0.06/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.06/0.13	% Command    : run_vampire %s %d
0.13/0.34	% Computer   : n008.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   : 1200
0.13/0.34	% WCLimit    : 120
0.13/0.34	% DateTime   : Tue Jul 13 15:30:14 EDT 2021
0.13/0.34	% CPUTime    : 
0.13/0.35	This is a THF_ problem
0.13/0.35	Running vampire --ignore_missing on --mode casc_hol --cores 0 -t 120 /export/starexec/sandbox/benchmark/theBenchmark.p
0.13/0.35	Running in auto input_syntax mode. Trying TPTP
0.13/0.38	% (26789)lrs+1011_5:1_acc=on:csup=on:inj=on:chr=on:cases=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:thsq=on_3 on theBenchmark
0.13/0.38	% (26789)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs.
0.13/0.39	% (26805)dis+10_4_av=off:bsr=on:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:cond=fast:er=filter:fde=none:gsp=input_only:lcm=reverse:lma=on:nwc=4:sp=occurrence:urr=on:thsq=on_8 on theBenchmark
0.21/0.39	% (26783)ott+1002_2_av=off:bd=preordered:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:irw=on:lma=on:nm=64:nwc=10:sp=reverse_arity:updr=off:thsq=on_2 on theBenchmark
0.21/0.39	% (26788)ott+1002_8:1_add=off:csup=on:inj=on:chr=on:cases=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:thsq=on_14 on theBenchmark
0.21/0.39	% (26791)dis+1010_3:2_av=off:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:gsp=input_only:nm=2:nwc=1:sp=reverse_arity:urr=ec_only:thsq=on_29 on theBenchmark
0.21/0.40	% (26793)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:thsq=on_40 on theBenchmark
0.21/0.40	% (26797)lrs+1002_1_av=off:er=filter:csup=on:inj=on:chr=on:cases=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:thsq=on_1 on theBenchmark
0.21/0.40	% (26792)dis+1_2:3_acc=on:add=large:csup=on:inj=on:chr=on:cases=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:thsq=on_3 on theBenchmark
0.21/0.40	% (26794)dis-11_3_add=off:afp=40000:csup=on:inj=on:chr=on:cases=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:thsq=on_2 on theBenchmark
0.21/0.40	% (26784)lrs-11_4:1_afp=4000:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:afq=2.0:anc=none:br=off:gs=on:lwlo=on:nm=64:nwc=3:stl=30:urr=on:thsq=on_2 on theBenchmark
0.21/0.40	% (26803)lrs+10_12_add=off:afp=100000:csup=on:inj=on:chr=on:cases=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:thsq=on_41 on theBenchmark
0.21/0.41	% (26797)Refutation not found, incomplete strategy% (26797)------------------------------
0.21/0.41	% (26797)Version: Vampire 4.6.0 (commit 0afb7ed4a on 2021-06-23 15:27:21 +0100)
0.21/0.42	% (26786)dis+10_128_acc=on:add=off:csup=on:inj=on:chr=on:cases=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:thsq=on_2 on theBenchmark
0.21/0.42	% (26811)dis+1002_4_add=large:csup=on:inj=on:chr=on:cases=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
0.21/0.42	% (26812)dis-11_3_add=off:afp=40000:csup=on:inj=on:chr=on:e2e=on:prag=on:cases=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:thsq=on_50 on theBenchmark
0.21/0.42	% (26806)lrs+1002_1_add=large:csup=on:inj=on:fe=off:chr=on:cases=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:thsq=on_50 on theBenchmark
0.21/0.42	% (26805)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
0.21/0.42	% (26787)lrs+1010_8_add=off:afp=100000:csup=on:inj=on:chr=on:cases=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:thsq=on_13 on theBenchmark
0.21/0.42	% (26785)lrs+1011_8_add=large:csup=on:inj=on:chr=on:cases=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:thsq=on_3 on theBenchmark
0.21/0.42	% (26798)ott+2_2_afp=10000:afq=1.4:csup=on:inj=on:chr=on:cases=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:thsq=on_7 on theBenchmark
0.21/0.42	% (26797)Termination reason: Refutation not found, incomplete strategy
0.21/0.42	
0.21/0.42	% (26797)Memory used [KB]: 5884
0.21/0.42	% (26797)Time elapsed: 0.049 s
0.21/0.42	% (26797)------------------------------
0.21/0.42	% (26797)------------------------------
0.21/0.43	% (26792)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs.
0.21/0.43	% (26795)dis+1002_6_add=large:csup=on:inj=on:chr=on:cases=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:thsq=on_2 on theBenchmark
0.21/0.43	% (26808)lrs+1010_8_add=off:afp=100000:csup=on:inj=off:cases=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:thsq=on_13 on theBenchmark
0.21/0.43	% (26800)lrs+1011_5:1_acc=on:csup=on:inj=on:e2e=on:prag=on:cases=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:thsq=on_30 on theBenchmark
0.21/0.43	% (26790)lrs+4_3_av=off:br=off:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:nm=0:newcnf=on:nwc=1:stl=30:sp=occurrence:urr=on:thsq=on_32 on theBenchmark
0.21/0.43	% (26791)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
0.21/0.43	% (26810)lrs-11_4:1_afp=4000:csup=on:inj=on:mXXn=1:cases=on:e2e=on:cnfonf=eager:afq=2.0:anc=none:br=off:gs=on:lwlo=on:nm=64:nwc=3:stl=30:urr=on:thsq=on_186 on theBenchmark
0.21/0.44	% (26796)lrs+1010_3_av=off:fsr=off:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:gs=on:gsem=off:nm=2:newcnf=on:nwc=2:stl=30:sp=reverse_arity:urr=on:updr=off:thsq=on_9 on theBenchmark
0.21/0.44	% (26802)dis+1002_3:1_acc=model:csup=on:inj=on:chr=on:cases=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:thsq=on_8 on theBenchmark
0.21/0.44	% (26809)lrs+1_4_afp=100000:afq=1.2:csup=on:inj=on:chr=on:cases=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:thsq=on_300 on theBenchmark
0.21/0.44	% (26799)lrs+1010_3:2_afr=on:csup=on:inj=on:chr=on:cases=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:thsq=on_300 on theBenchmark
0.21/0.44	% (26801)ott+11_20_afr=on:afp=100000:csup=on:inj=on:chr=on:cases=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:thsq=on_6 on theBenchmark
0.21/0.44	% (26804)lrs-11_4:1_afp=4000:csup=on:inj=on:chr=on:cases=on:cnfonf=lazy_gen:afq=2.0:anc=none:br=off:gs=on:lwlo=on:nm=64:nwc=3:stl=30:urr=on:thsq=on_30 on theBenchmark
0.21/0.44	% (26800)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs.
