0.06/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.06/0.12 % Command : run_vampire %s %d 0.11/0.33 % Computer : n024.cluster.edu 0.11/0.33 % Model : x86_64 x86_64 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.11/0.33 % Memory : 8042.1875MB 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64 0.11/0.33 % CPULimit : 960 0.11/0.33 % WCLimit : 120 0.11/0.33 % DateTime : Thu Jul 2 07:01:56 EDT 2020 0.11/0.33 % CPUTime : 0.11/0.36 % (29141)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 0.11/0.36 % (29140)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 % (29146)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 0.11/0.37 % (29155)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 0.11/0.38 % (29147)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 0.11/0.38 % (29135)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 0.11/0.38 % (29134)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 0.11/0.38 % (29136)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 0.11/0.38 % (29133)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 0.11/0.38 % (29131)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 0.11/0.38 % (29144)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 0.11/0.38 % (29132)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 0.11/0.38 % (29142)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 0.11/0.38 % (29143)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 0.11/0.38 % (29145)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 0.11/0.38 % (29137)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 0.17/0.39 % (29139)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 0.17/0.39 % (29160)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 0.17/0.39 % (29158)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 0.17/0.39 % (29159)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 0.17/0.39 % (29156)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 0.17/0.39 % (29157)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 0.17/0.39 % (29161)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 0.17/0.39 % (29154)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 0.17/0.40 % (29146)Refutation not found, incomplete strategy 0.17/0.40 % (29146)------------------------------ 0.17/0.40 % (29146)Version: Vampire 4.5.0 (commit 7ae30c7f on 2020-06-30 15:57:20 +0100) 0.17/0.40 % (29152)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 0.17/0.40 % (29151)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 0.17/0.40 % (29150)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 0.17/0.40 % (29148)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 0.17/0.40 % (29149)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 0.17/0.40 % (29153)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 0.17/0.42 % (29146)Termination reason: Refutation not found, incomplete strategy 0.17/0.42 0.17/0.42 % (29146)Memory used [KB]: 5373 0.17/0.42 % (29146)Time elapsed: 0.050 s 0.17/0.42 % (29146)------------------------------ 0.17/0.42 % (29146)------------------------------ 0.17/0.44 % (29155)Refutation found. Thanks to Tanya! 0.17/0.44 % SZS status Theorem for theBenchmark 0.17/0.44 % SZS output start Proof for theBenchmark 0.17/0.44 tff(func_def_3, type, ->: ('$tType' * '$tType') > '$tType'). 0.17/0.44 tff(func_def_4, type, in: '$i' -> '$i' -> '$o'). 0.17/0.44 tff(func_def_5, type, dsetconstr: '$i' -> ('$i' -> '$o') -> '$i'). 