0.03/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.03/0.13	% Command    : run_vampire %s %d
0.13/0.34	% Computer   : n026.cluster.edu
0.13/0.34	% Model      : x86_64 x86_64
0.13/0.34	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.34	% Memory     : 8042.1875MB
0.13/0.34	% OS         : Linux 3.10.0-693.el7.x86_64
0.13/0.34	% CPULimit   : 960
0.13/0.34	% WCLimit    : 120
0.13/0.34	% DateTime   : Thu Jul  2 08:34:39 EDT 2020
0.13/0.34	% CPUTime    : 
0.19/0.37	% (10478)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
0.19/0.37	% (10481)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
0.19/0.39	% (10502)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
0.19/0.39	% (10482)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
0.19/0.39	% (10485)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
0.19/0.40	% (10484)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
0.19/0.40	% (10474)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
0.19/0.40	% (10494)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
0.19/0.40	% (10479)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
0.19/0.40	% (10496)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
0.19/0.40	% (10486)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
0.19/0.41	% (10483)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
0.19/0.41	% (10488)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
0.19/0.41	% (10489)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
0.19/0.41	% (10476)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
0.19/0.41	% (10503)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
0.19/0.41	% (10477)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
0.19/0.41	% (10475)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
0.19/0.42	% (10491)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
0.19/0.42	% (10480)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
0.19/0.42	% (10492)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
0.19/0.43	% (10476)Refutation not found, incomplete strategy
0.19/0.43	% (10476)------------------------------
0.19/0.43	% (10476)Version: Vampire 4.5.0 (commit 7ae30c7f on 2020-06-30 15:57:20 +0100)
0.19/0.43	% (10500)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
0.19/0.43	% (10495)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
0.19/0.43	% (10501)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
0.19/0.43	% (10498)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
0.19/0.43	% (10497)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
0.19/0.43	% (10476)Termination reason: Refutation not found, incomplete strategy
0.19/0.43	
0.19/0.43	% (10476)Memory used [KB]: 9850
0.19/0.43	% (10476)Time elapsed: 0.066 s
0.19/0.43	% (10476)------------------------------
0.19/0.43	% (10476)------------------------------
0.19/0.43	% (10487)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
0.19/0.43	% (10488)Refutation not found, incomplete strategy
0.19/0.43	% (10488)------------------------------
0.19/0.43	% (10488)Version: Vampire 4.5.0 (commit 7ae30c7f on 2020-06-30 15:57:20 +0100)
0.19/0.43	% (10488)Termination reason: Refutation not found, incomplete strategy
0.19/0.43	
0.19/0.43	% (10488)Memory used [KB]: 5245
0.19/0.43	% (10488)Time elapsed: 0.062 s
0.19/0.43	% (10488)------------------------------
0.19/0.43	% (10488)------------------------------
0.19/0.44	% (10490)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
0.19/0.44	% (10493)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
0.19/0.44	% (10499)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
0.19/0.46	% (10484)Refutation not found, incomplete strategy
0.19/0.46	% (10484)------------------------------
0.19/0.46	% (10484)Version: Vampire 4.5.0 (commit 7ae30c7f on 2020-06-30 15:57:20 +0100)
0.19/0.46	% (10484)Termination reason: Refutation not found, incomplete strategy
0.19/0.46	
0.19/0.46	% (10484)Memory used [KB]: 10618
0.19/0.46	% (10484)Time elapsed: 0.106 s
0.19/0.46	% (10484)------------------------------
0.19/0.46	% (10484)------------------------------
0.19/0.47	% (10478)Refutation found. Thanks to Tanya!
0.19/0.47	% SZS status Theorem for theBenchmark
0.19/0.47	% SZS output start Proof for theBenchmark
0.19/0.47	tff(func_def_3, type, ->: ('$tType' * '$tType') > '$tType').
0.19/0.47	tff(func_def_4, type, in: '$i' -> '$i' -> '$o').
0.19/0.47	tff(func_def_6, type, setadjoin: '$i' -> '$i' -> '$i').
0.19/0.47	tff(func_def_7, type, powerset: '$i' -> '$i').
0.19/0.47	tff(func_def_8, type, dsetconstr: '$i' -> ('$i' -> '$o') -> '$i').
0.19/0.47	tff(func_def_10, type, vAPP: !>[X0: $ttype, X1: $ttype]:(X0 -> X1 * X0) > X1).
0.19/0.47	tff(func_def_11, type, subset: '$i' -> '$i' -> '$o').
0.19/0.47	tff(func_def_12, type, kpair: '$i' -> '$i' -> '$i').
0.19/0.47	tff(func_def_13, type, cartprod: '$i' -> '$i' -> '$i').
0.19/0.47	tff(func_def_14, type, singleton: '$i' -> '$o').
0.19/0.47	tff(func_def_15, type, ex1: '$i' -> ('$i' -> '$o') -> '$o').
0.19/0.47	tff(func_def_16, type, breln: '$i' -> '$i' -> '$i' -> '$o').
0.19/0.47	tff(func_def_17, type, func: '$i' -> '$i' -> '$i' -> '$o').
0.19/0.47	tff(func_def_18, type, funcSet: '$i' -> '$i' -> '$i').
0.19/0.47	tff(func_def_19, type, vEPSILON: !>[X0: $ttype]:(X0 -> '$o') -> X0).
0.19/0.47	tff(func_def_22, type, vAND: '$o' -> '$o' -> '$o').
0.19/0.47	tff(func_def_23, type, vEQ: !>[X0: $ttype]:X0 -> X0 -> '$o').
0.19/0.47	tff(func_def_24, type, vSIGMA: !>[X0: $ttype]:(X0 -> '$o') -> '$o').
0.19/0.47	tff(func_def_25, type, cCOMB: !>[X0: $ttype, X1: $ttype, X2: $ttype]:(X0 -> X1 -> X2) -> X1 -> X0 -> X2).
0.19/0.47	tff(func_def_26, type, bCOMB: !>[X0: $ttype, X1: $ttype, X2: $ttype]:(X1 -> X2) -> (X0 -> X1) -> X0 -> X2).
