type, mfunctional: ('$i' -> '$i' -> '$o') -> '$o').
1.22/0.59	tff(func_def_30, type, mweakly_dense: ('$i' -> '$i' -> '$o') -> '$o').
1.22/0.59	tff(func_def_31, type, mweakly_connected: ('$i' -> '$i' -> '$o') -> '$o').
1.22/0.59	tff(func_def_32, type, mweakly_directed: ('$i' -> '$i' -> '$o') -> '$o').
1.22/0.59	tff(func_def_33, type, mvalid: ('$i' -> '$o') -> '$o').
1.22/0.59	tff(func_def_34, type, minvalid: ('$i' -> '$o') -> '$o').
1.22/0.59	tff(func_def_35, type, msatisfiable: ('$i' -> '$o') -> '$o').
1.22/0.59	tff(func_def_36, type, mcountersatisfiable: ('$i' -> '$o') -> '$o').
1.22/0.59	tff(func_def_37, type, vEPSILON: !>[X0: $ttype]:(X0 -> '$o') -> X0).
1.22/0.59	tff(func_def_38, type, bCOMB: !>[X0: $ttype, X1: $ttype, X2: $ttype]:(X1 -> X2) -> (X0 -> X1) -> X0 -> X2).
1.22/0.59	tff(func_def_39, type, sCOMB: !>[X0: $ttype, X1: $ttype, X2: $ttype]:(X0 -> X1 -> X2) -> (X0 -> X1) -> X0 -> X2).
1.22/0.59	tff(func_def_42, type, vNOT: '$o' -> '$o').
1.22/0.59	tff(func_def_43, type, vPI: !>[X0: $ttype]:(X0 -> '$o') -> '$o').
1.22/0.59	tff(func_def_44, type, vAND: '$o' -> '$o' -> '$o').
1.22/0.59	tff(func_def_45, type, vIMP: '$o' -> '$o' -> '$o').
1.22/0.59	tff(func_def_46, type, vEQ: !>[X0: $ttype]:X0 -> X0 -> '$o').
1.22/0.59	tff(func_def_47, type, vSIGMA: !>[X0: $ttype]:(X0 -> '$o') -> '$o').
1.22/0.59	tff(func_def_48, type, cCOMB: !>[X0: $ttype, X1: $ttype, X2: $ttype]:(X0 -> X1 -> X2) -> X1 -> X0 -> X2).
1.22/0.59	tff(func_def_49, type, iCOMB: !>[X2: $ttype]:X2 -> X2).
1.22/0.59	tff(func_def_50, type, vOR: '$o' -> '$o' -> '$o').
1.22/0.59	tff(func_def_51, type, kCOMB: !>[X1: $ttype, X2: $ttype]:X1 -> X2 -> X1).
1.22/0.59	tff(func_def_52, type, sK0: '$i' -> '$i' -> '$o').
1.22/0.59	tff(func_def_54, type, sK2: '$i' -> ('$i' -> '$o') -> '$i').
1.22/0.59	tff(f3,axiom,(
1.22/0.59	  mnot = (^[X3 : '$i' -> '$o', X2 : '$i'] : ~X3 @ X2)),
1.22/0.59	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot)).
1.22/0.59	tff(f4,axiom,(
1.22/0.59	  mor = (^[X3 : '$i' -> '$o', X4 : '$i' -> '$o', X2 : '$i'] : X4 @ X2 | X3 @ X2)),
1.22/0.59	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor)).
1.22/0.59	tff(f6,axiom,(
1.22/0.59	  mimplies = (^[X3 : '$i' -> '$o', X4 : '$i' -> '$o'] : mor @ (mnot @ X3) @ X4)),
1.22/0.59	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies)).
1.22/0.59	tff(f11,axiom,(
1.22/0.59	  mforall_prop = (^[X3 : ('$i' -> '$o') -> '$i' -> '$o', X2 : '$i'] : ! [X5 : '$i' -> '$o'] : X3 @ X5 @ X2)),
1.22/0.59	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_prop)).
1.22/0.59	tff(f16,axiom,(
1.22/0.59	  mbox = (^[X6 : '$i' -> '$i' -> '$o', X3 : '$i' -> '$o', X2 : '$i'] : ! [X7] : (X3 @ X7 | ~X6 @ X2 @ X7))),
1.22/0.59	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox)).
1.22/0.59	tff(f17,axiom,(
1.22/0.59	  mdia = (^[X6 : '$i' -> '$i' -> '$o', X3 : '$i' -> '$o'] : mnot @ (mbox @ X6 @ (mnot @ X3)))),
1.22/0.59	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia)).