0.17/0.44 tff(func_def_7, type, vAPP: !>[X0: $ttype, X1: $ttype]:(X0 -> X1 * X0) > X1). 0.17/0.44 tff(func_def_9, type, kpair: '$i' -> '$i' -> '$i'). 0.17/0.44 tff(func_def_10, type, cartprod: '$i' -> '$i' -> '$i'). 0.17/0.44 tff(func_def_12, type, dpsetconstr: '$i' -> '$i' -> ('$i' -> '$i' -> '$o') -> '$i'). 0.17/0.44 tff(func_def_13, type, vEPSILON: !>[X0: $ttype]:(X0 -> '$o') -> X0). 0.17/0.44 tff(func_def_16, type, vIMP: '$o' -> '$o' -> '$o'). 0.17/0.44 tff(func_def_17, type, vPI: !>[X0: $ttype]:(X0 -> '$o') -> '$o'). 0.17/0.44 tff(func_def_18, type, cCOMB: !>[X0: $ttype, X1: $ttype, X2: $ttype]:(X0 -> X1 -> X2) -> X1 -> X0 -> X2). 0.17/0.44 tff(func_def_19, type, bCOMB: !>[X0: $ttype, X1: $ttype, X2: $ttype]:(X1 -> X2) -> (X0 -> X1) -> X0 -> X2). 0.17/0.44 tff(func_def_20, type, sCOMB: !>[X0: $ttype, X1: $ttype, X2: $ttype]:(X0 -> X1 -> X2) -> (X0 -> X1) -> X0 -> X2). 0.17/0.44 tff(func_def_21, type, vEQ: !>[X0: $ttype]:X0 -> X0 -> '$o'). 0.17/0.44 tff(func_def_22, type, iCOMB: !>[X2: $ttype]:X2 -> X2). 0.17/0.44 tff(func_def_23, type, vAND: '$o' -> '$o' -> '$o'). 0.17/0.44 tff(func_def_24, type, vSIGMA: !>[X0: $ttype]:(X0 -> '$o') -> '$o'). 0.17/0.44 tff(func_def_27, type, sK2: '$i' -> '$i' -> '$o'). 0.17/0.44 tff(func_def_31, type, kCOMB: !>[X1: $ttype, X2: $ttype]:X1 -> X2 -> X1). 0.17/0.44 tff(func_def_32, type, vOR: '$o' -> '$o' -> '$o'). 0.17/0.44 tff(func_def_33, type, vNOT: '$o' -> '$o'). 0.17/0.44 tff(func_def_34, type, sK6: '$i' -> '$i' -> '$i'). 0.17/0.44 tff(func_def_35, type, sK7: '$i' -> '$i' -> '$i'). 0.17/0.44 tff(f1,axiom,( 0.17/0.44 (dsetconstrI = ! [X0,X1 : '$i' -> '$o',X2] : (in @ X2 @ X0 => (X1 @ X2 => in @ X2 @ (dsetconstr @ X0 @ (^[X3 : '$i'] : X1 @ X3)))))), 0.17/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrI)). 0.17/0.44 tff(f3,axiom,( 0.17/0.44 (cartprodpairin = ! [X0,X4,X2] : (in @ X2 @ X0 => ! [X3] : (in @ X3 @ X4 => in @ (kpair @ X2 @ X3) @ (cartprod @ X0 @ X4))))), 0.17/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodpairin)). 0.17/0.44 tff(f4,axiom,( 0.17/0.44 dpsetconstr = (^[X0 : '$i', X4 : '$i', X1 : '$i' -> '$i' -> '$o'] : dsetconstr @ (cartprod @ X0 @ X4) @ (^[X5 : '$i'] : ? [X2] : (? [X3] : (kpair @ X2 @ X3 = X5 & X1 @ X2 @ X3 & in @ X3 @ X4) & in @ X2 @ X0)))), 0.17/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dpsetconstr)). 0.17/0.44 tff(f5,conjecture,( 0.17/0.44 dsetconstrI => (setext => (cartprodpairin => ! [X0,X4,X1 : '$i' -> '$i' -> '$o',X2] : (in @ X2 @ X0 => ! [X3] : (in @ X3 @ X4 => (X1 @ X2 @ X3 => in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X0 @ X4 @ (^[X6 : '$i', X5 : '$i'] : X1 @ X6 @ X5)))))))), 0.17/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dpsetconstrI)). 0.17/0.44 tff(f6,negated_conjecture,( 0.17/0.44 ~(dsetconstrI => (setext => (cartprodpairin => ! [X0,X4,X1 : '$i' -> '$i' -> '$o',X2] : (in @ X2 @ X0 => ! [X3] : (in @ X3 @ X4 => (X1 @ X2 @ X3 => in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X0 @ X4 @ (^[X6 : '$i', X5 : '$i'] : X1 @ X6 @ X5))))))))), 0.17/0.44 inference(negated_conjecture,[],[f5])). 0.17/0.44 tff(f7,plain,( 0.17/0.44 ~(dsetconstrI => (setext => (cartprodpairin => ! [X0,X1,X2 : '$i' -> '$i' -> '$o',X3] : (in @ X3 @ X0 => ! [X4] : (in @ X4 @ X1 => (X2 @ X3 @ X4 => in @ (kpair @ X3 @ X4) @ (dpsetconstr @ X0 @ X1 @ (^[X5 : '$i', X6 : '$i'] : X2 @ X5 @ X6))))))))), 0.17/0.44 inference(rectify,[],[f6])). 