0.07/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.13 % Command : run_vampire %s %d 0.12/0.34 % Computer : n005.cluster.edu 0.12/0.34 % Model : x86_64 x86_64 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.34 % Memory : 8042.1875MB 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.34 % CPULimit : 960 0.12/0.34 % WCLimit : 120 0.12/0.34 % DateTime : Wed Jul 1 17:20:21 EDT 2020 0.12/0.34 % CPUTime : 0.12/0.38 % (30017)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 0.20/0.39 % (30033)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 0.20/0.39 % (30008)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 0.20/0.39 % (30030)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 0.20/0.39 % (30018)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 0.20/0.39 % (30020)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 0.20/0.39 % (30016)dis+1010_3:2_av=off:csup=on:inj=on:chr=on:foolp=on:cnfonf=eager:gsp=input_only:nm=2:nwc=1:sp=reverse_arity:urr=ec_only_29 on theBenchmark 0.20/0.39 % (30019)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 0.20/0.39 % (30021)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 0.20/0.39 % (30025)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 0.20/0.40 % (30022)lrs+1002_1_av=off:er=filter:csup=on:inj=on:chr=on:foolp=on:cnfonf=eager:fsr=off:gs=on:gsem=off:irw=on:lma=on:nm=4:nwc=1:stl=30:sd=3:ss=axioms:st=1.5:sos=on_1 on theBenchmark 0.20/0.41 % (30014)lrs+1011_5:1_acc=on:csup=on:inj=on:chr=on:foolp=on:cnfonf=eager:amm=off:anc=all_dependent:bd=off:ccuc=small_ones:fde=unused:gs=on:gsaa=full_model:gsem=off:lcm=predicate:lwlo=on:nm=6:newcnf=on:nwc=2.5:stl=30:sp=occurrence:updr=off_3 on theBenchmark 0.20/0.41 % (30013)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 0.20/0.41 % (30031)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 0.20/0.41 % (30009)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 0.20/0.41 % (30010)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 0.20/0.41 % (30011)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 0.20/0.41 % (30012)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 0.20/0.42 % (30033)Refutation found. Thanks to Tanya! 0.20/0.42 % SZS status Theorem for theBenchmark 0.20/0.43 % (30015)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 0.20/0.43 % (30034)lrs+1_4_afp=100000:afq=1.2:csup=on:inj=on:chr=on:foolp=on:cnfonf=eager:anc=none:bd=off:cond=on:gs=on:gsem=off:nm=64:nwc=1:sd=2:ss=axioms:st=2.0:sos=all:updr=off_300 on theBenchmark 0.20/0.43 % SZS output start Proof for theBenchmark 0.20/0.43 % (30036)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 0.20/0.43 tff(func_def_3, type, ->: ('$tType' * '$tType') > '$tType'). 0.20/0.43 tff(func_def_4, type, in: '$i' -> '$i' -> '$o'). 0.20/0.43 tff(func_def_6, type, setadjoin: '$i' -> '$i' -> '$i'). 0.20/0.43 tff(func_def_7, type, setunion: '$i' -> '$i'). 0.20/0.43 tff(func_def_9, type, vAPP: !>[X0: $ttype, X1: $ttype]:(X0 -> X1 * X0) > X1). 0.20/0.43 tff(func_def_12, type, binunion: '$i' -> '$i' -> '$i'). 0.20/0.43 tff(func_def_15, type, cCOMB: !>[X0: $ttype, X1: $ttype, X2: $ttype]:(X0 -> X1 -> X2) -> X1 -> X0 -> X2). 0.20/0.43 tff(func_def_16, type, bCOMB: !>[X0: $ttype, X1: $ttype, X2: $ttype]:(X1 -> X2) -> (X0 -> X1) -> X0 -> X2). 0.20/0.43 tff(func_def_24, type, sK7: '$o' -> '$i' -> '$i' -> '$i'). 0.20/0.43 tff(func_def_32, type, kCOMB: !