1.22/0.59	tff(f22,axiom,(
1.22/0.59	  meuclidean = (^[X6 : '$i' -> '$i' -> '$o'] : ! [X8,X9,X10] : ((X6 @ X8 @ X10 & X6 @ X8 @ X9) => X6 @ X9 @ X10))),
1.22/0.59	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',meuclidean)).
1.22/0.59	tff(f28,axiom,(
1.22/0.59	  mvalid = (^[X3 : '$i' -> '$o'] : ! [X2] : X3 @ X2)),
1.22/0.59	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mvalid)).
1.22/0.59	tff(f32,conjecture,(
1.22/0.59	  ! [X6 : '$i' -> '$i' -> '$o'] : (mvalid @ (mforall_prop @ (^[X11 : '$i' -> '$o'] : mimplies @ (mdia @ X6 @ X11) @ (mbox @ X6 @ (mdia @ X6 @ X11)))) => meuclidean @ X6)),
1.22/0.59	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj)).
1.22/0.59	tff(f33,negated_conjecture,(
1.22/0.59	  ~! [X6 : '$i' -> '$i' -> '$o'] : (mvalid @ (mforall_prop @ (^[X11 : '$i' -> '$o'] : mimplies @ (mdia @ X6 @ X11) @ (mbox @ X6 @ (mdia @ X6 @ X11)))) => meuclidean @ X6)),
1.22/0.59	  inference(negated_conjecture,[],[f32])).
1.22/0.59	tff(f34,plain,(
1.22/0.59	  ~! [X0 : '$i' -> '$i' -> '$o'] : (mvalid @ (mforall_prop @ (^[X1 : '$i' -> '$o'] : mimplies @ (mdia @ X0 @ X1) @ (mbox @ X0 @ (mdia @ X0 @ X1)))) => meuclidean @ X0)),
1.22/0.59	  inference(rectify,[],[f33])).
1.22/0.59	tff(f35,plain,(
1.22/0.59	  ~! [X0 : '$i' -> '$i' -> '$o'] : ((mvalid @ (mforall_prop @ (sCOMB @ (bCOMB @ mimplies @ (mdia @ X0)) @ (bCOMB @ (mbox @ X0) @ (mdia @ X0)))) = $true) => (meuclidean @ X0 = $true))),
1.22/0.59	  inference(fool_elimination,[],[f34])).
1.22/0.59	tff(f70,plain,(
1.22/0.59	  mvalid = (^[X0 : '$i' -> '$o'] : ! [X1] : X0 @ X1)),
1.22/0.59	  inference(rectify,[],[f28])).
1.22/0.59	tff(f71,plain,(
1.22/0.59	  mvalid = vPI('$i')),
1.22/0.59	  inference(fool_elimination,[],[f70])).
1.22/0.59	tff(f72,plain,(
1.22/0.59	  meuclidean = (^[X0 : '$i' -> '$i' -> '$o'] : ! [X1,X2,X3] : ((X0 @ X1 @ X3 & X0 @ X1 @ X2) => X0 @ X2 @ X3))),
1.22/0.59	  inference(rectify,[],[f22])).
1.22/0.59	tff(f73,plain,(
1.22/0.59	  bCOMB @ vPI('$i') @ (bCOMB @ (bCOMB @ vPI('$i')) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i'))) @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ sCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ cCOMB)) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vIMP))) @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ sCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vAND)) @ cCOMB)))) @ cCOMB))))) @ cCOMB))) = meuclidean),
1.22/0.59	  inference(fool_elimination,[],[f72])).
1.22/0.59	tff(f82,plain,(
1.22/0.59	  mor = (^[X0 : '$i' -> '$o', X1 : '$i' -> '$o', X2 : '$i'] : X1 @ X2 | X0 @ X2)),
1.22/0.59	  inference(rectify,[],[f4])).
1.22/0.59	tff(f83,plain,(
1.22/0.59	  bCOMB @ sCOMB @ (bCOMB @ vOR) = mor),
1.22/0.59	  inference(fool_elimination,[],[f82])).
1.22/0.59	tff(f84,plain,(
1.22/0.59	  mbox = (^[X0 : '$i' -> '$i' -> '$o', X1 : '$i' -> '$o', X2 : '$i'] : ! [X3] : (X1 @ X3 | ~X0 @ X2 @ X3))),
1.22/0.59	  inference(rectify,[],[f16])).
1.22/0.59	tff(f85,plain,(
1.22/0.59	  bCOMB @ (bCOMB @ (bCOMB @ vPI('$i'))) @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ sCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vOR)) @ (bCOMB @ (bCOMB @ vNOT))))) = mbox),
1.22/0.59	  inference(fool_elimination,[],[f84])).
1.22/0.59	tff(f86,plain,(
1.22/0.59	  mimplies = (^[X0 : '$i' -> '$o', X1 : '$i' -> '$o'] : mor @ (mnot @ X0) @ X1)),
1.22/0.59	  inference(rectify,[],[f6])).