0.17/0.44 tff(f8,plain,( 0.17/0.44 ~((dsetconstrI = $true) => ((setext = $true) => ((cartprodpairin = $true) => ! [X0,X1,X2 : '$i' -> '$i' -> '$o',X3] : ((in @ X3 @ X0 = $true) => ! [X4] : ((in @ X4 @ X1 = $true) => ((X2 @ X3 @ X4 = $true) => (in @ (kpair @ X3 @ X4) @ (dpsetconstr @ X0 @ X1 @ X2) = $true)))))))), 0.17/0.44 inference(fool_elimination,[],[f7])). 0.17/0.44 tff(f11,plain,( 0.17/0.44 (dsetconstrI = ! [X0,X1 : '$i' -> '$o',X2] : (in @ X2 @ X0 => (X1 @ X2 => in @ X2 @ (dsetconstr @ X0 @ (^[X3 : '$i'] : X1 @ X3)))))), 0.17/0.44 inference(rectify,[],[f1])). 0.17/0.44 tff(f12,plain,( 0.17/0.44 (dsetconstrI = vPI('$i') @ (bCOMB @ vPI('$i' -> '$o') @ (bCOMB @ (bCOMB @ vPI('$i')) @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ in))) @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ bCOMB) @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ iCOMB)))) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ in)) @ (cCOMB @ dsetconstr)))))))), 0.17/0.44 inference(fool_elimination,[],[f11])). 0.17/0.44 tff(f13,plain,( 0.17/0.44 (cartprodpairin = ! [X0,X1,X2] : (in @ X2 @ X0 => ! [X3] : (in @ X3 @ X1 => in @ (kpair @ X2 @ X3) @ (cartprod @ X0 @ X1))))), 0.17/0.44 inference(rectify,[],[f3])). 0.17/0.44 tff(f14,plain,( 0.17/0.44 (vPI('$i') @ (bCOMB @ vPI('$i') @ (bCOMB @ (bCOMB @ vPI('$i')) @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ in))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i'))) @ (bCOMB @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ in))))) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ in) @ kpair)))) @ (cCOMB @ cartprod))))))) = cartprodpairin)), 0.17/0.44 inference(fool_elimination,[],[f13])). 0.17/0.44 tff(f15,plain,( 0.17/0.44 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)))), 0.17/0.44 inference(rectify,[],[f4])). 0.17/0.45 tff(f16,plain,( 0.17/0.45 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('$i')) @ kpair))))))) = dpsetconstr), 0.17/0.45 inference(fool_elimination,[],[f15])). 0.17/0.46 % (29133)Refutation not found, incomplete strategy 0.17/0.46 % (29133)------------------------------ 0.17/0.46 % (29133)Version: Vampire 4.5.0 (commit 7ae30c7f on 2020-06-30 15:57:20 +0100) 0.17/0.46 % (29133)Termination reason: Refutation not found, incomplete strategy 0.17/0.46 0.17/0.46 % (29133)Memory used [KB]: 9850 0.17/0.46 % (29133)Time elapsed: 0.087 s 0.17/0.46 % (29133)------------------------------ 0.17/0.46 % (29133)------------------------------ 0.17/0.46 tff(f17,plain,( 0.17/0.46 ((? [X0,X1,X2 : '$i' -> '$i' -> '$o',X3] : (? [X4] : (((in @ (kpair @ X3 @ X4) @ (dpsetconstr @ X0 @ X1 @ X2) != $true) & (X2 @ X3 @ X4 = $true)) & (in @ X4 @ X1 = $true)) & (in @ X3 @ X0 = $true)) & (cartprodpairin = $true)) & (setext = $true)) & (dsetconstrI = $true)), 0.17/0.46 inference(ennf_transformation,[],[f8])). 0.17/0.46 tff(f18,plain,( 0.17/0.46 ? [X0,X1,X2 : '$i' -> '$i' -> '$o',X3] : (? [X4] : ((in @ (kpair @ X3 @ X4) @ (dpsetconstr @ X0 @ X1 @ X2) != $true) & (X2 @ X3 @ X4 = $true) & (in @ X4 @ X1 = $true)) & (in @ X3 @ X0 = $true)) & (cartprodpairin = $true) & (setext = $true) & (dsetconstrI = $true)), 0.17/0.46 inference(flattening,[],[f17])). 0.17/0.46 tff(f19,plain,( 0.17/0.46 ? [X0,X1,X2 : '$i' -> '$i' -> '$o',X3] : (? [X4] : ((in @ (kpair @ X3 @ X4) @ (dpsetconstr @ X0 @ X1 @ X2) != $true) & (X2 @ X3 @ X4 = $true) & (in @ X4 @ X1 = $true)) & (in @ X3 @ X0 = $true)) => (? [X4] : ((in @ (kpair @ sK3 @ X4) @ (dpsetconstr @ sK0 @ sK1 @ sK2) != $true) & (sK2 @ sK3 @ X4 = $true) & (in @ X4 @ sK1 = $true)) & (in @ sK3 @ sK0 = $true))), 0.17/0.46 introduced(choice_axiom,[])). 