0.07/0.13	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.07/0.14	% Command    : run_vampire %s %d
0.13/0.35	% Computer   : n004.cluster.edu
0.13/0.35	% Model      : x86_64 x86_64
0.13/0.35	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.35	% Memory     : 8042.1875MB
0.13/0.35	% OS         : Linux 3.10.0-693.el7.x86_64
0.13/0.35	% CPULimit   : 960
0.13/0.35	% WCLimit    : 120
0.13/0.35	% DateTime   : Thu Jul  2 07:05:13 EDT 2020
0.13/0.35	% CPUTime    : 
0.21/0.40	% (17034)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
0.21/0.40	% (17024)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
0.21/0.40	% (17025)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
0.21/0.40	% (17023)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
0.21/0.40	% (17044)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
0.21/0.40	% (17030)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
0.21/0.40	% (17036)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
0.21/0.41	% (17035)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
0.21/0.41	% (17037)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
0.21/0.42	% (17047)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
0.21/0.42	% (17038)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
0.21/0.42	% (17031)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
0.21/0.42	% (17027)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
0.21/0.42	% (17028)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
0.21/0.43	% (17029)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
0.21/0.43	% (17040)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
0.21/0.43	% (17026)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
0.21/0.43	% (17049)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
0.21/0.43	% (17048)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
0.21/0.43	% (17046)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
0.21/0.44	% (17041)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
0.21/0.44	% (17052)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
0.21/0.44	% (17051)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
0.21/0.44	% (17039)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
0.21/0.44	% (17032)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
0.21/0.44	% (17050)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
0.21/0.44	% (17043)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
0.21/0.44	% (17033)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
0.21/0.45	% (17045)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
0.21/0.45	% (17042)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
0.21/0.52	% (17046)Refutation not found, incomplete strategy
0.21/0.52	% (17046)------------------------------
0.21/0.52	% (17046)Version: Vampire 4.5.0 (commit 7ae30c7f on 2020-06-30 15:57:20 +0100)
0.21/0.52	% (17046)Termination reason: Refutation not found, incomplete strategy
0.21/0.52	
0.21/0.52	% (17046)Memory used [KB]: 9978
0.21/0.52	% (17046)Time elapsed: 0.146 s
0.21/0.52	% (17046)------------------------------
0.21/0.52	% (17046)------------------------------
1.34/0.54	% (17034)Refutation found. Thanks to Tanya!
1.34/0.54	% SZS status Theorem for theBenchmark
1.34/0.54	% SZS output start Proof for theBenchmark
1.34/0.54	tff(func_def_3, type, ->: ('$tType' * '$tType') > '$tType').
1.34/0.54	tff(func_def_4, type, in: '$i' -> '$i' -> '$o').
1.34/0.54	tff(func_def_5, type, setunion: '$i' -> '$i').
1.34/0.54	tff(func_def_6, type, dsetconstr: '$i' -> ('$i' -> '$o') -> '$i').
1.34/0.54	tff(func_def_7, type, singleton: '$i' -> '$o').
1.34/0.54	tff(func_def_9, type, vAPP: !>[X0: $ttype, X1: $ttype]:(X0 -> X1 * X0) > X1).
1.34/0.54	tff(func_def_11, type, if: '$i' -> '$o' -> '$i' -> '$i' -> '$i').
1.34/0.54	tff(func_def_13, type, vEPSILON: !>[X0: $ttype]:(X0 -> '$o') -> X0).
1.34/0.54	tff(func_def_16, type, vOR: '$o' -> '$o' -> '$o').
1.34/0.54	tff(func_def_17, type, vAND: '$o' -> '$o' -> '$o').
1.34/0.54	tff(func_def_18, type, vEQ: !>[X0: $ttype]:X0 -> X0 -> '$o').
1.34/0.54	tff(func_def_19, type, vNOT: '$o' -> '$o').
1.34/0.54	tff(func_def_20, type, bCOMB: !>[X0: $ttype, X1: $ttype, X2: $ttype]:(X1 -> X2) -> (X0 -> X1) -> X0 -> X2).
1.34/0.54	tff(func_def_21, type, sCOMB: !>[X0: $ttype, X1: $ttype, X2: $ttype]:(X0 -> X1 -> X2) -> (X0 -> X1) -> X0 -> X2).
1.34/0.54	tff(func_def_22, type, cCOMB: !>[X0: $ttype, X1: $ttype, X2: $ttype]:(X0 -> X1 -> X2) -> X1 -> X0 -> X2).
1.34/0.54	tff(func_def_23, type, vIMP: '$o' -> '$o' -> '$o').
1.34/0.54	tff(func_def_24, type, vPI: !>[X0: $ttype]:(X0 -> '$o') -> '$o').
1.34/0.54	tff(func_def_30, type, kCOMB: !>[X1: $ttype, X2: $ttype]:X1 -> X2 -> X1).
1.34/0.54	tff(func_def_31, type, iCOMB: !>[X2: $ttype]:X2 -> X2).
1.34/0.54	tff(func_def_32, type, sK5: '$i' -> '$i' -> '$o' -> '$i' -> '$i' -> '$o' -> '$i').
1.34/0.54	tff(func_def_33, type, sK6: '$i' -> '$i' -> '$o' -> '$i').
1.34/0.54	tff(func_def_34, type, sK7: '$o' -> '$i' -> '$i').
1.34/0.54	tff(func_def_35, type, sK8: '$i' -> '$i' -> '$o' -> '$i' -> '$i' -> '$o' -> '$i').
1.34/0.55	tff(f1,axiom,(
1.34/0.55	  (iftrueProp1 = ! [X0,X1 : '$o',X2] : (in @ X2 @ X0 => ! [X3] : (in @ X3 @ X0 => (X1 => in @ X2 @ (dsetconstr @ X0 @ (^[X4 : '$i'] : (X3 = X4 & ~X1) | (X2 = X4 & X1)))))))),
1.34/0.55	  file('/export/starexec/sandbox/benchmark/theBenchmark.p',iftrueProp1)).
1.34/0.55	tff(f2,axiom,(
1.34/0.55	  (ifSingleton = ! [X0,X1 : '$o',X2] : (in @ X2 @ X0 => ! [X3] : (in @ X3 @ X0 => singleton @ (dsetconstr @ X0 @ (^[X4 : '$i'] : (X3 = X4 & ~X1) | (X2 = X4 & X1))))))),
1.34/0.55	  file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifSingleton)).
1.34/0.55	tff(f3,axiom,(
1.34/0.55	  if = (^[X0 : '$i', X1 : '$o', X2 : '$i', X3 : '$i'] : setunion @ (dsetconstr @ X0 @ (^[X4 : '$i'] : (X3 = X4 & ~X1) | (X2 = X4 & X1))))),
1.34/0.55	  file('/export/starexec/sandbox/benchmark/theBenchmark.p',if)).
1.34/0.55	tff(f4,axiom,(
1.34/0.55	  (theeq = ! [X5] : (singleton @ X5 => ! [X2] : (in @ X2 @ X5 => setunion @ X5 = X2)))),
1.34/0.55	  file('/export/starexec/sandbox/benchmark/theBenchmark.p',theeq)).
1.34/0.55	tff(f5,conjecture,(
1.34/0.55	  iftrueProp1 => (ifSingleton => (theeq => ! [X0,X1 : '$o',X2] : (in @ X2 @ X0 => ! [X3] : (in @ X3 @ X0 => (X1 => if @ X0 @ X1 @ X2 @ X3 = X2)))))),
1.34/0.55	  file('/export/starexec/sandbox/benchmark/theBenchmark.p',iftrue)).
1.34/0.55	tff(f6,negated_conjecture,(
1.34/0.55	  ~(iftrueProp1 => (ifSingleton => (theeq => ! [X0,X1 : '$o',X2] : (in @ X2 @ X0 => ! [X3] : (in @ X3 @ X0 => (X1 => if @ X0 @ X1 @ X2 @ X3 = X2))))))),
1.34/0.55	  inference(negated_conjecture,[],[f5])).