0.21/0.44	% (26787)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs.
0.21/0.45	% (26785)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
0.21/0.45	% (26792)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
0.21/0.45	% (26806)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs.
0.21/0.45	% (26807)lrs+1011_5_add=large:csup=on:inj=on:chr=on:cases=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:thsq=on_130 on theBenchmark
0.21/0.46	% (26808)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs.
0.21/0.46	% (26790)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs.
0.21/0.46	% (26796)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs.
0.21/0.46	% (26791)First to succeed.
0.21/0.46	% (26799)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs.
0.21/0.47	% (26802)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
0.21/0.47	% (26799)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
0.21/0.47	% (26798)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
0.21/0.47	% (26785)Refutation not found, incomplete strategy% (26785)------------------------------
0.21/0.47	% (26785)Version: Vampire 4.6.0 (commit 0afb7ed4a on 2021-06-23 15:27:21 +0100)
0.21/0.47	% (26785)Termination reason: Refutation not found, incomplete strategy
0.21/0.47	
0.21/0.47	% (26785)Memory used [KB]: 10362
0.21/0.47	% (26785)Time elapsed: 0.098 s
0.21/0.47	% (26785)------------------------------
0.21/0.47	% (26785)------------------------------
0.21/0.48	% (26791)Refutation found. Thanks to Tanya!
0.21/0.48	% SZS status Theorem for theBenchmark
0.21/0.48	% SZS output start Proof for theBenchmark
0.21/0.48	thf(type_def_6, type, >: ($tType * $tType) > $tType).
0.21/0.48	thf(func_def_7, type, in: $i > $i > $o).
0.21/0.48	thf(func_def_8, type, dsetconstr: $i > ($i > $o) > $i).
0.21/0.48	thf(func_def_11, type, kpair: $i > $i > $i).
0.21/0.48	thf(func_def_12, type, cartprod: $i > $i > $i).
0.21/0.48	thf(func_def_15, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
0.21/0.48	thf(func_def_16, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
0.21/0.48	thf(func_def_19, type, vIMP: $o > $o > $o).
0.21/0.48	thf(func_def_20, type, vPI: !>[X0: $tType]:((X0 > $o) > $o)).
0.21/0.48	thf(func_def_21, type, cCOMB: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > X1 > X0 > X2)).
0.21/0.48	thf(func_def_22, type, bCOMB: !>[X0: $tType, X1: $tType, X2: $tType]:((X1 > X2) > (X0 > X1) > X0 > X2)).
0.21/0.48	thf(func_def_23, type, iCOMB: !>[X0: $tType]:(X0 > X0)).
0.21/0.48	thf(func_def_24, type, sCOMB: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > (X0 > X1) > X0 > X2)).
0.21/0.48	thf(func_def_25, type, vEQ: !>[X0: $tType]:(X0 > X0 > $o)).
0.21/0.48	thf(func_def_26, type, vAND: $o > $o > $o).
0.21/0.48	thf(func_def_27, type, vSIGMA: !>[X0: $tType]:((X0 > $o) > $o)).
0.21/0.48	thf(func_def_30, type, sK2: $i > $i > $o).
0.21/0.48	thf(func_def_33, type, kCOMB: !>[X0: $tType, X1: $tType]:(X0 > X1 > X0)).
0.21/0.48	thf(func_def_34, type, vOR: $o > $o > $o).
0.21/0.48	thf(func_def_35, type, vNOT: $o > $o).
0.21/0.48	thf(f131,plain,(
0.21/0.48	  $false),
0.21/0.48	  inference(subsumption_resolution,[],[f129,f29])).
0.21/0.48	thf(f29,plain,(
0.21/0.48	  ($true != ((sK2 @ sK3) @ sK4))),
0.21/0.48	  inference(cnf_transformation,[],[f22])).
0.21/0.48	thf(f22,plain,(
0.21/0.48	  ((($true != ((sK2 @ sK3) @ sK4)) & ($true = ((in @ ((kpair @ sK3) @ sK4)) @ (((dpsetconstr @ sK0) @ sK1) @ sK2))) & ($true = ((in @ sK4) @ sK1))) & ($true = ((in @ sK3) @ sK0))) & (setukpairinjR = $true) & (setukpairinjL = $true) & (dsetconstrER = $true)),
0.21/0.48	  inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f19,f21,f20])).
0.21/0.48	thf(f20,plain,(
0.21/0.48	  ? [X0,X1,X2 : $i > $i > $o,X3] : (? [X4] : (($true != ((X2 @ X3) @ X4)) & ($true = ((in @ ((kpair @ X3) @ X4)) @ (((dpsetconstr @ X0) @ X1) @ X2))) & ($true = ((in @ X4) @ X1))) & ($true = ((in @ X3) @ X0))) => (? [X4] : (($true != ((sK2 @ sK3) @ X4)) & ($true = ((in @ ((kpair @ sK3) @ X4)) @ (((dpsetconstr @ sK0) @ sK1) @ sK2))) & ($true = ((in @ X4) @ sK1))) & ($true = ((in @ sK3) @ sK0)))),
0.21/0.48	  introduced(choice_axiom,[])).
0.21/0.48	thf(f21,plain,(
0.21/0.48	  ? [X4] : (($true != ((sK2 @ sK3) @ X4)) & ($true = ((in @ ((kpair @ sK3) @ X4)) @ (((dpsetconstr @ sK0) @ sK1) @ sK2))) & ($true = ((in @ X4) @ sK1))) => (($true != ((sK2 @ sK3) @ sK4)) & ($true = ((in @ ((kpair @ sK3) @ sK4)) @ (((dpsetconstr @ sK0) @ sK1) @ sK2))) & ($true = ((in @ sK4) @ sK1)))),
0.21/0.48	  introduced(choice_axiom,[])).