0.17/0.46 tff(f20,plain,( 0.17/0.46 ? [X4] : ((in @ (kpair @ sK3 @ X4) @ (dpsetconstr @ sK0 @ sK1 @ sK2) != $true) & (sK2 @ sK3 @ X4 = $true) & (in @ X4 @ sK1 = $true)) => ((in @ (kpair @ sK3 @ sK4) @ (dpsetconstr @ sK0 @ sK1 @ sK2) != $true) & (sK2 @ sK3 @ sK4 = $true) & (in @ sK4 @ sK1 = $true))), 0.17/0.46 introduced(choice_axiom,[])). 0.17/0.46 tff(f21,plain,( 0.17/0.46 (((in @ (kpair @ sK3 @ sK4) @ (dpsetconstr @ sK0 @ sK1 @ sK2) != $true) & (sK2 @ sK3 @ sK4 = $true) & (in @ sK4 @ sK1 = $true)) & (in @ sK3 @ sK0 = $true)) & (cartprodpairin = $true) & (setext = $true) & (dsetconstrI = $true)), 0.17/0.46 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f18,f20,f19])). 0.17/0.46 tff(f22,plain,( 0.17/0.46 (dsetconstrI = $true)), 0.17/0.46 inference(cnf_transformation,[],[f21])). 0.17/0.46 tff(f24,plain,( 0.17/0.46 (cartprodpairin = $true)), 0.17/0.46 inference(cnf_transformation,[],[f21])). 0.17/0.46 tff(f25,plain,( 0.17/0.46 (in @ sK3 @ sK0 = $true)), 0.17/0.46 inference(cnf_transformation,[],[f21])). 0.17/0.46 tff(f26,plain,( 0.17/0.46 (in @ sK4 @ sK1 = $true)), 0.17/0.46 inference(cnf_transformation,[],[f21])). 0.17/0.46 tff(f27,plain,( 0.17/0.46 (sK2 @ sK3 @ sK4 = $true)), 0.17/0.46 inference(cnf_transformation,[],[f21])). 0.17/0.46 tff(f28,plain,( 0.17/0.46 (in @ (kpair @ sK3 @ sK4) @ (dpsetconstr @ sK0 @ sK1 @ sK2) != $true)), 0.17/0.46 inference(cnf_transformation,[],[f21])). 0.17/0.46 tff(f29,plain,( 0.17/0.46 sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ bCOMB) @ (bCOMB @ (bCOMB @ dsetconstr) @ cartprod))) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vSIGMA('$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), 0.17/0.46 inference(cnf_transformation,[],[f16])). 0.17/0.46 tff(f30,plain,( 0.17/0.46 (vPI('$i') @ (bCOMB @ vPI('$i') @ (bCOMB @ (bCOMB @ vPI('$i')) @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ in))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i'))) @ (bCOMB @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ in))))) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ in) @ kpair)))) @ (cCOMB @ cartprod))))))) = cartprodpairin)), 0.17/0.46 inference(cnf_transformation,[],[f14])). 0.17/0.46 tff(f31,plain,( 0.17/0.46 (dsetconstrI = vPI('$i') @ (bCOMB @ vPI('$i' -> '$o') @ (bCOMB @ (bCOMB @ vPI('$i')) @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ in))) @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ bCOMB) @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ iCOMB)))) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ in)) @ (cCOMB @ dsetconstr)))))))), 0.17/0.46 inference(cnf_transformation,[],[f12])). 0.17/0.46 tff(f33,plain,( 0.17/0.46 (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) != $true)), 0.17/0.46 inference(definition_unfolding,[],[f28,f29])). 0.17/0.46 % (29142)Refutation not found, incomplete strategy 0.17/0.46 % (29142)------------------------------ 0.17/0.46 % (29142)Version: Vampire 4.5.0 (commit 7ae30c7f on 2020-06-30 15:57:20 +0100) 0.17/0.46 % (29162)dis+1011_10_add=large:csup=on:inj=on:chr=on:foolp=on:cnfonf=eager:afr=on:afp=4000:afq=1.0:amm=off:anc=none:lma=on:nm=64:nwc=4:sac=on:sp=occurrence_75 on theBenchmark 0.17/0.47 tff(f34,plain,( 0.17/0.47 (vPI('$i') @ (bCOMB @ vPI('$i') @ (bCOMB @ (bCOMB @ vPI('$i')) @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ in))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i'))) @ (bCOMB @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ in))))) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ in) @ kpair)))) @ (cCOMB @ cartprod))))))) = $true)), 0.17/0.47 inference(definition_unfolding,[],[f30,f24])). 