0.06/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.06/0.12 % Command : run_vampire %s %d 0.11/0.32 % Computer : n029.cluster.edu 0.11/0.32 % Model : x86_64 x86_64 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.11/0.32 % Memory : 8042.1875MB 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 0.11/0.32 % CPULimit : 960 0.11/0.32 % WCLimit : 120 0.11/0.32 % DateTime : Thu Jul 2 07:19:16 EDT 2020 0.11/0.32 % CPUTime : 0.11/0.35 % (27732)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 0.11/0.35 % (27729)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 0.11/0.35 % (27728)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 0.11/0.35 % (27731)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 0.11/0.36 % (27725)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 0.11/0.36 % (27727)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 0.11/0.36 % (27746)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 0.11/0.37 % (27726)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 0.11/0.37 % (27738)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 0.11/0.37 % (27723)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 0.11/0.37 % (27752)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 0.11/0.37 % (27745)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 0.11/0.37 % (27751)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 0.11/0.37 % (27724)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 0.11/0.37 % (27750)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 0.11/0.38 % (27737)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 0.11/0.38 % (27730)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 0.11/0.38 % (27743)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 0.11/0.38 % (27742)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 0.11/0.38 % (27741)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 0.11/0.38 % (27748)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 0.11/0.39 % (27747)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 0.11/0.39 % (27744)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 0.11/0.39 % (27734)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 0.11/0.39 % (27733)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 0.11/0.39 % (27740)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 0.11/0.39 % (27736)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 0.11/0.39 % (27739)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 0.16/0.39 % (27735)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 0.16/0.40 % (27749)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 0.16/0.41 % (27737)Refutation not found, incomplete strategy 0.16/0.41 % (27737)------------------------------ 0.16/0.41 % (27737)Version: Vampire 4.5.0 (commit 7ae30c7f on 2020-06-30 15:57:20 +0100) 0.16/0.41 % (27725)Refutation not found, incomplete strategy 0.16/0.41 % (27725)------------------------------ 0.16/0.41 % (27725)Version: Vampire 4.5.0 (commit 7ae30c7f on 2020-06-30 15:57:20 +0100) 0.16/0.41 % (27725)Termination reason: Refutation not found, incomplete strategy 0.16/0.41 0.16/0.41 % (27725)Memory used [KB]: 9850 0.16/0.41 % (27725)Time elapsed: 0.066 s 0.16/0.41 % (27725)------------------------------ 0.16/0.41 % (27725)------------------------------ 0.16/0.43 % (27737)Termination reason: Refutation not found, incomplete strategy 0.16/0.43 0.16/0.43 % (27737)Memory used [KB]: 5373 0.16/0.43 % (27737)Time elapsed: 0.068 s 0.16/0.43 % (27737)------------------------------ 0.16/0.43 % (27737)------------------------------ 0.16/0.43 % (27728)Refutation found. Thanks to Tanya! 