0.19/0.47	tff(func_def_27, type, sCOMB: !>[X0: $ttype, X1: $ttype, X2: $ttype]:(X0 -> X1 -> X2) -> (X0 -> X1) -> X0 -> X2).
0.19/0.47	tff(func_def_28, type, vIMP: '$o' -> '$o' -> '$o').
0.19/0.47	tff(func_def_29, type, vPI: !>[X0: $ttype]:(X0 -> '$o') -> '$o').
0.19/0.47	tff(func_def_30, type, iCOMB: !>[X2: $ttype]:X2 -> X2).
0.19/0.47	tff(func_def_35, type, kCOMB: !>[X1: $ttype, X2: $ttype]:X1 -> X2 -> X1).
0.19/0.47	tff(func_def_36, type, vOR: '$o' -> '$o' -> '$o').
0.19/0.47	tff(func_def_37, type, vNOT: '$o' -> '$o').
0.19/0.47	tff(func_def_39, type, sK5: '$i' -> '$i').
0.19/0.47	tff(func_def_40, type, sK6: '$i' -> '$i').
0.19/0.47	tff(func_def_41, type, sK7: '$i' -> '$i' -> '$i').
0.19/0.47	tff(func_def_42, type, sK8: '$i' -> '$i' -> '$i').
0.19/0.47	tff(func_def_43, type, sK9: '$i' -> '$i' -> '$i').
0.19/0.47	tff(func_def_44, type, sK10: '$i' -> '$i' -> '$i').
0.19/0.47	tff(func_def_45, type, sK11: '$i' -> '$i' -> '$i').
0.19/0.47	tff(func_def_46, type, sK12: '$i' -> '$i' -> '$i').
0.19/0.47	tff(func_def_47, type, sK13: '$i' -> '$i' -> '$i').
0.19/0.47	tff(func_def_48, type, sK14: '$i' -> '$i').
0.19/0.47	tff(func_def_49, type, sK15: '$i' -> '$i').
0.19/0.47	tff(f1,axiom,(
0.19/0.47	  (dsetconstrER = ! [X0,X1 : '$i' -> '$o',X2] : (in @ X2 @ (dsetconstr @ X0 @ (^[X3 : '$i'] : X1 @ X3)) => X1 @ X2))),
0.19/0.47	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrER)).
0.19/0.47	tff(f2,axiom,(
0.19/0.47	  singleton = (^[X0 : '$i'] : ? [X2] : (setadjoin @ X2 @ emptyset = X0 & in @ X2 @ X0))),
0.19/0.47	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton)).
0.19/0.47	tff(f3,axiom,(
0.19/0.47	  ex1 = (^[X0 : '$i', X1 : '$i' -> '$o'] : singleton @ (dsetconstr @ X0 @ (^[X2 : '$i'] : X1 @ X2)))),
0.19/0.47	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1)).
0.19/0.47	tff(f4,axiom,(
0.19/0.47	  breln = (^[X0 : '$i', X4 : '$i', X5 : '$i'] : subset @ X5 @ (cartprod @ X0 @ X4))),
0.19/0.47	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln)).
0.19/0.47	tff(f5,axiom,(
0.19/0.47	  func = (^[X0 : '$i', X4 : '$i', X6 : '$i'] : ! [X2] : (in @ X2 @ X0 => ex1 @ X4 @ (^[X3 : '$i'] : in @ (kpair @ X2 @ X3) @ X6)) & breln @ X0 @ X4 @ X6)),
0.19/0.47	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',func)).
0.19/0.47	tff(f6,axiom,(
0.19/0.47	  funcSet = (^[X0 : '$i', X4 : '$i'] : dsetconstr @ (powerset @ (cartprod @ X0 @ X4)) @ (^[X7 : '$i'] : func @ X0 @ X4 @ X7))),
0.19/0.47	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcSet)).
0.19/0.47	tff(f7,conjecture,(
0.19/0.47	  dsetconstrER => ! [X0,X4,X7] : (in @ X7 @ (funcSet @ X0 @ X4) => func @ X0 @ X4 @ X7)),
0.19/0.47	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',infuncsetfunc)).
0.19/0.47	tff(f8,negated_conjecture,(
0.19/0.47	  ~(dsetconstrER => ! [X0,X4,X7] : (in @ X7 @ (funcSet @ X0 @ X4) => func @ X0 @ X4 @ X7))),
0.19/0.47	  inference(negated_conjecture,[],[f7])).
0.19/0.47	tff(f9,plain,(
0.19/0.47	  ~(dsetconstrER => ! [X0,X1,X2] : (in @ X2 @ (funcSet @ X0 @ X1) => func @ X0 @ X1 @ X2))),
0.19/0.47	  inference(rectify,[],[f8])).
0.19/0.47	tff(f10,plain,(
0.19/0.47	  ~((dsetconstrER = $true) => ! [X0,X1,X2] : ((in @ X2 @ (funcSet @ X0 @ X1) = $true) => (func @ X0 @ X1 @ X2 = $true)))),
0.19/0.47	  inference(fool_elimination,[],[f9])).
0.19/0.47	tff(f11,plain,(
0.19/0.47	  singleton = (^[X0 : '$i'] : ? [X1] : (setadjoin @ X1 @ emptyset = X0 & in @ X1 @ X0))),
0.19/0.47	  inference(rectify,[],[f2])).
0.19/0.47	tff(f12,plain,(
0.19/0.47	  bCOMB @ vSIGMA('$i') @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vAND) @ (cCOMB @ in))) @ (cCOMB @ (bCOMB @ vEQ('$i') @ (cCOMB @ setadjoin @ emptyset)))) = singleton),
0.19/0.47	  inference(fool_elimination,[],[f11])).
0.19/0.47	tff(f13,plain,(
0.19/0.47	  funcSet = (^[X0 : '$i', X1 : '$i'] : dsetconstr @ (powerset @ (cartprod @ X0 @ X1)) @ (^[X2 : '$i'] : func @ X0 @ X1 @ X2))),
0.19/0.47	  inference(rectify,[],[f6])).
0.19/0.47	tff(f14,plain,(
0.19/0.47	  sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ dsetconstr) @ (bCOMB @ (bCOMB @ powerset) @ cartprod))) @ func = funcSet),
0.19/0.47	  inference(fool_elimination,[],[f13])).
