0.07/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.07/0.13	% Command    : run_vampire %s %d
0.13/0.34	% Computer   : n021.cluster.edu
0.13/0.34	% Model      : x86_64 x86_64
0.13/0.34	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.34	% Memory     : 8042.1875MB
0.13/0.34	% OS         : Linux 3.10.0-693.el7.x86_64
0.13/0.35	% CPULimit   : 960
0.13/0.35	% WCLimit    : 120
0.13/0.35	% DateTime   : Thu Jul  2 06:46:52 EDT 2020
0.13/0.35	% CPUTime    : 
0.20/0.40	% (22595)lrs+1011_8_add=large:csup=on:inj=on:chr=on:foolp=on:cnfonf=eager:afp=100000:afq=1.1:er=filter:gsp=input_only:gs=on:gsem=on:lma=on:nm=6:nwc=1:stl=30:sd=2:ss=axioms:st=1.5:sos=on_3 on theBenchmark
0.20/0.40	% (22597)lrs+1010_8_add=off:afp=100000:csup=on:inj=on:chr=on:foolp=on:cnfonf=eager:afq=1.0:amm=off:anc=none:irw=on:nm=16:newcnf=on:nwc=1.1:nicw=on:stl=30:sp=reverse_arity:urr=on_13 on theBenchmark
0.20/0.40	% (22602)dis+1_2:3_acc=on:add=large:csup=on:inj=on:chr=on:foolp=on:cnfonf=eager:afp=40000:afq=2.0:amm=sco:anc=none:er=filter:fsr=off:gsp=input_only:gs=on:gsem=off:nm=64:newcnf=on:nwc=1_3 on theBenchmark
0.20/0.40	% (22598)ott+1002_8:1_add=off:csup=on:inj=on:chr=on:foolp=on:cnfonf=eager:afr=on:afp=100000:afq=1.1:amm=off:anc=none:bd=off:bs=unit_only:fsr=off:gs=on:gsem=off:nm=32:nwc=10:sp=occurrence:urr=on:updr=off_14 on theBenchmark
0.20/0.40	% (22601)dis+1010_3:2_av=off:csup=on:inj=on:chr=on:foolp=on:cnfonf=eager:gsp=input_only:nm=2:nwc=1:sp=reverse_arity:urr=ec_only_29 on theBenchmark
0.20/0.41	% (22596)dis+10_128_acc=on:add=off:csup=on:inj=on:chr=on:foolp=on:cnfonf=eager:afp=4000:afq=1.4:amm=off:bd=preordered:cond=on:fsr=off:fde=unused:gs=on:gsem=on:irw=on:lma=on:nm=64:nwc=1.2:nicw=on:sos=on:sp=occurrence:updr=off:uhcvi=on_2 on theBenchmark
0.20/0.41	% (22615)dis+10_4_av=off:bsr=on:csup=on:inj=on:chr=on:foolp=on:cnfonf=eager:cond=fast:er=filter:fde=none:gsp=input_only:lcm=reverse:lma=on:nwc=4:sp=occurrence:urr=on_8 on theBenchmark
0.20/0.41	% (22607)lrs+1002_1_av=off:er=filter:csup=on:inj=on:chr=on:foolp=on:cnfonf=eager:fsr=off:gs=on:gsem=off:irw=on:lma=on:nm=4:nwc=1:stl=30:sd=3:ss=axioms:st=1.5:sos=on_1 on theBenchmark
0.20/0.41	% (22618)lrs+1010_8_add=off:afp=100000:csup=on:inj=off:foolp=on:chr=off:e2e=on:cnfonf=eager:afq=1.0:amm=off:anc=none:irw=on:nm=16:newcnf=on:nwc=1.1:nicw=on:stl=30:sp=reverse_arity:urr=on_13 on theBenchmark
0.20/0.42	% (22599)lrs+1011_5:1_acc=on:csup=on:inj=on:chr=on:foolp=on:cnfonf=eager:amm=off:anc=all_dependent:bd=off:ccuc=small_ones:fde=unused:gs=on:gsaa=full_model:gsem=off:lcm=predicate:lwlo=on:nm=6:newcnf=on:nwc=2.5:stl=30:sp=occurrence:updr=off_3 on theBenchmark
0.20/0.42	% (22600)lrs+4_3_av=off:br=off:csup=on:inj=on:chr=on:foolp=on:cnfonf=eager:nm=0:newcnf=on:nwc=1:stl=30:sp=occurrence:urr=on_32 on theBenchmark
0.20/0.42	% (22605)dis+1002_6_add=large:csup=on:inj=on:chr=on:foolp=on:cnfonf=eager:afp=40000:afq=2.0:bsr=on:cond=on:irw=on:lma=on:nm=2:nwc=2.5:nicw=on:sp=reverse_arity:updr=off_2 on theBenchmark
0.20/0.42	% (22614)lrs-11_4:1_afp=4000:csup=on:inj=on:chr=on:foolp=on:cnfonf=lazy_gen:afq=2.0:anc=none:br=off:gs=on:lwlo=on:nm=64:nwc=3:stl=30:urr=on_30 on theBenchmark
0.20/0.42	% (22611)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
0.20/0.42	% (22594)lrs-11_4:1_afp=4000:csup=on:inj=on:chr=on:foolp=on:cnfonf=eager:afq=2.0:anc=none:br=off:gs=on:lwlo=on:nm=64:nwc=3:stl=30:urr=on_2 on theBenchmark
0.20/0.42	% (22609)lrs+1010_3:2_afr=on:csup=on:inj=on:chr=on:foolp=on:cnfonf=eager:afp=100000:afq=1.1:anc=none:gsp=input_only:irw=on:lwlo=on:nm=2:newcnf=on:nwc=1.7:sac=on:sp=occurrence_300 on theBenchmark
0.20/0.42	% (22612)dis+1002_3:1_acc=model:csup=on:inj=on:chr=on:foolp=on:cnfonf=eager:afr=on:afp=40000:afq=1.1:anc=none:ccuc=first:fsr=off:gsp=input_only:irw=on:nm=16:nwc=1:sos=all_8 on theBenchmark
0.20/0.42	% (22619)lrs+1_4_afp=100000:afq=1.2:csup=on:inj=on:chr=on:foolp=on:cnfonf=eager:anc=none:bd=off:cond=on:gs=on:gsem=off:nm=64:nwc=1:sd=2:ss=axioms:st=2.0:sos=all:updr=off_300 on theBenchmark