0.17/0.47 tff(f35,plain,( 0.17/0.47 (vPI('$i') @ (bCOMB @ vPI('$i' -> '$o') @ (bCOMB @ (bCOMB @ vPI('$i')) @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ in))) @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ bCOMB) @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ iCOMB)))) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ in)) @ (cCOMB @ dsetconstr)))))) = $true)), 0.17/0.47 inference(definition_unfolding,[],[f31,f22])). 0.17/0.47 tff(f53,plain,( 0.17/0.47 ( ! [X1] : ((bCOMB @ vPI('$i' -> '$o') @ (bCOMB @ (bCOMB @ vPI('$i')) @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ in))) @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ bCOMB) @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ iCOMB)))) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ in)) @ (cCOMB @ dsetconstr))))) @ X1 = $true)) )), 0.17/0.47 inference(pi_clausification,[],[f35])). 0.17/0.47 tff(f54,plain,( 0.17/0.47 ( ! [X1] : ((vPI('$i' -> '$o') @ (bCOMB @ vPI('$i') @ (bCOMB @ (sCOMB @ (bCOMB @ vIMP @ (in @ X1))) @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ vIMP @ (cCOMB @ iCOMB @ X1))) @ (bCOMB @ (bCOMB @ (in @ X1)) @ (cCOMB @ dsetconstr))))) = $true)) )), 0.17/0.47 inference(combinator_demodulation,[],[f53])). 0.17/0.47 tff(f55,plain,( 0.17/0.47 ( ! [X2:'$i' -> '$o',X1] : ((bCOMB @ vPI('$i') @ (bCOMB @ (sCOMB @ (bCOMB @ vIMP @ (in @ X1))) @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ vIMP @ (cCOMB @ iCOMB @ X1))) @ (bCOMB @ (bCOMB @ (in @ X1)) @ (cCOMB @ dsetconstr)))) @ X2 = $true)) )), 0.17/0.47 inference(pi_clausification,[],[f54])). 0.17/0.47 tff(f56,plain,( 0.17/0.47 ( ! [X2:'$i' -> '$o',X1] : ((vPI('$i') @ (sCOMB @ (bCOMB @ vIMP @ (in @ X1)) @ (bCOMB @ (vIMP @ (X2 @ X1)) @ (bCOMB @ (in @ X1) @ (cCOMB @ dsetconstr @ X2)))) = $true)) )), 0.17/0.47 inference(combinator_demodulation,[],[f55])). 0.17/0.47 tff(f57,plain,( 0.17/0.47 ( ! [X2:'$i' -> '$o',X3,X1] : ((sCOMB @ (bCOMB @ vIMP @ (in @ X1)) @ (bCOMB @ (vIMP @ (X2 @ X1)) @ (bCOMB @ (in @ X1) @ (cCOMB @ dsetconstr @ X2))) @ X3 = $true)) )), 0.17/0.47 inference(pi_clausification,[],[f56])). 0.17/0.47 tff(f58,plain,( 0.17/0.47 ( ! [X2:'$i' -> '$o',X3,X1] : ((vIMP @ (in @ X1 @ X3) @ (vIMP @ (X2 @ X1) @ (in @ X1 @ (dsetconstr @ X3 @ X2))) = $true)) )), 0.17/0.47 inference(combinator_demodulation,[],[f57])). 0.17/0.47 tff(f59,plain,( 0.17/0.47 ( ! [X2:'$i' -> '$o',X3,X1] : ((in @ X1 @ X3 = $false) | (vIMP @ (X2 @ X1) @ (in @ X1 @ (dsetconstr @ X3 @ X2)) = $true)) )), 0.17/0.47 inference(binary_proxy_clausification,[],[f58])). 0.17/0.47 tff(f60,plain,( 0.17/0.47 ( ! [X2:'$i' -> '$o',X3,X1] : ((in @ X1 @ (dsetconstr @ X3 @ X2) = $true) | (X2 @ X1 = $false) | (in @ X1 @ X3 = $false)) )), 0.17/0.47 inference(binary_proxy_clausification,[],[f59])). 0.17/0.47 tff(f61,plain,( 0.17/0.47 ( ! [X1] : ((bCOMB @ vPI('$i') @ (bCOMB @ (bCOMB @ vPI('$i')) @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ in))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i'))) @ (bCOMB @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ in))))) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ in) @ kpair)))) @ (cCOMB @ cartprod)))))) @ X1 = $true)) )), 0.17/0.47 inference(pi_clausification,[],[f34])). 