0.16/0.43 % SZS status Theorem for theBenchmark 0.16/0.43 % SZS output start Proof for theBenchmark 0.16/0.43 tff(func_def_3, type, ->: ('$tType' * '$tType') > '$tType'). 0.16/0.43 tff(func_def_4, type, in: '$i' -> '$i' -> '$o'). 0.16/0.43 tff(func_def_5, type, dsetconstr: '$i' -> ('$i' -> '$o') -> '$i'). 0.16/0.43 tff(func_def_7, type, vAPP: !>[X0: $ttype, X1: $ttype]:(X0 -> X1 * X0) > X1). 0.16/0.43 tff(func_def_8, type, kpair: '$i' -> '$i' -> '$i'). 0.16/0.43 tff(func_def_9, type, cartprod: '$i' -> '$i' -> '$i'). 0.16/0.43 tff(func_def_12, type, dpsetconstr: '$i' -> '$i' -> ('$i' -> '$i' -> '$o') -> '$i'). 0.16/0.43 tff(func_def_13, type, vEPSILON: !>[X0: $ttype]:(X0 -> '$o') -> X0). 0.16/0.43 tff(func_def_16, type, vIMP: '$o' -> '$o' -> '$o'). 0.16/0.43 tff(func_def_17, type, vPI: !>[X0: $ttype]:(X0 -> '$o') -> '$o'). 0.16/0.43 tff(func_def_18, type, cCOMB: !>[X0: $ttype, X1: $ttype, X2: $ttype]:(X0 -> X1 -> X2) -> X1 -> X0 -> X2). 0.16/0.43 tff(func_def_19, type, bCOMB: !>[X0: $ttype, X1: $ttype, X2: $ttype]:(X1 -> X2) -> (X0 -> X1) -> X0 -> X2). 0.16/0.43 tff(func_def_20, type, iCOMB: !>[X2: $ttype]:X2 -> X2). 0.16/0.43 tff(func_def_21, type, sCOMB: !>[X0: $ttype, X1: $ttype, X2: $ttype]:(X0 -> X1 -> X2) -> (X0 -> X1) -> X0 -> X2). 0.16/0.43 tff(func_def_22, type, vEQ: !>[X0: $ttype]:X0 -> X0 -> '$o'). 0.16/0.43 tff(func_def_23, type, vAND: '$o' -> '$o' -> '$o'). 0.16/0.43 tff(func_def_24, type, vSIGMA: !>[X0: $ttype]:(X0 -> '$o') -> '$o'). 0.16/0.43 tff(func_def_27, type, sK2: '$i' -> '$i' -> '$o'). 0.16/0.43 tff(func_def_31, type, kCOMB: !>[X1: $ttype, X2: $ttype]:X1 -> X2 -> X1). 0.16/0.43 tff(func_def_32, type, vOR: '$o' -> '$o' -> '$o'). 0.16/0.43 tff(func_def_33, type, vNOT: '$o' -> '$o'). 0.16/0.43 tff(f1,axiom,( 0.16/0.43 (dsetconstrER = ! [X0,X1 : '$i' -> '$o',X2] : (in @ X2 @ (dsetconstr @ X0 @ (^[X3 : '$i'] : X1 @ X3)) => X1 @ X2))), 0.16/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrER)). 0.16/0.43 tff(f2,axiom,( 0.16/0.43 (setukpairinjL = ! [X2,X3,X4,X5] : (kpair @ X2 @ X3 = kpair @ X4 @ X5 => X2 = X4))), 0.16/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjL)). 0.16/0.43 tff(f3,axiom,( 0.16/0.43 (setukpairinjR = ! [X2,X3,X4,X5] : (kpair @ X2 @ X3 = kpair @ X4 @ X5 => X3 = X5))), 0.16/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjR)). 0.16/0.43 tff(f4,axiom,( 0.16/0.43 dpsetconstr = (^[X0 : '$i', X6 : '$i', X1 : '$i' -> '$i' -> '$o'] : dsetconstr @ (cartprod @ X0 @ X6) @ (^[X5 : '$i'] : ? [X2] : (? [X3] : (kpair @ X2 @ X3 = X5 & X1 @ X2 @ X3 & in @ X3 @ X6) & in @ X2 @ X0)))), 0.16/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dpsetconstr)). 0.16/0.43 tff(f5,conjecture,( 0.16/0.43 dsetconstrER => (setukpairinjL => (setukpairinjR => ! [X0,X6,X1 : '$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)))))), 0.16/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dpsetconstrERa)). 0.16/0.43 tff(f6,negated_conjecture,( 0.16/0.43 ~(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 : '$i'] : X1 @ X4 @ X5)) => X1 @ X2 @ X3))))))), 0.16/0.43 inference(negated_conjecture,[],[f5])). 