0.19/0.47	tff(f15,plain,(
0.19/0.47	  breln = (^[X0 : '$i', X1 : '$i', X2 : '$i'] : subset @ X2 @ (cartprod @ X0 @ X1))),
0.19/0.47	  inference(rectify,[],[f4])).
0.19/0.47	tff(f16,plain,(
0.19/0.47	  bCOMB @ (bCOMB @ (cCOMB @ subset)) @ cartprod = breln),
0.19/0.47	  inference(fool_elimination,[],[f15])).
0.19/0.47	tff(f17,plain,(
0.19/0.47	  (dsetconstrER = ! [X0,X1 : '$i' -> '$o',X2] : (in @ X2 @ (dsetconstr @ X0 @ (^[X3 : '$i'] : X1 @ X3)) => X1 @ X2))),
0.19/0.47	  inference(rectify,[],[f1])).
0.19/0.47	tff(f18,plain,(
0.19/0.47	  (dsetconstrER = vPI('$i') @ (bCOMB @ vPI('$i' -> '$o') @ (bCOMB @ (bCOMB @ vPI('$i')) @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ cCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vIMP)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ in)) @ (cCOMB @ dsetconstr))))) @ (cCOMB @ iCOMB)))))),
0.19/0.47	  inference(fool_elimination,[],[f17])).
0.19/0.47	tff(f19,plain,(
0.19/0.47	  bCOMB @ (bCOMB @ singleton) @ (cCOMB @ (bCOMB @ bCOMB @ dsetconstr) @ iCOMB) = ex1),
0.19/0.47	  inference(fool_elimination,[],[f3])).
0.19/0.47	tff(f20,plain,(
0.19/0.47	  func = (^[X0 : '$i', X1 : '$i', X2 : '$i'] : ! [X3] : (in @ X3 @ X0 => ex1 @ X1 @ (^[X4 : '$i'] : in @ (kpair @ X3 @ X4) @ X2)) & breln @ X0 @ X1 @ X2)),
0.19/0.47	  inference(rectify,[],[f5])).
0.19/0.47	tff(f21,plain,(
0.19/0.47	  sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ sCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vAND)) @ breln))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i'))) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ in))))) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ ex1)) @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ in) @ kpair)))))) = func),
0.19/0.47	  inference(fool_elimination,[],[f20])).
0.19/0.47	tff(f22,plain,(
0.19/0.47	  ? [X0,X1,X2] : ((func @ X0 @ X1 @ X2 != $true) & (in @ X2 @ (funcSet @ X0 @ X1) = $true)) & (dsetconstrER = $true)),
0.19/0.47	  inference(ennf_transformation,[],[f10])).
0.19/0.47	tff(f23,plain,(
0.19/0.47	  ? [X0,X1,X2] : ((func @ X0 @ X1 @ X2 != $true) & (in @ X2 @ (funcSet @ X0 @ X1) = $true)) => ((func @ sK0 @ sK1 @ sK2 != $true) & (in @ sK2 @ (funcSet @ sK0 @ sK1) = $true))),
0.19/0.47	  introduced(choice_axiom,[])).
0.19/0.47	tff(f24,plain,(
0.19/0.47	  ((func @ sK0 @ sK1 @ sK2 != $true) & (in @ sK2 @ (funcSet @ sK0 @ sK1) = $true)) & (dsetconstrER = $true)),
0.19/0.47	  inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f22,f23])).
0.19/0.47	tff(f25,plain,(
0.19/0.47	  (dsetconstrER = $true)),
0.19/0.47	  inference(cnf_transformation,[],[f24])).
0.19/0.47	tff(f26,plain,(
0.19/0.47	  (in @ sK2 @ (funcSet @ sK0 @ sK1) = $true)),
0.19/0.47	  inference(cnf_transformation,[],[f24])).
0.19/0.47	tff(f27,plain,(
0.19/0.47	  (func @ sK0 @ sK1 @ sK2 != $true)),
0.19/0.47	  inference(cnf_transformation,[],[f24])).
0.19/0.47	tff(f28,plain,(
0.19/0.47	  bCOMB @ vSIGMA('$i') @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vAND) @ (cCOMB @ in))) @ (cCOMB @ (bCOMB @ vEQ('$i') @ (cCOMB @ setadjoin @ emptyset)))) = singleton),
0.19/0.47	  inference(cnf_transformation,[],[f12])).
0.19/0.47	tff(f29,plain,(
0.19/0.47	  sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ dsetconstr) @ (bCOMB @ (bCOMB @ powerset) @ cartprod))) @ func = funcSet),
0.19/0.47	  inference(cnf_transformation,[],[f14])).
0.19/0.47	tff(f30,plain,(
0.19/0.47	  bCOMB @ (bCOMB @ (cCOMB @ subset)) @ cartprod = breln),
0.19/0.47	  inference(cnf_transformation,[],[f16])).
0.19/0.47	tff(f31,plain,(
0.19/0.47	  (dsetconstrER = vPI('$i') @ (bCOMB @ vPI('$i' -> '$o') @ (bCOMB @ (bCOMB @ vPI('$i')) @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ cCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vIMP)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ in)) @ (cCOMB @ dsetconstr))))) @ (cCOMB @ iCOMB)))))),
0.19/0.47	  inference(cnf_transformation,[],[f18])).
0.19/0.47	tff(f32,plain,(
0.19/0.47	  bCOMB @ (bCOMB @ singleton) @ (cCOMB @ (bCOMB @ bCOMB @ dsetconstr) @ iCOMB) = ex1),
0.19/0.47	  inference(cnf_transformation,[],[f19])).
0.19/0.47	tff(f33,plain,(
0.19/0.47	  sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ sCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vAND)) @ breln))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i'))) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ in))))) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ ex1)) @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ in) @ kpair)))))) = func),
0.19/0.47	  inference(cnf_transformation,[],[f21])).
0.19/0.47	tff(f34,plain,(
0.19/0.47	  bCOMB @ (bCOMB @ (bCOMB @ vSIGMA('$i') @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vAND) @ (cCOMB @ in))) @ (cCOMB @ (bCOMB @ vEQ('$i') @ (cCOMB @ setadjoin @ emptyset)))))) @ (cCOMB @ (bCOMB @ bCOMB @ dsetconstr) @ iCOMB) = ex1),
0.19/0.47	  inference(definition_unfolding,[],[f32,f28])).