0.17/0.47 tff(f62,plain,( 0.17/0.47 ( ! [X1] : ((vPI('$i') @ (bCOMB @ vPI('$i') @ (bCOMB @ (sCOMB @ (bCOMB @ vIMP @ (in @ X1))) @ (bCOMB @ (bCOMB @ vPI('$i')) @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ in)))) @ (bCOMB @ (bCOMB @ (cCOMB @ (bCOMB @ in @ (kpair @ X1)))) @ (cCOMB @ cartprod)))))) = $true)) )), 0.17/0.47 inference(combinator_demodulation,[],[f61])). 0.17/0.47 tff(f63,plain,( 0.17/0.47 ( ! [X2,X1] : ((bCOMB @ vPI('$i') @ (bCOMB @ (sCOMB @ (bCOMB @ vIMP @ (in @ X1))) @ (bCOMB @ (bCOMB @ vPI('$i')) @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ in)))) @ (bCOMB @ (bCOMB @ (cCOMB @ (bCOMB @ in @ (kpair @ X1)))) @ (cCOMB @ cartprod))))) @ X2 = $true)) )), 0.17/0.47 inference(pi_clausification,[],[f62])). 0.17/0.47 tff(f64,plain,( 0.17/0.47 ( ! [X2,X1] : ((vPI('$i') @ (sCOMB @ (bCOMB @ vIMP @ (in @ X1)) @ (bCOMB @ vPI('$i') @ (bCOMB @ (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ in @ X2))) @ (bCOMB @ (cCOMB @ (bCOMB @ in @ (kpair @ X1))) @ (cCOMB @ cartprod @ X2))))) = $true)) )), 0.17/0.47 inference(combinator_demodulation,[],[f63])). 0.17/0.47 tff(f65,plain,( 0.17/0.47 ( ! [X2,X3,X1] : ((sCOMB @ (bCOMB @ vIMP @ (in @ X1)) @ (bCOMB @ vPI('$i') @ (bCOMB @ (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ in @ X2))) @ (bCOMB @ (cCOMB @ (bCOMB @ in @ (kpair @ X1))) @ (cCOMB @ cartprod @ X2)))) @ X3 = $true)) )), 0.17/0.47 inference(pi_clausification,[],[f64])). 0.17/0.47 tff(f66,plain,( 0.17/0.47 ( ! [X2,X3,X1] : ((vIMP @ (in @ X1 @ X3) @ (vPI('$i') @ (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ in @ X2)) @ (cCOMB @ (bCOMB @ in @ (kpair @ X1)) @ (cartprod @ X3 @ X2)))) = $true)) )), 0.17/0.47 inference(combinator_demodulation,[],[f65])). 0.17/0.47 tff(f67,plain,( 0.17/0.47 ( ! [X2,X3,X1] : ((in @ X1 @ X3 = $false) | (vPI('$i') @ (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ in @ X2)) @ (cCOMB @ (bCOMB @ in @ (kpair @ X1)) @ (cartprod @ X3 @ X2))) = $true)) )), 0.17/0.47 inference(binary_proxy_clausification,[],[f66])). 0.17/0.47 tff(f68,plain,( 0.17/0.47 ( ! [X4,X2,X3,X1] : ((in @ X1 @ X3 = $false) | (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ in @ X2)) @ (cCOMB @ (bCOMB @ in @ (kpair @ X1)) @ (cartprod @ X3 @ X2)) @ X4 = $true)) )), 0.17/0.47 inference(pi_clausification,[],[f67])). 0.17/0.47 tff(f69,plain,( 0.17/0.47 ( ! [X4,X2,X3,X1] : ((in @ X1 @ X3 = $false) | (vIMP @ (in @ X4 @ X2) @ (in @ (kpair @ X1 @ X4) @ (cartprod @ X3 @ X2)) = $true)) )), 0.17/0.47 inference(combinator_demodulation,[],[f68])). 0.17/0.47 tff(f70,plain,( 0.17/0.47 ( ! [X4,X2,X3,X1] : ((in @ (kpair @ X1 @ X4) @ (cartprod @ X3 @ X2) = $true) | (in @ X4 @ X2 = $false) | (in @ X1 @ X3 = $false)) )), 0.17/0.47 inference(binary_proxy_clausification,[],[f69])). 0.17/0.47 tff(f71,plain,( 0.17/0.47 (in @ (kpair @ sK3 @ sK4) @ (dsetconstr @ (cartprod @ sK0 @ sK1) @ (bCOMB @ vSIGMA('$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)))))))) != $true)), 0.17/0.47 inference(combinator_demodulation,[],[f33])). 0.17/0.47 tff(f85,plain,( 0.17/0.47 ($true != $true) | (bCOMB @ vSIGMA('$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) = $false) | (in @ (kpair @ sK3 @ sK4) @ (cartprod @ sK0 @ sK1) = $false)), 0.17/0.47 inference(superposition,[],[f71,f60])). 0.17/0.47 tff(f86,plain,( 0.17/0.47 (bCOMB @ vSIGMA('$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) = $false) | (in @ (kpair @ sK3 @ sK4) @ (cartprod @ sK0 @ sK1) = $false)), 0.17/0.47 inference(trivial_inequality_removal,[],[f85])). 