1.34/0.55	tff(f7,plain,(
1.34/0.55	  ~(iftrueProp1 => (ifSingleton => (theeq => ! [X0,X1 : '$o',X2] : (in @ X2 @ X0 => ! [X3] : (in @ X3 @ X0 => (X1 => if @ X0 @ X1 @ X2 @ X3 = X2))))))),
1.34/0.55	  inference(rectify,[],[f6])).
1.34/0.55	tff(f8,plain,(
1.34/0.55	  ~((iftrueProp1 = $true) => ((ifSingleton = $true) => ((theeq = $true) => ! [X0,X1 : '$o',X2] : ((in @ X2 @ X0 = $true) => ! [X3] : ((in @ X3 @ X0 = $true) => (($true = X1) => if @ X0 @ X1 @ X2 @ X3 = X2))))))),
1.34/0.55	  inference(fool_elimination,[],[f7])).
1.34/0.55	tff(f9,plain,(
1.34/0.55	  if = (^[X0 : '$i', X1 : '$o', X2 : '$i', X3 : '$i'] : setunion @ (dsetconstr @ X0 @ (^[X4 : '$i'] : (X3 = X4 & ~X1) | (X2 = X4 & X1))))),
1.34/0.55	  inference(rectify,[],[f3])).
1.34/0.55	tff(f10,plain,(
1.34/0.55	  bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ setunion))) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ dsetconstr))) @ (sCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ bCOMB) @ (bCOMB @ (bCOMB @ sCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vOR)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ vAND)) @ vEQ('$i')))))) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ (bCOMB @ vAND @ vNOT))) @ vEQ('$i')))) = if),
1.34/0.55	  inference(fool_elimination,[],[f9])).
1.34/0.55	tff(f11,plain,(
1.34/0.55	  (theeq = ! [X0] : (singleton @ X0 => ! [X1] : (in @ X1 @ X0 => setunion @ X0 = X1)))),
1.34/0.55	  inference(rectify,[],[f4])).
1.34/0.55	tff(f12,plain,(
1.34/0.55	  (vPI('$i') @ (sCOMB @ (bCOMB @ vIMP @ singleton) @ (bCOMB @ vPI('$i') @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ in))) @ (bCOMB @ vEQ('$i') @ setunion)))) = theeq)),
1.34/0.55	  inference(fool_elimination,[],[f11])).
1.34/0.55	tff(f13,plain,(
1.34/0.55	  (iftrueProp1 = ! [X0,X1 : '$o',X2] : (in @ X2 @ X0 => ! [X3] : (in @ X3 @ X0 => (X1 => in @ X2 @ (dsetconstr @ X0 @ (^[X4 : '$i'] : (X3 = X4 & ~X1) | (X2 = X4 & X1)))))))),
1.34/0.55	  inference(rectify,[],[f1])).
1.34/0.55	tff(f14,plain,(
1.34/0.55	  (iftrueProp1 = vPI('$i') @ (bCOMB @ vPI('$o') @ (bCOMB @ (bCOMB @ vPI('$i')) @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ in))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i'))) @ (bCOMB @ (bCOMB @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ in))))) @ (bCOMB @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ vIMP))) @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ in))) @ (bCOMB @ (bCOMB @ (cCOMB @ (bCOMB @ bCOMB @ dsetconstr))) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ bCOMB) @ (bCOMB @ (bCOMB @ sCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vOR)) @ (bCOMB @ (cCOMB @ (bCOMB @ bCOMB @ vAND)) @ vEQ('$i')))))) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ (bCOMB @ vAND @ vNOT))) @ vEQ('$i'))))))))))))),
1.34/0.55	  inference(fool_elimination,[],[f13])).
1.34/0.55	tff(f15,plain,(
1.34/0.55	  (ifSingleton = ! [X0,X1 : '$o',X2] : (in @ X2 @ X0 => ! [X3] : (in @ X3 @ X0 => singleton @ (dsetconstr @ X0 @ (^[X4 : '$i'] : (X3 = X4 & ~X1) | (X2 = X4 & X1))))))),
1.34/0.55	  inference(rectify,[],[f2])).
1.34/0.55	tff(f16,plain,(
1.34/0.55	  (vPI('$i') @ (bCOMB @ vPI('$o') @ (bCOMB @ (bCOMB @ vPI('$i')) @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ in))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i'))) @ (bCOMB @ (bCOMB @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ in))))) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ singleton))) @ (bCOMB @ (bCOMB @ (cCOMB @ (bCOMB @ bCOMB @ dsetconstr))) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ bCOMB) @ (bCOMB @ (bCOMB @ sCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vOR)) @ (bCOMB @ (cCOMB @ (bCOMB @ bCOMB @ vAND)) @ vEQ('$i')))))) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ (bCOMB @ vAND @ vNOT))) @ vEQ('$i')))))))))) = ifSingleton)),
1.34/0.55	  inference(fool_elimination,[],[f15])).
1.34/0.55	tff(f17,plain,(
1.34/0.55	  ((? [X0,X1 : '$o',X2] : (? [X3] : ((if @ X0 @ X1 @ X2 @ X3 != X2 & ($true = X1)) & (in @ X3 @ X0 = $true)) & (in @ X2 @ X0 = $true)) & (theeq = $true)) & (ifSingleton = $true)) & (iftrueProp1 = $true)),
1.34/0.55	  inference(ennf_transformation,[],[f8])).
1.34/0.55	tff(f18,plain,(
1.34/0.55	  ? [X0,X1 : '$o',X2] : (? [X3] : (if @ X0 @ X1 @ X2 @ X3 != X2 & ($true = X1) & (in @ X3 @ X0 = $true)) & (in @ X2 @ X0 = $true)) & (theeq = $true) & (ifSingleton = $true) & (iftrueProp1 = $true)),
1.34/0.55	  inference(flattening,[],[f17])).
1.34/0.55	tff(f19,plain,(
1.34/0.55	  ? [X0,X1 : '$o',X2] : (? [X3] : (if @ X0 @ X1 @ X2 @ X3 != X2 & ($true = X1) & (in @ X3 @ X0 = $true)) & (in @ X2 @ X0 = $true)) => (? [X3] : (if @ sK0 @ sK1 @ sK2 @ X3 != sK2 & ($true = sK1) & (in @ X3 @ sK0 = $true)) & (in @ sK2 @ sK0 = $true))),
1.34/0.55	  introduced(choice_axiom,[])).
1.34/0.55	tff(f20,plain,(
1.34/0.55	  ? [X3] : (if @ sK0 @ sK1 @ sK2 @ X3 != sK2 & ($true = sK1) & (in @ X3 @ sK0 = $true)) => (if @ sK0 @ sK1 @ sK2 @ sK3 != sK2 & ($true = sK1) & (in @ sK3 @ sK0 = $true))),
1.34/0.55	  introduced(choice_axiom,[])).
1.34/0.55	tff(f21,plain,(
1.34/0.55	  ((if @ sK0 @ sK1 @ sK2 @ sK3 != sK2 & ($true = sK1) & (in @ sK3 @ sK0 = $true)) & (in @ sK2 @ sK0 = $true)) & (theeq = $true) & (ifSingleton = $true) & (iftrueProp1 = $true)),
1.34/0.55	  inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f18,f20,f19])).
1.34/0.55	tff(f22,plain,(
1.34/0.55	  (iftrueProp1 = $true)),
1.34/0.55	  inference(cnf_transformation,[],[f21])).
1.34/0.55	tff(f23,plain,(
1.34/0.55	  (ifSingleton = $true)),
1.34/0.55	  inference(cnf_transformation,[],[f21])).