0.19/0.47	tff(f35,plain,(
0.19/0.47	  sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ sCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vAND)) @ (bCOMB @ (bCOMB @ (cCOMB @ subset)) @ cartprod)))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i'))) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ in))))) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vSIGMA('$i') @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vAND) @ (cCOMB @ in))) @ (cCOMB @ (bCOMB @ vEQ('$i') @ (cCOMB @ setadjoin @ emptyset)))))) @ (cCOMB @ (bCOMB @ bCOMB @ dsetconstr) @ iCOMB)))) @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ in) @ kpair)))))) = func),
0.19/0.47	  inference(definition_unfolding,[],[f33,f30,f34])).
0.19/0.47	tff(f36,plain,(
0.19/0.47	  sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ dsetconstr) @ (bCOMB @ (bCOMB @ powerset) @ cartprod))) @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ sCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vAND)) @ (bCOMB @ (bCOMB @ (cCOMB @ subset)) @ cartprod)))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i'))) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ in))))) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vSIGMA('$i') @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vAND) @ (cCOMB @ in))) @ (cCOMB @ (bCOMB @ vEQ('$i') @ (cCOMB @ setadjoin @ emptyset)))))) @ (cCOMB @ (bCOMB @ bCOMB @ dsetconstr) @ iCOMB)))) @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ in) @ kpair))))))) = funcSet),
0.19/0.47	  inference(definition_unfolding,[],[f29,f35])).
0.19/0.47	tff(f37,plain,(
0.19/0.47	  (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ sCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vAND)) @ (bCOMB @ (bCOMB @ (cCOMB @ subset)) @ cartprod)))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i'))) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ in))))) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vSIGMA('$i') @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vAND) @ (cCOMB @ in))) @ (cCOMB @ (bCOMB @ vEQ('$i') @ (cCOMB @ setadjoin @ emptyset)))))) @ (cCOMB @ (bCOMB @ bCOMB @ dsetconstr) @ iCOMB)))) @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ in) @ kpair)))))) @ sK0 @ sK1 @ sK2 != $true)),
0.19/0.47	  inference(definition_unfolding,[],[f27,f35])).
0.19/0.47	tff(f38,plain,(
0.19/0.47	  (in @ sK2 @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ dsetconstr) @ (bCOMB @ (bCOMB @ powerset) @ cartprod))) @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ sCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vAND)) @ (bCOMB @ (bCOMB @ (cCOMB @ subset)) @ cartprod)))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i'))) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ in))))) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vSIGMA('$i') @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vAND) @ (cCOMB @ in))) @ (cCOMB @ (bCOMB @ vEQ('$i') @ (cCOMB @ setadjoin @ emptyset)))))) @ (cCOMB @ (bCOMB @ bCOMB @ dsetconstr) @ iCOMB)))) @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ in) @ kpair))))))) @ sK0 @ sK1) = $true)),
0.19/0.47	  inference(definition_unfolding,[],[f26,f36])).
0.19/0.49	% (10512)dis+1010_3:2_av=off:csup=on:prag=on:chr=on:foolp=on:bet=on:cnfonf=lazy_not_be_gen:gsp=input_only:nm=2:nwc=1:sp=reverse_arity:urr=ec_only_29 on theBenchmark
0.19/0.49	% (10511)dis+1011_10_add=large:csup=on:inj=on:chr=on:foolp=on:cnfonf=eager:afr=on:afp=4000:afq=1.0:amm=off:anc=none:lma=on:nm=64:nwc=4:sac=on:sp=occurrence_75 on theBenchmark
0.19/0.49	tff(f39,plain,(
0.19/0.49	  (vPI('$i') @ (bCOMB @ vPI('$i' -> '$o') @ (bCOMB @ (bCOMB @ vPI('$i')) @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ cCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vIMP)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ in)) @ (cCOMB @ dsetconstr))))) @ (cCOMB @ iCOMB)))) = $true)),
0.19/0.49	  inference(definition_unfolding,[],[f31,f25])).
0.19/0.49	tff(f40,plain,(
0.19/0.49	  ( ! [X1] : ((bCOMB @ vPI('$i' -> '$o') @ (bCOMB @ (bCOMB @ vPI('$i')) @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ cCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vIMP)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ in)) @ (cCOMB @ dsetconstr))))) @ (cCOMB @ iCOMB))) @ X1 = $true)) )),
0.19/0.49	  inference(pi_clausification,[],[f39])).
0.19/0.49	tff(f41,plain,(
0.19/0.49	  ( ! [X1] : ((vPI('$i' -> '$o') @ (bCOMB @ vPI('$i') @ (sCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (bCOMB @ (bCOMB @ (in @ X1)) @ (cCOMB @ dsetconstr)))) @ (cCOMB @ iCOMB @ X1))) = $true)) )),
0.19/0.49	  inference(combinator_demodulation,[],[f40])).
0.19/0.49	tff(f42,plain,(
0.19/0.49	  ( ! [X2:'$i' -> '$o',X1] : ((bCOMB @ vPI('$i') @ (sCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (bCOMB @ (bCOMB @ (in @ X1)) @ (cCOMB @ dsetconstr)))) @ (cCOMB @ iCOMB @ X1)) @ X2 = $true)) )),
0.19/0.49	  inference(pi_clausification,[],[f41])).
0.19/0.49	tff(f43,plain,(
0.19/0.49	  ( ! [X2:'$i' -> '$o',X1] : ((vPI('$i') @ (cCOMB @ (bCOMB @ vIMP @ (bCOMB @ (in @ X1) @ (cCOMB @ dsetconstr @ X2))) @ (X2 @ X1)) = $true)) )),
0.19/0.49	  inference(combinator_demodulation,[],[f42])).
0.19/0.49	tff(f44,plain,(
0.19/0.49	  ( ! [X2:'$i' -> '$o',X3,X1] : ((cCOMB @ (bCOMB @ vIMP @ (bCOMB @ (in @ X1) @ (cCOMB @ dsetconstr @ X2))) @ (X2 @ X1) @ X3 = $true)) )),
0.19/0.49	  inference(pi_clausification,[],[f43])).