>[X1: $ttype, X2: $ttype]:X1 -> X2 -> X1). 0.20/0.43 tff(func_def_33, type, vAND: '$o' -> '$o' -> '$o'). 0.20/0.43 tff(func_def_34, type, vOR: '$o' -> '$o' -> '$o'). 0.20/0.43 tff(func_def_35, type, vIMP: '$o' -> '$o' -> '$o'). 0.20/0.43 tff(func_def_36, type, vNOT: '$o' -> '$o'). 0.20/0.43 tff(func_def_37, type, vEQ: !>[X0: $ttype]:X0 -> X0 -> '$o'). 0.20/0.43 tff(func_def_38, type, sCOMB: !>[X0: $ttype, X1: $ttype, X2: $ttype]:(X0 -> X1 -> X2) -> (X0 -> X1) -> X0 -> X2). 0.20/0.43 tff(func_def_39, type, iCOMB: !>[X2: $ttype]:X2 -> X2). 0.20/0.43 tff(f1,axiom,( 0.20/0.43 (setadjoinE = ! [X0,X1,X2] : (in @ X2 @ (setadjoin @ X0 @ X1) => ! [X3 : '$o'] : ((X0 = X2 => X3) => ((in @ X2 @ X1 => X3) => X3))))), 0.20/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinE)). 0.20/0.43 tff(f2,axiom,( 0.20/0.43 (setunionE = ! [X1,X0] : (in @ X0 @ (setunion @ X1) => ! [X3 : '$o'] : (! [X4] : (in @ X0 @ X4 => (in @ X4 @ X1 => X3)) => X3)))), 0.20/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionE)). 0.20/0.43 tff(f3,axiom,( 0.20/0.43 (uniqinunit = ! [X0,X2] : (in @ X0 @ (setadjoin @ X2 @ emptyset) => X0 = X2))), 0.20/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',uniqinunit)). 0.20/0.43 tff(f4,axiom,( 0.20/0.43 binunion = (^[X0 : '$i', X2 : '$i'] : setunion @ (setadjoin @ X0 @ (setadjoin @ X2 @ emptyset)))), 0.20/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunion)). 0.20/0.43 tff(f5,conjecture,( 0.20/0.43 setadjoinE => (setunionE => (uniqinunit => ! [X1,X4,X0,X3 : '$o'] : (in @ X0 @ (binunion @ X1 @ X4) => ((in @ X0 @ X1 => X3) => ((in @ X0 @ X4 => X3) => X3)))))), 0.20/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionEcases)). 0.20/0.43 tff(f6,negated_conjecture,( 0.20/0.43 ~(setadjoinE => (setunionE => (uniqinunit => ! [X1,X4,X0,X3 : '$o'] : (in @ X0 @ (binunion @ X1 @ X4) => ((in @ X0 @ X1 => X3) => ((in @ X0 @ X4 => X3) => X3))))))), 0.20/0.43 inference(negated_conjecture,[],[f5])). 0.20/0.43 tff(f7,plain,( 0.20/0.43 ~(setadjoinE => (setunionE => (uniqinunit => ! [X0,X1,X2,X3 : '$o'] : (in @ X2 @ (binunion @ X0 @ X1) => ((in @ X2 @ X0 => X3) => ((in @ X2 @ X1 => X3) => X3))))))), 0.20/0.43 inference(rectify,[],[f6])). 0.20/0.43 tff(f8,plain,( 0.20/0.43 ~((setadjoinE = $true) => ((setunionE = $true) => ((uniqinunit = $true) => ! [X0,X1,X2,X3 : '$o'] : ((in @ X2 @ (binunion @ X0 @ X1) = $true) => (((in @ X2 @ X0 = $true) => ($true = X3)) => (((in @ X2 @ X1 = $true) => ($true = X3)) => ($true = X3)))))))), 0.20/0.43 inference(fool_elimination,[],[f7])). 0.20/0.43 tff(f9,plain,( 0.20/0.43 binunion = (^[X0 : '$i', X1 : '$i'] : setunion @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)))), 0.20/0.43 inference(rectify,[],[f4])). 0.20/0.43 tff(f10,plain,( 0.20/0.43 bCOMB @ (bCOMB @ setunion) @ (cCOMB @ (bCOMB @ bCOMB @ setadjoin) @ (cCOMB @ setadjoin @ emptyset)) = binunion), 0.20/0.43 inference(fool_elimination,[],[f9])). 0.20/0.43 tff(f11,plain,( 0.20/0.43 (setunionE = ! [X0,X1] : (in @ X1 @ (setunion @ X0) => ! [X2 : '$o'] : (! [X3] : (in @ X1 @ X3 => (in @ X3 @ X0 => X2)) => X2)))), 0.20/0.43 inference(rectify,[],[f2])). 0.20/0.43 tff(f12,plain,( 0.20/0.43 (setunionE = $true) <=> ! [X0,X1] : ((in @ X1 @ (setunion @ X0) = $true) => ! [X2 : '$o'] : (! [X3] : ((in @ X1 @ X3 = $true) => ((in @ X3 @ X0 = $true) => ($true = X2))) => ($true = X2)))), 0.20/0.43 inference(fool_elimination,[],[f11])). 