0.17/0.47 tff(f87,plain,( 0.17/0.47 (vSIGMA('$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))))) = $false) | (in @ (kpair @ sK3 @ sK4) @ (cartprod @ sK0 @ sK1) = $false)), 0.17/0.47 inference(combinator_demodulation,[],[f86])). 0.17/0.47 tff(f88,plain,( 0.17/0.47 ( ! [X1] : ((sCOMB @ (bCOMB @ vAND @ (cCOMB @ in @ sK0)) @ (bCOMB @ vSIGMA('$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)))) @ X1 = $false) | (in @ (kpair @ sK3 @ sK4) @ (cartprod @ sK0 @ sK1) = $false)) )), 0.17/0.47 inference(pi_clausification,[],[f87])). 0.17/0.47 tff(f89,plain,( 0.17/0.47 ( ! [X1] : ((vAND @ (in @ X1 @ sK0) @ (vSIGMA('$i') @ (sCOMB @ (bCOMB @ vAND @ (sCOMB @ (bCOMB @ vAND @ (cCOMB @ in @ sK1)) @ (sK2 @ X1))) @ (cCOMB @ (bCOMB @ vEQ('$i') @ (kpair @ X1)) @ (kpair @ sK3 @ sK4)))) = $false) | (in @ (kpair @ sK3 @ sK4) @ (cartprod @ sK0 @ sK1) = $false)) )), 0.17/0.47 inference(combinator_demodulation,[],[f88])). 0.17/0.47 tff(f90,plain,( 0.17/0.47 ( ! [X1] : ((in @ X1 @ sK0 = $false) | (in @ (kpair @ sK3 @ sK4) @ (cartprod @ sK0 @ sK1) = $false) | (vSIGMA('$i') @ (sCOMB @ (bCOMB @ vAND @ (sCOMB @ (bCOMB @ vAND @ (cCOMB @ in @ sK1)) @ (sK2 @ X1))) @ (cCOMB @ (bCOMB @ vEQ('$i') @ (kpair @ X1)) @ (kpair @ sK3 @ sK4))) = $false)) )), 0.17/0.47 inference(binary_proxy_clausification,[],[f89])). 0.17/0.47 % (29142)Termination reason: Refutation not found, incomplete strategy 0.17/0.47 0.17/0.47 % (29142)Memory used [KB]: 11641 0.17/0.47 % (29142)Time elapsed: 0.096 s 0.17/0.47 % (29142)------------------------------ 0.17/0.47 % (29142)------------------------------ 0.17/0.47 tff(f91,plain,( 0.17/0.47 ( ! [X2,X1] : ((in @ X1 @ sK0 = $false) | (in @ (kpair @ sK3 @ sK4) @ (cartprod @ sK0 @ sK1) = $false) | (sCOMB @ (bCOMB @ vAND @ (sCOMB @ (bCOMB @ vAND @ (cCOMB @ in @ sK1)) @ (sK2 @ X1))) @ (cCOMB @ (bCOMB @ vEQ('$i') @ (kpair @ X1)) @ (kpair @ sK3 @ sK4)) @ X2 = $false)) )), 0.17/0.47 inference(pi_clausification,[],[f90])). 0.17/0.47 tff(f92,plain,( 0.17/0.47 ( ! [X2,X1] : ((in @ X1 @ sK0 = $false) | (in @ (kpair @ sK3 @ sK4) @ (cartprod @ sK0 @ sK1) = $false) | (vAND @ (vAND @ (in @ X2 @ sK1) @ (sK2 @ X1 @ X2)) @ (vEQ('$i') @ (kpair @ X1 @ X2) @ (kpair @ sK3 @ sK4)) = $false)) )), 0.17/0.47 inference(combinator_demodulation,[],[f91])). 0.17/0.47 tff(f93,plain,( 0.17/0.47 ( ! [X2,X1] : ((in @ X1 @ sK0 = $false) | (in @ (kpair @ sK3 @ sK4) @ (cartprod @ sK0 @ sK1) = $false) | (vAND @ (in @ X2 @ sK1) @ (sK2 @ X1 @ X2) = $false) | (vEQ('$i') @ (kpair @ X1 @ X2) @ (kpair @ sK3 @ sK4) = $false)) )), 0.17/0.47 inference(binary_proxy_clausification,[],[f92])). 0.17/0.47 tff(f94,plain,( 0.17/0.47 ( ! [X2,X1] : ((in @ X1 @ sK0 = $false) | (in @ (kpair @ sK3 @ sK4) @ (cartprod @ sK0 @ sK1) = $false) | (vAND @ (in @ X2 @ sK1) @ (sK2 @ X1 @ X2) = $false) | kpair @ sK3 @ sK4 != kpair @ X1 @ X2) )), 0.17/0.47 inference(equality_proxy_clausification,[],[f93])). 0.17/0.47 tff(f95,plain,( 0.17/0.47 ( ! [X2,X1] : ((in @ X1 @ sK0 = $false) | (in @ (kpair @ sK3 @ sK4) @ (cartprod @ sK0 @ sK1) = $false) | (in @ X2 @ sK1 = $false) | kpair @ sK3 @ sK4 != kpair @ X1 @ X2 | (sK2 @ X1 @ X2 = $false)) )), 0.17/0.47 inference(binary_proxy_clausification,[],[f94])). 0.17/0.47 tff(f102,plain,( 0.17/0.47 spl5_0 <=> (in @ (kpair @ sK3 @ sK4) @ (cartprod @ sK0 @ sK1) = $false)), 0.17/0.47 introduced(avatar_definition,[new_symbols(naming,[spl5_0])])). 