0.20/0.42	% (22593)ott+1002_2_av=off:bd=preordered:csup=on:inj=on:chr=on:foolp=on:cnfonf=eager:irw=on:lma=on:nm=64:nwc=10:sp=reverse_arity:updr=off_2 on theBenchmark
0.20/0.42	% (22621)dis+1002_4_add=large:csup=on:inj=on:chr=on:foolp=on:cnfonf=eager:afp=40000:afq=1.0:anc=none:cond=fast:fde=none:gs=on:gsaa=full_model:lma=on:lwlo=on:nm=0:nwc=1.5:sp=reverse_arity:tha=off_300 on theBenchmark
0.20/0.43	% (22622)dis-11_3_add=off:afp=40000:csup=on:inj=on:chr=on:e2e=on:prag=on:foolp=on:cnfonf=eager:afq=1.0:fde=all:amm=sco:anc=none:gs=on:irw=on:lcm=reverse:nm=6:nwc=1:sd=4:ss=axioms:st=3.0:sos=on:sac=on_50 on theBenchmark
0.20/0.43	% (22603)dis+10_128_acc=on:add=off:add=off:afp=4000:afq=1.4:amm=off:bd=preordered:cond=on:fsr=off:fde=unused:gs=on:gsem=on:irw=on:lma=on:nm=64:nwc=1.2:nicw=on:sos=on:sp=occurrence:updr=off:uhcvi=on_40 on theBenchmark
0.20/0.43	% (22616)lrs+1002_1_add=large:csup=on:inj=on:fe=off:chr=on:foolp=on:cnfonf=eager:afr=on:afp=1000:afq=1.1:amm=sco:anc=none:er=known:fsr=off:gs=on:gsem=off:lma=on:nm=2:newcnf=on:nwc=2:stl=30:sd=1:ss=axioms:st=5.0:sp=reverse_arity:updr=off_50 on theBenchmark
0.20/0.43	% (22620)lrs-11_4:1_afp=4000:csup=on:inj=on:mXXn=1:foolp=on:e2e=on:cnfonf=eager:afq=2.0:anc=none:br=off:gs=on:lwlo=on:nm=64:nwc=3:stl=30:urr=on_186 on theBenchmark
0.20/0.44	% (22613)lrs+10_12_add=off:afp=100000:csup=on:inj=on:chr=on:foolp=on:cnfonf=eager:afq=1.4:amm=sco:anc=none:cond=on:lma=on:nm=64:nwc=1.3:stl=30:sac=on:urr=on_41 on theBenchmark
0.20/0.44	% (22606)lrs+1010_3_av=off:fsr=off:csup=on:inj=on:chr=on:foolp=on:cnfonf=eager:gs=on:gsem=off:nm=2:newcnf=on:nwc=2:stl=30:sp=reverse_arity:urr=on:updr=off_9 on theBenchmark
0.20/0.44	% (22604)dis-11_3_add=off:afp=40000:csup=on:inj=on:chr=on:foolp=on:cnfonf=eager:afq=1.0:amm=sco:anc=none:gs=on:irw=on:lcm=reverse:nm=6:nwc=1:sd=4:ss=axioms:st=3.0:sos=on:sac=on_2 on theBenchmark
0.20/0.44	% (22617)lrs+1011_5_add=large:csup=on:inj=on:chr=on:foolp=on:cnfonf=eager:afp=1000:afq=1.2:anc=none:fsr=off:irw=on:lma=on:nm=64:newcnf=on:nwc=1:stl=30:sd=3:ss=axioms:st=2.0:sos=on:sac=on:sp=reverse_arity:urr=on:updr=off_130 on theBenchmark
0.20/0.44	% (22608)ott+2_2_afp=10000:afq=1.4:csup=on:inj=on:chr=on:foolp=on:cnfonf=eager:amm=off:anc=none:gsp=input_only:gs=on:gsem=off:irw=on:lcm=predicate:nm=32:nwc=1.5:sos=on:sp=reverse_arity_7 on theBenchmark
0.20/0.45	% (22610)lrs+1011_5:1_acc=on:csup=on:inj=on:e2e=on:prag=on:foolp=on:cnfonf=eager:amm=off:anc=all_dependent:bd=off:ccuc=small_ones:fde=unused:gs=on:gsaa=full_model:gsem=off:lcm=predicate:lwlo=on:nm=6:newcnf=on:nwc=2.5:stl=30:sp=occurrence:updr=off_30 on theBenchmark
0.20/0.46	% (22607)Refutation not found, incomplete strategy
0.20/0.46	% (22607)------------------------------
0.20/0.46	% (22607)Version: Vampire 4.5.0 (commit 7ae30c7f on 2020-06-30 15:57:20 +0100)
0.20/0.46	% (22607)Termination reason: Refutation not found, incomplete strategy
0.20/0.46	
0.20/0.46	% (22607)Memory used [KB]: 5500
0.20/0.46	% (22607)Time elapsed: 0.055 s
0.20/0.46	% (22607)------------------------------
0.20/0.46	% (22607)------------------------------
0.20/0.49	% (22595)Refutation not found, incomplete strategy
0.20/0.49	% (22595)------------------------------
0.20/0.49	% (22595)Version: Vampire 4.5.0 (commit 7ae30c7f on 2020-06-30 15:57:20 +0100)
0.20/0.49	% (22623)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
0.20/0.50	% (22593)Refutation found. Thanks to Tanya!
0.20/0.50	% SZS status Theorem for theBenchmark
0.20/0.50	% SZS output start Proof for theBenchmark
0.20/0.50	tff(func_def_3, type, ->: ('$tType' * '$tType') > '$tType').
0.20/0.50	tff(func_def_4, type, in: '$i' -> '$i' -> '$o').
0.20/0.50	tff(func_def_5, type, kpair: '$i' -> '$i' -> '$i').
0.20/0.50	tff(func_def_6, type, dpsetconstr: '$i' -> '$i' -> ('$i' -> '$i' -> '$o') -> '$i').