0.16/0.43 tff(f7,plain,( 0.16/0.43 ~(dsetconstrER => (setukpairinjL => (setukpairinjR => ! [X0,X1,X2 : '$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))))))), 0.16/0.43 inference(rectify,[],[f6])). 0.16/0.43 tff(f8,plain,( 0.16/0.43 ~((dsetconstrER = $true) => ((setukpairinjL = $true) => ((setukpairinjR = $true) => ! [X0,X1,X2 : '$i' -> '$i' -> '$o',X3] : ((in @ X3 @ X0 = $true) => ! [X4] : ((in @ X4 @ X1 = $true) => ((in @ (kpair @ X3 @ X4) @ (dpsetconstr @ X0 @ X1 @ X2) = $true) => (X2 @ X3 @ X4 = $true)))))))), 0.16/0.43 inference(fool_elimination,[],[f7])). 0.16/0.43 tff(f9,plain,( 0.16/0.43 (dsetconstrER = ! [X0,X1 : '$i' -> '$o',X2] : (in @ X2 @ (dsetconstr @ X0 @ (^[X3 : '$i'] : X1 @ X3)) => X1 @ X2))), 0.16/0.43 inference(rectify,[],[f1])). 0.16/0.43 tff(f10,plain,( 0.16/0.43 (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)))))), 0.16/0.43 inference(fool_elimination,[],[f9])). 0.16/0.43 tff(f11,plain,( 0.16/0.43 (setukpairinjL = ! [X0,X1,X2,X3] : (kpair @ X0 @ X1 = kpair @ X2 @ X3 => X0 = X2))), 0.16/0.43 inference(rectify,[],[f2])). 0.16/0.44 tff(f12,plain,( 0.16/0.44 (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))) @ (bCOMB @ (bCOMB @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ vEQ('$i')) @ (cCOMB @ kpair))))) @ (cCOMB @ kpair)))))) @ (cCOMB @ vEQ('$i')))))) = setukpairinjL)), 0.16/0.44 inference(fool_elimination,[],[f11])). 0.16/0.44 tff(f13,plain,( 0.16/0.44 (setukpairinjR = ! [X0,X1,X2,X3] : (kpair @ X0 @ X1 = kpair @ X2 @ X3 => X1 = X3))), 0.16/0.44 inference(rectify,[],[f3])). 0.16/0.44 tff(f14,plain,( 0.16/0.44 (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))) @ (bCOMB @ (bCOMB @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ vEQ('$i')) @ (cCOMB @ kpair))))) @ (cCOMB @ kpair)))))) @ (cCOMB @ vEQ('$i')))))) = setukpairinjR)), 0.16/0.44 inference(fool_elimination,[],[f13])). 0.16/0.44 tff(f15,plain,( 0.16/0.44 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)))), 0.16/0.44 inference(rectify,[],[f4])). 0.16/0.46 tff(f16,plain,( 0.16/0.46 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('$i')) @ kpair))))))) = dpsetconstr), 0.16/0.46 inference(fool_elimination,[],[f15])). 0.16/0.46 tff(f17,plain,( 0.16/0.46 ((? [X0,X1,X2 : '$i' -> '$i' -> '$o',X3] : (? [X4] : (((X2 @ X3 @ X4 != $true) & (in @ (kpair @ X3 @ X4) @ (dpsetconstr @ X0 @ X1 @ X2) = $true)) & (in @ X4 @ X1 = $true)) & (in @ X3 @ X0 = $true)) & (setukpairinjR = $true)) & (setukpairinjL = $true)) & (dsetconstrER = $true)), 0.16/0.46 inference(ennf_transformation,[],[f8])). 0.16/0.46 tff(f18,plain,( 0.16/0.46 ? [X0,X1,X2 : '$i' -> '$i' -> '$o',X3] : (? [X4] : ((X2 @ X3 @ X4 != $true) & (in @ (kpair @ X3 @ X4) @ (dpsetconstr @ X0 @ X1 @ X2) = $true) & (in @ X4 @ X1 = $true)) & (in @ X3 @ X0 = $true)) & (setukpairinjR = $true) & (setukpairinjL = $true) & (dsetconstrER = $true)), 0.16/0.46 inference(flattening,[],[f17])). 0.16/0.46 tff(f19,plain,( 0.16/0.46 ? [X0,X1,X2 : '$i' -> '$i' -> '$o',X3] : (? [X4] : ((X2 @ X3 @ X4 != $true) & (in @ (kpair @ X3 @ X4) @ (dpsetconstr @ X0 @ X1 @ X2) = $true) & (in @ X4 @ X1 = $true)) & (in @ X3 @ X0 = $true)) => (? [X4] : ((sK2 @ sK3 @ X4 != $true) & (in @ (kpair @ sK3 @ X4) @ (dpsetconstr @ sK0 @ sK1 @ sK2) = $true) & (in @ X4 @ sK1 = $true)) & (in @ sK3 @ sK0 = $true))), 0.16/0.46 introduced(choice_axiom,[])). 0.16/0.46 tff(f20,plain,( 0.16/0.46 ? [X4] : ((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 = $true))), 0.16/0.46 introduced(choice_axiom,[])). 