1.34/0.55	tff(f24,plain,(
1.34/0.55	  (theeq = $true)),
1.34/0.55	  inference(cnf_transformation,[],[f21])).
1.34/0.55	tff(f25,plain,(
1.34/0.55	  (in @ sK2 @ sK0 = $true)),
1.34/0.55	  inference(cnf_transformation,[],[f21])).
1.34/0.55	tff(f27,plain,(
1.34/0.55	  ($true = sK1)),
1.34/0.55	  inference(cnf_transformation,[],[f21])).
1.34/0.55	tff(f28,plain,(
1.34/0.55	  if @ sK0 @ sK1 @ sK2 @ sK3 != sK2),
1.34/0.55	  inference(cnf_transformation,[],[f21])).
1.34/0.55	tff(f29,plain,(
1.34/0.55	  bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ setunion))) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ dsetconstr))) @ (sCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ bCOMB) @ (bCOMB @ (bCOMB @ sCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vOR)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ vAND)) @ vEQ('$i')))))) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ (bCOMB @ vAND @ vNOT))) @ vEQ('$i')))) = if),
1.34/0.55	  inference(cnf_transformation,[],[f10])).
1.34/0.55	tff(f30,plain,(
1.34/0.55	  (vPI('$i') @ (bCOMB @ vPI('$o') @ (bCOMB @ (bCOMB @ vPI('$i')) @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ in))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i'))) @ (bCOMB @ (bCOMB @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ in))))) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ singleton))) @ (bCOMB @ (bCOMB @ (cCOMB @ (bCOMB @ bCOMB @ dsetconstr))) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ bCOMB) @ (bCOMB @ (bCOMB @ sCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vOR)) @ (bCOMB @ (cCOMB @ (bCOMB @ bCOMB @ vAND)) @ vEQ('$i')))))) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ (bCOMB @ vAND @ vNOT))) @ vEQ('$i')))))))))) = ifSingleton)),
1.34/0.55	  inference(cnf_transformation,[],[f16])).
1.34/0.55	tff(f31,plain,(
1.34/0.55	  (iftrueProp1 = vPI('$i') @ (bCOMB @ vPI('$o') @ (bCOMB @ (bCOMB @ vPI('$i')) @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ in))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i'))) @ (bCOMB @ (bCOMB @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ in))))) @ (bCOMB @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ vIMP))) @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ in))) @ (bCOMB @ (bCOMB @ (cCOMB @ (bCOMB @ bCOMB @ dsetconstr))) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ bCOMB) @ (bCOMB @ (bCOMB @ sCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vOR)) @ (bCOMB @ (cCOMB @ (bCOMB @ bCOMB @ vAND)) @ vEQ('$i')))))) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ (bCOMB @ vAND @ vNOT))) @ vEQ('$i'))))))))))))),
1.34/0.55	  inference(cnf_transformation,[],[f14])).
1.34/0.55	tff(f32,plain,(
1.34/0.55	  (vPI('$i') @ (sCOMB @ (bCOMB @ vIMP @ singleton) @ (bCOMB @ vPI('$i') @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ in))) @ (bCOMB @ vEQ('$i') @ setunion)))) = theeq)),
1.34/0.55	  inference(cnf_transformation,[],[f12])).
1.34/0.55	tff(f33,plain,(
1.34/0.55	  bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ setunion))) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ dsetconstr))) @ (sCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ bCOMB) @ (bCOMB @ (bCOMB @ sCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vOR)) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ vAND)) @ vEQ('$i')))))) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ (bCOMB @ vAND @ vNOT))) @ vEQ('$i')))) @ sK0 @ $true @ sK2 @ sK3 != sK2),
1.34/0.55	  inference(definition_unfolding,[],[f28,f29,f27])).
1.34/0.55	tff(f34,plain,(
1.34/0.55	  (vPI('$i') @ (bCOMB @ vPI('$o') @ (bCOMB @ (bCOMB @ vPI('$i')) @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ in))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i'))) @ (bCOMB @ (bCOMB @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ in))))) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ singleton))) @ (bCOMB @ (bCOMB @ (cCOMB @ (bCOMB @ bCOMB @ dsetconstr))) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ bCOMB) @ (bCOMB @ (bCOMB @ sCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vOR)) @ (bCOMB @ (cCOMB @ (bCOMB @ bCOMB @ vAND)) @ vEQ('$i')))))) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ (bCOMB @ vAND @ vNOT))) @ vEQ('$i')))))))))) = $true)),
1.34/0.55	  inference(definition_unfolding,[],[f30,f23])).
1.34/0.55	tff(f35,plain,(
1.34/0.55	  (vPI('$i') @ (bCOMB @ vPI('$o') @ (bCOMB @ (bCOMB @ vPI('$i')) @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ in))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i'))) @ (bCOMB @ (bCOMB @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ in))))) @ (bCOMB @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ vIMP))) @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ in))) @ (bCOMB @ (bCOMB @ (cCOMB @ (bCOMB @ bCOMB @ dsetconstr))) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ bCOMB) @ (bCOMB @ (bCOMB @ sCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vOR)) @ (bCOMB @ (cCOMB @ (bCOMB @ bCOMB @ vAND)) @ vEQ('$i')))))) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ (bCOMB @ vAND @ vNOT))) @ vEQ('$i'))))))))))) = $true)),
1.34/0.55	  inference(definition_unfolding,[],[f31,f22])).
1.34/0.56	tff(f36,plain,(
1.34/0.56	  (vPI('$i') @ (sCOMB @ (bCOMB @ vIMP @ singleton) @ (bCOMB @ vPI('$i') @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ in))) @ (bCOMB @ vEQ('$i') @ setunion)))) = $true)),
1.34/0.56	  inference(definition_unfolding,[],[f32,f24])).
1.34/0.56	tff(f37,plain,(
1.34/0.56	  ( ! [X1] : ((sCOMB @ (bCOMB @ vIMP @ singleton) @ (bCOMB @ vPI('$i') @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ in))) @ (bCOMB @ vEQ('$i') @ setunion))) @ X1 = $true)) )),
1.34/0.56	  inference(pi_clausification,[],[f36])).
1.34/0.56	tff(f38,plain,(
1.34/0.56	  ( ! [X1] : ((vIMP @ (singleton @ X1) @ (vPI('$i') @ (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ in @ X1)) @ (vEQ('$i') @ (setunion @ X1)))) = $true)) )),
1.34/0.56	  inference(combinator_demodulation,[],[f37])).
1.34/0.56	tff(f39,plain,(
1.34/0.56	  ( ! [X1] : ((singleton @ X1 = $false) | (vPI('$i') @ (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ in @ X1)) @ (vEQ('$i') @ (setunion @ X1))) = $true)) )),
1.34/0.56	  inference(binary_proxy_clausification,[],[f38])).
1.34/0.56	tff(f40,plain,(
1.34/0.56	  ( ! [X2,X1] : ((singleton @ X1 = $false) | (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ in @ X1)) @ (vEQ('$i') @ (setunion @ X1)) @ X2 = $true)) )),
1.34/0.56	  inference(pi_clausification,[],[f39])).
1.34/0.56	tff(f41,plain,(
1.34/0.56	  ( ! [X2,X1] : ((singleton @ X1 = $false) | (vIMP @ (in @ X2 @ X1) @ (vEQ('$i') @ (setunion @ X1) @ X2) = $true)) )),
1.34/0.56	  inference(combinator_demodulation,[],[f40])).
1.34/0.56	tff(f42,plain,(
1.34/0.56	  ( ! [X2,X1] : ((singleton @ X1 = $false) | (in @ X2 @ X1 = $false) | (vEQ('$i') @ (setunion @ X1) @ X2 = $true)) )),
1.34/0.56	  inference(binary_proxy_clausification,[],[f41])).