0.20/0.50	tff(func_def_8, type, vAPP: !>[X0: $ttype, X1: $ttype]:(X0 -> X1 * X0) > X1).
0.20/0.50	tff(func_def_9, type, func: '$i' -> '$i' -> '$i' -> '$o').
0.20/0.50	tff(func_def_10, type, ap: '$i' -> '$i' -> '$i' -> '$i' -> '$i').
0.20/0.50	tff(func_def_11, type, lam: '$i' -> '$i' -> ('$i' -> '$i') -> '$i').
0.20/0.50	tff(func_def_14, type, vEPSILON: !>[X0: $ttype]:(X0 -> '$o') -> X0).
0.20/0.50	tff(func_def_17, type, vIMP: '$o' -> '$o' -> '$o').
0.20/0.50	tff(func_def_18, type, vPI: !>[X0: $ttype]:(X0 -> '$o') -> '$o').
0.20/0.50	tff(func_def_19, type, bCOMB: !>[X0: $ttype, X1: $ttype, X2: $ttype]:(X1 -> X2) -> (X0 -> X1) -> X0 -> X2).
0.20/0.50	tff(func_def_20, type, cCOMB: !>[X0: $ttype, X1: $ttype, X2: $ttype]:(X0 -> X1 -> X2) -> X1 -> X0 -> X2).
0.20/0.50	tff(func_def_21, type, sCOMB: !>[X0: $ttype, X1: $ttype, X2: $ttype]:(X0 -> X1 -> X2) -> (X0 -> X1) -> X0 -> X2).
0.20/0.50	tff(func_def_22, type, vEQ: !>[X0: $ttype]:X0 -> X0 -> '$o').
0.20/0.50	tff(func_def_23, type, iCOMB: !>[X2: $ttype]:X2 -> X2).
0.20/0.50	tff(func_def_26, type, sK2: '$i' -> '$i').
0.20/0.50	tff(func_def_28, type, kCOMB: !>[X1: $ttype, X2: $ttype]:X1 -> X2 -> X1).
0.20/0.50	tff(func_def_29, type, vAND: '$o' -> '$o' -> '$o').
0.20/0.50	tff(func_def_30, type, vOR: '$o' -> '$o' -> '$o').
0.20/0.50	tff(func_def_31, type, vNOT: '$o' -> '$o').
0.20/0.50	tff(func_def_32, type, sK4: '$i' -> '$i' -> ('$i' -> '$i') -> '$i').
0.20/0.50	tff(func_def_33, type, sK5: ('$i' -> '$i') -> '$i').
0.20/0.50	tff(func_def_34, type, sK6: ('$i' -> '$i') -> '$i').
0.20/0.50	tff(f1,axiom,(
0.20/0.50	  (dpsetconstrI = ! [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 : '$i'] : X2 @ X5 @ X6))))))),
0.20/0.50	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dpsetconstrI)).
0.20/0.50	tff(f2,axiom,(
0.20/0.50	  lam = (^[X0 : '$i', X1 : '$i', X7 : '$i' -> '$i'] : dpsetconstr @ X0 @ X1 @ (^[X3 : '$i', X4 : '$i'] : X7 @ X3 = X4))),
0.20/0.50	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lam)).
0.20/0.50	tff(f3,axiom,(
0.20/0.50	  (lamp = ! [X0,X1,X7 : '$i' -> '$i'] : (! [X3] : (in @ X3 @ X0 => in @ (X7 @ X3) @ X1) => func @ X0 @ X1 @ (lam @ X0 @ X1 @ (^[X3 : '$i'] : X7 @ X3))))),
0.20/0.50	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lamp)).
0.20/0.50	tff(f4,axiom,(
0.20/0.50	  (funcGraphProp2 = ! [X0,X1,X7] : (func @ X0 @ X1 @ X7 => ! [X3] : (in @ X3 @ X0 => ! [X4] : (in @ X4 @ X1 => (in @ (kpair @ X3 @ X4) @ X7 => ap @ X0 @ X1 @ X7 @ X3 = X4)))))),
0.20/0.50	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcGraphProp2)).
0.20/0.50	tff(f5,conjecture,(
0.20/0.50	  dpsetconstrI => (lamp => (funcGraphProp2 => ! [X0,X1,X7 : '$i' -> '$i'] : (! [X3] : (in @ X3 @ X0 => in @ (X7 @ X3) @ X1) => ! [X3] : (in @ X3 @ X0 => ap @ X0 @ X1 @ (lam @ X0 @ X1 @ (^[X4 : '$i'] : X7 @ X4)) @ X3 = X7 @ X3))))),
0.20/0.50	  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',beta1)).
0.20/0.50	tff(f6,negated_conjecture,(
0.20/0.50	  ~(dpsetconstrI => (lamp => (funcGraphProp2 => ! [X0,X1,X7 : '$i' -> '$i'] : (! [X3] : (in @ X3 @ X0 => in @ (X7 @ X3) @ X1) => ! [X3] : (in @ X3 @ X0 => ap @ X0 @ X1 @ (lam @ X0 @ X1 @ (^[X4 : '$i'] : X7 @ X4)) @ X3 = X7 @ X3)))))),
0.20/0.50	  inference(negated_conjecture,[],[f5])).
0.20/0.50	tff(f7,plain,(
0.20/0.50	  ~(dpsetconstrI => (lamp => (funcGraphProp2 => ! [X0,X1,X2 : '$i' -> '$i'] : (! [X3] : (in @ X3 @ X0 => in @ (X2 @ X3) @ X1) => ! [X4] : (in @ X4 @ X0 => ap @ X0 @ X1 @ (lam @ X0 @ X1 @ (^[X5 : '$i'] : X2 @ X5)) @ X4 = X2 @ X4)))))),
0.20/0.50	  inference(rectify,[],[f6])).
0.20/0.50	tff(f8,plain,(
0.20/0.50	  ~((dpsetconstrI = $true) => ((lamp = $true) => ((funcGraphProp2 = $true) => ! [X0,X1,X2 : '$i' -> '$i'] : (! [X3] : ((in @ X3 @ X0 = $true) => (in @ (X2 @ X3) @ X1 = $true)) => ! [X4] : ((in @ X4 @ X0 = $true) => X2 @ X4 = ap @ X0 @ X1 @ (lam @ X0 @ X1 @ X2) @ X4)))))),
0.20/0.50	  inference(fool_elimination,[],[f7])).