0.19/0.49	tff(f45,plain,(
0.19/0.49	  ( ! [X2:'$i' -> '$o',X3,X1] : ((vIMP @ (in @ X1 @ (dsetconstr @ X3 @ X2)) @ (X2 @ X1) = $true)) )),
0.19/0.49	  inference(combinator_demodulation,[],[f44])).
0.19/0.49	tff(f46,plain,(
0.19/0.49	  ( ! [X2:'$i' -> '$o',X3,X1] : ((in @ X1 @ (dsetconstr @ X3 @ X2) = $false) | (X2 @ X1 = $true)) )),
0.19/0.49	  inference(binary_proxy_clausification,[],[f45])).
0.19/0.49	tff(f47,plain,(
0.19/0.49	  (in @ sK2 @ (dsetconstr @ (powerset @ (cartprod @ sK0 @ sK1)) @ (sCOMB @ (bCOMB @ vAND @ (cCOMB @ subset @ (cartprod @ sK0 @ sK1))) @ (bCOMB @ vPI('$i') @ (bCOMB @ (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ in @ sK0))) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vSIGMA('$i') @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vAND) @ (cCOMB @ in))) @ (cCOMB @ (bCOMB @ vEQ('$i') @ (cCOMB @ setadjoin @ emptyset))))) @ (bCOMB @ (dsetconstr @ sK1) @ iCOMB))) @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ in) @ kpair)))))))) = $true)),
0.19/0.49	  inference(combinator_demodulation,[],[f38])).
0.19/0.49	tff(f48,plain,(
0.19/0.49	  (in @ sK2 @ (dsetconstr @ (powerset @ (cartprod @ sK0 @ sK1)) @ (sCOMB @ (bCOMB @ vAND @ (cCOMB @ subset @ (cartprod @ sK0 @ sK1))) @ (bCOMB @ vPI('$i') @ (bCOMB @ (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ in @ sK0))) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vSIGMA('$i') @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vAND) @ (cCOMB @ in))) @ (cCOMB @ (bCOMB @ vEQ('$i') @ (cCOMB @ setadjoin @ emptyset))))) @ (dsetconstr @ sK1))) @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ in) @ kpair)))))))) = $true)),
0.19/0.49	  inference(combinator_normalisation,[],[f47])).
0.19/0.49	tff(f49,plain,(
0.19/0.49	  (vAND @ (subset @ sK2 @ (cartprod @ sK0 @ sK1)) @ (vPI('$i') @ (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ in @ sK0)) @ (bCOMB @ (bCOMB @ (bCOMB @ vSIGMA('$i') @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vAND) @ (cCOMB @ in))) @ (cCOMB @ (bCOMB @ vEQ('$i') @ (cCOMB @ setadjoin @ emptyset))))) @ (bCOMB @ (dsetconstr @ sK1) @ iCOMB)) @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ in) @ kpair)) @ sK2)))) != $true)),
0.19/0.49	  inference(combinator_demodulation,[],[f37])).
0.19/0.49	tff(f50,plain,(
0.19/0.49	  (subset @ sK2 @ (cartprod @ sK0 @ sK1) = $false) | (vPI('$i') @ (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ in @ sK0)) @ (bCOMB @ (bCOMB @ (bCOMB @ vSIGMA('$i') @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vAND) @ (cCOMB @ in))) @ (cCOMB @ (bCOMB @ vEQ('$i') @ (cCOMB @ setadjoin @ emptyset))))) @ (bCOMB @ (dsetconstr @ sK1) @ iCOMB)) @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ in) @ kpair)) @ sK2))) = $false)),
0.19/0.49	  inference(binary_proxy_clausification,[],[f49])).
0.19/0.49	tff(f51,plain,(
0.19/0.49	  (subset @ sK2 @ (cartprod @ sK0 @ sK1) = $false) | (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ in @ sK0)) @ (bCOMB @ (bCOMB @ (bCOMB @ vSIGMA('$i') @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vAND) @ (cCOMB @ in))) @ (cCOMB @ (bCOMB @ vEQ('$i') @ (cCOMB @ setadjoin @ emptyset))))) @ (bCOMB @ (dsetconstr @ sK1) @ iCOMB)) @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ in) @ kpair)) @ sK2)) @ sK4 = $false)),
0.19/0.49	  inference(sigma_clausification,[],[f50])).
0.19/0.49	tff(f52,plain,(
0.19/0.49	  (subset @ sK2 @ (cartprod @ sK0 @ sK1) = $false) | (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ in @ sK0)) @ (bCOMB @ (bCOMB @ (bCOMB @ vSIGMA('$i') @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vAND) @ (cCOMB @ in))) @ (cCOMB @ (bCOMB @ vEQ('$i') @ (cCOMB @ setadjoin @ emptyset))))) @ (dsetconstr @ sK1)) @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ in) @ kpair)) @ sK2)) @ sK4 = $false)),
0.19/0.49	  inference(combinator_normalisation,[],[f51])).
0.19/0.49	tff(f53,plain,(
0.19/0.49	  (subset @ sK2 @ (cartprod @ sK0 @ sK1) = $false) | (vIMP @ (in @ sK4 @ sK0) @ (vSIGMA('$i') @ (sCOMB @ (bCOMB @ vAND @ (cCOMB @ in @ (dsetconstr @ sK1 @ (cCOMB @ (bCOMB @ in @ (kpair @ sK4)) @ sK2)))) @ (cCOMB @ (bCOMB @ vEQ('$i') @ (cCOMB @ setadjoin @ emptyset)) @ (dsetconstr @ sK1 @ (cCOMB @ (bCOMB @ in @ (kpair @ sK4)) @ sK2))))) = $false)),
0.19/0.49	  inference(combinator_demodulation,[],[f52])).
0.19/0.49	tff(f54,plain,(
0.19/0.49	  (subset @ sK2 @ (cartprod @ sK0 @ sK1) = $false) | (in @ sK4 @ sK0 = $true)),
0.19/0.49	  inference(binary_proxy_clausification,[],[f53])).