1.34/0.56	tff(f43,plain,(
1.34/0.56	  ( ! [X2,X1] : ((in @ X2 @ X1 = $false) | (singleton @ X1 = $false) | setunion @ X1 = X2) )),
1.34/0.56	  inference(equality_proxy_clausification,[],[f42])).
1.34/0.56	% (17033)Refutation not found, incomplete strategy
1.34/0.56	% (17033)------------------------------
1.34/0.56	% (17033)Version: Vampire 4.5.0 (commit 7ae30c7f on 2020-06-30 15:57:20 +0100)
1.34/0.56	% (17033)Termination reason: Refutation not found, incomplete strategy
1.34/0.56	
1.34/0.56	% (17033)Memory used [KB]: 13304
1.34/0.56	% (17033)Time elapsed: 0.186 s
1.34/0.56	% (17033)------------------------------
1.34/0.56	% (17033)------------------------------
1.34/0.56	tff(f44,plain,(
1.34/0.56	  ( ! [X1] : ((bCOMB @ vPI('$o') @ (bCOMB @ (bCOMB @ vPI('$i')) @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ in))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i'))) @ (bCOMB @ (bCOMB @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ in))))) @ (bCOMB @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ vIMP))) @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ in))) @ (bCOMB @ (bCOMB @ (cCOMB @ (bCOMB @ bCOMB @ dsetconstr))) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ bCOMB) @ (bCOMB @ (bCOMB @ sCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vOR)) @ (bCOMB @ (cCOMB @ (bCOMB @ bCOMB @ vAND)) @ vEQ('$i')))))) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ (bCOMB @ vAND @ vNOT))) @ vEQ('$i')))))))))) @ X1 = $true)) )),
1.34/0.56	  inference(pi_clausification,[],[f35])).
1.34/0.56	tff(f45,plain,(
1.34/0.56	  ( ! [X1] : ((vPI('$o') @ (bCOMB @ vPI('$i') @ (bCOMB @ (sCOMB @ (bCOMB @ vIMP @ (in @ X1))) @ (bCOMB @ (bCOMB @ vPI('$i')) @ (bCOMB @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ in)))) @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ vIMP)) @ (bCOMB @ (bCOMB @ (bCOMB @ (in @ X1))) @ (bCOMB @ (cCOMB @ (bCOMB @ bCOMB @ dsetconstr)) @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (cCOMB @ (bCOMB @ bCOMB @ vAND) @ (vEQ('$i') @ X1))))) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ (bCOMB @ vAND @ vNOT))) @ vEQ('$i')))))))))) = $true)) )),
1.34/0.56	  inference(combinator_demodulation,[],[f44])).
1.34/0.56	tff(f46,plain,(
1.34/0.56	  ( ! [X2:'$o',X1] : ((bCOMB @ vPI('$i') @ (bCOMB @ (sCOMB @ (bCOMB @ vIMP @ (in @ X1))) @ (bCOMB @ (bCOMB @ vPI('$i')) @ (bCOMB @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ in)))) @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ vIMP)) @ (bCOMB @ (bCOMB @ (bCOMB @ (in @ X1))) @ (bCOMB @ (cCOMB @ (bCOMB @ bCOMB @ dsetconstr)) @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (cCOMB @ (bCOMB @ bCOMB @ vAND) @ (vEQ('$i') @ X1))))) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ (bCOMB @ vAND @ vNOT))) @ vEQ('$i'))))))))) @ X2 = $true)) )),
1.34/0.56	  inference(pi_clausification,[],[f45])).
1.34/0.56	% (17059)dis+1011_10_add=large:csup=on:inj=on:chr=on:foolp=on:cnfonf=eager:afr=on:afp=4000:afq=1.0:amm=off:anc=none:lma=on:nm=64:nwc=4:sac=on:sp=occurrence_75 on theBenchmark
1.34/0.56	tff(f47,plain,(
1.34/0.56	  ( ! [X2:'$o',X1] : ((vPI('$i') @ (sCOMB @ (bCOMB @ vIMP @ (in @ X1)) @ (bCOMB @ vPI('$i') @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ in))) @ (bCOMB @ (bCOMB @ (vIMP @ X2)) @ (bCOMB @ (bCOMB @ (in @ X1)) @ (cCOMB @ (bCOMB @ bCOMB @ dsetconstr) @ (bCOMB @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ (vAND @ X2) @ (vEQ('$i') @ X1)))) @ (bCOMB @ (bCOMB @ (vAND @ (vNOT @ X2))) @ vEQ('$i'))))))))) = $true)) )),
1.34/0.56	  inference(combinator_demodulation,[],[f46])).
1.34/0.56	tff(f48,plain,(
1.34/0.56	  ( ! [X2:'$o',X3,X1] : ((sCOMB @ (bCOMB @ vIMP @ (in @ X1)) @ (bCOMB @ vPI('$i') @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ in))) @ (bCOMB @ (bCOMB @ (vIMP @ X2)) @ (bCOMB @ (bCOMB @ (in @ X1)) @ (cCOMB @ (bCOMB @ bCOMB @ dsetconstr) @ (bCOMB @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ (vAND @ X2) @ (vEQ('$i') @ X1)))) @ (bCOMB @ (bCOMB @ (vAND @ (vNOT @ X2))) @ vEQ('$i')))))))) @ X3 = $true)) )),
1.34/0.56	  inference(pi_clausification,[],[f47])).
1.34/0.56	tff(f49,plain,(
1.34/0.56	  ( ! [X2:'$o',X3,X1] : ((vIMP @ (in @ X1 @ X3) @ (vPI('$i') @ (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ in @ X3)) @ (bCOMB @ (vIMP @ X2) @ (bCOMB @ (in @ X1) @ (bCOMB @ (dsetconstr @ X3) @ (bCOMB @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ (vAND @ X2) @ (vEQ('$i') @ X1)))) @ (bCOMB @ (bCOMB @ (vAND @ (vNOT @ X2))) @ vEQ('$i')))))))) = $true)) )),
1.34/0.56	  inference(combinator_demodulation,[],[f48])).
1.34/0.56	tff(f50,plain,(
1.34/0.56	  ( ! [X2:'$o',X3,X1] : ((in @ X1 @ X3 = $false) | (vPI('$i') @ (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ in @ X3)) @ (bCOMB @ (vIMP @ X2) @ (bCOMB @ (in @ X1) @ (bCOMB @ (dsetconstr @ X3) @ (bCOMB @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ (vAND @ X2) @ (vEQ('$i') @ X1)))) @ (bCOMB @ (bCOMB @ (vAND @ (vNOT @ X2))) @ vEQ('$i'))))))) = $true)) )),
1.34/0.56	  inference(binary_proxy_clausification,[],[f49])).
1.34/0.56	tff(f51,plain,(
1.34/0.56	  ( ! [X4,X2:'$o',X3,X1] : ((in @ X1 @ X3 = $false) | (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ in @ X3)) @ (bCOMB @ (vIMP @ X2) @ (bCOMB @ (in @ X1) @ (bCOMB @ (dsetconstr @ X3) @ (bCOMB @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ (vAND @ X2) @ (vEQ('$i') @ X1)))) @ (bCOMB @ (bCOMB @ (vAND @ (vNOT @ X2))) @ vEQ('$i')))))) @ X4 = $true)) )),
1.34/0.56	  inference(pi_clausification,[],[f50])).
1.34/0.56	tff(f52,plain,(
1.34/0.56	  ( ! [X4,X2:'$o',X3,X1] : ((in @ X1 @ X3 = $false) | (vIMP @ (in @ X4 @ X3) @ (vIMP @ X2 @ (in @ X1 @ (dsetconstr @ X3 @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ (vAND @ X2) @ (vEQ('$i') @ X1))) @ (bCOMB @ (vAND @ (vNOT @ X2)) @ (vEQ('$i') @ X4)))))) = $true)) )),
1.34/0.56	  inference(combinator_demodulation,[],[f51])).