0.20/0.50	tff(f9,plain,(
0.20/0.50	  (lamp = ! [X0,X1,X2 : '$i' -> '$i'] : (! [X3] : (in @ X3 @ X0 => in @ (X2 @ X3) @ X1) => func @ X0 @ X1 @ (lam @ X0 @ X1 @ (^[X4 : '$i'] : X2 @ X4))))),
0.20/0.50	  inference(rectify,[],[f3])).
0.20/0.50	tff(f10,plain,(
0.20/0.50	  (vPI('$i' -> '$i') @ (bCOMB @ vPI('$i') @ (bCOMB @ (bCOMB @ vPI('$i')) @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ sCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vIMP)) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i'))) @ (bCOMB @ (bCOMB @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ in))))) @ (bCOMB @ cCOMB @ (bCOMB @ in))))))) @ (bCOMB @ (sCOMB @ (bCOMB @ sCOMB @ (cCOMB @ func))) @ (cCOMB @ (bCOMB @ cCOMB @ (cCOMB @ lam))))))) = lamp)),
0.20/0.50	  inference(fool_elimination,[],[f9])).
0.20/0.50	tff(f11,plain,(
0.20/0.50	  (funcGraphProp2 = ! [X0,X1,X2] : (func @ X0 @ X1 @ X2 => ! [X3] : (in @ X3 @ X0 => ! [X4] : (in @ X4 @ X1 => (in @ (kpair @ X3 @ X4) @ X2 => ap @ X0 @ X1 @ X2 @ X3 = X4)))))),
0.20/0.50	  inference(rectify,[],[f4])).
0.20/0.51	% (22595)Termination reason: Refutation not found, incomplete strategy
0.20/0.51	
0.20/0.51	% (22595)Memory used [KB]: 9978
0.20/0.51	% (22595)Time elapsed: 0.117 s
0.20/0.51	% (22595)------------------------------
0.20/0.51	% (22595)------------------------------
0.20/0.52	tff(f12,plain,(
0.20/0.52	  (vPI('$i') @ (bCOMB @ vPI('$i') @ (bCOMB @ (bCOMB @ vPI('$i')) @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ sCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vIMP)) @ (cCOMB @ (bCOMB @ cCOMB @ (cCOMB @ func)))))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i'))) @ (bCOMB @ (bCOMB @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ in))))) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')))) @ (bCOMB @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ in)))))) @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ sCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vIMP)) @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ in) @ kpair)))))))) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vEQ('$i')))) @ (cCOMB @ (bCOMB @ cCOMB @ (cCOMB @ ap)))))))))))) = funcGraphProp2)),
0.20/0.52	  inference(fool_elimination,[],[f11])).
0.20/0.52	tff(f13,plain,(
0.20/0.52	  (dpsetconstrI = ! [X0,X1,X2 : '$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))))))),
0.20/0.52	  inference(rectify,[],[f1])).
0.20/0.52	tff(f14,plain,(
0.20/0.52	  (dpsetconstrI = vPI('$i') @ (bCOMB @ vPI('$i' -> '$i' -> '$o') @ (bCOMB @ (bCOMB @ vPI('$i')) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i'))) @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ in)))) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')))) @ (bCOMB @ (bCOMB @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ in)))))) @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ bCOMB) @ (bCOMB @ (bCOMB @ bCOMB) @ (bCOMB @ (bCOMB @ sCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vIMP)) @ (cCOMB @ iCOMB)))))) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ in) @ kpair))))) @ (cCOMB @ (bCOMB @ cCOMB @ (cCOMB @ dpsetconstr))))))))))))),
0.20/0.52	  inference(fool_elimination,[],[f13])).
0.20/0.52	tff(f15,plain,(
0.20/0.52	  lam = (^[X0 : '$i', X1 : '$i', X2 : '$i' -> '$i'] : dpsetconstr @ X0 @ X1 @ (^[X3 : '$i', X4 : '$i'] : X2 @ X3 = X4))),
0.20/0.52	  inference(rectify,[],[f2])).
0.20/0.52	tff(f16,plain,(
0.20/0.52	  cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ bCOMB) @ dpsetconstr)) @ (bCOMB @ vEQ('$i')) = lam),
0.20/0.52	  inference(fool_elimination,[],[f15])).
0.20/0.52	tff(f17,plain,(
0.20/0.52	  ((? [X0,X1,X2 : '$i' -> '$i'] : (? [X4] : (X2 @ X4 != ap @ X0 @ X1 @ (lam @ X0 @ X1 @ X2) @ X4 & (in @ X4 @ X0 = $true)) & ! [X3] : ((in @ (X2 @ X3) @ X1 = $true) | (in @ X3 @ X0 != $true))) & (funcGraphProp2 = $true)) & (lamp = $true)) & (dpsetconstrI = $true)),
0.20/0.52	  inference(ennf_transformation,[],[f8])).
0.20/0.52	tff(f18,plain,(
0.20/0.52	  ? [X0,X1,X2 : '$i' -> '$i'] : (? [X4] : (X2 @ X4 != ap @ X0 @ X1 @ (lam @ X0 @ X1 @ X2) @ X4 & (in @ X4 @ X0 = $true)) & ! [X3] : ((in @ (X2 @ X3) @ X1 = $true) | (in @ X3 @ X0 != $true))) & (funcGraphProp2 = $true) & (lamp = $true) & (dpsetconstrI = $true)),
0.20/0.52	  inference(flattening,[],[f17])).
0.20/0.52	tff(f19,plain,(
0.20/0.52	  ? [X0,X1,X2 : '$i' -> '$i'] : (? [X3] : (X2 @ X3 != ap @ X0 @ X1 @ (lam @ X0 @ X1 @ X2) @ X3 & (in @ X3 @ X0 = $true)) & ! [X4] : ((in @ (X2 @ X4) @ X1 = $true) | (in @ X4 @ X0 != $true))) & (funcGraphProp2 = $true) & (lamp = $true) & (dpsetconstrI = $true)),
0.20/0.52	  inference(rectify,[],[f18])).