1.22/0.59	tff(f87,plain,(
1.22/0.59	  bCOMB @ mor @ mnot = mimplies),
1.22/0.59	  inference(fool_elimination,[],[f86])).
1.22/0.59	tff(f88,plain,(
1.22/0.59	  mdia = (^[X0 : '$i' -> '$i' -> '$o', X1 : '$i' -> '$o'] : mnot @ (mbox @ X0 @ (mnot @ X1)))),
1.22/0.59	  inference(rectify,[],[f17])).
1.22/0.59	tff(f89,plain,(
1.22/0.59	  bCOMB @ (bCOMB @ mnot) @ (cCOMB @ (bCOMB @ bCOMB @ mbox) @ mnot) = mdia),
1.22/0.59	  inference(fool_elimination,[],[f88])).
1.22/0.59	tff(f90,plain,(
1.22/0.59	  mforall_prop = (^[X0 : ('$i' -> '$o') -> '$i' -> '$o', X1 : '$i'] : ! [X2 : '$i' -> '$o'] : X0 @ X2 @ X1)),
1.22/0.59	  inference(rectify,[],[f11])).
1.22/0.59	tff(f91,plain,(
1.22/0.59	  bCOMB @ (bCOMB @ vPI('$i' -> '$o')) @ cCOMB = mforall_prop),
1.22/0.59	  inference(fool_elimination,[],[f90])).
1.22/0.59	tff(f92,plain,(
1.22/0.59	  mnot = (^[X0 : '$i' -> '$o', X1 : '$i'] : ~X0 @ X1)),
1.22/0.59	  inference(rectify,[],[f3])).
1.22/0.59	tff(f93,plain,(
1.22/0.59	  bCOMB @ vNOT = mnot),
1.22/0.59	  inference(fool_elimination,[],[f92])).
1.22/0.59	tff(f94,plain,(
1.22/0.59	  ? [X0 : '$i' -> '$i' -> '$o'] : ((meuclidean @ X0 != $true) & (mvalid @ (mforall_prop @ (sCOMB @ (bCOMB @ mimplies @ (mdia @ X0)) @ (bCOMB @ (mbox @ X0) @ (mdia @ X0)))) = $true))),
1.22/0.59	  inference(ennf_transformation,[],[f35])).
1.22/0.59	tff(f95,plain,(
1.22/0.59	  ? [X0 : '$i' -> '$i' -> '$o'] : ((meuclidean @ X0 != $true) & (mvalid @ (mforall_prop @ (sCOMB @ (bCOMB @ mimplies @ (mdia @ X0)) @ (bCOMB @ (mbox @ X0) @ (mdia @ X0)))) = $true)) => ((meuclidean @ sK0 != $true) & (mvalid @ (mforall_prop @ (sCOMB @ (bCOMB @ mimplies @ (mdia @ sK0)) @ (bCOMB @ (mbox @ sK0) @ (mdia @ sK0)))) = $true))),
1.22/0.59	  introduced(choice_axiom,[])).
1.22/0.59	tff(f96,plain,(
1.22/0.59	  (meuclidean @ sK0 != $true) & (mvalid @ (mforall_prop @ (sCOMB @ (bCOMB @ mimplies @ (mdia @ sK0)) @ (bCOMB @ (mbox @ sK0) @ (mdia @ sK0)))) = $true)),
1.22/0.59	  inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f94,f95])).
1.22/0.59	tff(f97,plain,(
1.22/0.59	  (mvalid @ (mforall_prop @ (sCOMB @ (bCOMB @ mimplies @ (mdia @ sK0)) @ (bCOMB @ (mbox @ sK0) @ (mdia @ sK0)))) = $true)),
1.22/0.59	  inference(cnf_transformation,[],[f96])).
1.22/0.59	tff(f98,plain,(
1.22/0.59	  (meuclidean @ sK0 != $true)),
1.22/0.59	  inference(cnf_transformation,[],[f96])).
1.22/0.59	tff(f118,plain,(
1.22/0.59	  mvalid = vPI('$i')),
1.22/0.59	  inference(cnf_transformation,[],[f71])).
1.22/0.59	tff(f119,plain,(
1.22/0.59	  bCOMB @ vPI('$i') @ (bCOMB @ (bCOMB @ vPI('$i')) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i'))) @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ sCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ cCOMB)) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vIMP))) @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ sCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vAND)) @ cCOMB)))) @ cCOMB))))) @ cCOMB))) = meuclidean),
1.22/0.59	  inference(cnf_transformation,[],[f73])).