0.20/0.43 tff(f13,plain,( 0.20/0.43 (uniqinunit = ! [X0,X1] : (in @ X0 @ (setadjoin @ X1 @ emptyset) => X0 = X1))), 0.20/0.43 inference(rectify,[],[f3])). 0.20/0.43 tff(f14,plain,( 0.20/0.43 (uniqinunit = $true) <=> ! [X0,X1] : ((in @ X0 @ (setadjoin @ X1 @ emptyset) = $true) => X0 = X1)), 0.20/0.43 inference(fool_elimination,[],[f13])). 0.20/0.43 % (30035)lrs-11_4:1_afp=4000:csup=on:inj=on:mXXn=1:foolp=on:e2e=on:cnfonf=eager:afq=2.0:anc=none:br=off:gs=on:lwlo=on:nm=64:nwc=3:stl=30:urr=on_186 on theBenchmark 0.20/0.43 tff(f15,plain,( 0.20/0.43 (setadjoinE = ! [X0,X1,X2] : (in @ X2 @ (setadjoin @ X0 @ X1) => ! [X3 : '$o'] : ((X0 = X2 => X3) => ((in @ X2 @ X1 => X3) => X3))))), 0.20/0.43 inference(rectify,[],[f1])). 0.20/0.43 % (30032)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 0.20/0.43 tff(f16,plain,( 0.20/0.43 (setadjoinE = $true) <=> ! [X0,X1,X2] : ((in @ X2 @ (setadjoin @ X0 @ X1) = $true) => ! [X3 : '$o'] : ((X0 = X2 => ($true = X3)) => (((in @ X2 @ X1 = $true) => ($true = X3)) => ($true = X3))))), 0.20/0.43 inference(fool_elimination,[],[f15])). 0.20/0.43 % (30037)dis-11_3_add=off:afp=40000:csup=on:inj=on:chr=on:e2e=on:prag=on:foolp=on:cnfonf=eager:afq=1.0:fde=all:amm=sco:anc=none:gs=on:irw=on:lcm=reverse:nm=6:nwc=1:sd=4:ss=axioms:st=3.0:sos=on:sac=on_50 on theBenchmark 0.20/0.43 tff(f17,plain,( 0.20/0.43 ((? [X0,X1,X2,X3 : '$o'] : (((($true != X3) & (($true = X3) | (in @ X2 @ X1 != $true))) & (($true = X3) | (in @ X2 @ X0 != $true))) & (in @ X2 @ (binunion @ X0 @ X1) = $true)) & (uniqinunit = $true)) & (setunionE = $true)) & (setadjoinE = $true)), 0.20/0.43 inference(ennf_transformation,[],[f8])). 0.20/0.43 tff(f18,plain,( 0.20/0.43 ? [X0,X1,X2,X3 : '$o'] : (($true != X3) & (($true = X3) | (in @ X2 @ X1 != $true)) & (($true = X3) | (in @ X2 @ X0 != $true)) & (in @ X2 @ (binunion @ X0 @ X1) = $true)) & (uniqinunit = $true) & (setunionE = $true) & (setadjoinE = $true)), 0.20/0.43 inference(flattening,[],[f17])). 0.20/0.43 tff(f19,plain,( 0.20/0.43 (setunionE = $true) <=> ! [X0,X1] : (! [X2 : '$o'] : (($true = X2) | ? [X3] : ((($true != X2) & (in @ X3 @ X0 = $true)) & (in @ X1 @ X3 = $true))) | (in @ X1 @ (setunion @ X0) != $true))), 0.20/0.43 inference(ennf_transformation,[],[f12])). 0.20/0.43 tff(f20,plain,( 0.20/0.43 (setunionE = $true) <=> ! [X0,X1] : (! [X2 : '$o'] : (($true = X2) | ? [X3] : (($true != X2) & (in @ X3 @ X0 = $true) & (in @ X1 @ X3 = $true))) | (in @ X1 @ (setunion @ X0) != $true))), 0.20/0.43 inference(flattening,[],[f19])). 0.20/0.43 tff(f21,plain,( 0.20/0.43 (uniqinunit = $true) <=> ! [X0,X1] : (X0 = X1 | (in @ X0 @ (setadjoin @ X1 @ emptyset) != $true))), 0.20/0.43 inference(ennf_transformation,[],[f14])). 0.20/0.43 tff(f22,plain,( 0.20/0.43 (setadjoinE = $true) <=> ! [X0,X1,X2] : (! [X3 : '$o'] : ((($true = X3) | (($true != X3) & (in @ X2 @ X1 = $true))) | (($true != X3) & X0 = X2)) | (in @ X2 @ (setadjoin @ X0 @ X1) != $true))), 0.20/0.43 inference(ennf_transformation,[],[f16])). 0.20/0.43 tff(f23,plain,( 0.20/0.43 (setadjoinE = $true) <=> ! [X0,X1,X2] : (! [X3 : '$o'] : (($true = X3) | (($true != X3) & (in @ X2 @ X1 = $true)) | (($true != X3) & X0 = X2)) | (in @ X2 @ (setadjoin @ X0 @ X1) != $true))), 0.20/0.43 inference(flattening,[],[f22])). 