0.20/0.52	tff(f20,plain,(
0.20/0.52	  ? [X0,X1,X2 : '$i' -> '$i'] : (? [X3] : (X2 @ X3 != ap @ X0 @ X1 @ (lam @ X0 @ X1 @ X2) @ X3 & (in @ X3 @ X0 = $true)) & ! [X4] : ((in @ (X2 @ X4) @ X1 = $true) | (in @ X4 @ X0 != $true))) => (? [X3] : (sK2 @ X3 != ap @ sK0 @ sK1 @ (lam @ sK0 @ sK1 @ sK2) @ X3 & (in @ X3 @ sK0 = $true)) & ! [X4] : ((in @ (sK2 @ X4) @ sK1 = $true) | (in @ X4 @ sK0 != $true)))),
0.20/0.52	  introduced(choice_axiom,[])).
0.20/0.52	tff(f21,plain,(
0.20/0.52	  ? [X3] : (sK2 @ X3 != ap @ sK0 @ sK1 @ (lam @ sK0 @ sK1 @ sK2) @ X3 & (in @ X3 @ sK0 = $true)) => (sK2 @ sK3 != ap @ sK0 @ sK1 @ (lam @ sK0 @ sK1 @ sK2) @ sK3 & (in @ sK3 @ sK0 = $true))),
0.20/0.52	  introduced(choice_axiom,[])).
0.20/0.52	tff(f22,plain,(
0.20/0.52	  ((sK2 @ sK3 != ap @ sK0 @ sK1 @ (lam @ sK0 @ sK1 @ sK2) @ sK3 & (in @ sK3 @ sK0 = $true)) & ! [X4] : ((in @ (sK2 @ X4) @ sK1 = $true) | (in @ X4 @ sK0 != $true))) & (funcGraphProp2 = $true) & (lamp = $true) & (dpsetconstrI = $true)),
0.20/0.52	  inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f19,f21,f20])).
0.20/0.52	tff(f23,plain,(
0.20/0.52	  (dpsetconstrI = $true)),
0.20/0.52	  inference(cnf_transformation,[],[f22])).
0.20/0.52	tff(f24,plain,(
0.20/0.52	  (lamp = $true)),
0.20/0.52	  inference(cnf_transformation,[],[f22])).
0.20/0.52	tff(f25,plain,(
0.20/0.52	  (funcGraphProp2 = $true)),
0.20/0.52	  inference(cnf_transformation,[],[f22])).
0.20/0.52	tff(f26,plain,(
0.20/0.52	  ( ! [X4] : ((in @ (sK2 @ X4) @ sK1 = $true) | (in @ X4 @ sK0 != $true)) )),
0.20/0.52	  inference(cnf_transformation,[],[f22])).
0.20/0.52	tff(f27,plain,(
0.20/0.52	  (in @ sK3 @ sK0 = $true)),
0.20/0.52	  inference(cnf_transformation,[],[f22])).
0.20/0.52	tff(f28,plain,(
0.20/0.52	  sK2 @ sK3 != ap @ sK0 @ sK1 @ (lam @ sK0 @ sK1 @ sK2) @ sK3),
0.20/0.52	  inference(cnf_transformation,[],[f22])).
0.20/0.52	tff(f29,plain,(
0.20/0.52	  (vPI('$i' -> '$i') @ (bCOMB @ vPI('$i') @ (bCOMB @ (bCOMB @ vPI('$i')) @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ sCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vIMP)) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i'))) @ (bCOMB @ (bCOMB @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ in))))) @ (bCOMB @ cCOMB @ (bCOMB @ in))))))) @ (bCOMB @ (sCOMB @ (bCOMB @ sCOMB @ (cCOMB @ func))) @ (cCOMB @ (bCOMB @ cCOMB @ (cCOMB @ lam))))))) = lamp)),
0.20/0.52	  inference(cnf_transformation,[],[f10])).
0.20/0.52	tff(f30,plain,(
0.20/0.52	  (vPI('$i') @ (bCOMB @ vPI('$i') @ (bCOMB @ (bCOMB @ vPI('$i')) @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ sCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vIMP)) @ (cCOMB @ (bCOMB @ cCOMB @ (cCOMB @ func)))))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i'))) @ (bCOMB @ (bCOMB @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ in))))) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')))) @ (bCOMB @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ in)))))) @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ sCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vIMP)) @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ in) @ kpair)))))))) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vEQ('$i')))) @ (cCOMB @ (bCOMB @ cCOMB @ (cCOMB @ ap)))))))))))) = funcGraphProp2)),
0.20/0.52	  inference(cnf_transformation,[],[f12])).
0.20/0.52	tff(f31,plain,(
0.20/0.52	  (dpsetconstrI = vPI('$i') @ (bCOMB @ vPI('$i' -> '$i' -> '$o') @ (bCOMB @ (bCOMB @ vPI('$i')) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i'))) @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ in)))) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')))) @ (bCOMB @ (bCOMB @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ in)))))) @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ bCOMB) @ (bCOMB @ (bCOMB @ bCOMB) @ (bCOMB @ (bCOMB @ sCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vIMP)) @ (cCOMB @ iCOMB)))))) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ in) @ kpair))))) @ (cCOMB @ (bCOMB @ cCOMB @ (cCOMB @ dpsetconstr))))))))))))),
0.20/0.52	  inference(cnf_transformation,[],[f14])).
0.20/0.52	tff(f32,plain,(
0.20/0.52	  cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ bCOMB) @ dpsetconstr)) @ (bCOMB @ vEQ('$i')) = lam),
0.20/0.52	  inference(cnf_transformation,[],[f16])).
0.20/0.52	tff(f33,plain,(
0.20/0.52	  sK2 @ sK3 != ap @ sK0 @ sK1 @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ bCOMB) @ dpsetconstr)) @ (bCOMB @ vEQ('$i')) @ sK0 @ sK1 @ sK2) @ sK3),
0.20/0.52	  inference(definition_unfolding,[],[f28,f32])).