0.21/0.48	thf(f19,plain,(
0.21/0.48	  ? [X0,X1,X2 : $i > $i > $o,X3] : (? [X4] : (($true != ((X2 @ X3) @ X4)) & ($true = ((in @ ((kpair @ X3) @ X4)) @ (((dpsetconstr @ X0) @ X1) @ X2))) & ($true = ((in @ X4) @ X1))) & ($true = ((in @ X3) @ X0))) & (setukpairinjR = $true) & (setukpairinjL = $true) & (dsetconstrER = $true)),
0.21/0.48	  inference(flattening,[],[f18])).
0.21/0.48	thf(f18,plain,(
0.21/0.48	  ((? [X0,X1,X2 : $i > $i > $o,X3] : (? [X4] : ((($true != ((X2 @ X3) @ X4)) & ($true = ((in @ ((kpair @ X3) @ X4)) @ (((dpsetconstr @ X0) @ X1) @ X2)))) & ($true = ((in @ X4) @ X1))) & ($true = ((in @ X3) @ X0))) & (setukpairinjR = $true)) & (setukpairinjL = $true)) & (dsetconstrER = $true)),
0.21/0.48	  inference(ennf_transformation,[],[f9])).
0.21/0.48	thf(f9,plain,(
0.21/0.48	  ~((dsetconstrER = $true) => ((setukpairinjL = $true) => ((setukpairinjR = $true) => ! [X0,X1,X2 : $i > $i > $o,X3] : (($true = ((in @ X3) @ X0)) => ! [X4] : (($true = ((in @ X4) @ X1)) => (($true = ((in @ ((kpair @ X3) @ X4)) @ (((dpsetconstr @ X0) @ X1) @ X2))) => ($true = ((X2 @ X3) @ X4))))))))),
0.21/0.48	  inference(fool_elimination,[],[f8])).
0.21/0.48	thf(f8,plain,(
0.21/0.48	  ~(dsetconstrER => (setukpairinjL => (setukpairinjR => ! [X0,X1,X2 : $i > $i > $o,X3] : (((in @ X3) @ X0) => ! [X4] : (((in @ X4) @ X1) => (((in @ ((kpair @ X3) @ X4)) @ (((dpsetconstr @ X0) @ X1) @ (^[X5 : $i, X6 : $i] : (((X2 @ X5) @ X6))))) => ((X2 @ X3) @ X4)))))))),
0.21/0.48	  inference(rectify,[],[f6])).
0.21/0.48	thf(f6,negated_conjecture,(
0.21/0.48	  ~(dsetconstrER => (setukpairinjL => (setukpairinjR => ! [X0,X6,X1 : $i > $i > $o,X2] : (((in @ X2) @ X0) => ! [X3] : (((in @ X3) @ X6) => (((in @ ((kpair @ X2) @ X3)) @ (((dpsetconstr @ X0) @ X6) @ (^[X4 : $i, X5 : $i] : (((X1 @ X4) @ X5))))) => ((X1 @ X2) @ X3)))))))),
0.21/0.48	  inference(negated_conjecture,[],[f5])).
0.21/0.48	thf(f5,conjecture,(
0.21/0.48	  dsetconstrER => (setukpairinjL => (setukpairinjR => ! [X0,X6,X1 : $i > $i > $o,X2] : (((in @ X2) @ X0) => ! [X3] : (((in @ X3) @ X6) => (((in @ ((kpair @ X2) @ X3)) @ (((dpsetconstr @ X0) @ X6) @ (^[X4 : $i, X5 : $i] : (((X1 @ X4) @ X5))))) => ((X1 @ X2) @ X3))))))),
0.21/0.48	  file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrERa)).
0.21/0.48	thf(f129,plain,(
0.21/0.48	  ($true = ((sK2 @ sK3) @ sK4))),
0.21/0.48	  inference(backward_demodulation,[],[f111,f121])).
0.21/0.48	thf(f121,plain,(
0.21/0.48	  (sK4 = sK6)),
0.21/0.48	  inference(equality_resolution,[],[f100])).
0.21/0.48	thf(f100,plain,(
0.21/0.48	  ( ! [X4 : $i,X5 : $i] : ((((kpair @ X4) @ X5) != ((kpair @ sK3) @ sK4)) | (sK6 = X5)) )),
0.21/0.48	  inference(superposition,[],[f48,f84])).
0.21/0.48	thf(f84,plain,(
0.21/0.48	  (((kpair @ sK3) @ sK4) = ((kpair @ sK5) @ sK6))),
0.21/0.48	  inference(equality_proxy_clausification,[],[f80])).
0.21/0.48	thf(f80,plain,(
0.21/0.48	  ($true = ((vEQ($i) @ ((kpair @ sK5) @ sK6)) @ ((kpair @ sK3) @ sK4)))),
0.21/0.48	  inference(binary_proxy_clausification,[],[f79])).
0.21/0.48	thf(f79,plain,(
0.21/0.48	  ($true = ((vAND @ ((vAND @ ((in @ sK6) @ sK1)) @ ((sK2 @ sK5) @ sK6))) @ ((vEQ($i) @ ((kpair @ sK5) @ sK6)) @ ((kpair @ sK3) @ sK4))))),
0.21/0.48	  inference(combinator_demodulation,[],[f78])).
0.21/0.48	thf(f78,plain,(
0.21/0.48	  ($true = (((sCOMB @ ((bCOMB @ vAND) @ ((sCOMB @ ((bCOMB @ vAND) @ ((cCOMB @ in) @ sK1))) @ (sK2 @ sK5)))) @ ((cCOMB @ ((bCOMB @ vEQ($i)) @ (kpair @ sK5))) @ ((kpair @ sK3) @ sK4))) @ sK6))),
0.21/0.48	  inference(sigma_clausification,[],[f76])).