0.20/0.43 tff(f24,plain,( 0.20/0.43 ? [X0,X1,X2,X3 : '$o'] : (($true != X3) & (($true = X3) | (in @ X2 @ X1 != $true)) & (($true = X3) | (in @ X2 @ X0 != $true)) & (in @ X2 @ (binunion @ X0 @ X1) = $true)) => (($true != sK3) & (($true = sK3) | (in @ sK2 @ sK1 != $true)) & (($true = sK3) | (in @ sK2 @ sK0 != $true)) & (in @ sK2 @ (binunion @ sK0 @ sK1) = $true))), 0.20/0.43 introduced(choice_axiom,[])). 0.20/0.43 tff(f25,plain,( 0.20/0.43 (($true != sK3) & (($true = sK3) | (in @ sK2 @ sK1 != $true)) & (($true = sK3) | (in @ sK2 @ sK0 != $true)) & (in @ sK2 @ (binunion @ sK0 @ sK1) = $true)) & (uniqinunit = $true) & (setunionE = $true) & (setadjoinE = $true)), 0.20/0.43 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f18,f24])). 0.20/0.43 % (30023)ott+2_2_afp=10000:afq=1.4:csup=on:inj=on:chr=on:foolp=on:cnfonf=eager:amm=off:anc=none:gsp=input_only:gs=on:gsem=off:irw=on:lcm=predicate:nm=32:nwc=1.5:sos=on:sp=reverse_arity_7 on theBenchmark 0.20/0.43 tff(f26,plain,( 0.20/0.43 ((setunionE = $true) | ? [X0,X1] : (? [X2 : '$o'] : (($true != X2) & ! [X3] : (($true = X2) | (in @ X3 @ X0 != $true) | (in @ X1 @ X3 != $true))) & (in @ X1 @ (setunion @ X0) = $true))) & (! [X0,X1] : (! [X2 : '$o'] : (($true = X2) | ? [X3] : (($true != X2) & (in @ X3 @ X0 = $true) & (in @ X1 @ X3 = $true))) | (in @ X1 @ (setunion @ X0) != $true)) | (setunionE != $true))), 0.20/0.43 inference(nnf_transformation,[],[f20])). 0.20/0.43 tff(f27,plain,( 0.20/0.43 ((setunionE = $true) | ? [X0,X1] : (? [X2 : '$o'] : (($true != X2) & ! [X3] : (($true = X2) | (in @ X3 @ X0 != $true) | (in @ X1 @ X3 != $true))) & (in @ X1 @ (setunion @ X0) = $true))) & (! [X4,X5] : (! [X6 : '$o'] : (($true = X6) | ? [X7] : (($true != X6) & (in @ X7 @ X4 = $true) & (in @ X5 @ X7 = $true))) | (in @ X5 @ (setunion @ X4) != $true)) | (setunionE != $true))), 0.20/0.43 inference(rectify,[],[f26])). 0.20/0.43 tff(f28,plain,( 0.20/0.43 ? [X0,X1] : (? [X2 : '$o'] : (($true != X2) & ! [X3] : (($true = X2) | (in @ X3 @ X0 != $true) | (in @ X1 @ X3 != $true))) & (in @ X1 @ (setunion @ X0) = $true)) => (? [X2 : '$o'] : (($true != X2) & ! [X3] : (($true = X2) | (in @ X3 @ sK4 != $true) | (in @ sK5 @ X3 != $true))) & (in @ sK5 @ (setunion @ sK4) = $true))), 0.20/0.43 introduced(choice_axiom,[])). 0.20/0.43 tff(f29,plain,( 0.20/0.43 ? [X2 : '$o'] : (($true != X2) & ! [X3] : (($true = X2) | (in @ X3 @ sK4 != $true) | (in @ sK5 @ X3 != $true))) => (($true != sK6) & ! [X3] : (($true = sK6) | (in @ X3 @ sK4 != $true) | (in @ sK5 @ X3 != $true)))), 0.20/0.43 introduced(choice_axiom,[])). 0.20/0.43 tff(f30,plain,( 0.20/0.43 ! [X6 : '$o',X5,X4] : (? [X7] : (($true != X6) & (in @ X7 @ X4 = $true) & (in @ X5 @ X7 = $true)) => (($true != X6) & (in @ (sK7 @ X6 @ X5 @ X4) @ X4 = $true) & (in @ X5 @ (sK7 @ X6 @ X5 @ X4) = $true)))), 0.20/0.43 introduced(choice_axiom,[])). 0.20/0.43 tff(f31,plain,( 0.20/0.43 ((setunionE = $true) | ((($true != sK6) & ! [X3] : (($true = sK6) | (in @ X3 @ sK4 != $true) | (in @ sK5 @ X3 != $true))) & (in @ sK5 @ (setunion @ sK4) = $true))) & (! [X4,X5] : (! [X6 : '$o'] : (($true = X6) | (($true != X6) & (in @ (sK7 @ X6 @ X5 @ X4) @ X4 = $true) & (in @ X5 @ (sK7 @ X6 @ X5 @ X4) = $true))) | (in @ X5 @ (setunion @ X4) != $true)) | (setunionE != $true))), 0.20/0.43 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7])],[f27,f30,f29,f28])). 0.20/0.43 tff(f32,plain,( 0.20/0.43 ((uniqinunit = $true) | ? [X0,X1] : (X0 != X1 & (in @ X0 @ (setadjoin @ X1 @ emptyset) = $true))) & (! [X0,X1] : (X0 = X1 | (in @ X0 @ (setadjoin @ X1 @ emptyset) != $true)) | (uniqinunit != $true))), 0.20/0.43 inference(nnf_transformation,[],[f21])). 