0.20/0.52	tff(f34,plain,(
0.20/0.52	  (vPI('$i' -> '$i') @ (bCOMB @ vPI('$i') @ (bCOMB @ (bCOMB @ vPI('$i')) @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ sCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vIMP)) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i'))) @ (bCOMB @ (bCOMB @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ in))))) @ (bCOMB @ cCOMB @ (bCOMB @ in))))))) @ (bCOMB @ (sCOMB @ (bCOMB @ sCOMB @ (cCOMB @ func))) @ (cCOMB @ (bCOMB @ cCOMB @ (cCOMB @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ bCOMB) @ dpsetconstr)) @ (bCOMB @ vEQ('$i')))))))))) = $true)),
0.20/0.52	  inference(definition_unfolding,[],[f29,f32,f24])).
0.20/0.52	tff(f35,plain,(
0.20/0.52	  (vPI('$i') @ (bCOMB @ vPI('$i') @ (bCOMB @ (bCOMB @ vPI('$i')) @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ sCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vIMP)) @ (cCOMB @ (bCOMB @ cCOMB @ (cCOMB @ func)))))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i'))) @ (bCOMB @ (bCOMB @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ in))))) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')))) @ (bCOMB @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ in)))))) @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ sCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vIMP)) @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ in) @ kpair)))))))) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vEQ('$i')))) @ (cCOMB @ (bCOMB @ cCOMB @ (cCOMB @ ap)))))))))))) = $true)),
0.20/0.52	  inference(definition_unfolding,[],[f30,f25])).
0.20/0.52	tff(f36,plain,(
0.20/0.52	  (vPI('$i') @ (bCOMB @ vPI('$i' -> '$i' -> '$o') @ (bCOMB @ (bCOMB @ vPI('$i')) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i'))) @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ in)))) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')))) @ (bCOMB @ (bCOMB @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ in)))))) @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ bCOMB) @ (bCOMB @ (bCOMB @ bCOMB) @ (bCOMB @ (bCOMB @ sCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vIMP)) @ (cCOMB @ iCOMB)))))) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ in) @ kpair))))) @ (cCOMB @ (bCOMB @ cCOMB @ (cCOMB @ dpsetconstr))))))))))) = $true)),
0.20/0.52	  inference(definition_unfolding,[],[f31,f23])).
0.20/0.52	tff(f37,plain,(
0.20/0.52	  ( ! [X1] : ((bCOMB @ vPI('$i' -> '$i' -> '$o') @ (bCOMB @ (bCOMB @ vPI('$i')) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i'))) @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ in)))) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')))) @ (bCOMB @ (bCOMB @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ in)))))) @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ bCOMB) @ (bCOMB @ (bCOMB @ bCOMB) @ (bCOMB @ (bCOMB @ sCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vIMP)) @ (cCOMB @ iCOMB)))))) @ (cCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ in) @ kpair))))) @ (cCOMB @ (bCOMB @ cCOMB @ (cCOMB @ dpsetconstr)))))))))) @ X1 = $true)) )),
0.20/0.52	  inference(pi_clausification,[],[f36])).
0.20/0.52	tff(f38,plain,(
0.20/0.52	  ( ! [X1] : ((vPI('$i' -> '$i' -> '$o') @ (bCOMB @ vPI('$i') @ (bCOMB @ (bCOMB @ vPI('$i')) @ (bCOMB @ (bCOMB @ (sCOMB @ (bCOMB @ vIMP @ (in @ X1)))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i'))) @ (bCOMB @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ in))))) @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ iCOMB @ X1))))) @ (bCOMB @ (bCOMB @ (bCOMB @ (cCOMB @ (bCOMB @ in @ (kpair @ X1))))) @ (cCOMB @ (bCOMB @ cCOMB @ (cCOMB @ dpsetconstr)))))))))) = $true)) )),
0.20/0.52	  inference(combinator_demodulation,[],[f37])).
0.20/0.52	tff(f39,plain,(
0.20/0.52	  ( ! [X2:'$i' -> '$i' -> '$o',X1] : ((bCOMB @ vPI('$i') @ (bCOMB @ (bCOMB @ vPI('$i')) @ (bCOMB @ (bCOMB @ (sCOMB @ (bCOMB @ vIMP @ (in @ X1)))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i'))) @ (bCOMB @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ in))))) @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ iCOMB @ X1))))) @ (bCOMB @ (bCOMB @ (bCOMB @ (cCOMB @ (bCOMB @ in @ (kpair @ X1))))) @ (cCOMB @ (bCOMB @ cCOMB @ (cCOMB @ dpsetconstr))))))))) @ X2 = $true)) )),
0.20/0.52	  inference(pi_clausification,[],[f38])).
0.20/0.52	tff(f40,plain,(
0.20/0.52	  ( ! [X2:'$i' -> '$i' -> '$o',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 @ (sCOMB @ (bCOMB @ vIMP @ (X2 @ X1)))) @ (bCOMB @ (bCOMB @ (cCOMB @ (bCOMB @ in @ (kpair @ X1)))) @ (cCOMB @ (bCOMB @ cCOMB @ (cCOMB @ dpsetconstr)) @ X2))))))) = $true)) )),
0.20/0.52	  inference(combinator_demodulation,[],[f39])).
0.20/0.52	tff(f41,plain,(
0.20/0.52	  ( ! [X2:'$i' -> '$i' -> '$o',X3,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 @ (sCOMB @ (bCOMB @ vIMP @ (X2 @ X1)))) @ (bCOMB @ (bCOMB @ (cCOMB @ (bCOMB @ in @ (kpair @ X1)))) @ (cCOMB @ (bCOMB @ cCOMB @ (cCOMB @ dpsetconstr)) @ X2)))))) @ X3 = $true)) )),
0.20/0.52	  inference(pi_clausification,[],[f40])).
0.20/0.52	tff(f42,plain,(
0.20/0.52	  ( ! [X2:'$i' -> '$i' -> '$o',X3,X1] : ((vPI('$i') @ (sCOMB @ (bCOMB @ vIMP @ (in @ X1)) @ (bCOMB @ vPI('$i') @ (bCOMB @ (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ in @ X3))) @ (bCOMB @ (sCOMB @ (bCOMB @ vIMP @ (X2 @ X1))) @ (bCOMB @ (cCOMB @ (bCOMB @ in @ (kpair @ X1))) @ (cCOMB @ (cCOMB @ dpsetconstr @ X3) @ X2)))))) = $true)) )),
0.20/0.52	  inference(combinator_demodulation,[],[f41])).