1.34/0.56	tff(f53,plain,(
1.34/0.56	  ( ! [X4,X2:'$o',X3,X1] : ((in @ X1 @ X3 = $false) | (in @ X4 @ X3 = $false) | (vIMP @ X2 @ (in @ X1 @ (dsetconstr @ X3 @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ (vAND @ X2) @ (vEQ('$i') @ X1))) @ (bCOMB @ (vAND @ (vNOT @ X2)) @ (vEQ('$i') @ X4))))) = $true)) )),
1.34/0.56	  inference(binary_proxy_clausification,[],[f52])).
1.34/0.56	tff(f54,plain,(
1.34/0.56	  ( ! [X4,X2:'$o',X3,X1] : ((in @ X1 @ (dsetconstr @ X3 @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ (vAND @ X2) @ (vEQ('$i') @ X1))) @ (bCOMB @ (vAND @ (vNOT @ X2)) @ (vEQ('$i') @ X4)))) = $true) | (in @ X4 @ X3 = $false) | ($false = X2) | (in @ X1 @ X3 = $false)) )),
1.34/0.56	  inference(binary_proxy_clausification,[],[f53])).
1.34/0.56	tff(f55,plain,(
1.34/0.56	  ( ! [X1] : ((bCOMB @ vPI('$o') @ (bCOMB @ (bCOMB @ vPI('$i')) @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ in))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i'))) @ (bCOMB @ (bCOMB @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ in))))) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ singleton))) @ (bCOMB @ (bCOMB @ (cCOMB @ (bCOMB @ bCOMB @ dsetconstr))) @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ bCOMB) @ (bCOMB @ (bCOMB @ sCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vOR)) @ (bCOMB @ (cCOMB @ (bCOMB @ bCOMB @ vAND)) @ vEQ('$i')))))) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ (bCOMB @ vAND @ vNOT))) @ vEQ('$i'))))))))) @ X1 = $true)) )),
1.34/0.56	  inference(pi_clausification,[],[f34])).
1.34/0.56	tff(f56,plain,(
1.34/0.56	  ( ! [X1] : ((vPI('$o') @ (bCOMB @ vPI('$i') @ (bCOMB @ (sCOMB @ (bCOMB @ vIMP @ (in @ X1))) @ (bCOMB @ (bCOMB @ vPI('$i')) @ (bCOMB @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ in)))) @ (bCOMB @ (bCOMB @ (bCOMB @ singleton)) @ (bCOMB @ (cCOMB @ (bCOMB @ bCOMB @ dsetconstr)) @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (cCOMB @ (bCOMB @ bCOMB @ vAND) @ (vEQ('$i') @ X1))))) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ (bCOMB @ vAND @ vNOT))) @ vEQ('$i'))))))))) = $true)) )),
1.34/0.56	  inference(combinator_demodulation,[],[f55])).
1.34/0.56	tff(f57,plain,(
1.34/0.56	  ( ! [X2:'$o',X1] : ((bCOMB @ vPI('$i') @ (bCOMB @ (sCOMB @ (bCOMB @ vIMP @ (in @ X1))) @ (bCOMB @ (bCOMB @ vPI('$i')) @ (bCOMB @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ in)))) @ (bCOMB @ (bCOMB @ (bCOMB @ singleton)) @ (bCOMB @ (cCOMB @ (bCOMB @ bCOMB @ dsetconstr)) @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vOR) @ (cCOMB @ (bCOMB @ bCOMB @ vAND) @ (vEQ('$i') @ X1))))) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ (bCOMB @ vAND @ vNOT))) @ vEQ('$i')))))))) @ X2 = $true)) )),
1.34/0.56	  inference(pi_clausification,[],[f56])).
1.34/0.57	tff(f58,plain,(
1.34/0.57	  ( ! [X2:'$o',X1] : ((vPI('$i') @ (sCOMB @ (bCOMB @ vIMP @ (in @ X1)) @ (bCOMB @ vPI('$i') @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ in))) @ (bCOMB @ (bCOMB @ singleton) @ (cCOMB @ (bCOMB @ bCOMB @ dsetconstr) @ (bCOMB @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ (vAND @ X2) @ (vEQ('$i') @ X1)))) @ (bCOMB @ (bCOMB @ (vAND @ (vNOT @ X2))) @ vEQ('$i')))))))) = $true)) )),
1.34/0.57	  inference(combinator_demodulation,[],[f57])).
1.34/0.57	tff(f59,plain,(
1.34/0.57	  ( ! [X2:'$o',X3,X1] : ((sCOMB @ (bCOMB @ vIMP @ (in @ X1)) @ (bCOMB @ vPI('$i') @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ in))) @ (bCOMB @ (bCOMB @ singleton) @ (cCOMB @ (bCOMB @ bCOMB @ dsetconstr) @ (bCOMB @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ (vAND @ X2) @ (vEQ('$i') @ X1)))) @ (bCOMB @ (bCOMB @ (vAND @ (vNOT @ X2))) @ vEQ('$i'))))))) @ X3 = $true)) )),
1.34/0.57	  inference(pi_clausification,[],[f58])).
1.34/0.57	tff(f60,plain,(
1.34/0.57	  ( ! [X2:'$o',X3,X1] : ((vIMP @ (in @ X1 @ X3) @ (vPI('$i') @ (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ in @ X3)) @ (bCOMB @ singleton @ (bCOMB @ (dsetconstr @ X3) @ (bCOMB @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ (vAND @ X2) @ (vEQ('$i') @ X1)))) @ (bCOMB @ (bCOMB @ (vAND @ (vNOT @ X2))) @ vEQ('$i'))))))) = $true)) )),
1.34/0.57	  inference(combinator_demodulation,[],[f59])).
1.34/0.57	tff(f61,plain,(
1.34/0.57	  ( ! [X2:'$o',X3,X1] : ((in @ X1 @ X3 = $false) | (vPI('$i') @ (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ in @ X3)) @ (bCOMB @ singleton @ (bCOMB @ (dsetconstr @ X3) @ (bCOMB @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ (vAND @ X2) @ (vEQ('$i') @ X1)))) @ (bCOMB @ (bCOMB @ (vAND @ (vNOT @ X2))) @ vEQ('$i')))))) = $true)) )),
1.34/0.57	  inference(binary_proxy_clausification,[],[f60])).
1.34/0.57	tff(f62,plain,(
1.34/0.57	  ( ! [X4,X2:'$o',X3,X1] : ((in @ X1 @ X3 = $false) | (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ in @ X3)) @ (bCOMB @ singleton @ (bCOMB @ (dsetconstr @ X3) @ (bCOMB @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ (vAND @ X2) @ (vEQ('$i') @ X1)))) @ (bCOMB @ (bCOMB @ (vAND @ (vNOT @ X2))) @ vEQ('$i'))))) @ X4 = $true)) )),
1.34/0.57	  inference(pi_clausification,[],[f61])).
1.34/0.57	tff(f63,plain,(
1.34/0.57	  ( ! [X4,X2:'$o',X3,X1] : ((in @ X1 @ X3 = $false) | (vIMP @ (in @ X4 @ X3) @ (singleton @ (dsetconstr @ X3 @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ (vAND @ X2) @ (vEQ('$i') @ X1))) @ (bCOMB @ (vAND @ (vNOT @ X2)) @ (vEQ('$i') @ X4))))) = $true)) )),
1.34/0.57	  inference(combinator_demodulation,[],[f62])).
1.34/0.57	tff(f64,plain,(
1.34/0.57	  ( ! [X4,X2:'$o',X3,X1] : ((singleton @ (dsetconstr @ X3 @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ (vAND @ X2) @ (vEQ('$i') @ X1))) @ (bCOMB @ (vAND @ (vNOT @ X2)) @ (vEQ('$i') @ X4)))) = $true) | (in @ X4 @ X3 = $false) | (in @ X1 @ X3 = $false)) )),
1.34/0.57	  inference(binary_proxy_clausification,[],[f63])).