1.22/0.59	tff(f124,plain,(
1.22/0.59	  bCOMB @ sCOMB @ (bCOMB @ vOR) = mor),
1.22/0.59	  inference(cnf_transformation,[],[f83])).
1.22/0.59	tff(f125,plain,(
1.22/0.59	  bCOMB @ (bCOMB @ (bCOMB @ vPI('$i'))) @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ sCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vOR)) @ (bCOMB @ (bCOMB @ vNOT))))) = mbox),
1.22/0.59	  inference(cnf_transformation,[],[f85])).
1.22/0.60	tff(f126,plain,(
1.22/0.60	  bCOMB @ mor @ mnot = mimplies),
1.22/0.60	  inference(cnf_transformation,[],[f87])).
1.22/0.60	tff(f127,plain,(
1.22/0.60	  bCOMB @ (bCOMB @ mnot) @ (cCOMB @ (bCOMB @ bCOMB @ mbox) @ mnot) = mdia),
1.22/0.60	  inference(cnf_transformation,[],[f89])).
1.22/0.60	tff(f128,plain,(
1.22/0.60	  bCOMB @ (bCOMB @ vPI('$i' -> '$o')) @ cCOMB = mforall_prop),
1.22/0.60	  inference(cnf_transformation,[],[f91])).
1.22/0.60	tff(f129,plain,(
1.22/0.60	  bCOMB @ vNOT = mnot),
1.22/0.60	  inference(cnf_transformation,[],[f93])).
1.22/0.60	tff(f131,plain,(
1.22/0.60	  bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT) = mimplies),
1.22/0.60	  inference(definition_unfolding,[],[f126,f124,f129])).
1.22/0.60	tff(f138,plain,(
1.22/0.60	  bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i'))) @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ sCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vOR)) @ (bCOMB @ (bCOMB @ vNOT))))))) @ (bCOMB @ vNOT)) = mdia),
1.22/0.60	  inference(definition_unfolding,[],[f127,f129,f125,f129])).
1.22/0.60	tff(f139,plain,(
1.22/0.60	  (bCOMB @ vPI('$i') @ (bCOMB @ (bCOMB @ vPI('$i')) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i'))) @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ sCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ cCOMB)) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vIMP))) @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ sCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vAND)) @ cCOMB)))) @ cCOMB))))) @ cCOMB))) @ sK0 != $true)),
1.22/0.60	  inference(definition_unfolding,[],[f98,f119])).
1.22/0.60	tff(f140,plain,(
1.22/0.60	  (vPI('$i') @ (bCOMB @ (bCOMB @ vPI('$i' -> '$o')) @ cCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT)) @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i'))) @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ sCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vOR)) @ (bCOMB @ (bCOMB @ vNOT))))))) @ (bCOMB @ vNOT)) @ sK0)) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i'))) @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ sCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vOR)) @ (bCOMB @ (bCOMB @ vNOT))))) @ sK0) @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i'))) @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ sCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vOR)) @ (bCOMB @ (bCOMB @ vNOT))))))) @ (bCOMB @ vNOT)) @ sK0)))) = $true)),
1.22/0.60	  inference(definition_unfolding,[],[f97,f118,f128,f131,f138,f125,f138])).
1.22/0.60	tff(f141,plain,(
1.22/0.60	  ( ! [X1] : ((bCOMB @ (bCOMB @ vPI('$i' -> '$o')) @ cCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT)) @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i'))) @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ sCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vOR)) @ (bCOMB @ (bCOMB @ vNOT))))))) @ (bCOMB @ vNOT)) @ sK0)) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i'))) @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ sCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vOR)) @ (bCOMB @ (bCOMB @ vNOT))))) @ sK0) @ (bCOMB @ (bCOMB @ (bCOMB @ vNOT)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i'))) @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ sCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vOR)) @ (bCOMB @ (bCOMB @ vNOT))))))) @ (bCOMB @ vNOT)) @ sK0))) @ X1 = $true)) )),
1.22/0.60	  inference(pi_clausification,[],[f140])).
1.22/0.60	tff(f142,plain,(
1.22/0.60	  ( ! [X1] : ((vPI('$i' -> '$o') @ (cCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT)) @ (bCOMB @ (bCOMB @ vNOT) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ sK0))))) @ (bCOMB @ vNOT)))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ sK0))))) @ (bCOMB @ (bCOMB @ vNOT) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ sK0))))) @ (bCOMB @ vNOT))))) @ X1) = $true)) )),
1.22/0.60	  inference(combinator_demodulation,[],[f141])).