0.16/0.46 tff(f21,plain,( 0.16/0.46 (((sK2 @ sK3 @ sK4 != $true) & (in @ (kpair @ sK3 @ sK4) @ (dpsetconstr @ sK0 @ sK1 @ sK2) = $true) & (in @ sK4 @ sK1 = $true)) & (in @ sK3 @ sK0 = $true)) & (setukpairinjR = $true) & (setukpairinjL = $true) & (dsetconstrER = $true)), 0.16/0.46 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f18,f20,f19])). 0.16/0.46 tff(f22,plain,( 0.16/0.46 (dsetconstrER = $true)), 0.16/0.46 inference(cnf_transformation,[],[f21])). 0.16/0.46 tff(f23,plain,( 0.16/0.46 (setukpairinjL = $true)), 0.16/0.46 inference(cnf_transformation,[],[f21])). 0.16/0.46 tff(f24,plain,( 0.16/0.46 (setukpairinjR = $true)), 0.16/0.46 inference(cnf_transformation,[],[f21])). 0.16/0.46 tff(f27,plain,( 0.16/0.46 (in @ (kpair @ sK3 @ sK4) @ (dpsetconstr @ sK0 @ sK1 @ sK2) = $true)), 0.16/0.46 inference(cnf_transformation,[],[f21])). 0.16/0.46 tff(f28,plain,( 0.16/0.46 (sK2 @ sK3 @ sK4 != $true)), 0.16/0.46 inference(cnf_transformation,[],[f21])). 0.16/0.46 tff(f29,plain,( 0.16/0.46 (dsetconstrER = vPI('$i') @ (bCOMB @ vPI('$i' -> '$o') @ (bCOMB @ (bCOMB @ vPI('$i')) @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ cCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vIMP)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ in)) @ (cCOMB @ dsetconstr))))) @ (cCOMB @ iCOMB)))))), 0.16/0.46 inference(cnf_transformation,[],[f10])). 0.16/0.46 tff(f30,plain,( 0.16/0.46 (vPI('$i') @ (bCOMB @ vPI('$i') @ (bCOMB @ (bCOMB @ vPI('$i')) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i'))) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ cCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ sCOMB)) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vIMP))) @ (bCOMB @ (bCOMB @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ vEQ('$i')) @ (cCOMB @ kpair))))) @ (cCOMB @ kpair)))))) @ (cCOMB @ vEQ('$i')))))) = setukpairinjL)), 0.16/0.46 inference(cnf_transformation,[],[f12])). 0.16/0.46 tff(f31,plain,( 0.16/0.46 (vPI('$i') @ (bCOMB @ vPI('$i') @ (bCOMB @ (bCOMB @ vPI('$i')) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i'))) @ (sCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ sCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ cCOMB)) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vIMP))) @ (bCOMB @ (bCOMB @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ vEQ('$i')) @ (cCOMB @ kpair))))) @ (cCOMB @ kpair)))))) @ (cCOMB @ vEQ('$i')))))) = setukpairinjR)), 0.16/0.46 inference(cnf_transformation,[],[f14])). 0.16/0.46 tff(f32,plain,( 0.16/0.46 sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ bCOMB) @ (bCOMB @ (bCOMB @ dsetconstr) @ cartprod))) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vSIGMA('$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))))))) = dpsetconstr), 0.16/0.46 inference(cnf_transformation,[],[f16])). 0.16/0.46 tff(f33,plain,( 0.16/0.46 (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) = $true)), 0.16/0.46 inference(definition_unfolding,[],[f27,f32])). 0.16/0.46 tff(f34,plain,( 0.16/0.46 (vPI('$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)))) = $true)), 0.16/0.46 inference(definition_unfolding,[],[f29,f22])). 