0.21/0.48	thf(f76,plain,(
0.21/0.48	  ($true = (vSIGMA($i) @ ((sCOMB @ ((bCOMB @ vAND) @ ((sCOMB @ ((bCOMB @ vAND) @ ((cCOMB @ in) @ sK1))) @ (sK2 @ sK5)))) @ ((cCOMB @ ((bCOMB @ vEQ($i)) @ (kpair @ sK5))) @ ((kpair @ sK3) @ sK4)))))),
0.21/0.48	  inference(binary_proxy_clausification,[],[f75])).
0.21/0.48	thf(f75,plain,(
0.21/0.48	  ($true = ((vAND @ ((in @ sK5) @ sK0)) @ (vSIGMA($i) @ ((sCOMB @ ((bCOMB @ vAND) @ ((sCOMB @ ((bCOMB @ vAND) @ ((cCOMB @ in) @ sK1))) @ (sK2 @ sK5)))) @ ((cCOMB @ ((bCOMB @ vEQ($i)) @ (kpair @ sK5))) @ ((kpair @ sK3) @ sK4))))))),
0.21/0.48	  inference(combinator_demodulation,[],[f74])).
0.21/0.48	thf(f74,plain,(
0.21/0.48	  ($true = (((sCOMB @ ((bCOMB @ vAND) @ ((cCOMB @ in) @ sK0))) @ ((bCOMB @ vSIGMA($i)) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vAND)) @ ((bCOMB @ (sCOMB @ ((bCOMB @ vAND) @ ((cCOMB @ in) @ sK1)))) @ sK2)))) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ vEQ($i))) @ kpair))) @ ((kpair @ sK3) @ sK4))))) @ sK5))),
0.21/0.48	  inference(sigma_clausification,[],[f73])).
0.21/0.48	thf(f73,plain,(
0.21/0.48	  ($true = (vSIGMA($i) @ ((sCOMB @ ((bCOMB @ vAND) @ ((cCOMB @ in) @ sK0))) @ ((bCOMB @ vSIGMA($i)) @ ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vAND)) @ ((bCOMB @ (sCOMB @ ((bCOMB @ vAND) @ ((cCOMB @ in) @ sK1)))) @ sK2)))) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ vEQ($i))) @ kpair))) @ ((kpair @ sK3) @ sK4)))))))),
0.21/0.48	  inference(combinator_demodulation,[],[f72])).
0.21/0.48	thf(f72,plain,(
0.21/0.48	  ($true = (((bCOMB @ vSIGMA($i)) @ ((bCOMB @ (sCOMB @ ((bCOMB @ vAND) @ ((cCOMB @ in) @ sK0)))) @ ((bCOMB @ (bCOMB @ vSIGMA($i))) @ ((bCOMB @ (sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vAND)) @ ((bCOMB @ (sCOMB @ ((bCOMB @ vAND) @ ((cCOMB @ in) @ sK1)))) @ sK2))))) @ (cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ vEQ($i))) @ kpair))))))) @ ((kpair @ sK3) @ sK4)))),
0.21/0.48	  inference(trivial_inequality_removal,[],[f71])).
0.21/0.48	thf(f71,plain,(
0.21/0.48	  ($true = $false) | ($true = (((bCOMB @ vSIGMA($i)) @ ((bCOMB @ (sCOMB @ ((bCOMB @ vAND) @ ((cCOMB @ in) @ sK0)))) @ ((bCOMB @ (bCOMB @ vSIGMA($i))) @ ((bCOMB @ (sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vAND)) @ ((bCOMB @ (sCOMB @ ((bCOMB @ vAND) @ ((cCOMB @ in) @ sK1)))) @ sK2))))) @ (cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ vEQ($i))) @ kpair))))))) @ ((kpair @ sK3) @ sK4)))),
0.21/0.48	  inference(superposition,[],[f66,f67])).
0.21/0.48	thf(f67,plain,(
0.21/0.48	  ($true = ((in @ ((kpair @ sK3) @ sK4)) @ ((dsetconstr @ ((cartprod @ sK0) @ sK1)) @ ((bCOMB @ vSIGMA($i)) @ ((bCOMB @ (sCOMB @ ((bCOMB @ vAND) @ ((cCOMB @ in) @ sK0)))) @ ((bCOMB @ (bCOMB @ vSIGMA($i))) @ ((bCOMB @ (sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vAND)) @ ((bCOMB @ (sCOMB @ ((bCOMB @ vAND) @ ((cCOMB @ in) @ sK1)))) @ sK2))))) @ (cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ vEQ($i))) @ kpair))))))))))),
0.21/0.48	  inference(combinator_demodulation,[],[f34])).
0.21/0.48	thf(f34,plain,(
0.21/0.48	  ($true = ((in @ ((kpair @ sK3) @ sK4)) @ (((((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ bCOMB)) @ ((bCOMB @ (bCOMB @ dsetconstr)) @ cartprod)))) @ ((bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vSIGMA($i))))) @ ((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ bCOMB) @ ((bCOMB @ bCOMB) @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vAND)) @ (cCOMB @ in))))))) @ ((bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vSIGMA($i))))) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ bCOMB)) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ sCOMB))) @ ((bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vAND)))) @ ((bCOMB @ bCOMB) @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vAND)) @ (cCOMB @ in)))))))))) @ (cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ vEQ($i))) @ kpair)))))))) @ sK0) @ sK1) @ sK2)))),
0.21/0.48	  inference(definition_unfolding,[],[f28,f33])).
0.21/0.48	thf(f33,plain,(
0.21/0.48	  (dpsetconstr = ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ bCOMB)) @ ((bCOMB @ (bCOMB @ dsetconstr)) @ cartprod)))) @ ((bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vSIGMA($i))))) @ ((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ bCOMB) @ ((bCOMB @ bCOMB) @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vAND)) @ (cCOMB @ in))))))) @ ((bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vSIGMA($i))))) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ bCOMB)) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ sCOMB))) @ ((bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vAND)))) @ ((bCOMB @ bCOMB) @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vAND)) @ (cCOMB @ in)))))))))) @ (cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ vEQ($i))) @ kpair)))))))))),
0.21/0.48	  inference(cnf_transformation,[],[f17])).