0.19/0.49	tff(f55,plain,(
0.19/0.49	  (subset @ sK2 @ (cartprod @ sK0 @ sK1) = $false) | (vSIGMA('$i') @ (sCOMB @ (bCOMB @ vAND @ (cCOMB @ in @ (dsetconstr @ sK1 @ (cCOMB @ (bCOMB @ in @ (kpair @ sK4)) @ sK2)))) @ (cCOMB @ (bCOMB @ vEQ('$i') @ (cCOMB @ setadjoin @ emptyset)) @ (dsetconstr @ sK1 @ (cCOMB @ (bCOMB @ in @ (kpair @ sK4)) @ sK2)))) = $false)),
0.19/0.49	  inference(binary_proxy_clausification,[],[f53])).
0.19/0.49	tff(f56,plain,(
0.19/0.49	  ( ! [X1] : ((subset @ sK2 @ (cartprod @ sK0 @ sK1) = $false) | (sCOMB @ (bCOMB @ vAND @ (cCOMB @ in @ (dsetconstr @ sK1 @ (cCOMB @ (bCOMB @ in @ (kpair @ sK4)) @ sK2)))) @ (cCOMB @ (bCOMB @ vEQ('$i') @ (cCOMB @ setadjoin @ emptyset)) @ (dsetconstr @ sK1 @ (cCOMB @ (bCOMB @ in @ (kpair @ sK4)) @ sK2))) @ X1 = $false)) )),
0.19/0.49	  inference(pi_clausification,[],[f55])).
0.19/0.49	tff(f57,plain,(
0.19/0.49	  ( ! [X1] : ((subset @ sK2 @ (cartprod @ sK0 @ sK1) = $false) | (vAND @ (in @ X1 @ (dsetconstr @ sK1 @ (cCOMB @ (bCOMB @ in @ (kpair @ sK4)) @ sK2))) @ (vEQ('$i') @ (setadjoin @ X1 @ emptyset) @ (dsetconstr @ sK1 @ (cCOMB @ (bCOMB @ in @ (kpair @ sK4)) @ sK2))) = $false)) )),
0.19/0.49	  inference(combinator_demodulation,[],[f56])).
0.19/0.49	tff(f58,plain,(
0.19/0.49	  ( ! [X1] : ((subset @ sK2 @ (cartprod @ sK0 @ sK1) = $false) | (in @ X1 @ (dsetconstr @ sK1 @ (cCOMB @ (bCOMB @ in @ (kpair @ sK4)) @ sK2)) = $false) | (vEQ('$i') @ (setadjoin @ X1 @ emptyset) @ (dsetconstr @ sK1 @ (cCOMB @ (bCOMB @ in @ (kpair @ sK4)) @ sK2)) = $false)) )),
0.19/0.49	  inference(binary_proxy_clausification,[],[f57])).
0.19/0.49	tff(f59,plain,(
0.19/0.49	  ( ! [X1] : ((subset @ sK2 @ (cartprod @ sK0 @ sK1) = $false) | (in @ X1 @ (dsetconstr @ sK1 @ (cCOMB @ (bCOMB @ in @ (kpair @ sK4)) @ sK2)) = $false) | setadjoin @ X1 @ emptyset != dsetconstr @ sK1 @ (cCOMB @ (bCOMB @ in @ (kpair @ sK4)) @ sK2)) )),
0.19/0.49	  inference(equality_proxy_clausification,[],[f58])).
0.19/0.49	tff(f64,plain,(
0.19/0.49	  spl3_0 <=> (in @ sK4 @ sK0 = $true)),
0.19/0.49	  introduced(avatar_definition,[new_symbols(naming,[spl3_0])])).
0.19/0.49	tff(f65,plain,(
0.19/0.49	  (in @ sK4 @ sK0 = $true) | ~spl3_0),
0.19/0.49	  inference(avatar_component_clause,[],[f64])).
0.19/0.49	tff(f70,plain,(
0.19/0.49	  spl3_2 <=> (subset @ sK2 @ (cartprod @ sK0 @ sK1) = $false)),
0.19/0.49	  introduced(avatar_definition,[new_symbols(naming,[spl3_2])])).
0.19/0.49	tff(f71,plain,(
0.19/0.49	  (subset @ sK2 @ (cartprod @ sK0 @ sK1) = $false) | ~spl3_2),
0.19/0.49	  inference(avatar_component_clause,[],[f70])).
0.19/0.49	tff(f72,plain,(
0.19/0.49	  spl3_0 | spl3_2),
0.19/0.49	  inference(avatar_split_clause,[],[f54,f70,f64])).
0.19/0.49	tff(f74,plain,(
0.19/0.49	  spl3_4 <=> ! [X1] : ((in @ X1 @ (dsetconstr @ sK1 @ (cCOMB @ (bCOMB @ in @ (kpair @ sK4)) @ sK2)) = $false) | setadjoin @ X1 @ emptyset != dsetconstr @ sK1 @ (cCOMB @ (bCOMB @ in @ (kpair @ sK4)) @ sK2))),
0.19/0.49	  introduced(avatar_definition,[new_symbols(naming,[spl3_4])])).
0.19/0.49	tff(f75,plain,(
0.19/0.49	  ( ! [X1] : (setadjoin @ X1 @ emptyset != dsetconstr @ sK1 @ (cCOMB @ (bCOMB @ in @ (kpair @ sK4)) @ sK2) | (in @ X1 @ (dsetconstr @ sK1 @ (cCOMB @ (bCOMB @ in @ (kpair @ sK4)) @ sK2)) = $false)) ) | ~spl3_4),
0.19/0.49	  inference(avatar_component_clause,[],[f74])).
0.19/0.49	tff(f76,plain,(
0.19/0.49	  spl3_4 | spl3_2),
0.19/0.49	  inference(avatar_split_clause,[],[f59,f70,f74])).
0.19/0.49	tff(f82,plain,(
0.19/0.49	  ($false = $true) | (sCOMB @ (bCOMB @ vAND @ (cCOMB @ subset @ (cartprod @ sK0 @ sK1))) @ (bCOMB @ vPI('$i') @ (bCOMB @ (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ in @ sK0))) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vSIGMA('$i') @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vAND) @ (cCOMB @ in))) @ (cCOMB @ (bCOMB @ vEQ('$i') @ (cCOMB @ setadjoin @ emptyset))))) @ (dsetconstr @ sK1))) @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ in) @ kpair)))))) @ sK2 = $true)),
0.19/0.49	  inference(superposition,[],[f46,f48])).