0.17/0.47 tff(f103,plain,( 0.17/0.47 (in @ (kpair @ sK3 @ sK4) @ (cartprod @ sK0 @ sK1) = $false) | ~spl5_0), 0.17/0.47 inference(avatar_component_clause,[],[f102])). 0.17/0.47 tff(f105,plain,( 0.17/0.47 spl5_2 <=> ! [X1,X2] : ((in @ X1 @ sK0 = $false) | (sK2 @ X1 @ X2 = $false) | kpair @ sK3 @ sK4 != kpair @ X1 @ X2 | (in @ X2 @ sK1 = $false))), 0.17/0.47 introduced(avatar_definition,[new_symbols(naming,[spl5_2])])). 0.17/0.47 tff(f106,plain,( 0.17/0.47 ( ! [X2,X1] : (kpair @ sK3 @ sK4 != kpair @ X1 @ X2 | (sK2 @ X1 @ X2 = $false) | (in @ X1 @ sK0 = $false) | (in @ X2 @ sK1 = $false)) ) | ~spl5_2), 0.17/0.47 inference(avatar_component_clause,[],[f105])). 0.17/0.47 tff(f107,plain,( 0.17/0.47 spl5_0 | spl5_2), 0.17/0.47 inference(avatar_split_clause,[],[f95,f105,f102])). 0.17/0.47 tff(f108,plain,( 0.17/0.47 (sK2 @ sK3 @ sK4 = $false) | (in @ sK3 @ sK0 = $false) | (in @ sK4 @ sK1 = $false) | ~spl5_2), 0.17/0.47 inference(equality_resolution,[],[f106])). 0.17/0.47 tff(f109,plain,( 0.17/0.47 ($false = $true) | (sK2 @ sK3 @ sK4 = $false) | (in @ sK4 @ sK1 = $false) | ~spl5_2), 0.17/0.47 inference(forward_demodulation,[],[f108,f25])). 0.17/0.47 tff(f110,plain,( 0.17/0.47 (sK2 @ sK3 @ sK4 = $false) | (in @ sK4 @ sK1 = $false) | ~spl5_2), 0.17/0.47 inference(trivial_inequality_removal,[],[f109])). 0.17/0.47 tff(f111,plain,( 0.17/0.47 ($false = $true) | (sK2 @ sK3 @ sK4 = $false) | ~spl5_2), 0.17/0.47 inference(forward_demodulation,[],[f110,f26])). 0.17/0.47 tff(f112,plain,( 0.17/0.47 (sK2 @ sK3 @ sK4 = $false) | ~spl5_2), 0.17/0.47 inference(trivial_inequality_removal,[],[f111])). 0.17/0.47 tff(f113,plain,( 0.17/0.47 ($false = $true) | ~spl5_2), 0.17/0.47 inference(backward_demodulation,[],[f112,f27])). 0.17/0.47 tff(f114,plain,( 0.17/0.47 $false | ~spl5_2), 0.17/0.47 inference(trivial_inequality_removal,[],[f113])). 0.17/0.47 tff(f115,plain,( 0.17/0.47 ~spl5_2), 0.17/0.47 inference(avatar_contradiction_clause,[],[f114])). 0.17/0.47 tff(f117,plain,( 0.17/0.47 ($false = $true) | (in @ sK4 @ sK1 = $false) | (in @ sK3 @ sK0 = $false) | ~spl5_0), 0.17/0.47 inference(superposition,[],[f103,f70])). 0.17/0.47 tff(f120,plain,( 0.17/0.47 (in @ sK4 @ sK1 = $false) | (in @ sK3 @ sK0 = $false) | ~spl5_0), 0.17/0.47 inference(trivial_inequality_removal,[],[f117])). 0.17/0.47 tff(f121,plain,( 0.17/0.47 ($false = $true) | (in @ sK4 @ sK1 = $false) | ~spl5_0), 0.17/0.47 inference(forward_demodulation,[],[f120,f25])). 0.17/0.47 tff(f122,plain,( 0.17/0.47 (in @ sK4 @ sK1 = $false) | ~spl5_0), 0.17/0.47 inference(trivial_inequality_removal,[],[f121])). 0.17/0.47 tff(f123,plain,( 0.17/0.47 ($false = $true) | ~spl5_0), 0.17/0.47 inference(backward_demodulation,[],[f122,f26])). 0.17/0.47 tff(f124,plain,( 0.17/0.47 $false | ~spl5_0), 0.17/0.47 inference(trivial_inequality_removal,[],[f123])). 0.17/0.47 tff(f125,plain,( 0.17/0.47 ~spl5_0), 0.17/0.47 inference(avatar_contradiction_clause,[],[f124])). 0.17/0.47 tff(f126,plain,( 0.17/0.47 $false), 0.17/0.47 inference(avatar_sat_refutation,[],[f107,f115,f125])). 0.17/0.47 % SZS output end Proof for theBenchmark 0.17/0.47 % (29155)------------------------------ 0.17/0.47 % (29155)Version: Vampire 4.5.0 (commit 7ae30c7f on 2020-06-30 15:57:20 +0100) 0.17/0.47 % (29155)Termination reason: Refutation 0.17/0.47 0.17/0.47 % (29155)Memory used [KB]: 10234 0.17/0.47 % (29155)Time elapsed: 0.094 s 0.17/0.47 % (29155)------------------------------ 0.17/0.47 % (29155)------------------------------ 0.17/0.47 % (29130)Success in time 0.133 s 0.17/0.48 EOF