1.22/0.60	tff(f143,plain,(
1.22/0.60	  ( ! [X2:'$i' -> '$o',X1] : ((cCOMB @ (sCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ vOR)) @ (bCOMB @ vNOT)) @ (bCOMB @ (bCOMB @ vNOT) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ sK0))))) @ (bCOMB @ vNOT)))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ sK0))))) @ (bCOMB @ (bCOMB @ vNOT) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ sK0))))) @ (bCOMB @ vNOT))))) @ X1 @ X2 = $true)) )),
1.22/0.60	  inference(pi_clausification,[],[f142])).
1.22/0.60	tff(f144,plain,(
1.22/0.60	  ( ! [X2:'$i' -> '$o',X1] : ((vOR @ (vNOT @ (vNOT @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (sK0 @ X1))) @ (bCOMB @ vNOT @ X2))))) @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (sK0 @ X1))) @ (bCOMB @ vNOT @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ sK0))) @ (bCOMB @ vNOT @ X2)))))) = $true)) )),
1.22/0.60	  inference(combinator_demodulation,[],[f143])).
1.22/0.60	tff(f145,plain,(
1.22/0.60	  ( ! [X2:'$i' -> '$o',X1] : ((vOR @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (sK0 @ X1))) @ (bCOMB @ vNOT @ X2))) @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (sK0 @ X1))) @ (bCOMB @ vNOT @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ sK0))) @ (bCOMB @ vNOT @ X2)))))) = $true)) )),
1.22/0.60	  inference(boolean_simplification,[],[f144])).
1.22/0.60	tff(f146,plain,(
1.22/0.60	  ( ! [X2:'$i' -> '$o',X1] : ((vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (sK0 @ X1))) @ (bCOMB @ vNOT @ X2)) = $true) | (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (sK0 @ X1))) @ (bCOMB @ vNOT @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ sK0))) @ (bCOMB @ vNOT @ X2))))) = $true)) )),
1.22/0.60	  inference(binary_proxy_clausification,[],[f145])).
1.22/0.60	tff(f147,plain,(
1.22/0.60	  ( ! [X2:'$i' -> '$o',X3,X1] : ((vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (sK0 @ X1))) @ (bCOMB @ vNOT @ X2)) = $true) | (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (sK0 @ X1))) @ (bCOMB @ vNOT @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ sK0))) @ (bCOMB @ vNOT @ X2)))) @ X3 = $true)) )),
1.22/0.60	  inference(pi_clausification,[],[f146])).
1.22/0.60	tff(f148,plain,(
1.22/0.60	  ( ! [X4,X2:'$i' -> '$o',X3,X1] : ((sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (sK0 @ X1))) @ (bCOMB @ vNOT @ X2) @ X4 = $true) | (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (sK0 @ X1))) @ (bCOMB @ vNOT @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (bCOMB @ (bCOMB @ vNOT) @ sK0))) @ (bCOMB @ vNOT @ X2)))) @ X3 = $true)) )),
1.22/0.60	  inference(pi_clausification,[],[f147])).
1.22/0.61	tff(f149,plain,(
1.22/0.61	  ( ! [X4,X2:'$i' -> '$o',X3,X1] : ((vOR @ (vNOT @ (sK0 @ X1 @ X4)) @ (vNOT @ (X2 @ X4)) = $true) | (vOR @ (vNOT @ (sK0 @ X1 @ X3)) @ (vNOT @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (sK0 @ X3))) @ (bCOMB @ vNOT @ X2)))) = $true)) )),
1.22/0.61	  inference(combinator_demodulation,[],[f148])).
1.22/0.61	tff(f150,plain,(
1.22/0.61	  ( ! [X4,X2:'$i' -> '$o',X3,X1] : ((vOR @ (vNOT @ (sK0 @ X1 @ X4)) @ (vNOT @ (X2 @ X4)) = $true) | (vNOT @ (sK0 @ X1 @ X3) = $true) | (vNOT @ (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (sK0 @ X3))) @ (bCOMB @ vNOT @ X2))) = $true)) )),
1.22/0.61	  inference(binary_proxy_clausification,[],[f149])).
1.22/0.61	tff(f151,plain,(
1.22/0.61	  ( ! [X4,X2:'$i' -> '$o',X3,X1] : ((vOR @ (vNOT @ (sK0 @ X1 @ X4)) @ (vNOT @ (X2 @ X4)) = $true) | (vNOT @ (sK0 @ X1 @ X3) = $true) | (vPI('$i') @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (sK0 @ X3))) @ (bCOMB @ vNOT @ X2)) = $false)) )),
1.22/0.61	  inference(not_proxy_clausification,[],[f150])).
1.22/0.61	tff(f152,plain,(
1.22/0.61	  ( ! [X4,X2:'$i' -> '$o',X3,X1] : ((vOR @ (vNOT @ (sK0 @ X1 @ X4)) @ (vNOT @ (X2 @ X4)) = $true) | (vNOT @ (sK0 @ X1 @ X3) = $true) | (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (sK0 @ X3))) @ (bCOMB @ vNOT @ X2) @ (sK2 @ X3 @ X2) = $false)) )),
1.22/0.61	  inference(sigma_clausification,[],[f151])).