0.20/0.52	tff(f43,plain,(
0.20/0.52	  ( ! [X4,X2:'$i' -> '$i' -> '$o',X3,X1] : ((sCOMB @ (bCOMB @ vIMP @ (in @ X1)) @ (bCOMB @ vPI('$i') @ (bCOMB @ (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ in @ X3))) @ (bCOMB @ (sCOMB @ (bCOMB @ vIMP @ (X2 @ X1))) @ (bCOMB @ (cCOMB @ (bCOMB @ in @ (kpair @ X1))) @ (cCOMB @ (cCOMB @ dpsetconstr @ X3) @ X2))))) @ X4 = $true)) )),
0.20/0.52	  inference(pi_clausification,[],[f42])).
0.20/0.52	tff(f44,plain,(
0.20/0.52	  ( ! [X4,X2:'$i' -> '$i' -> '$o',X3,X1] : ((vIMP @ (in @ X1 @ X4) @ (vPI('$i') @ (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ in @ X3)) @ (sCOMB @ (bCOMB @ vIMP @ (X2 @ X1)) @ (cCOMB @ (bCOMB @ in @ (kpair @ X1)) @ (dpsetconstr @ X4 @ X3 @ X2))))) = $true)) )),
0.20/0.52	  inference(combinator_demodulation,[],[f43])).
0.20/0.52	tff(f45,plain,(
0.20/0.52	  ( ! [X4,X2:'$i' -> '$i' -> '$o',X3,X1] : ((in @ X1 @ X4 = $false) | (vPI('$i') @ (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ in @ X3)) @ (sCOMB @ (bCOMB @ vIMP @ (X2 @ X1)) @ (cCOMB @ (bCOMB @ in @ (kpair @ X1)) @ (dpsetconstr @ X4 @ X3 @ X2)))) = $true)) )),
0.20/0.52	  inference(binary_proxy_clausification,[],[f44])).
0.20/0.52	tff(f46,plain,(
0.20/0.52	  ( ! [X4,X2:'$i' -> '$i' -> '$o',X5,X3,X1] : ((in @ X1 @ X4 = $false) | (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ in @ X3)) @ (sCOMB @ (bCOMB @ vIMP @ (X2 @ X1)) @ (cCOMB @ (bCOMB @ in @ (kpair @ X1)) @ (dpsetconstr @ X4 @ X3 @ X2))) @ X5 = $true)) )),
0.20/0.52	  inference(pi_clausification,[],[f45])).
0.20/0.52	tff(f47,plain,(
0.20/0.52	  ( ! [X4,X2:'$i' -> '$i' -> '$o',X5,X3,X1] : ((in @ X1 @ X4 = $false) | (vIMP @ (in @ X5 @ X3) @ (vIMP @ (X2 @ X1 @ X5) @ (in @ (kpair @ X1 @ X5) @ (dpsetconstr @ X4 @ X3 @ X2))) = $true)) )),
0.20/0.52	  inference(combinator_demodulation,[],[f46])).
0.20/0.52	tff(f48,plain,(
0.20/0.52	  ( ! [X4,X2:'$i' -> '$i' -> '$o',X5,X3,X1] : ((in @ X1 @ X4 = $false) | (in @ X5 @ X3 = $false) | (vIMP @ (X2 @ X1 @ X5) @ (in @ (kpair @ X1 @ X5) @ (dpsetconstr @ X4 @ X3 @ X2)) = $true)) )),
0.20/0.52	  inference(binary_proxy_clausification,[],[f47])).
0.20/0.52	tff(f49,plain,(
0.20/0.52	  ( ! [X4,X2:'$i' -> '$i' -> '$o',X5,X3,X1] : ((in @ (kpair @ X1 @ X5) @ (dpsetconstr @ X4 @ X3 @ X2) = $true) | (in @ X5 @ X3 = $false) | (X2 @ X1 @ X5 = $false) | (in @ X1 @ X4 = $false)) )),
0.20/0.52	  inference(binary_proxy_clausification,[],[f48])).
0.20/0.52	tff(f50,plain,(
0.20/0.52	  ( ! [X1] : ((bCOMB @ vPI('$i') @ (bCOMB @ (bCOMB @ vPI('$i')) @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ sCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vIMP)) @ (cCOMB @ (bCOMB @ cCOMB @ (cCOMB @ func)))))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i'))) @ (bCOMB @ (bCOMB @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ in))))) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i')))) @ (bCOMB @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ in)))))) @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ sCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vIMP)) @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ in) @ kpair)))))))) @ (bCOMB @ (bCOMB @ (bCOMB @ (bCOMB @ vEQ('$i')))) @ (cCOMB @ (bCOMB @ cCOMB @ (cCOMB @ ap))))))))))) @ X1 = $true)) )),
0.20/0.52	  inference(pi_clausification,[],[f35])).
0.20/0.52	tff(f51,plain,(
0.20/0.52	  ( ! [X1] : ((vPI('$i') @ (bCOMB @ vPI('$i') @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ (bCOMB @ cCOMB @ (cCOMB @ func)) @ X1))) @ (bCOMB @ (bCOMB @ vPI('$i')) @ (bCOMB @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ in)))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i'))) @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ in))))) @ (bCOMB @ (bCOMB @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ in) @ kpair)) @ X1))))) @ (bCOMB @ (bCOMB @ (bCOMB @ vEQ('$i'))) @ (cCOMB @ (bCOMB @ cCOMB @ (cCOMB @ ap)) @ X1))))))))) = $true)) )),
0.20/0.52	  inference(combinator_demodulation,[],[f50])).
0.20/0.52	tff(f52,plain,(
0.20/0.52	  ( ! [X2,X1] : ((bCOMB @ vPI('$i') @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ (bCOMB @ cCOMB @ (cCOMB @ func)) @ X1))) @ (bCOMB @ (bCOMB @ vPI('$i')) @ (bCOMB @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ in)))) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i'))) @ (sCOMB @ (bCOMB @ bCOMB @ (bCOMB @ bCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ in))))) @ (bCOMB @ (bCOMB @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ in) @ kpair)) @ X1))))) @ (bCOMB @ (bCOMB @ (bCOMB @ vEQ('$i'))) @ (cCOMB @ (bCOMB @ cCOMB @ (cCOMB @ ap)) @ X1)))))))) @ X2 = $true)) )),
0.20/0.52	  inference(pi_clausification,[],[f51])).