1.34/0.57	tff(f65,plain,(
1.34/0.57	  setunion @ (dsetconstr @ sK0 @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ (vAND @ $true) @ (vEQ('$i') @ sK2))) @ (bCOMB @ (vAND @ (vNOT @ $true)) @ (vEQ('$i') @ sK3)))) != sK2),
1.34/0.57	  inference(combinator_demodulation,[],[f33])).
1.34/0.57	tff(f66,plain,(
1.34/0.57	  setunion @ (dsetconstr @ sK0 @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ (vAND @ $true) @ (vEQ('$i') @ sK2))) @ (bCOMB @ (vAND @ $false) @ (vEQ('$i') @ sK3)))) != sK2),
1.34/0.57	  inference(boolean_simplification,[],[f65])).
1.34/0.57	tff(f93,plain,(
1.34/0.57	  ( ! [X2:'$o',X0,X3,X1] : (($false = $true) | (singleton @ (dsetconstr @ X1 @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ (vAND @ X2) @ (vEQ('$i') @ X0))) @ (bCOMB @ (vAND @ (vNOT @ X2)) @ (vEQ('$i') @ X3)))) = $false) | setunion @ (dsetconstr @ X1 @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ (vAND @ X2) @ (vEQ('$i') @ X0))) @ (bCOMB @ (vAND @ (vNOT @ X2)) @ (vEQ('$i') @ X3)))) = X0 | (in @ X3 @ X1 = $false) | ($false = X2) | (in @ X0 @ X1 = $false)) )),
1.34/0.57	  inference(superposition,[],[f43,f54])).
1.34/0.57	tff(f94,plain,(
1.34/0.57	  ( ! [X2:'$o',X0,X3,X1] : ((singleton @ (dsetconstr @ X1 @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ (vAND @ X2) @ (vEQ('$i') @ X0))) @ (bCOMB @ (vAND @ (vNOT @ X2)) @ (vEQ('$i') @ X3)))) = $false) | setunion @ (dsetconstr @ X1 @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ (vAND @ X2) @ (vEQ('$i') @ X0))) @ (bCOMB @ (vAND @ (vNOT @ X2)) @ (vEQ('$i') @ X3)))) = X0 | (in @ X3 @ X1 = $false) | ($false = X2) | (in @ X0 @ X1 = $false)) )),
1.34/0.57	  inference(trivial_inequality_removal,[],[f93])).
1.34/0.57	tff(f97,plain,(
1.34/0.57	  ( ! [X6,X4:'$o',X2,X0,X5,X3,X1:'$o'] : (($false = $true) | (in @ X6 @ X0 = $false) | (in @ X5 @ X0 = $false) | setunion @ (dsetconstr @ X0 @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ (vAND @ X1) @ (vEQ('$i') @ X2))) @ (bCOMB @ (vAND @ (vNOT @ X1)) @ (vEQ('$i') @ X3)))) = X2 | (in @ X3 @ X0 = $false) | ($false = X1) | (in @ X2 @ X0 = $false) | sCOMB @ (bCOMB @ vOR @ (bCOMB @ (vAND @ X1) @ (vEQ('$i') @ X2))) @ (bCOMB @ (vAND @ (vNOT @ X1)) @ (vEQ('$i') @ X3)) != sCOMB @ (bCOMB @ vOR @ (bCOMB @ (vAND @ X4) @ (vEQ('$i') @ X5))) @ (bCOMB @ (vAND @ (vNOT @ X4)) @ (vEQ('$i') @ X6))) )),
1.34/0.57	  inference(superposition,[],[f64,f94])).
1.34/0.57	tff(f98,plain,(
1.34/0.57	  ( ! [X6,X4:'$o',X2,X0,X5,X3,X1:'$o'] : (sCOMB @ (bCOMB @ vOR @ (bCOMB @ (vAND @ X1) @ (vEQ('$i') @ X2))) @ (bCOMB @ (vAND @ (vNOT @ X1)) @ (vEQ('$i') @ X3)) != sCOMB @ (bCOMB @ vOR @ (bCOMB @ (vAND @ X4) @ (vEQ('$i') @ X5))) @ (bCOMB @ (vAND @ (vNOT @ X4)) @ (vEQ('$i') @ X6)) | (in @ X5 @ X0 = $false) | setunion @ (dsetconstr @ X0 @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ (vAND @ X1) @ (vEQ('$i') @ X2))) @ (bCOMB @ (vAND @ (vNOT @ X1)) @ (vEQ('$i') @ X3)))) = X2 | (in @ X3 @ X0 = $false) | ($false = X1) | (in @ X2 @ X0 = $false) | (in @ X6 @ X0 = $false)) )),
1.34/0.57	  inference(trivial_inequality_removal,[],[f97])).
1.34/0.57	tff(f102,plain,(
1.34/0.57	  ( ! [X2:'$o',X0,X3,X1] : ((in @ X0 @ X1 = $false) | setunion @ (dsetconstr @ X1 @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ (vAND @ X2) @ (vEQ('$i') @ X0))) @ (bCOMB @ (vAND @ (vNOT @ X2)) @ (vEQ('$i') @ X3)))) = X0 | (in @ X3 @ X1 = $false) | ($false = X2) | (in @ X0 @ X1 = $false) | (in @ X3 @ X1 = $false)) )),
1.34/0.57	  inference(equality_resolution,[],[f98])).
1.34/0.57	tff(f103,plain,(
1.34/0.57	  ( ! [X2:'$o',X0,X3,X1] : (setunion @ (dsetconstr @ X1 @ (sCOMB @ (bCOMB @ vOR @ (bCOMB @ (vAND @ X2) @ (vEQ('$i') @ X0))) @ (bCOMB @ (vAND @ (vNOT @ X2)) @ (vEQ('$i') @ X3)))) = X0 | (in @ X0 @ X1 = $false) | (in @ X3 @ X1 = $false) | ($false = X2)) )),
1.34/0.57	  inference(duplicate_literal_removal,[],[f102])).
1.34/0.57	tff(f211,plain,(
1.34/0.57	  ( ! [X2,X0:'$o',X1] : (sK2 != X1 | (in @ X1 @ sK0 = $false) | (in @ X2 @ sK0 = $false) | ($false = X0) | sCOMB @ (bCOMB @ vOR @ (bCOMB @ (vAND @ $true) @ (vEQ('$i') @ sK2))) @ (bCOMB @ (vAND @ $false) @ (vEQ('$i') @ sK3)) != sCOMB @ (bCOMB @ vOR @ (bCOMB @ (vAND @ X0) @ (vEQ('$i') @ X1))) @ (bCOMB @ (vAND @ (vNOT @ X0)) @ (vEQ('$i') @ X2))) )),
1.34/0.57	  inference(superposition,[],[f66,f103])).
1.34/0.57	tff(f303,plain,(
1.34/0.57	  spl4_8 <=> ! [X0 : '$o'] : ($false = X0)),
1.34/0.57	  introduced(avatar_definition,[new_symbols(naming,[spl4_8])])).
1.34/0.57	tff(f304,plain,(
1.34/0.57	  ( ! [X0:'$o'] : (($false = X0)) ) | ~spl4_8),
1.34/0.57	  inference(avatar_component_clause,[],[f303])).
1.34/0.57	tff(f315,plain,(
1.34/0.57	  ( ! [X0,X1:'$o'] : ((in @ sK2 @ sK0 = $false) | (in @ X0 @ sK0 = $false) | ($false = X1) | sCOMB @ (bCOMB @ vOR @ (bCOMB @ (vAND @ $true) @ (vEQ('$i') @ sK2))) @ (bCOMB @ (vAND @ $false) @ (vEQ('$i') @ sK3)) != sCOMB @ (bCOMB @ vOR @ (bCOMB @ (vAND @ X1) @ (vEQ('$i') @ sK2))) @ (bCOMB @ (vAND @ (vNOT @ X1)) @ (vEQ('$i') @ X0))) )),
1.34/0.57	  inference(equality_resolution,[],[f211])).