0.20/0.43 tff(f33,plain,( 0.20/0.43 ((uniqinunit = $true) | ? [X0,X1] : (X0 != X1 & (in @ X0 @ (setadjoin @ X1 @ emptyset) = $true))) & (! [X2,X3] : (X2 = X3 | (in @ X2 @ (setadjoin @ X3 @ emptyset) != $true)) | (uniqinunit != $true))), 0.20/0.43 inference(rectify,[],[f32])). 0.20/0.43 tff(f34,plain,( 0.20/0.43 ? [X0,X1] : (X0 != X1 & (in @ X0 @ (setadjoin @ X1 @ emptyset) = $true)) => (sK8 != sK9 & (in @ sK8 @ (setadjoin @ sK9 @ emptyset) = $true))), 0.20/0.43 introduced(choice_axiom,[])). 0.20/0.43 tff(f35,plain,( 0.20/0.43 ((uniqinunit = $true) | (sK8 != sK9 & (in @ sK8 @ (setadjoin @ sK9 @ emptyset) = $true))) & (! [X2,X3] : (X2 = X3 | (in @ X2 @ (setadjoin @ X3 @ emptyset) != $true)) | (uniqinunit != $true))), 0.20/0.43 inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9])],[f33,f34])). 0.20/0.43 tff(f36,plain,( 0.20/0.43 ((setadjoinE = $true) | ? [X0,X1,X2] : (? [X3 : '$o'] : (($true != X3) & (($true = X3) | (in @ X2 @ X1 != $true)) & (($true = X3) | X0 != X2)) & (in @ X2 @ (setadjoin @ X0 @ X1) = $true))) & (! [X0,X1,X2] : (! [X3 : '$o'] : (($true = X3) | (($true != X3) & (in @ X2 @ X1 = $true)) | (($true != X3) & X0 = X2)) | (in @ X2 @ (setadjoin @ X0 @ X1) != $true)) | (setadjoinE != $true))), 0.20/0.43 inference(nnf_transformation,[],[f23])). 0.20/0.43 tff(f37,plain,( 0.20/0.43 ((setadjoinE = $true) | ? [X0,X1,X2] : (? [X3 : '$o'] : (($true != X3) & (($true = X3) | (in @ X2 @ X1 != $true)) & (($true = X3) | X0 != X2)) & (in @ X2 @ (setadjoin @ X0 @ X1) = $true))) & (! [X4,X5,X6] : (! [X7 : '$o'] : (($true = X7) | (($true != X7) & (in @ X6 @ X5 = $true)) | (($true != X7) & X4 = X6)) | (in @ X6 @ (setadjoin @ X4 @ X5) != $true)) | (setadjoinE != $true))), 0.20/0.43 inference(rectify,[],[f36])). 0.20/0.43 tff(f38,plain,( 0.20/0.43 ? [X0,X1,X2] : (? [X3 : '$o'] : (($true != X3) & (($true = X3) | (in @ X2 @ X1 != $true)) & (($true = X3) | X0 != X2)) & (in @ X2 @ (setadjoin @ X0 @ X1) = $true)) => (? [X3 : '$o'] : (($true != X3) & (($true = X3) | (in @ sK12 @ sK11 != $true)) & (($true = X3) | sK10 != sK12)) & (in @ sK12 @ (setadjoin @ sK10 @ sK11) = $true))), 0.20/0.43 introduced(choice_axiom,[])). 0.20/0.43 tff(f39,plain,( 0.20/0.43 ? [X3 : '$o'] : (($true != X3) & (($true = X3) | (in @ sK12 @ sK11 != $true)) & (($true = X3) | sK10 != sK12)) => (($true != sK13) & (($true = sK13) | (in @ sK12 @ sK11 != $true)) & (($true = sK13) | sK10 != sK12))), 0.20/0.43 introduced(choice_axiom,[])). 0.20/0.43 tff(f40,plain,( 0.20/0.43 ((setadjoinE = $true) | ((($true != sK13) & (($true = sK13) | (in @ sK12 @ sK11 != $true)) & (($true = sK13) | sK10 != sK12)) & (in @ sK12 @ (setadjoin @ sK10 @ sK11) = $true))) & (! [X4,X5,X6] : (! [X7 : '$o'] : (($true = X7) | (($true != X7) & (in @ X6 @ X5 = $true)) | (($true != X7) & X4 = X6)) | (in @ X6 @ (setadjoin @ X4 @ X5) != $true)) | (setadjoinE != $true))), 0.20/0.43 inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12,sK13])],[f37,f39,f38])). 0.20/0.43 tff(f41,plain,( 0.20/0.43 (setadjoinE = $true)), 0.20/0.43 inference(cnf_transformation,[],[f25])). 0.20/0.43 tff(f42,plain,( 0.20/0.43 (setunionE = $true)), 0.20/0.43 inference(cnf_transformation,[],[f25])). 0.20/0.43 tff(f43,plain,( 0.20/0.43 (uniqinunit = $true)), 0.20/0.43 inference(cnf_transformation,[],[f25])). 0.20/0.43 tff(f44,plain,( 0.20/0.43 (in @ sK2 @ (binunion @ sK0 @ sK1) = $true)), 0.20/0.43 inference(cnf_transformation,[],[f25])). 