0.16/0.46 tff(f35,plain,( 0.16/0.46 (vPI('$i') @ (bCOMB @ vPI('$i') @ (bCOMB @ (bCOMB @ vPI('$i')) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i'))) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ cCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ sCOMB)) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vIMP))) @ (bCOMB @ (bCOMB @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ vEQ('$i')) @ (cCOMB @ kpair))))) @ (cCOMB @ kpair)))))) @ (cCOMB @ vEQ('$i')))))) = $true)), 0.16/0.46 inference(definition_unfolding,[],[f30,f23])). 0.16/0.46 tff(f36,plain,( 0.16/0.46 (vPI('$i') @ (bCOMB @ vPI('$i') @ (bCOMB @ (bCOMB @ vPI('$i')) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i'))) @ (sCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ sCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ cCOMB)) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vIMP))) @ (bCOMB @ (bCOMB @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ vEQ('$i')) @ (cCOMB @ kpair))))) @ (cCOMB @ kpair)))))) @ (cCOMB @ vEQ('$i')))))) = $true)), 0.16/0.46 inference(definition_unfolding,[],[f31,f24])). 0.16/0.46 tff(f37,plain,( 0.16/0.46 ( ! [X1] : ((bCOMB @ vPI('$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))) @ (bCOMB @ (bCOMB @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ vEQ('$i')) @ (cCOMB @ kpair))))) @ (cCOMB @ kpair)))))) @ (cCOMB @ vEQ('$i'))))) @ X1 = $true)) )), 0.16/0.46 inference(pi_clausification,[],[f36])). 0.16/0.46 tff(f38,plain,( 0.16/0.46 ( ! [X1] : ((vPI('$i') @ (bCOMB @ vPI('$i') @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ cCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vIMP)) @ (bCOMB @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ vEQ('$i')) @ (cCOMB @ kpair)))) @ (cCOMB @ kpair @ X1))))) @ (cCOMB @ vEQ('$i') @ X1)))) = $true)) )), 0.16/0.46 inference(combinator_demodulation,[],[f37])). 0.16/0.46 tff(f39,plain,( 0.16/0.46 ( ! [X2,X1] : ((bCOMB @ vPI('$i') @ (bCOMB @ (bCOMB @ vPI('$i')) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ cCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vIMP)) @ (bCOMB @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ vEQ('$i')) @ (cCOMB @ kpair)))) @ (cCOMB @ kpair @ X1))))) @ (cCOMB @ vEQ('$i') @ X1))) @ X2 = $true)) )), 0.16/0.46 inference(pi_clausification,[],[f38])). 0.16/0.46 tff(f40,plain,( 0.16/0.46 ( ! [X2,X1] : ((vPI('$i') @ (bCOMB @ vPI('$i') @ (sCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ vEQ('$i')) @ (cCOMB @ kpair))) @ (kpair @ X2 @ X1)))) @ (cCOMB @ vEQ('$i') @ X1))) = $true)) )), 0.16/0.46 inference(combinator_demodulation,[],[f39])). 0.16/0.46 tff(f41,plain,( 0.16/0.46 ( ! [X2,X3,X1] : ((bCOMB @ vPI('$i') @ (sCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ vEQ('$i')) @ (cCOMB @ kpair))) @ (kpair @ X2 @ X1)))) @ (cCOMB @ vEQ('$i') @ X1)) @ X3 = $true)) )), 0.16/0.46 inference(pi_clausification,[],[f40])). 0.16/0.46 tff(f42,plain,( 0.16/0.46 ( ! [X2,X3,X1] : ((vPI('$i') @ (cCOMB @ (bCOMB @ vIMP @ (cCOMB @ (bCOMB @ vEQ('$i') @ (cCOMB @ kpair @ X3)) @ (kpair @ X2 @ X1))) @ (vEQ('$i') @ X3 @ X1)) = $true)) )), 0.16/0.46 inference(combinator_demodulation,[],[f41])). 0.16/0.46 tff(f43,plain,( 0.16/0.46 ( ! [X4,X2,X3,X1] : ((cCOMB @ (bCOMB @ vIMP @ (cCOMB @ (bCOMB @ vEQ('$i') @ (cCOMB @ kpair @ X3)) @ (kpair @ X2 @ X1))) @ (vEQ('$i') @ X3 @ X1) @ X4 = $true)) )), 0.16/0.46 inference(pi_clausification,[],[f42])). 0.16/0.46 tff(f44,plain,( 0.16/0.46 ( ! [X4,X2,X3,X1] : ((vIMP @ (vEQ('$i') @ (kpair @ X4 @ X3) @ (kpair @ X2 @ X1)) @ (vEQ('$i') @ X3 @ X1) = $true)) )), 0.16/0.46 inference(combinator_demodulation,[],[f43])). 