1.34/0.57	tff(f316,plain,(
1.34/0.57	  ( ! [X0,X1:'$o'] : (($false = $true) | (in @ X0 @ sK0 = $false) | ($false = X1) | sCOMB @ (bCOMB @ vOR @ (bCOMB @ (vAND @ $true) @ (vEQ('$i') @ sK2))) @ (bCOMB @ (vAND @ $false) @ (vEQ('$i') @ sK3)) != sCOMB @ (bCOMB @ vOR @ (bCOMB @ (vAND @ X1) @ (vEQ('$i') @ sK2))) @ (bCOMB @ (vAND @ (vNOT @ X1)) @ (vEQ('$i') @ X0))) )),
1.34/0.57	  inference(forward_demodulation,[],[f315,f25])).
1.34/0.57	tff(f317,plain,(
1.34/0.57	  ( ! [X0,X1:'$o'] : (sCOMB @ (bCOMB @ vOR @ (bCOMB @ (vAND @ $true) @ (vEQ('$i') @ sK2))) @ (bCOMB @ (vAND @ $false) @ (vEQ('$i') @ sK3)) != sCOMB @ (bCOMB @ vOR @ (bCOMB @ (vAND @ X1) @ (vEQ('$i') @ sK2))) @ (bCOMB @ (vAND @ (vNOT @ X1)) @ (vEQ('$i') @ X0)) | ($false = X1) | (in @ X0 @ sK0 = $false)) )),
1.34/0.57	  inference(trivial_inequality_removal,[],[f316])).
1.34/0.57	tff(f333,plain,(
1.34/0.57	  ( ! [X0,X1:'$o'] : ((sCOMB @ (bCOMB @ vOR @ (bCOMB @ (vAND @ $true) @ (vEQ('$i') @ sK2))) @ (bCOMB @ (vAND @ $false) @ (vEQ('$i') @ sK3)) @ (sK7 @ X1 @ X0) != sCOMB @ (bCOMB @ vOR @ (bCOMB @ (vAND @ X1) @ (vEQ('$i') @ sK2))) @ (bCOMB @ (vAND @ (vNOT @ X1)) @ (vEQ('$i') @ X0)) @ (sK7 @ X1 @ X0)) | ($false = X1) | (in @ X0 @ sK0 = $false)) )),
1.34/0.57	  inference(negative_extensionality,[],[f317])).
1.34/0.58	tff(f336,plain,(
1.34/0.58	  ( ! [X0,X1:'$o'] : ((vOR @ (vAND @ $true @ (vEQ('$i') @ sK2 @ (sK7 @ X1 @ X0))) @ (vAND @ $false @ (vEQ('$i') @ sK3 @ (sK7 @ X1 @ X0))) != vOR @ (vAND @ X1 @ (vEQ('$i') @ sK2 @ (sK7 @ X1 @ X0))) @ (vAND @ (vNOT @ X1) @ (vEQ('$i') @ X0 @ (sK7 @ X1 @ X0)))) | ($false = X1) | (in @ X0 @ sK0 = $false)) )),
1.34/0.58	  inference(combinator_demodulation,[],[f333])).
1.34/0.58	tff(f337,plain,(
1.34/0.58	  ( ! [X0,X1:'$o'] : ((vOR @ (vAND @ $true @ (vEQ('$i') @ sK2 @ (sK7 @ X1 @ X0))) @ $false != vOR @ (vAND @ X1 @ (vEQ('$i') @ sK2 @ (sK7 @ X1 @ X0))) @ (vAND @ (vNOT @ X1) @ (vEQ('$i') @ X0 @ (sK7 @ X1 @ X0)))) | ($false = X1) | (in @ X0 @ sK0 = $false)) )),
1.34/0.58	  inference(boolean_simplification,[],[f336])).
1.34/0.58	tff(f338,plain,(
1.34/0.58	  ( ! [X0,X1:'$o'] : ((vAND @ $true @ (vEQ('$i') @ sK2 @ (sK7 @ X1 @ X0)) != vOR @ (vAND @ X1 @ (vEQ('$i') @ sK2 @ (sK7 @ X1 @ X0))) @ (vAND @ (vNOT @ X1) @ (vEQ('$i') @ X0 @ (sK7 @ X1 @ X0)))) | ($false = X1) | (in @ X0 @ sK0 = $false)) )),
1.34/0.58	  inference(boolean_simplification,[],[f337])).
1.34/0.58	tff(f339,plain,(
1.34/0.58	  ( ! [X0,X1:'$o'] : ((vEQ('$i') @ sK2 @ (sK7 @ X1 @ X0) != vOR @ (vAND @ X1 @ (vEQ('$i') @ sK2 @ (sK7 @ X1 @ X0))) @ (vAND @ (vNOT @ X1) @ (vEQ('$i') @ X0 @ (sK7 @ X1 @ X0)))) | ($false = X1) | (in @ X0 @ sK0 = $false)) )),
1.34/0.58	  inference(boolean_simplification,[],[f338])).
1.34/0.58	tff(f340,plain,(
1.34/0.58	  ( ! [X0,X1:'$o'] : ((vEQ('$i') @ sK2 @ (sK7 @ X1 @ X0) = $true) | ($false = X1) | (in @ X0 @ sK0 = $false) | (vOR @ (vAND @ X1 @ (vEQ('$i') @ sK2 @ (sK7 @ X1 @ X0))) @ (vAND @ (vNOT @ X1) @ (vEQ('$i') @ X0 @ (sK7 @ X1 @ X0))) = $true)) )),
1.34/0.58	  inference(binary_proxy_clausification,[],[f339])).
1.34/0.58	tff(f341,plain,(
1.34/0.58	  ( ! [X0,X1:'$o'] : ((vEQ('$i') @ sK2 @ (sK7 @ X1 @ X0) = $false) | ($false = X1) | (in @ X0 @ sK0 = $false) | (vOR @ (vAND @ X1 @ (vEQ('$i') @ sK2 @ (sK7 @ X1 @ X0))) @ (vAND @ (vNOT @ X1) @ (vEQ('$i') @ X0 @ (sK7 @ X1 @ X0))) = $false)) )),
1.34/0.58	  inference(binary_proxy_clausification,[],[f339])).
1.34/0.58	tff(f342,plain,(
1.34/0.58	  ( ! [X0,X1:'$o'] : (sK7 @ X1 @ X0 != sK2 | ($false = X1) | (in @ X0 @ sK0 = $false) | (vOR @ (vAND @ X1 @ (vEQ('$i') @ sK2 @ (sK7 @ X1 @ X0))) @ (vAND @ (vNOT @ X1) @ (vEQ('$i') @ X0 @ (sK7 @ X1 @ X0))) = $false)) )),
1.34/0.58	  inference(equality_proxy_clausification,[],[f341])).
1.34/0.58	tff(f343,plain,(
1.34/0.58	  ( ! [X0,X1:'$o'] : (sK7 @ X1 @ X0 != sK2 | ($false = X1) | (in @ X0 @ sK0 = $false) | (vAND @ X1 @ (vEQ('$i') @ sK2 @ (sK7 @ X1 @ X0)) = $false)) )),
1.34/0.58	  inference(binary_proxy_clausification,[],[f342])).
1.34/0.58	tff(f348,plain,(
1.34/0.58	  ( ! [X0,X1:'$o'] : (sK7 @ X1 @ X0 != sK2 | ($false = X1) | (in @ X0 @ sK0 = $false) | ($false = X1) | (vEQ('$i') @ sK2 @ (sK7 @ X1 @ X0) = $false)) )),
1.34/0.58	  inference(binary_proxy_clausification,[],[f343])).