0.20/0.43 tff(f45,plain,( 0.20/0.43 ($true = sK3) | (in @ sK2 @ sK0 != $true)), 0.20/0.43 inference(cnf_transformation,[],[f25])). 0.20/0.43 tff(f46,plain,( 0.20/0.43 ($true = sK3) | (in @ sK2 @ sK1 != $true)), 0.20/0.43 inference(cnf_transformation,[],[f25])). 0.20/0.43 tff(f47,plain,( 0.20/0.43 ($true != sK3)), 0.20/0.43 inference(cnf_transformation,[],[f25])). 0.20/0.43 tff(f48,plain,( 0.20/0.43 bCOMB @ (bCOMB @ setunion) @ (cCOMB @ (bCOMB @ bCOMB @ setadjoin) @ (cCOMB @ setadjoin @ emptyset)) = binunion), 0.20/0.43 inference(cnf_transformation,[],[f10])). 0.20/0.43 tff(f49,plain,( 0.20/0.43 ( ! [X6:'$o',X4,X5] : (($true = X6) | (in @ X5 @ (sK7 @ X6 @ X5 @ X4) = $true) | (in @ X5 @ (setunion @ X4) != $true) | (setunionE != $true)) )), 0.20/0.43 inference(cnf_transformation,[],[f31])). 0.20/0.43 % (30028)lrs+10_12_add=off:afp=100000:csup=on:inj=on:chr=on:foolp=on:cnfonf=eager:afq=1.4:amm=sco:anc=none:cond=on:lma=on:nm=64:nwc=1.3:stl=30:sac=on:urr=on_41 on theBenchmark 0.20/0.43 tff(f50,plain,( 0.20/0.43 ( ! [X6:'$o',X4,X5] : (($true = X6) | (in @ (sK7 @ X6 @ X5 @ X4) @ X4 = $true) | (in @ X5 @ (setunion @ X4) != $true) | (setunionE != $true)) )), 0.20/0.43 inference(cnf_transformation,[],[f31])). 0.20/0.43 % (30029)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 0.20/0.43 % (30024)lrs+1010_3:2_afr=on:csup=on:inj=on:chr=on:foolp=on:cnfonf=eager:afp=100000:afq=1.1:anc=none:gsp=input_only:irw=on:lwlo=on:nm=2:newcnf=on:nwc=1.7:sac=on:sp=occurrence_300 on theBenchmark 0.20/0.43 % (30027)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 0.20/0.43 tff(f55,plain,( 0.20/0.43 ( ! [X2,X3] : (X2 = X3 | (in @ X2 @ (setadjoin @ X3 @ emptyset) != $true) | (uniqinunit != $true)) )), 0.20/0.43 inference(cnf_transformation,[],[f35])). 0.20/0.43 tff(f58,plain,( 0.20/0.43 ( ! [X6,X4,X7:'$o',X5] : (($true = X7) | (in @ X6 @ X5 = $true) | X4 = X6 | (in @ X6 @ (setadjoin @ X4 @ X5) != $true) | (setadjoinE != $true)) )), 0.20/0.43 inference(cnf_transformation,[],[f40])). 0.20/0.43 tff(f66,plain,( 0.20/0.43 (in @ sK2 @ (bCOMB @ (bCOMB @ setunion) @ (cCOMB @ (bCOMB @ bCOMB @ setadjoin) @ (cCOMB @ setadjoin @ emptyset)) @ sK0 @ sK1) = $true)), 0.20/0.43 inference(definition_unfolding,[],[f44,f48])). 0.20/0.43 tff(f71,plain,( 0.20/0.43 ( ! [X6:'$o',X4,X5] : (($true = X6) | (in @ (sK7 @ X6 @ X5 @ X4) @ X4 = $true) | (in @ X5 @ (setunion @ X4) != $true) | ($true != $true)) )), 0.20/0.43 inference(definition_unfolding,[],[f50,f42])). 0.20/0.43 tff(f72,plain,( 0.20/0.43 ( ! [X6:'$o',X4,X5] : (($true = X6) | (in @ X5 @ (sK7 @ X6 @ X5 @ X4) = $true) | (in @ X5 @ (setunion @ X4) != $true) | ($true != $true)) )), 0.20/0.43 inference(definition_unfolding,[],[f49,f42])). 0.20/0.43 tff(f75,plain,( 0.20/0.43 ( ! [X2,X3] : (X2 = X3 | (in @ X2 @ (setadjoin @ X3 @ emptyset) != $true) | ($true != $true)) )), 0.20/0.43 inference(definition_unfolding,[],[f55,f43])). 0.20/0.43 tff(f83,plain,( 0.20/0.43 ( ! [X6,X4,X7:'$o',X5] : (($true = X7) | (in @ X6 @ X5 = $true) | X4 = X6 | (in @ X6 @ (setadjoin @ X4 @ X5) != $true) | ($true != $true)) )), 0.20/0.43 inference(definition_unfolding,[],[f58,f41])). 0.20/0.43 tff(f88,plain,( 0.20/0.43 ( ! [X6,X4,X7:'$o',X5] : (($true = X7) | (in @ X6 @ X5 = $true) | X4 = X6 | (in @ X6 @ (setadjoin @ X4 @ X5) != $true)) )), 0.20/0.43 inference(trivial_inequality_removal,[],[f83])). 