1.22/0.61	tff(f153,plain,(
1.22/0.61	  ( ! [X4,X2:'$i' -> '$o',X3,X1] : ((vOR @ (vNOT @ (sK0 @ X1 @ X4)) @ (vNOT @ (X2 @ X4)) = $true) | (sK0 @ X1 @ X3 = $false) | (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (sK0 @ X3))) @ (bCOMB @ vNOT @ X2) @ (sK2 @ X3 @ X2) = $false)) )),
1.22/0.61	  inference(not_proxy_clausification,[],[f152])).
1.22/0.61	tff(f154,plain,(
1.22/0.61	  ( ! [X4,X2:'$i' -> '$o',X3,X1] : ((vNOT @ (sK0 @ X1 @ X4) = $true) | (sK0 @ X1 @ X3 = $false) | (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (sK0 @ X3))) @ (bCOMB @ vNOT @ X2) @ (sK2 @ X3 @ X2) = $false) | (vNOT @ (X2 @ X4) = $true)) )),
1.22/0.61	  inference(binary_proxy_clausification,[],[f153])).
1.22/0.61	tff(f155,plain,(
1.22/0.61	  ( ! [X4,X2:'$i' -> '$o',X3,X1] : ((vNOT @ (sK0 @ X1 @ X4) = $true) | (sK0 @ X1 @ X3 = $false) | (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (sK0 @ X3))) @ (bCOMB @ vNOT @ X2) @ (sK2 @ X3 @ X2) = $false) | (X2 @ X4 = $false)) )),
1.22/0.61	  inference(not_proxy_clausification,[],[f154])).
1.22/0.61	tff(f156,plain,(
1.22/0.61	  ( ! [X4,X2:'$i' -> '$o',X3,X1] : ((sK0 @ X1 @ X4 = $false) | (sK0 @ X1 @ X3 = $false) | (sCOMB @ (bCOMB @ vOR @ (bCOMB @ vNOT @ (sK0 @ X3))) @ (bCOMB @ vNOT @ X2) @ (sK2 @ X3 @ X2) = $false) | (X2 @ X4 = $false)) )),
1.22/0.61	  inference(not_proxy_clausification,[],[f155])).
1.22/0.61	tff(f157,plain,(
1.22/0.61	  ( ! [X4,X2:'$i' -> '$o',X3,X1] : ((sK0 @ X1 @ X4 = $false) | (sK0 @ X1 @ X3 = $false) | (vOR @ (vNOT @ (sK0 @ X3 @ (sK2 @ X3 @ X2))) @ (vNOT @ (X2 @ (sK2 @ X3 @ X2))) = $false) | (X2 @ X4 = $false)) )),
1.22/0.61	  inference(combinator_demodulation,[],[f156])).
1.22/0.61	tff(f158,plain,(
1.22/0.61	  ( ! [X4,X2:'$i' -> '$o',X3,X1] : ((sK0 @ X1 @ X4 = $false) | (sK0 @ X1 @ X3 = $false) | (vNOT @ (sK0 @ X3 @ (sK2 @ X3 @ X2)) = $false) | (X2 @ X4 = $false)) )),
1.22/0.61	  inference(binary_proxy_clausification,[],[f157])).
1.22/0.61	tff(f159,plain,(
1.22/0.61	  ( ! [X4,X2:'$i' -> '$o',X3,X1] : ((sK0 @ X1 @ X4 = $false) | (sK0 @ X1 @ X3 = $false) | (vNOT @ (X2 @ (sK2 @ X3 @ X2)) = $false) | (X2 @ X4 = $false)) )),
1.22/0.61	  inference(binary_proxy_clausification,[],[f157])).
1.22/0.61	tff(f160,plain,(
1.22/0.61	  ( ! [X4,X2:'$i' -> '$o',X3,X1] : ((X2 @ (sK2 @ X3 @ X2) = $true) | (sK0 @ X1 @ X3 = $false) | (sK0 @ X1 @ X4 = $false) | (X2 @ X4 = $false)) )),
1.22/0.61	  inference(not_proxy_clausification,[],[f159])).
1.22/0.61	tff(f161,plain,(
1.22/0.61	  ( ! [X4,X2:'$i' -> '$o',X3,X1] : ((sK0 @ X3 @ (sK2 @ X3 @ X2) = $true) | (sK0 @ X1 @ X3 = $false) | (sK0 @ X1 @ X4 = $false) | (X2 @ X4 = $false)) )),
1.22/0.61	  inference(not_proxy_clausification,[],[f158])).