1.34/0.58	tff(f349,plain,(
1.34/0.58	  ( ! [X0,X1:'$o'] : (sK7 @ X1 @ X0 != sK2 | ($false = X1) | (in @ X0 @ sK0 = $false) | (vEQ('$i') @ sK2 @ (sK7 @ X1 @ X0) = $false)) )),
1.34/0.58	  inference(duplicate_literal_removal,[],[f348])).
1.34/0.58	tff(f350,plain,(
1.34/0.58	  ( ! [X0,X1:'$o'] : (sK7 @ X1 @ X0 != sK2 | ($false = X1) | (in @ X0 @ sK0 = $false) | sK7 @ X1 @ X0 != sK2) )),
1.34/0.58	  inference(equality_proxy_clausification,[],[f349])).
1.34/0.58	tff(f351,plain,(
1.34/0.58	  ( ! [X0,X1:'$o'] : (sK7 @ X1 @ X0 != sK2 | ($false = X1) | (in @ X0 @ sK0 = $false)) )),
1.34/0.58	  inference(duplicate_literal_removal,[],[f350])).
1.34/0.58	tff(f352,plain,(
1.34/0.58	  ( ! [X0,X1:'$o'] : (sK7 @ X1 @ X0 = sK2 | ($false = X1) | (in @ X0 @ sK0 = $false) | (vOR @ (vAND @ X1 @ (vEQ('$i') @ sK2 @ (sK7 @ X1 @ X0))) @ (vAND @ (vNOT @ X1) @ (vEQ('$i') @ X0 @ (sK7 @ X1 @ X0))) = $true)) )),
1.34/0.58	  inference(equality_proxy_clausification,[],[f340])).
1.34/0.58	tff(f353,plain,(
1.34/0.58	  ( ! [X0,X1:'$o'] : (sK7 @ X1 @ X0 = sK2 | ($false = X1) | (in @ X0 @ sK0 = $false) | (vAND @ X1 @ (vEQ('$i') @ sK2 @ (sK7 @ X1 @ X0)) = $true) | (vAND @ (vNOT @ X1) @ (vEQ('$i') @ X0 @ (sK7 @ X1 @ X0)) = $true)) )),
1.34/0.58	  inference(binary_proxy_clausification,[],[f352])).
1.34/0.58	tff(f355,plain,(
1.34/0.58	  ( ! [X0,X1:'$o'] : (sK7 @ X1 @ X0 = sK2 | ($false = X1) | (in @ X0 @ sK0 = $false) | (vEQ('$i') @ sK2 @ (sK7 @ X1 @ X0) = $true) | (vAND @ (vNOT @ X1) @ (vEQ('$i') @ X0 @ (sK7 @ X1 @ X0)) = $true)) )),
1.34/0.58	  inference(binary_proxy_clausification,[],[f353])).
1.34/0.58	tff(f356,plain,(
1.34/0.58	  ( ! [X0,X1:'$o'] : (sK7 @ X1 @ X0 = sK2 | ($false = X1) | (in @ X0 @ sK0 = $false) | sK7 @ X1 @ X0 = sK2 | (vAND @ (vNOT @ X1) @ (vEQ('$i') @ X0 @ (sK7 @ X1 @ X0)) = $true)) )),
1.34/0.58	  inference(equality_proxy_clausification,[],[f355])).
1.34/0.58	tff(f357,plain,(
1.34/0.58	  ( ! [X0,X1:'$o'] : (sK7 @ X1 @ X0 = sK2 | ($false = X1) | (in @ X0 @ sK0 = $false) | (vAND @ (vNOT @ X1) @ (vEQ('$i') @ X0 @ (sK7 @ X1 @ X0)) = $true)) )),
1.34/0.58	  inference(duplicate_literal_removal,[],[f356])).
1.34/0.58	tff(f358,plain,(
1.34/0.58	  ( ! [X0,X1:'$o'] : (sK7 @ X1 @ X0 = sK2 | ($false = X1) | (in @ X0 @ sK0 = $false) | (vNOT @ X1 = $true)) )),
1.34/0.58	  inference(binary_proxy_clausification,[],[f357])).
1.34/0.58	tff(f361,plain,(
1.34/0.58	  ( ! [X0,X1:'$o'] : (sK7 @ X1 @ X0 = sK2 | ($false = X1) | (in @ X0 @ sK0 = $false) | ($false = X1)) )),
1.34/0.58	  inference(not_proxy_clausification,[],[f358])).
1.34/0.58	tff(f362,plain,(
1.34/0.58	  ( ! [X0,X1:'$o'] : (sK7 @ X1 @ X0 = sK2 | ($false = X1) | (in @ X0 @ sK0 = $false)) )),
1.34/0.58	  inference(duplicate_literal_removal,[],[f361])).
1.34/0.58	tff(f369,plain,(
1.34/0.58	  ( ! [X0,X1:'$o'] : (($false = X1) | (in @ X0 @ sK0 = $false) | sK7 @ X1 @ X0 = sK2) )),
1.34/0.58	  inference(global_subsumption,[],[f362])).
1.34/0.58	tff(f370,plain,(
1.34/0.58	  ( ! [X0,X1:'$o'] : ((in @ X0 @ sK0 = $false) | ($false = X1)) )),
1.34/0.58	  inference(global_subsumption,[],[f369,f351])).
1.34/0.58	tff(f483,plain,(
1.34/0.58	  spl4_12 <=> ! [X0] : (in @ X0 @ sK0 = $false)),
1.34/0.58	  introduced(avatar_definition,[new_symbols(naming,[spl4_12])])).
1.34/0.58	tff(f484,plain,(
1.34/0.58	  ( ! [X0] : ((in @ X0 @ sK0 = $false)) ) | ~spl4_12),
1.34/0.58	  inference(avatar_component_clause,[],[f483])).
1.34/0.58	tff(f485,plain,(
1.34/0.58	  spl4_8 | spl4_12),
1.34/0.58	  inference(avatar_split_clause,[],[f370,f483,f303])).
1.34/0.58	tff(f486,plain,(
1.34/0.58	  ($false = $true) | ~spl4_8),
1.34/0.58	  inference(backward_demodulation,[],[f304,f25])).
1.34/0.58	tff(f519,plain,(
1.34/0.58	  $false | ~spl4_8),
1.34/0.58	  inference(trivial_inequality_removal,[],[f486])).
1.34/0.58	tff(f520,plain,(
1.34/0.58	  ~spl4_8),
1.34/0.58	  inference(avatar_contradiction_clause,[],[f519])).
1.34/0.58	tff(f526,plain,(
1.34/0.58	  ($false = $true) | ~spl4_12),
1.34/0.58	  inference(backward_demodulation,[],[f484,f25])).
1.34/0.58	tff(f532,plain,(
1.34/0.58	  $false | ~spl4_12),
1.34/0.58	  inference(trivial_inequality_removal,[],[f526])).
1.34/0.58	tff(f533,plain,(
1.34/0.58	  ~spl4_12),
1.34/0.58	  inference(avatar_contradiction_clause,[],[f532])).
1.34/0.58	tff(f534,plain,(
1.34/0.58	  $false),
1.34/0.58	  inference(avatar_sat_refutation,[],[f485,f520,f533])).
1.34/0.58	% SZS output end Proof for theBenchmark
1.34/0.58	% (17034)------------------------------
1.34/0.58	% (17034)Version: Vampire 4.5.0 (commit 7ae30c7f on 2020-06-30 15:57:20 +0100)
1.34/0.58	% (17034)Termination reason: Refutation
1.34/0.58	
1.34/0.58	% (17034)Memory used [KB]: 10618
1.34/0.58	% (17034)Time elapsed: 0.154 s
1.34/0.58	% (17034)------------------------------
1.34/0.58	% (17034)------------------------------
1.34/0.58	% (17021)Success in time 0.214 s
1.34/0.58	EOF