0.20/0.43 tff(f90,plain,( 0.20/0.43 ( ! [X2,X3] : ((in @ X2 @ (setadjoin @ X3 @ emptyset) != $true) | X2 = X3) )), 0.20/0.43 inference(trivial_inequality_removal,[],[f75])). 0.20/0.43 tff(f91,plain,( 0.20/0.43 ( ! [X6:'$o',X4,X5] : ((in @ X5 @ (setunion @ X4) != $true) | (in @ X5 @ (sK7 @ X6 @ X5 @ X4) = $true) | ($true = X6)) )), 0.20/0.43 inference(trivial_inequality_removal,[],[f72])). 0.20/0.43 tff(f92,plain,( 0.20/0.43 ( ! [X6:'$o',X4,X5] : ((in @ X5 @ (setunion @ X4) != $true) | (in @ (sK7 @ X6 @ X5 @ X4) @ X4 = $true) | ($true = X6)) )), 0.20/0.43 inference(trivial_inequality_removal,[],[f71])). 0.20/0.43 tff(f93,plain,( 0.20/0.43 (in @ sK2 @ (setunion @ (setadjoin @ sK0 @ (setadjoin @ sK1 @ emptyset))) = $true)), 0.20/0.43 inference(combinator_demodulation,[],[f66])). 0.20/0.43 tff(f94,plain,( 0.20/0.43 (in @ sK2 @ sK1 != $true)), 0.20/0.43 inference(subsumption_resolution,[],[f46,f47])). 0.20/0.43 tff(f95,plain,( 0.20/0.43 (in @ sK2 @ sK0 != $true)), 0.20/0.43 inference(subsumption_resolution,[],[f45,f47])). 0.20/0.43 tff(f97,plain,( 0.20/0.43 spl14_0 <=> ! [X5,X4,X6] : ((in @ X6 @ X5 = $true) | (in @ X6 @ (setadjoin @ X4 @ X5) != $true) | X4 = X6)), 0.20/0.43 introduced(avatar_definition,[new_symbols(naming,[spl14_0])])). 0.20/0.43 tff(f98,plain,( 0.20/0.43 ( ! [X6,X4,X5] : ((in @ X6 @ (setadjoin @ X4 @ X5) != $true) | (in @ X6 @ X5 = $true) | X4 = X6) ) | ~spl14_0), 0.20/0.43 inference(avatar_component_clause,[],[f97])). 0.20/0.43 tff(f100,plain,( 0.20/0.43 spl14_2 <=> ! [X7 : '$o'] : ($true = X7)), 0.20/0.43 introduced(avatar_definition,[new_symbols(naming,[spl14_2])])). 0.20/0.43 tff(f101,plain,( 0.20/0.43 ( ! [X7:'$o'] : (($true = X7)) ) | ~spl14_2), 0.20/0.43 inference(avatar_component_clause,[],[f100])). 0.20/0.43 tff(f102,plain,( 0.20/0.43 spl14_0 | spl14_2), 0.20/0.43 inference(avatar_split_clause,[],[f88,f100,f97])). 0.20/0.43 tff(f107,plain,( 0.20/0.43 ($true != $true) | ($false = sK3)), 0.20/0.43 inference(fool_paramodulation,[],[f47])). 0.20/0.43 tff(f108,plain,( 0.20/0.43 ($false = sK3)), 0.20/0.43 inference(trivial_inequality_removal,[],[f107])). 0.20/0.43 tff(f109,plain,( 0.20/0.43 ($false != $true)), 0.20/0.43 inference(backward_demodulation,[],[f108,f47])). 0.20/0.43 tff(f110,plain,( 0.20/0.43 $false | ~spl14_2), 0.20/0.43 inference(subsumption_resolution,[],[f109,f101])). 0.20/0.43 tff(f111,plain,( 0.20/0.43 ~spl14_2), 0.20/0.43 inference(avatar_contradiction_clause,[],[f110])). 0.20/0.43 tff(f112,plain,( 0.20/0.43 ($true != $true) | (in @ sK2 @ sK1 = $false)), 0.20/0.43 inference(fool_paramodulation,[],[f94])). 0.20/0.43 tff(f113,plain,( 0.20/0.43 (in @ sK2 @ sK1 = $false)), 0.20/0.43 inference(trivial_inequality_removal,[],[f112])). 0.20/0.44 tff(f115,plain,( 0.20/0.44 ($true != $true) | (in @ sK2 @ sK0 = $false)), 0.20/0.44 inference(fool_paramodulation,[],[f95])). 0.20/0.44 tff(f116,plain,( 0.20/0.44 (in @ sK2 @ sK0 = $false)), 0.20/0.44 inference(trivial_inequality_removal,[],[f115])). 0.20/0.44 tff(f132,plain,( 0.20/0.44 (in @ sK2 @ (sK7 @ $false @ sK2 @ (setadjoin @ sK0 @ (setadjoin @ sK1 @ emptyset))) = $true)), 0.20/0.44 inference(unit_resulting_resolution,[],[f109,f93,f91])). 0.20/0.44 tff(f137,plain,( 0.20/0.44 (in @ (sK7 @ $false @ sK2 @ (setadjoin @ sK0 @ (setadjoin @ sK1 @ emptyset))) @ (setadjoin @ sK0 @ (setadjoin @ sK1 @ emptyset)) = $true)), 0.20/0.44 inference(unit_resulting_resolution,[],[f109,f93,f92])). 