0.16/0.46 tff(f45,plain,( 0.16/0.46 ( ! [X4,X2,X3,X1] : ((vEQ('$i') @ (kpair @ X4 @ X3) @ (kpair @ X2 @ X1) = $false) | (vEQ('$i') @ X3 @ X1 = $true)) )), 0.16/0.46 inference(binary_proxy_clausification,[],[f44])). 0.16/0.46 tff(f46,plain,( 0.16/0.46 ( ! [X4,X2,X3,X1] : ((vEQ('$i') @ (kpair @ X4 @ X3) @ (kpair @ X2 @ X1) = $false) | X1 = X3) )), 0.16/0.46 inference(equality_proxy_clausification,[],[f45])). 0.16/0.46 tff(f47,plain,( 0.16/0.46 ( ! [X4,X2,X3,X1] : (kpair @ X2 @ X1 != kpair @ X4 @ X3 | X1 = X3) )), 0.16/0.46 inference(equality_proxy_clausification,[],[f46])). 0.16/0.46 tff(f48,plain,( 0.16/0.46 ( ! [X1] : ((bCOMB @ vPI('$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))) @ (bCOMB @ (bCOMB @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ vEQ('$i')) @ (cCOMB @ kpair))))) @ (cCOMB @ kpair)))))) @ (cCOMB @ vEQ('$i'))))) @ X1 = $true)) )), 0.16/0.46 inference(pi_clausification,[],[f35])). 0.16/0.46 tff(f49,plain,( 0.16/0.46 ( ! [X1] : ((vPI('$i') @ (bCOMB @ vPI('$i') @ (bCOMB @ (bCOMB @ vPI('$i')) @ (sCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ sCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vIMP)) @ (bCOMB @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ vEQ('$i')) @ (cCOMB @ kpair)))) @ (cCOMB @ kpair @ X1))))) @ (cCOMB @ vEQ('$i'))))) = $true)) )), 0.16/0.46 inference(combinator_demodulation,[],[f48])). 0.16/0.46 tff(f50,plain,( 0.16/0.46 ( ! [X2,X1] : ((bCOMB @ vPI('$i') @ (bCOMB @ (bCOMB @ vPI('$i')) @ (sCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ sCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vIMP)) @ (bCOMB @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ vEQ('$i')) @ (cCOMB @ kpair)))) @ (cCOMB @ kpair @ X1))))) @ (cCOMB @ vEQ('$i')))) @ X2 = $true)) )), 0.16/0.46 inference(pi_clausification,[],[f49])). 0.16/0.46 tff(f51,plain,( 0.16/0.46 ( ! [X2,X1] : ((vPI('$i') @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ vEQ('$i')) @ (cCOMB @ kpair))) @ (kpair @ X2 @ X1)))) @ (cCOMB @ vEQ('$i') @ X2))) = $true)) )), 0.16/0.46 inference(combinator_demodulation,[],[f50])). 0.16/0.46 tff(f52,plain,( 0.16/0.46 ( ! [X2,X3,X1] : ((bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ vEQ('$i')) @ (cCOMB @ kpair))) @ (kpair @ X2 @ X1)))) @ (cCOMB @ vEQ('$i') @ X2)) @ X3 = $true)) )), 0.16/0.46 inference(pi_clausification,[],[f51])). 0.16/0.46 tff(f53,plain,( 0.16/0.46 ( ! [X2,X3,X1] : ((vPI('$i') @ (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ (bCOMB @ vEQ('$i') @ (cCOMB @ kpair @ X3)) @ (kpair @ X2 @ X1))) @ (cCOMB @ vEQ('$i') @ X2)) = $true)) )), 0.16/0.46 inference(combinator_demodulation,[],[f52])). 0.16/0.46 tff(f54,plain,( 0.16/0.46 ( ! [X4,X2,X3,X1] : ((sCOMB @ (bCOMB @ vIMP @ (cCOMB @ (bCOMB @ vEQ('$i') @ (cCOMB @ kpair @ X3)) @ (kpair @ X2 @ X1))) @ (cCOMB @ vEQ('$i') @ X2) @ X4 = $true)) )), 0.16/0.46 inference(pi_clausification,[],[f53])). 0.16/0.46 tff(f55,plain,( 0.16/0.46 ( ! [X4,X2,X3,X1] : ((vIMP @ (vEQ('$i') @ (kpair @ X4 @ X3) @ (kpair @ X2 @ X1)) @ (vEQ('$i') @ X4 @ X2) = $true)) )), 0.16/0.46 inference(combinator_demodulation,[],[f54])). 0.16/0.46 tff(f56,plain,( 0.16/0.46 ( ! [X4,X2,X3,X1] : ((vEQ('$i') @ (kpair @ X4 @ X3) @ (kpair @ X2 @ X1) = $false) | (vEQ('$i') @ X4 @ X2 = $true)) )), 0.16/0.46 inference(binary_proxy_clausification,[],[f55])). 