0.21/0.48	thf(f17,plain,(
0.21/0.48	  (dpsetconstr = ((sCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ bCOMB)) @ ((bCOMB @ (bCOMB @ dsetconstr)) @ cartprod)))) @ ((bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vSIGMA($i))))) @ ((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ bCOMB) @ ((bCOMB @ bCOMB) @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vAND)) @ (cCOMB @ in))))))) @ ((bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vSIGMA($i))))) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ bCOMB)) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ sCOMB))) @ ((bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vAND)))) @ ((bCOMB @ bCOMB) @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vAND)) @ (cCOMB @ in)))))))))) @ (cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ vEQ($i))) @ kpair)))))))))),
0.21/0.48	  inference(fool_elimination,[],[f16])).
0.21/0.48	thf(f16,plain,(
0.21/0.48	  (dpsetconstr = (^[X0 : $i, X1 : $i, X2 : $i > $i > $o] : (((dsetconstr @ ((cartprod @ X0) @ X1)) @ (^[X3 : $i] : (? [X4] : (? [X5] : ((((kpair @ X4) @ X5) = X3) & ((X2 @ X4) @ X5) & ((in @ X5) @ X1)) & ((in @ X4) @ X0))))))))),
0.21/0.48	  inference(rectify,[],[f4])).
0.21/0.48	thf(f4,axiom,(
0.21/0.48	  (dpsetconstr = (^[X0 : $i, X6 : $i, X1 : $i > $i > $o] : (((dsetconstr @ ((cartprod @ X0) @ X6)) @ (^[X5 : $i] : (? [X2] : (? [X3] : ((((kpair @ X2) @ X3) = X5) & ((X1 @ X2) @ X3) & ((in @ X3) @ X6)) & ((in @ X2) @ X0))))))))),
0.21/0.48	  file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstr)).
0.21/0.48	thf(f28,plain,(
0.21/0.48	  ($true = ((in @ ((kpair @ sK3) @ sK4)) @ (((dpsetconstr @ sK0) @ sK1) @ sK2)))),
0.21/0.48	  inference(cnf_transformation,[],[f22])).
0.21/0.48	thf(f66,plain,(
0.21/0.48	  ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (($false = ((in @ X1) @ ((dsetconstr @ X3) @ X2))) | ($true = (X2 @ X1))) )),
0.21/0.48	  inference(binary_proxy_clausification,[],[f65])).
0.21/0.48	thf(f65,plain,(
0.21/0.48	  ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (($true = ((vIMP @ ((in @ X1) @ ((dsetconstr @ X3) @ X2))) @ (X2 @ X1)))) )),
0.21/0.48	  inference(combinator_demodulation,[],[f64])).
0.21/0.48	thf(f64,plain,(
0.21/0.48	  ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (($true = (((cCOMB @ ((bCOMB @ vIMP) @ ((bCOMB @ (in @ X1)) @ ((cCOMB @ dsetconstr) @ X2)))) @ (X2 @ X1)) @ X3))) )),
0.21/0.48	  inference(pi_clausification,[],[f63])).
0.21/0.48	thf(f63,plain,(
0.21/0.48	  ( ! [X2 : $i > $o,X1 : $i] : (($true = (vPI($i) @ ((cCOMB @ ((bCOMB @ vIMP) @ ((bCOMB @ (in @ X1)) @ ((cCOMB @ dsetconstr) @ X2)))) @ (X2 @ X1))))) )),
0.21/0.48	  inference(combinator_demodulation,[],[f62])).
0.21/0.48	thf(f62,plain,(
0.21/0.48	  ( ! [X2 : $i > $o,X1 : $i] : (($true = (((bCOMB @ vPI($i)) @ ((sCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ vIMP)) @ ((bCOMB @ (bCOMB @ (in @ X1))) @ (cCOMB @ dsetconstr))))) @ ((cCOMB @ iCOMB) @ X1))) @ X2))) )),
0.21/0.48	  inference(pi_clausification,[],[f61])).
0.21/0.48	thf(f61,plain,(
0.21/0.48	  ( ! [X1 : $i] : (($true = (vPI($i > $o) @ ((bCOMB @ vPI($i)) @ ((sCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ vIMP)) @ ((bCOMB @ (bCOMB @ (in @ X1))) @ (cCOMB @ dsetconstr))))) @ ((cCOMB @ iCOMB) @ X1)))))) )),
0.21/0.48	  inference(combinator_demodulation,[],[f60])).
0.21/0.48	thf(f60,plain,(
0.21/0.48	  ( ! [X1 : $i] : (($true = (((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))) )),
0.21/0.48	  inference(pi_clausification,[],[f35])).
0.21/0.48	thf(f35,plain,(
0.21/0.48	  ($true = (vPI($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))))))),
0.21/0.48	  inference(definition_unfolding,[],[f30,f23])).
0.21/0.48	thf(f23,plain,(
0.21/0.48	  (dsetconstrER = $true)),
0.21/0.48	  inference(cnf_transformation,[],[f22])).
0.21/0.48	thf(f30,plain,(
0.21/0.48	  (dsetconstrER = (vPI($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))))))),
0.21/0.48	  inference(cnf_transformation,[],[f11])).
0.21/0.48	thf(f11,plain,(
0.21/0.48	  (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))))))),
0.21/0.48	  inference(fool_elimination,[],[f10])).
0.21/0.48	thf(f10,plain,(
0.21/0.48	  (dsetconstrER = ! [X0,X1 : $i > $o,X2] : (((in @ X2) @ ((dsetconstr @ X0) @ (^[X3 : $i] : ((X1 @ X3))))) => (X1 @ X2)))),
0.21/0.48	  inference(rectify,[],[f1])).
0.21/0.48	thf(f1,axiom,(
0.21/0.48	  (dsetconstrER = ! [X0,X1 : $i > $o,X2] : (((in @ X2) @ ((dsetconstr @ X0) @ (^[X3 : $i] : ((X1 @ X3))))) => (X1 @ X2)))),
0.21/0.48	  file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrER)).
0.21/0.48	thf(f48,plain,(
0.21/0.48	  ( ! [X4 : $i,X2 : $i,X3 : $i,X1 : $i] : ((((kpair @ X2) @ X1) != ((kpair @ X4) @ X3)) | (X1 = X3)) )),
0.21/0.48	  inference(equality_proxy_clausification,[],[f47])).