1.22/0.61	tff(f162,plain,(
1.22/0.61	  (vPI('$i') @ (bCOMB @ vPI('$i') @ (bCOMB @ (bCOMB @ vPI('$i')) @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ cCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vIMP)) @ (bCOMB @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vAND) @ (cCOMB @ sK0)))) @ (cCOMB @ sK0))))) @ (cCOMB @ sK0)))) != $true)),
1.22/0.61	  inference(combinator_demodulation,[],[f139])).
1.22/0.61	tff(f163,plain,(
1.22/0.61	  (bCOMB @ vPI('$i') @ (bCOMB @ (bCOMB @ vPI('$i')) @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ cCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vIMP)) @ (bCOMB @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vAND) @ (cCOMB @ sK0)))) @ (cCOMB @ sK0))))) @ (cCOMB @ sK0))) @ sK3 = $false)),
1.22/0.61	  inference(sigma_clausification,[],[f162])).
1.22/0.61	tff(f164,plain,(
1.22/0.61	  (vPI('$i') @ (bCOMB @ vPI('$i') @ (sCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vAND) @ (cCOMB @ sK0))) @ (cCOMB @ sK0 @ sK3)))) @ (cCOMB @ sK0 @ sK3))) = $false)),
1.22/0.61	  inference(combinator_demodulation,[],[f163])).
1.22/0.61	tff(f165,plain,(
1.22/0.61	  (bCOMB @ vPI('$i') @ (sCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vAND) @ (cCOMB @ sK0))) @ (cCOMB @ sK0 @ sK3)))) @ (cCOMB @ sK0 @ sK3)) @ sK4 = $false)),
1.22/0.61	  inference(sigma_clausification,[],[f164])).
1.22/0.61	tff(f166,plain,(
1.22/0.61	  (vPI('$i') @ (cCOMB @ (bCOMB @ vIMP @ (sCOMB @ (bCOMB @ vAND @ (cCOMB @ sK0 @ sK4)) @ (cCOMB @ sK0 @ sK3))) @ (sK0 @ sK4 @ sK3)) = $false)),
1.22/0.61	  inference(combinator_demodulation,[],[f165])).
1.22/0.61	tff(f167,plain,(
1.22/0.61	  (cCOMB @ (bCOMB @ vIMP @ (sCOMB @ (bCOMB @ vAND @ (cCOMB @ sK0 @ sK4)) @ (cCOMB @ sK0 @ sK3))) @ (sK0 @ sK4 @ sK3) @ sK5 = $false)),
1.22/0.61	  inference(sigma_clausification,[],[f166])).
1.22/0.61	tff(f168,plain,(
1.22/0.61	  (vIMP @ (vAND @ (sK0 @ sK5 @ sK4) @ (sK0 @ sK5 @ sK3)) @ (sK0 @ sK4 @ sK3) = $false)),
1.22/0.61	  inference(combinator_demodulation,[],[f167])).
1.22/0.61	tff(f169,plain,(
1.22/0.61	  (vAND @ (sK0 @ sK5 @ sK4) @ (sK0 @ sK5 @ sK3) = $true)),
1.22/0.61	  inference(binary_proxy_clausification,[],[f168])).
1.22/0.61	tff(f170,plain,(
1.22/0.61	  (sK0 @ sK4 @ sK3 = $false)),
1.22/0.61	  inference(binary_proxy_clausification,[],[f168])).
1.22/0.61	tff(f171,plain,(
1.22/0.61	  (sK0 @ sK5 @ sK4 = $true)),
1.22/0.61	  inference(binary_proxy_clausification,[],[f169])).
1.22/0.61	tff(f172,plain,(
1.22/0.61	  (sK0 @ sK5 @ sK3 = $true)),
1.22/0.61	  inference(binary_proxy_clausification,[],[f169])).
1.22/0.61	tff(f179,plain,(
1.22/0.61	  ( ! [X6,X8,X7,X9] : ((vEQ('$i') @ X6 @ (sK2 @ X7 @ (vEQ('$i') @ X6)) = $true) | (sK0 @ X8 @ X7 = $false) | (sK0 @ X8 @ X9 = $false) | (vEQ('$i') @ X6 @ X9 = $false)) )),
1.22/0.61	  inference(primitive_instantiation,[],[f160])).
1.22/0.61	tff(f192,plain,(
1.22/0.61	  ( ! [X6,X8,X7,X9] : ((vEQ('$i') @ X6 @ (sK2 @ X7 @ (vEQ('$i') @ X6)) = $true) | (sK0 @ X8 @ X7 = $false) | (sK0 @ X8 @ X9 = $false) | X6 != X9) )),
1.22/0.61	  inference(equality_proxy_clausification,[],[f179])).