0.16/0.46 tff(f57,plain,( 0.16/0.46 ( ! [X4,X2,X3,X1] : ((vEQ('$i') @ (kpair @ X4 @ X3) @ (kpair @ X2 @ X1) = $false) | X2 = X4) )), 0.16/0.46 inference(equality_proxy_clausification,[],[f56])). 0.16/0.46 tff(f58,plain,( 0.16/0.46 ( ! [X4,X2,X3,X1] : (kpair @ X2 @ X1 != kpair @ X4 @ X3 | X2 = X4) )), 0.16/0.46 inference(equality_proxy_clausification,[],[f57])). 0.16/0.46 tff(f59,plain,( 0.16/0.46 ( ! [X1] : ((bCOMB @ vPI('$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 = $true)) )), 0.16/0.46 inference(pi_clausification,[],[f34])). 0.16/0.46 tff(f60,plain,( 0.16/0.46 ( ! [X1] : ((vPI('$i' -> '$o') @ (bCOMB @ vPI('$i') @ (sCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (bCOMB @ (bCOMB @ (in @ X1)) @ (cCOMB @ dsetconstr)))) @ (cCOMB @ iCOMB @ X1))) = $true)) )), 0.16/0.46 inference(combinator_demodulation,[],[f59])). 0.16/0.46 tff(f61,plain,( 0.16/0.46 ( ! [X2:'$i' -> '$o',X1] : ((bCOMB @ vPI('$i') @ (sCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (bCOMB @ (bCOMB @ (in @ X1)) @ (cCOMB @ dsetconstr)))) @ (cCOMB @ iCOMB @ X1)) @ X2 = $true)) )), 0.16/0.46 inference(pi_clausification,[],[f60])). 0.16/0.46 tff(f62,plain,( 0.16/0.46 ( ! [X2:'$i' -> '$o',X1] : ((vPI('$i') @ (cCOMB @ (bCOMB @ vIMP @ (bCOMB @ (in @ X1) @ (cCOMB @ dsetconstr @ X2))) @ (X2 @ X1)) = $true)) )), 0.16/0.46 inference(combinator_demodulation,[],[f61])). 0.16/0.46 tff(f63,plain,( 0.16/0.46 ( ! [X2:'$i' -> '$o',X3,X1] : ((cCOMB @ (bCOMB @ vIMP @ (bCOMB @ (in @ X1) @ (cCOMB @ dsetconstr @ X2))) @ (X2 @ X1) @ X3 = $true)) )), 0.16/0.46 inference(pi_clausification,[],[f62])). 0.16/0.46 tff(f64,plain,( 0.16/0.46 ( ! [X2:'$i' -> '$o',X3,X1] : ((vIMP @ (in @ X1 @ (dsetconstr @ X3 @ X2)) @ (X2 @ X1) = $true)) )), 0.16/0.46 inference(combinator_demodulation,[],[f63])). 0.16/0.46 % (27754)dis+1011_10_add=large:csup=on:inj=on:chr=on:foolp=on:cnfonf=eager:afr=on:afp=4000:afq=1.0:amm=off:anc=none:lma=on:nm=64:nwc=4:sac=on:sp=occurrence_75 on theBenchmark 0.16/0.47 % (27755)dis+1010_3:2_av=off:csup=on:prag=on:chr=on:foolp=on:bet=on:cnfonf=lazy_not_be_gen:gsp=input_only:nm=2:nwc=1:sp=reverse_arity:urr=ec_only_29 on theBenchmark 0.16/0.47 tff(f65,plain,( 0.16/0.47 ( ! [X2:'$i' -> '$o',X3,X1] : ((in @ X1 @ (dsetconstr @ X3 @ X2) = $false) | (X2 @ X1 = $true)) )), 0.16/0.47 inference(binary_proxy_clausification,[],[f64])). 0.16/0.47 tff(f66,plain,( 0.16/0.47 (in @ (kpair @ sK3 @ sK4) @ (dsetconstr @ (cartprod @ sK0 @ sK1) @ (bCOMB @ vSIGMA('$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)))))))) = $true)), 0.16/0.47 inference(combinator_demodulation,[],[f33])). 0.16/0.47 tff(f69,plain,( 0.16/0.47 ($true != $true) | (sK2 @ sK3 @ sK4 = $false)), 0.16/0.47 inference(fool_paramodulation,[],[f28])). 0.16/0.47 tff(f70,plain,( 0.16/0.47 (sK2 @ sK3 @ sK4 = $false)), 0.16/0.47 inference(trivial_inequality_removal,[],[f69])). 0.16/0.47 tff(f76,plain,( 0.16/0.47 ($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) = $true)), 0.16/0.47 inference(superposition,[],[f65,f66])). 0.16/0.47 tff(f77,plain,( 0.16/0.47 (bCOMB @ vSIGMA('$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) = $true)), 0.16/0.47 inference(trivial_inequality_removal,[],[f76])). 0.16/0.47 tff(f78,plain,( 0.16/0.47 (vSIGMA('$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))))) = $true)), 0.16/0.47 inference(combinator_demodulation,[],[f77])). 0.16/0.47 tff(f79,plain,( 0.16/0.47 (sCOMB @ (bCOMB @ vAND @ (cCOMB @ in @ sK0)) @ (bCOMB @ vSIGMA('$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)))) @ sK6 = $true)), 0.16/0.47 inference(sigma_clausification,[],[f78])). 