0.21/0.48	thf(f47,plain,(
0.21/0.48	  ( ! [X4 : $i,X2 : $i,X3 : $i,X1 : $i] : ((((kpair @ X2) @ X1) != ((kpair @ X4) @ X3)) | ($true = ((vEQ($i) @ X3) @ X1))) )),
0.21/0.48	  inference(equality_proxy_clausification,[],[f46])).
0.21/0.48	thf(f46,plain,(
0.21/0.48	  ( ! [X4 : $i,X2 : $i,X3 : $i,X1 : $i] : (($false = ((vEQ($i) @ ((kpair @ X2) @ X1)) @ ((kpair @ X4) @ X3))) | ($true = ((vEQ($i) @ X3) @ X1))) )),
0.21/0.48	  inference(binary_proxy_clausification,[],[f45])).
0.21/0.48	thf(f45,plain,(
0.21/0.48	  ( ! [X4 : $i,X2 : $i,X3 : $i,X1 : $i] : (($true = ((vIMP @ ((vEQ($i) @ ((kpair @ X2) @ X1)) @ ((kpair @ X4) @ X3))) @ ((vEQ($i) @ X3) @ X1)))) )),
0.21/0.48	  inference(combinator_demodulation,[],[f44])).
0.21/0.48	thf(f44,plain,(
0.21/0.48	  ( ! [X4 : $i,X2 : $i,X3 : $i,X1 : $i] : (($true = (((cCOMB @ ((bCOMB @ vIMP) @ ((bCOMB @ (vEQ($i) @ ((kpair @ X2) @ X1))) @ ((cCOMB @ kpair) @ X3)))) @ ((vEQ($i) @ X3) @ X1)) @ X4))) )),
0.21/0.48	  inference(pi_clausification,[],[f43])).
0.21/0.48	thf(f43,plain,(
0.21/0.48	  ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (vPI($i) @ ((cCOMB @ ((bCOMB @ vIMP) @ ((bCOMB @ (vEQ($i) @ ((kpair @ X2) @ X1))) @ ((cCOMB @ kpair) @ X3)))) @ ((vEQ($i) @ X3) @ X1))))) )),
0.21/0.48	  inference(combinator_demodulation,[],[f42])).
0.21/0.48	thf(f42,plain,(
0.21/0.48	  ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((bCOMB @ vPI($i)) @ ((sCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ vIMP)) @ ((bCOMB @ (bCOMB @ (vEQ($i) @ ((kpair @ X2) @ X1)))) @ (cCOMB @ kpair))))) @ ((cCOMB @ vEQ($i)) @ X1))) @ X3))) )),
0.21/0.48	  inference(pi_clausification,[],[f41])).
0.21/0.48	thf(f41,plain,(
0.21/0.48	  ( ! [X2 : $i,X1 : $i] : (($true = (vPI($i) @ ((bCOMB @ vPI($i)) @ ((sCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ vIMP)) @ ((bCOMB @ (bCOMB @ (vEQ($i) @ ((kpair @ X2) @ X1)))) @ (cCOMB @ kpair))))) @ ((cCOMB @ vEQ($i)) @ X1)))))) )),
0.21/0.48	  inference(combinator_demodulation,[],[f40])).
0.21/0.48	thf(f40,plain,(
0.21/0.48	  ( ! [X2 : $i,X1 : $i] : (($true = (((bCOMB @ vPI($i)) @ ((bCOMB @ (bCOMB @ vPI($i))) @ ((cCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ cCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vIMP))) @ ((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ bCOMB) @ ((bCOMB @ vEQ($i)) @ ((cCOMB @ kpair) @ X1))))) @ (cCOMB @ kpair)))))) @ ((cCOMB @ vEQ($i)) @ X1)))) @ X2))) )),
0.21/0.48	  inference(pi_clausification,[],[f39])).
0.21/0.48	thf(f39,plain,(
0.21/0.48	  ( ! [X1 : $i] : (($true = (vPI($i) @ ((bCOMB @ vPI($i)) @ ((bCOMB @ (bCOMB @ vPI($i))) @ ((cCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ cCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vIMP))) @ ((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ bCOMB) @ ((bCOMB @ vEQ($i)) @ ((cCOMB @ kpair) @ X1))))) @ (cCOMB @ kpair)))))) @ ((cCOMB @ vEQ($i)) @ X1))))))) )),
0.21/0.48	  inference(combinator_demodulation,[],[f38])).
0.21/0.48	thf(f38,plain,(
0.21/0.48	  ( ! [X1 : $i] : (($true = (((bCOMB @ vPI($i)) @ ((bCOMB @ (bCOMB @ vPI($i))) @ ((bCOMB @ (bCOMB @ (bCOMB @ vPI($i)))) @ ((sCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ cCOMB))) @ ((bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vIMP)))) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ bCOMB)) @ ((bCOMB @ (bCOMB @ bCOMB)) @ ((bCOMB @ (bCOMB @ vEQ($i))) @ (cCOMB @ kpair)))))) @ (cCOMB @ kpair))))))) @ (cCOMB @ vEQ($i)))))) @ X1))) )),
0.21/0.48	  inference(pi_clausification,[],[f37])).
0.21/0.48	thf(f37,plain,(
0.21/0.48	  ($true = (vPI($i) @ ((bCOMB @ vPI($i)) @ ((bCOMB @ (bCOMB @ vPI($i))) @ ((bCOMB @ (bCOMB @ (bCOMB @ vPI($i)))) @ ((sCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ cCOMB))) @ ((bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vIMP)))) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ bCOMB)) @ ((bCOMB @ (bCOMB @ bCOMB)) @ ((bCOMB @ (bCOMB @ vEQ($i))) @ (cCOMB @ kpair)))))) @ (cCOMB @ kpair))))))) @ (cCOMB @ vEQ($i))))))))),
0.21/0.48	  inference(definition_unfolding,[],[f32,f25])).
0.21/0.48	thf(f25,plain,(
0.21/0.48	  (setukpairinjR = $true)),
0.21/0.48	  inference(cnf_transformation,[],[f22])).