1.22/0.61	tff(f193,plain,(
1.22/0.61	  ( ! [X6,X8,X7,X9] : (sK2 @ X7 @ (vEQ('$i') @ X6) = X6 | (sK0 @ X8 @ X7 = $false) | (sK0 @ X8 @ X9 = $false) | X6 != X9) )),
1.22/0.61	  inference(equality_proxy_clausification,[],[f192])).
1.22/0.61	tff(f276,plain,(
1.22/0.61	  ( ! [X4,X2,X0,X5,X3,X1] : ((sK0 @ X0 @ X1 = $true) | (sK0 @ X2 @ X0 = $false) | (sK0 @ X2 @ X3 = $false) | (vEQ('$i') @ X1 @ X3 = $false) | (sK0 @ X4 @ X0 = $false) | (sK0 @ X4 @ X5 = $false) | X1 != X5) )),
1.22/0.61	  inference(superposition,[],[f161,f193])).
1.22/0.61	tff(f279,plain,(
1.22/0.61	  ( ! [X4,X2,X0,X5,X3,X1] : ((sK0 @ X0 @ X1 = $true) | (sK0 @ X2 @ X0 = $false) | (sK0 @ X2 @ X3 = $false) | X1 != X3 | (sK0 @ X4 @ X0 = $false) | (sK0 @ X4 @ X5 = $false) | X1 != X5) )),
1.22/0.61	  inference(equality_proxy_clausification,[],[f276])).
1.22/0.61	tff(f280,plain,(
1.22/0.61	  ( ! [X4,X2,X0,X3,X1] : ((sK0 @ X0 @ X1 = $false) | (sK0 @ X1 @ X2 = $true) | (sK0 @ X0 @ X3 = $false) | X2 != X3 | (sK0 @ X0 @ X4 = $false) | X2 != X4) )),
1.22/0.61	  inference(condensation,[],[f279])).
1.22/0.61	tff(f281,plain,(
1.22/0.61	  ( ! [X2,X0,X3,X1] : ((sK0 @ X0 @ X1 = $false) | (sK0 @ X0 @ X2 = $false) | (sK0 @ X2 @ X3 = $true) | X1 != X3 | X1 != X3) )),
1.22/0.61	  inference(condensation,[],[f280])).
1.22/0.61	tff(f282,plain,(
1.22/0.61	  ( ! [X2,X0,X3,X1] : ((sK0 @ X2 @ X3 = $true) | (sK0 @ X0 @ X2 = $false) | (sK0 @ X0 @ X1 = $false) | X1 != X3) )),
1.22/0.61	  inference(duplicate_literal_removal,[],[f281])).
1.22/0.61	tff(f285,plain,(
1.22/0.61	  ( ! [X2,X3] : (($false = $true) | (sK0 @ X2 @ sK4 = $false) | (sK0 @ X2 @ X3 = $false) | sK3 != X3) )),
1.22/0.61	  inference(superposition,[],[f170,f282])).
1.22/0.61	tff(f290,plain,(
1.22/0.61	  ( ! [X2,X3] : ((sK0 @ X2 @ sK4 = $false) | (sK0 @ X2 @ X3 = $false) | sK3 != X3) )),
1.22/0.61	  inference(trivial_inequality_removal,[],[f285])).
1.22/0.61	tff(f295,plain,(
1.22/0.61	  ( ! [X0] : (($false = $true) | (sK0 @ sK5 @ X0 = $false) | sK3 != X0) )),
1.22/0.61	  inference(superposition,[],[f171,f290])).
1.22/0.61	tff(f300,plain,(
1.22/0.61	  ( ! [X0] : ((sK0 @ sK5 @ X0 = $false) | sK3 != X0) )),
1.22/0.61	  inference(trivial_inequality_removal,[],[f295])).
1.22/0.61	tff(f323,plain,(
1.22/0.61	  ($false = $true) | sK3 != sK3),
1.22/0.61	  inference(superposition,[],[f172,f300])).
1.22/0.61	tff(f328,plain,(
1.22/0.61	  $false),
1.22/0.61	  inference(trivial_inequality_removal,[],[f323])).
1.22/0.61	% SZS output end Proof for theBenchmark
1.22/0.61	% (26657)------------------------------
1.22/0.61	% (26657)Version: Vampire 4.5.0 (commit 7ae30c7f on 2020-06-30 15:57:20 +0100)
1.22/0.61	% (26657)Termination reason: Refutation
1.22/0.61	
1.22/0.61	% (26657)Memory used [KB]: 5628
1.22/0.61	% (26657)Time elapsed: 0.155 s
1.22/0.61	% (26657)------------------------------
1.22/0.61	% (26657)------------------------------
1.22/0.61	% (26644)Success in time 0.201 s
1.22/0.61	EOF