0.20/0.44 tff(f177,plain,( 0.20/0.44 ($true != $true) | (in @ (sK7 @ $false @ sK2 @ (setadjoin @ sK0 @ (setadjoin @ sK1 @ emptyset))) @ (setadjoin @ sK1 @ emptyset) = $true) | sK7 @ $false @ sK2 @ (setadjoin @ sK0 @ (setadjoin @ sK1 @ emptyset)) = sK0 | ~spl14_0), 0.20/0.44 inference(superposition,[],[f98,f137])). 0.20/0.44 tff(f178,plain,( 0.20/0.44 (in @ (sK7 @ $false @ sK2 @ (setadjoin @ sK0 @ (setadjoin @ sK1 @ emptyset))) @ (setadjoin @ sK1 @ emptyset) = $true) | sK7 @ $false @ sK2 @ (setadjoin @ sK0 @ (setadjoin @ sK1 @ emptyset)) = sK0 | ~spl14_0), 0.20/0.44 inference(trivial_inequality_removal,[],[f177])). 0.20/0.44 tff(f185,plain,( 0.20/0.44 spl14_8 <=> (in @ (sK7 @ $false @ sK2 @ (setadjoin @ sK0 @ (setadjoin @ sK1 @ emptyset))) @ (setadjoin @ sK1 @ emptyset) = $true)), 0.20/0.44 introduced(avatar_definition,[new_symbols(naming,[spl14_8])])). 0.20/0.44 tff(f186,plain,( 0.20/0.44 (in @ (sK7 @ $false @ sK2 @ (setadjoin @ sK0 @ (setadjoin @ sK1 @ emptyset))) @ (setadjoin @ sK1 @ emptyset) = $true) | ~spl14_8), 0.20/0.44 inference(avatar_component_clause,[],[f185])). 0.20/0.44 tff(f191,plain,( 0.20/0.44 spl14_10 <=> sK7 @ $false @ sK2 @ (setadjoin @ sK0 @ (setadjoin @ sK1 @ emptyset)) = sK0), 0.20/0.44 introduced(avatar_definition,[new_symbols(naming,[spl14_10])])). 0.20/0.44 tff(f192,plain,( 0.20/0.44 sK7 @ $false @ sK2 @ (setadjoin @ sK0 @ (setadjoin @ sK1 @ emptyset)) = sK0 | ~spl14_10), 0.20/0.44 inference(avatar_component_clause,[],[f191])). 0.20/0.44 tff(f195,plain,( 0.20/0.44 spl14_10 | spl14_8 | ~spl14_0), 0.20/0.44 inference(avatar_split_clause,[],[f178,f97,f185,f191])). 0.20/0.44 tff(f197,plain,( 0.20/0.44 (in @ sK2 @ sK0 = $true) | ~spl14_10), 0.20/0.44 inference(backward_demodulation,[],[f192,f132])). 0.20/0.44 tff(f198,plain,( 0.20/0.44 ($false = $true) | ~spl14_10), 0.20/0.44 inference(forward_demodulation,[],[f197,f116])). 0.20/0.44 tff(f199,plain,( 0.20/0.44 $false | ~spl14_10), 0.20/0.44 inference(trivial_inequality_removal,[],[f198])). 0.20/0.44 tff(f200,plain,( 0.20/0.44 ~spl14_10), 0.20/0.44 inference(avatar_contradiction_clause,[],[f199])). 0.20/0.44 tff(f249,plain,( 0.20/0.44 sK7 @ $false @ sK2 @ (setadjoin @ sK0 @ (setadjoin @ sK1 @ emptyset)) = sK1 | ~spl14_8), 0.20/0.44 inference(unit_resulting_resolution,[],[f186,f90])). 0.20/0.44 tff(f266,plain,( 0.20/0.44 (in @ sK2 @ sK1 = $true) | ~spl14_8), 0.20/0.44 inference(backward_demodulation,[],[f249,f132])). 0.20/0.44 tff(f267,plain,( 0.20/0.44 ($false = $true) | ~spl14_8), 0.20/0.44 inference(forward_demodulation,[],[f266,f113])). 0.20/0.44 tff(f268,plain,( 0.20/0.44 $false | ~spl14_8), 0.20/0.44 inference(trivial_inequality_removal,[],[f267])). 0.20/0.44 tff(f269,plain,( 0.20/0.44 ~spl14_8), 0.20/0.44 inference(avatar_contradiction_clause,[],[f268])). 0.20/0.44 tff(f270,plain,( 0.20/0.44 $false), 0.20/0.44 inference(avatar_sat_refutation,[],[f102,f111,f195,f200,f269])). 0.20/0.44 % SZS output end Proof for theBenchmark 0.20/0.44 % (30033)------------------------------ 0.20/0.44 % (30033)Version: Vampire 4.5.0 (commit 7ae30c7f on 2020-06-30 15:57:20 +0100) 0.20/0.44 % (30033)Termination reason: Refutation 0.20/0.44 0.20/0.44 % (30033)Memory used [KB]: 5500 0.20/0.44 % (30033)Time elapsed: 0.077 s 0.20/0.44 % (30033)------------------------------ 0.20/0.44 % (30033)------------------------------ 0.20/0.44 % (30007)Success in time 0.086 s 0.20/0.44 EOF