0.21/0.48	thf(f32,plain,(
0.21/0.48	  (setukpairinjR = (vPI($i) @ ((bCOMB @ vPI($i)) @ ((bCOMB @ (bCOMB @ vPI($i))) @ ((bCOMB @ (bCOMB @ (bCOMB @ vPI($i)))) @ ((sCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ cCOMB))) @ ((bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vIMP)))) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ bCOMB)) @ ((bCOMB @ (bCOMB @ bCOMB)) @ ((bCOMB @ (bCOMB @ vEQ($i))) @ (cCOMB @ kpair)))))) @ (cCOMB @ kpair))))))) @ (cCOMB @ vEQ($i))))))))),
0.21/0.48	  inference(cnf_transformation,[],[f15])).
0.21/0.48	thf(f15,plain,(
0.21/0.48	  (setukpairinjR = (vPI($i) @ ((bCOMB @ vPI($i)) @ ((bCOMB @ (bCOMB @ vPI($i))) @ ((bCOMB @ (bCOMB @ (bCOMB @ vPI($i)))) @ ((sCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ cCOMB))) @ ((bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vIMP)))) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ bCOMB)) @ ((bCOMB @ (bCOMB @ bCOMB)) @ ((bCOMB @ (bCOMB @ vEQ($i))) @ (cCOMB @ kpair)))))) @ (cCOMB @ kpair))))))) @ (cCOMB @ vEQ($i))))))))),
0.21/0.48	  inference(fool_elimination,[],[f14])).
0.21/0.48	thf(f14,plain,(
0.21/0.48	  (setukpairinjR = ! [X0,X1,X2,X3] : ((((kpair @ X2) @ X3) = ((kpair @ X0) @ X1)) => (X1 = X3)))),
0.21/0.48	  inference(rectify,[],[f3])).
0.21/0.48	thf(f3,axiom,(
0.21/0.48	  (setukpairinjR = ! [X2,X3,X4,X5] : ((((kpair @ X2) @ X3) = ((kpair @ X4) @ X5)) => (X3 = X5)))),
0.21/0.48	  file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR)).
0.21/0.48	thf(f111,plain,(
0.21/0.48	  ($true = ((sK2 @ sK3) @ sK6))),
0.21/0.48	  inference(backward_demodulation,[],[f82,f108])).
0.21/0.48	thf(f108,plain,(
0.21/0.48	  (sK3 = sK5)),
0.21/0.48	  inference(equality_resolution,[],[f98])).
0.21/0.48	thf(f98,plain,(
0.21/0.48	  ( ! [X0 : $i,X1 : $i] : ((((kpair @ X0) @ X1) != ((kpair @ sK3) @ sK4)) | (sK5 = X0)) )),
0.21/0.48	  inference(superposition,[],[f59,f84])).
0.21/0.48	thf(f59,plain,(
0.21/0.48	  ( ! [X4 : $i,X2 : $i,X3 : $i,X1 : $i] : ((((kpair @ X2) @ X1) != ((kpair @ X4) @ X3)) | (X2 = X4)) )),
0.21/0.48	  inference(equality_proxy_clausification,[],[f58])).
0.21/0.48	thf(f58,plain,(
0.21/0.48	  ( ! [X4 : $i,X2 : $i,X3 : $i,X1 : $i] : ((((kpair @ X2) @ X1) != ((kpair @ X4) @ X3)) | ($true = ((vEQ($i) @ X4) @ X2))) )),
0.21/0.48	  inference(equality_proxy_clausification,[],[f57])).
0.21/0.48	thf(f57,plain,(
0.21/0.48	  ( ! [X4 : $i,X2 : $i,X3 : $i,X1 : $i] : (($false = ((vEQ($i) @ ((kpair @ X2) @ X1)) @ ((kpair @ X4) @ X3))) | ($true = ((vEQ($i) @ X4) @ X2))) )),
0.21/0.48	  inference(binary_proxy_clausification,[],[f56])).
0.21/0.48	thf(f56,plain,(
0.21/0.48	  ( ! [X4 : $i,X2 : $i,X3 : $i,X1 : $i] : (($true = ((vIMP @ ((vEQ($i) @ ((kpair @ X2) @ X1)) @ ((kpair @ X4) @ X3))) @ ((vEQ($i) @ X4) @ X2)))) )),
0.21/0.48	  inference(combinator_demodulation,[],[f55])).
0.21/0.48	thf(f55,plain,(
0.21/0.48	  ( ! [X4 : $i,X2 : $i,X3 : $i,X1 : $i] : (($true = (((sCOMB @ ((bCOMB @ vIMP) @ ((bCOMB @ (vEQ($i) @ ((kpair @ X2) @ X1))) @ ((cCOMB @ kpair) @ X3)))) @ ((cCOMB @ vEQ($i)) @ X2)) @ X4))) )),
0.21/0.48	  inference(pi_clausification,[],[f54])).
0.21/0.48	thf(f54,plain,(
0.21/0.48	  ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (vPI($i) @ ((sCOMB @ ((bCOMB @ vIMP) @ ((bCOMB @ (vEQ($i) @ ((kpair @ X2) @ X1))) @ ((cCOMB @ kpair) @ X3)))) @ ((cCOMB @ vEQ($i)) @ X2))))) )),
0.21/0.48	  inference(combinator_demodulation,[],[f53])).
0.21/0.48	thf(f53,plain,(
0.21/0.48	  ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((bCOMB @ vPI($i)) @ ((cCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vIMP)) @ ((bCOMB @ (bCOMB @ (vEQ($i) @ ((kpair @ X2) @ X1)))) @ (cCOMB @ kpair))))) @ ((cCOMB @ vEQ($i)) @ X2))) @ X3))) )),
0.21/0.48	  inference(pi_clausification,[],[f52])).
0.21/0.48	thf(f52,plain,(
0.21/0.48	  ( ! [X2 : $i,X1 : $i] : (($true = (vPI($i) @ ((bCOMB @ vPI($i)) @ ((cCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vIMP)) @ ((bCOMB @ (bCOMB @ (vEQ($i) @ ((kpair @ X2) @ X1)))) @ (cCOMB @ kpair))))) @ ((cCOMB @ vEQ($i)) @ X2)))))) )),
0.21/0.48	  inference(combinator_demodulation,[],[f51])).