0.19/0.49	tff(f83,plain,(
0.19/0.49	  (sCOMB @ (bCOMB @ vAND @ (cCOMB @ subset @ (cartprod @ sK0 @ sK1))) @ (bCOMB @ vPI('$i') @ (bCOMB @ (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ in @ sK0))) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vSIGMA('$i') @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vAND) @ (cCOMB @ in))) @ (cCOMB @ (bCOMB @ vEQ('$i') @ (cCOMB @ setadjoin @ emptyset))))) @ (dsetconstr @ sK1))) @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ in) @ kpair)))))) @ sK2 = $true)),
0.19/0.49	  inference(trivial_inequality_removal,[],[f82])).
0.19/0.49	tff(f84,plain,(
0.19/0.49	  (vAND @ (subset @ sK2 @ (cartprod @ sK0 @ sK1)) @ (vPI('$i') @ (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ in @ sK0)) @ (bCOMB @ (bCOMB @ (bCOMB @ vSIGMA('$i') @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vAND) @ (cCOMB @ in))) @ (cCOMB @ (bCOMB @ vEQ('$i') @ (cCOMB @ setadjoin @ emptyset))))) @ (dsetconstr @ sK1)) @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ in) @ kpair)) @ sK2)))) = $true)),
0.19/0.49	  inference(combinator_demodulation,[],[f83])).
0.19/0.49	tff(f85,plain,(
0.19/0.49	  (subset @ sK2 @ (cartprod @ sK0 @ sK1) = $true)),
0.19/0.49	  inference(binary_proxy_clausification,[],[f84])).
0.19/0.49	tff(f86,plain,(
0.19/0.49	  (vPI('$i') @ (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ in @ sK0)) @ (bCOMB @ (bCOMB @ (bCOMB @ vSIGMA('$i') @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vAND) @ (cCOMB @ in))) @ (cCOMB @ (bCOMB @ vEQ('$i') @ (cCOMB @ setadjoin @ emptyset))))) @ (dsetconstr @ sK1)) @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ in) @ kpair)) @ sK2))) = $true)),
0.19/0.49	  inference(binary_proxy_clausification,[],[f84])).
0.19/0.49	tff(f87,plain,(
0.19/0.49	  ( ! [X1] : ((sCOMB @ (bCOMB @ vIMP @ (cCOMB @ in @ sK0)) @ (bCOMB @ (bCOMB @ (bCOMB @ vSIGMA('$i') @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vAND) @ (cCOMB @ in))) @ (cCOMB @ (bCOMB @ vEQ('$i') @ (cCOMB @ setadjoin @ emptyset))))) @ (dsetconstr @ sK1)) @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ in) @ kpair)) @ sK2)) @ X1 = $true)) )),
0.19/0.49	  inference(pi_clausification,[],[f86])).
0.19/0.49	tff(f88,plain,(
0.19/0.49	  ( ! [X1] : ((vIMP @ (in @ X1 @ sK0) @ (vSIGMA('$i') @ (sCOMB @ (bCOMB @ vAND @ (cCOMB @ in @ (dsetconstr @ sK1 @ (cCOMB @ (bCOMB @ in @ (kpair @ X1)) @ sK2)))) @ (cCOMB @ (bCOMB @ vEQ('$i') @ (cCOMB @ setadjoin @ emptyset)) @ (dsetconstr @ sK1 @ (cCOMB @ (bCOMB @ in @ (kpair @ X1)) @ sK2))))) = $true)) )),
0.19/0.49	  inference(combinator_demodulation,[],[f87])).
0.19/0.49	tff(f89,plain,(
0.19/0.49	  ( ! [X1] : ((in @ X1 @ sK0 = $false) | (vSIGMA('$i') @ (sCOMB @ (bCOMB @ vAND @ (cCOMB @ in @ (dsetconstr @ sK1 @ (cCOMB @ (bCOMB @ in @ (kpair @ X1)) @ sK2)))) @ (cCOMB @ (bCOMB @ vEQ('$i') @ (cCOMB @ setadjoin @ emptyset)) @ (dsetconstr @ sK1 @ (cCOMB @ (bCOMB @ in @ (kpair @ X1)) @ sK2)))) = $true)) )),
0.19/0.49	  inference(binary_proxy_clausification,[],[f88])).
0.19/0.49	tff(f90,plain,(
0.19/0.49	  ( ! [X1] : ((in @ X1 @ sK0 = $false) | (sCOMB @ (bCOMB @ vAND @ (cCOMB @ in @ (dsetconstr @ sK1 @ (cCOMB @ (bCOMB @ in @ (kpair @ X1)) @ sK2)))) @ (cCOMB @ (bCOMB @ vEQ('$i') @ (cCOMB @ setadjoin @ emptyset)) @ (dsetconstr @ sK1 @ (cCOMB @ (bCOMB @ in @ (kpair @ X1)) @ sK2))) @ (sK5 @ X1) = $true)) )),
0.19/0.49	  inference(sigma_clausification,[],[f89])).
0.19/0.49	tff(f91,plain,(
0.19/0.49	  ( ! [X1] : ((in @ X1 @ sK0 = $false) | (vAND @ (in @ (sK5 @ X1) @ (dsetconstr @ sK1 @ (cCOMB @ (bCOMB @ in @ (kpair @ X1)) @ sK2))) @ (vEQ('$i') @ (setadjoin @ (sK5 @ X1) @ emptyset) @ (dsetconstr @ sK1 @ (cCOMB @ (bCOMB @ in @ (kpair @ X1)) @ sK2))) = $true)) )),
0.19/0.49	  inference(combinator_demodulation,[],[f90])).
0.19/0.49	tff(f92,plain,(
0.19/0.49	  ( ! [X1] : ((in @ (sK5 @ X1) @ (dsetconstr @ sK1 @ (cCOMB @ (bCOMB @ in @ (kpair @ X1)) @ sK2)) = $true) | (in @ X1 @ sK0 = $false)) )),
0.19/0.49	  inference(binary_proxy_clausification,[],[f91])).