0.16/0.47 tff(f80,plain,( 0.16/0.47 (vAND @ (in @ sK6 @ sK0) @ (vSIGMA('$i') @ (sCOMB @ (bCOMB @ vAND @ (sCOMB @ (bCOMB @ vAND @ (cCOMB @ in @ sK1)) @ (sK2 @ sK6))) @ (cCOMB @ (bCOMB @ vEQ('$i') @ (kpair @ sK6)) @ (kpair @ sK3 @ sK4)))) = $true)), 0.16/0.47 inference(combinator_demodulation,[],[f79])). 0.16/0.47 tff(f82,plain,( 0.16/0.47 (vSIGMA('$i') @ (sCOMB @ (bCOMB @ vAND @ (sCOMB @ (bCOMB @ vAND @ (cCOMB @ in @ sK1)) @ (sK2 @ sK6))) @ (cCOMB @ (bCOMB @ vEQ('$i') @ (kpair @ sK6)) @ (kpair @ sK3 @ sK4))) = $true)), 0.16/0.47 inference(binary_proxy_clausification,[],[f80])). 0.16/0.47 tff(f83,plain,( 0.16/0.47 (sCOMB @ (bCOMB @ vAND @ (sCOMB @ (bCOMB @ vAND @ (cCOMB @ in @ sK1)) @ (sK2 @ sK6))) @ (cCOMB @ (bCOMB @ vEQ('$i') @ (kpair @ sK6)) @ (kpair @ sK3 @ sK4)) @ sK7 = $true)), 0.16/0.47 inference(sigma_clausification,[],[f82])). 0.16/0.47 tff(f84,plain,( 0.16/0.47 (vAND @ (vAND @ (in @ sK7 @ sK1) @ (sK2 @ sK6 @ sK7)) @ (vEQ('$i') @ (kpair @ sK6 @ sK7) @ (kpair @ sK3 @ sK4)) = $true)), 0.16/0.47 inference(combinator_demodulation,[],[f83])). 0.16/0.47 tff(f85,plain,( 0.16/0.47 (vAND @ (in @ sK7 @ sK1) @ (sK2 @ sK6 @ sK7) = $true)), 0.16/0.47 inference(binary_proxy_clausification,[],[f84])). 0.16/0.47 tff(f86,plain,( 0.16/0.47 (vEQ('$i') @ (kpair @ sK6 @ sK7) @ (kpair @ sK3 @ sK4) = $true)), 0.16/0.47 inference(binary_proxy_clausification,[],[f84])). 0.16/0.47 tff(f87,plain,( 0.16/0.47 kpair @ sK3 @ sK4 = kpair @ sK6 @ sK7), 0.16/0.47 inference(equality_proxy_clausification,[],[f86])). 0.16/0.47 tff(f89,plain,( 0.16/0.47 (sK2 @ sK6 @ sK7 = $true)), 0.16/0.47 inference(binary_proxy_clausification,[],[f85])). 0.16/0.47 tff(f108,plain,( 0.16/0.47 sK3 = sK6), 0.16/0.47 inference(unit_resulting_resolution,[],[f87,f58])). 0.16/0.47 tff(f109,plain,( 0.16/0.47 sK4 = sK7), 0.16/0.47 inference(unit_resulting_resolution,[],[f87,f47])). 0.16/0.47 tff(f139,plain,( 0.16/0.47 (sK2 @ sK6 @ sK4 = $true)), 0.16/0.47 inference(superposition,[],[f89,f109])). 0.16/0.47 tff(f141,plain,( 0.16/0.47 (sK2 @ sK3 @ sK4 = $true)), 0.16/0.47 inference(forward_demodulation,[],[f139,f108])). 0.16/0.47 tff(f142,plain,( 0.16/0.47 ($false = $true)), 0.16/0.47 inference(forward_demodulation,[],[f141,f70])). 0.16/0.47 tff(f143,plain,( 0.16/0.47 $false), 0.16/0.47 inference(trivial_inequality_removal,[],[f142])). 0.16/0.47 % SZS output end Proof for theBenchmark 0.16/0.47 % (27728)------------------------------ 0.16/0.47 % (27728)Version: Vampire 4.5.0 (commit 7ae30c7f on 2020-06-30 15:57:20 +0100) 0.16/0.47 % (27728)Termination reason: Refutation 0.16/0.47 0.16/0.47 % (27728)Memory used [KB]: 9978 0.16/0.47 % (27728)Time elapsed: 0.102 s 0.16/0.47 % (27728)------------------------------ 0.16/0.47 % (27728)------------------------------ 0.16/0.48 % (27733)Refutation not found, incomplete strategy 0.16/0.48 % (27733)------------------------------ 0.16/0.48 % (27733)Version: Vampire 4.5.0 (commit 7ae30c7f on 2020-06-30 15:57:20 +0100) 0.16/0.48 % (27733)Termination reason: Refutation not found, incomplete strategy 0.16/0.48 0.16/0.48 % (27733)Memory used [KB]: 11769 0.16/0.48 % (27733)Time elapsed: 0.115 s 0.16/0.48 % (27733)------------------------------ 0.16/0.48 % (27733)------------------------------ 0.16/0.48 % (27722)Success in time 0.142 s 0.26/0.48 EOF