0.21/0.48	thf(f51,plain,(
0.21/0.48	  ( ! [X2 : $i,X1 : $i] : (($true = (((bCOMB @ vPI($i)) @ ((bCOMB @ (bCOMB @ vPI($i))) @ ((sCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vIMP))) @ ((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ bCOMB) @ ((bCOMB @ vEQ($i)) @ ((cCOMB @ kpair) @ X1))))) @ (cCOMB @ kpair)))))) @ (cCOMB @ vEQ($i))))) @ X2))) )),
0.21/0.48	  inference(pi_clausification,[],[f50])).
0.21/0.48	thf(f50,plain,(
0.21/0.48	  ( ! [X1 : $i] : (($true = (vPI($i) @ ((bCOMB @ vPI($i)) @ ((bCOMB @ (bCOMB @ vPI($i))) @ ((sCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ sCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ vIMP))) @ ((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ bCOMB) @ ((bCOMB @ vEQ($i)) @ ((cCOMB @ kpair) @ X1))))) @ (cCOMB @ kpair)))))) @ (cCOMB @ vEQ($i)))))))) )),
0.21/0.48	  inference(combinator_demodulation,[],[f49])).
0.21/0.48	thf(f49,plain,(
0.21/0.48	  ( ! [X1 : $i] : (($true = (((bCOMB @ vPI($i)) @ ((bCOMB @ (bCOMB @ vPI($i))) @ ((bCOMB @ (bCOMB @ (bCOMB @ vPI($i)))) @ ((cCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ cCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ sCOMB))) @ ((bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vIMP)))) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ bCOMB)) @ ((bCOMB @ (bCOMB @ bCOMB)) @ ((bCOMB @ (bCOMB @ vEQ($i))) @ (cCOMB @ kpair)))))) @ (cCOMB @ kpair))))))) @ (cCOMB @ vEQ($i)))))) @ X1))) )),
0.21/0.48	  inference(pi_clausification,[],[f36])).
0.21/0.48	thf(f36,plain,(
0.21/0.48	  ($true = (vPI($i) @ ((bCOMB @ vPI($i)) @ ((bCOMB @ (bCOMB @ vPI($i))) @ ((bCOMB @ (bCOMB @ (bCOMB @ vPI($i)))) @ ((cCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ cCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ sCOMB))) @ ((bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vIMP)))) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ bCOMB)) @ ((bCOMB @ (bCOMB @ bCOMB)) @ ((bCOMB @ (bCOMB @ vEQ($i))) @ (cCOMB @ kpair)))))) @ (cCOMB @ kpair))))))) @ (cCOMB @ vEQ($i))))))))),
0.21/0.48	  inference(definition_unfolding,[],[f31,f24])).
0.21/0.48	thf(f24,plain,(
0.21/0.48	  (setukpairinjL = $true)),
0.21/0.48	  inference(cnf_transformation,[],[f22])).
0.21/0.48	thf(f31,plain,(
0.21/0.48	  (setukpairinjL = (vPI($i) @ ((bCOMB @ vPI($i)) @ ((bCOMB @ (bCOMB @ vPI($i))) @ ((bCOMB @ (bCOMB @ (bCOMB @ vPI($i)))) @ ((cCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ cCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ sCOMB))) @ ((bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vIMP)))) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ bCOMB)) @ ((bCOMB @ (bCOMB @ bCOMB)) @ ((bCOMB @ (bCOMB @ vEQ($i))) @ (cCOMB @ kpair)))))) @ (cCOMB @ kpair))))))) @ (cCOMB @ vEQ($i))))))))),
0.21/0.48	  inference(cnf_transformation,[],[f13])).
0.21/0.48	thf(f13,plain,(
0.21/0.48	  (setukpairinjL = (vPI($i) @ ((bCOMB @ vPI($i)) @ ((bCOMB @ (bCOMB @ vPI($i))) @ ((bCOMB @ (bCOMB @ (bCOMB @ vPI($i)))) @ ((cCOMB @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ cCOMB)) @ ((bCOMB @ (bCOMB @ (bCOMB @ sCOMB))) @ ((bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vIMP)))) @ ((cCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ bCOMB)) @ ((bCOMB @ (bCOMB @ bCOMB)) @ ((bCOMB @ (bCOMB @ vEQ($i))) @ (cCOMB @ kpair)))))) @ (cCOMB @ kpair))))))) @ (cCOMB @ vEQ($i))))))))),
0.21/0.48	  inference(fool_elimination,[],[f12])).
0.21/0.48	thf(f12,plain,(
0.21/0.48	  (setukpairinjL = ! [X0,X1,X2,X3] : ((((kpair @ X2) @ X3) = ((kpair @ X0) @ X1)) => (X0 = X2)))),
0.21/0.48	  inference(rectify,[],[f2])).
0.21/0.48	thf(f2,axiom,(
0.21/0.48	  (setukpairinjL = ! [X2,X3,X4,X5] : ((((kpair @ X2) @ X3) = ((kpair @ X4) @ X5)) => (X2 = X4)))),
0.21/0.48	  file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjL)).
0.21/0.48	thf(f82,plain,(
0.21/0.48	  ($true = ((sK2 @ sK5) @ sK6))),
0.21/0.48	  inference(binary_proxy_clausification,[],[f81])).
0.21/0.48	thf(f81,plain,(
0.21/0.48	  ($true = ((vAND @ ((in @ sK6) @ sK1)) @ ((sK2 @ sK5) @ sK6)))),
0.21/0.48	  inference(binary_proxy_clausification,[],[f79])).
0.21/0.48	% SZS output end Proof for theBenchmark
0.21/0.48	% (26791)------------------------------
0.21/0.48	% (26791)Version: Vampire 4.6.0 (commit 0afb7ed4a on 2021-06-23 15:27:21 +0100)
0.21/0.48	% (26791)Termination reason: Refutation
0.21/0.48	
0.21/0.48	% (26791)Memory used [KB]: 1791
0.21/0.48	% (26791)Time elapsed: 0.093 s
0.21/0.48	% (26791)------------------------------
0.21/0.48	% (26791)------------------------------
0.21/0.48	% (26781)Success in time 0.123 s
0.21/0.48	EOF