0.19/0.49	tff(f93,plain,(
0.19/0.49	  ( ! [X1] : ((in @ X1 @ sK0 = $false) | (vEQ('$i') @ (setadjoin @ (sK5 @ X1) @ emptyset) @ (dsetconstr @ sK1 @ (cCOMB @ (bCOMB @ in @ (kpair @ X1)) @ sK2)) = $true)) )),
0.19/0.49	  inference(binary_proxy_clausification,[],[f91])).
0.19/0.49	tff(f94,plain,(
0.19/0.49	  ( ! [X1] : (setadjoin @ (sK5 @ X1) @ emptyset = dsetconstr @ sK1 @ (cCOMB @ (bCOMB @ in @ (kpair @ X1)) @ sK2) | (in @ X1 @ sK0 = $false)) )),
0.19/0.49	  inference(equality_proxy_clausification,[],[f93])).
0.19/0.49	tff(f110,plain,(
0.19/0.49	  ($false = $true) | ~spl3_2),
0.19/0.49	  inference(forward_demodulation,[],[f85,f71])).
0.19/0.49	tff(f111,plain,(
0.19/0.49	  $false | ~spl3_2),
0.19/0.49	  inference(trivial_inequality_removal,[],[f110])).
0.19/0.49	tff(f112,plain,(
0.19/0.49	  ~spl3_2),
0.19/0.49	  inference(avatar_contradiction_clause,[],[f111])).
0.19/0.49	tff(f127,plain,(
0.19/0.49	  ( ! [X0,X1] : (cCOMB @ (bCOMB @ in @ (kpair @ sK4)) @ sK2 != cCOMB @ (bCOMB @ in @ (kpair @ X0)) @ sK2 | (in @ X1 @ (dsetconstr @ sK1 @ (cCOMB @ (bCOMB @ in @ (kpair @ sK4)) @ sK2)) = $false) | (in @ X0 @ sK0 = $false) | setadjoin @ X1 @ emptyset != setadjoin @ (sK5 @ X0) @ emptyset) ) | ~spl3_4),
0.19/0.49	  inference(superposition,[],[f75,f94])).
0.19/0.49	tff(f370,plain,(
0.19/0.49	  ( ! [X0] : ((in @ X0 @ (dsetconstr @ sK1 @ (cCOMB @ (bCOMB @ in @ (kpair @ sK4)) @ sK2)) = $false) | (in @ sK4 @ sK0 = $false) | setadjoin @ X0 @ emptyset != setadjoin @ (sK5 @ sK4) @ emptyset) ) | ~spl3_4),
0.19/0.49	  inference(equality_resolution,[],[f127])).
0.19/0.49	tff(f374,plain,(
0.19/0.49	  ( ! [X0] : (($false = $true) | (in @ X0 @ (dsetconstr @ sK1 @ (cCOMB @ (bCOMB @ in @ (kpair @ sK4)) @ sK2)) = $false) | setadjoin @ X0 @ emptyset != setadjoin @ (sK5 @ sK4) @ emptyset) ) | (~spl3_0 | ~spl3_4)),
0.19/0.49	  inference(forward_demodulation,[],[f370,f65])).
0.19/0.49	tff(f375,plain,(
0.19/0.49	  ( ! [X0] : (setadjoin @ X0 @ emptyset != setadjoin @ (sK5 @ sK4) @ emptyset | (in @ X0 @ (dsetconstr @ sK1 @ (cCOMB @ (bCOMB @ in @ (kpair @ sK4)) @ sK2)) = $false)) ) | (~spl3_0 | ~spl3_4)),
0.19/0.49	  inference(trivial_inequality_removal,[],[f374])).
0.19/0.49	tff(f377,plain,(
0.19/0.49	  (in @ (sK5 @ sK4) @ (dsetconstr @ sK1 @ (cCOMB @ (bCOMB @ in @ (kpair @ sK4)) @ sK2)) = $false) | (~spl3_0 | ~spl3_4)),
0.19/0.49	  inference(equality_resolution,[],[f375])).
0.19/0.49	tff(f387,plain,(
0.19/0.49	  ($false = $true) | (in @ sK4 @ sK0 = $false) | cCOMB @ (bCOMB @ in @ (kpair @ sK4)) @ sK2 != cCOMB @ (bCOMB @ in @ (kpair @ sK4)) @ sK2 | (~spl3_0 | ~spl3_4)),
0.19/0.49	  inference(superposition,[],[f377,f92])).
0.19/0.49	tff(f390,plain,(
0.19/0.49	  (in @ sK4 @ sK0 = $false) | (~spl3_0 | ~spl3_4)),
0.19/0.49	  inference(trivial_inequality_removal,[],[f387])).
0.19/0.49	tff(f391,plain,(
0.19/0.49	  ($false = $true) | (~spl3_0 | ~spl3_4)),
0.19/0.49	  inference(backward_demodulation,[],[f390,f65])).
0.19/0.49	tff(f392,plain,(
0.19/0.49	  $false | (~spl3_0 | ~spl3_4)),
0.19/0.49	  inference(trivial_inequality_removal,[],[f391])).
0.19/0.49	tff(f393,plain,(
0.19/0.49	  ~spl3_0 | ~spl3_4),
0.19/0.49	  inference(avatar_contradiction_clause,[],[f392])).
0.19/0.49	tff(f394,plain,(
0.19/0.49	  $false),
0.19/0.49	  inference(avatar_sat_refutation,[],[f72,f76,f112,f393])).
0.19/0.49	% SZS output end Proof for theBenchmark
0.19/0.49	% (10478)------------------------------
0.19/0.49	% (10478)Version: Vampire 4.5.0 (commit 7ae30c7f on 2020-06-30 15:57:20 +0100)
0.19/0.49	% (10478)Termination reason: Refutation
0.19/0.49	
0.19/0.49	% (10478)Memory used [KB]: 5884
0.19/0.49	% (10478)Time elapsed: 0.106 s
0.19/0.49	% (10478)------------------------------
0.19/0.49	% (10478)------------------------------
0.19/0.49	% (10473)Success in time 0.139 s
0.19/0.50	EOF