0.20/0.52	tff(f53,plain,(
0.20/0.52	  ( ! [X2,X1] : ((vPI('$i') @ (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ (cCOMB @ func @ X2) @ X1)) @ (bCOMB @ vPI('$i') @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ in))) @ (bCOMB @ (bCOMB @ vPI('$i')) @ (bCOMB @ (bCOMB @ (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ in @ X2)))) @ (bCOMB @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ in) @ kpair)) @ X1)))) @ (bCOMB @ (bCOMB @ vEQ('$i')) @ (cCOMB @ (cCOMB @ ap @ X2) @ X1)))))))) = $true)) )),
0.20/0.52	  inference(combinator_demodulation,[],[f52])).
0.20/0.53	tff(f54,plain,(
0.20/0.53	  ( ! [X2,X3,X1] : ((sCOMB @ (bCOMB @ vIMP @ (cCOMB @ (cCOMB @ func @ X2) @ X1)) @ (bCOMB @ vPI('$i') @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ in))) @ (bCOMB @ (bCOMB @ vPI('$i')) @ (bCOMB @ (bCOMB @ (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ in @ X2)))) @ (bCOMB @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ in) @ kpair)) @ X1)))) @ (bCOMB @ (bCOMB @ vEQ('$i')) @ (cCOMB @ (cCOMB @ ap @ X2) @ X1))))))) @ X3 = $true)) )),
0.20/0.53	  inference(pi_clausification,[],[f53])).
0.20/0.53	tff(f55,plain,(
0.20/0.53	  ( ! [X2,X3,X1] : ((vIMP @ (func @ X3 @ X2 @ X1) @ (vPI('$i') @ (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ in @ X3)) @ (bCOMB @ vPI('$i') @ (bCOMB @ (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ in @ X2))) @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ in) @ kpair)) @ X1))) @ (bCOMB @ vEQ('$i') @ (ap @ X3 @ X2 @ X1))))))) = $true)) )),
0.20/0.53	  inference(combinator_demodulation,[],[f54])).
0.20/0.53	tff(f56,plain,(
0.20/0.53	  ( ! [X2,X3,X1] : ((func @ X3 @ X2 @ X1 = $false) | (vPI('$i') @ (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ in @ X3)) @ (bCOMB @ vPI('$i') @ (bCOMB @ (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ in @ X2))) @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ in) @ kpair)) @ X1))) @ (bCOMB @ vEQ('$i') @ (ap @ X3 @ X2 @ X1)))))) = $true)) )),
0.20/0.53	  inference(binary_proxy_clausification,[],[f55])).
0.20/0.53	tff(f57,plain,(
0.20/0.53	  ( ! [X4,X2,X3,X1] : ((func @ X3 @ X2 @ X1 = $false) | (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ in @ X3)) @ (bCOMB @ vPI('$i') @ (bCOMB @ (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ in @ X2))) @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ in) @ kpair)) @ X1))) @ (bCOMB @ vEQ('$i') @ (ap @ X3 @ X2 @ X1))))) @ X4 = $true)) )),
0.20/0.53	  inference(pi_clausification,[],[f56])).
0.20/0.53	tff(f58,plain,(
0.20/0.53	  ( ! [X4,X2,X3,X1] : ((func @ X3 @ X2 @ X1 = $false) | (vIMP @ (in @ X4 @ X3) @ (vPI('$i') @ (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ in @ X2)) @ (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ (bCOMB @ in @ (kpair @ X4)) @ X1)) @ (vEQ('$i') @ (ap @ X3 @ X2 @ X1 @ X4))))) = $true)) )),
0.20/0.53	  inference(combinator_demodulation,[],[f57])).
0.20/0.53	tff(f59,plain,(
0.20/0.53	  ( ! [X4,X2,X3,X1] : ((func @ X3 @ X2 @ X1 = $false) | (in @ X4 @ X3 = $false) | (vPI('$i') @ (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ in @ X2)) @ (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ (bCOMB @ in @ (kpair @ X4)) @ X1)) @ (vEQ('$i') @ (ap @ X3 @ X2 @ X1 @ X4)))) = $true)) )),
0.20/0.53	  inference(binary_proxy_clausification,[],[f58])).
0.20/0.53	tff(f60,plain,(
0.20/0.53	  ( ! [X4,X2,X5,X3,X1] : ((func @ X3 @ X2 @ X1 = $false) | (in @ X4 @ X3 = $false) | (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ in @ X2)) @ (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ (bCOMB @ in @ (kpair @ X4)) @ X1)) @ (vEQ('$i') @ (ap @ X3 @ X2 @ X1 @ X4))) @ X5 = $true)) )),
0.20/0.53	  inference(pi_clausification,[],[f59])).
0.20/0.53	tff(f61,plain,(
0.20/0.53	  ( ! [X4,X2,X5,X3,X1] : ((func @ X3 @ X2 @ X1 = $false) | (in @ X4 @ X3 = $false) | (vIMP @ (in @ X5 @ X2) @ (vIMP @ (in @ (kpair @ X4 @ X5) @ X1) @ (vEQ('$i') @ (ap @ X3 @ X2 @ X1 @ X4) @ X5)) = $true)) )),
0.20/0.53	  inference(combinator_demodulation,[],[f60])).
0.20/0.53	tff(f62,plain,(
0.20/0.53	  ( ! [X4,X2,X5,X3,X1] : ((func @ X3 @ X2 @ X1 = $false) | (in @ X4 @ X3 = $false) | (in @ X5 @ X2 = $false) | (vIMP @ (in @ (kpair @ X4 @ X5) @ X1) @ (vEQ('$i') @ (ap @ X3 @ X2 @ X1 @ X4) @ X5) = $true)) )),
0.20/0.53	  inference(binary_proxy_clausification,[],[f61])).
0.20/0.53	tff(f63,plain,(
0.20/0.53	  ( ! [X4,X2,X5,X3,X1] : ((func @ X3 @ X2 @ X1 = $false) | (in @ X4 @ X3 = $false) | (in @ X5 @ X2 = $false) | (in @ (kpair @ X4 @ X5) @ X1 = $false) | (vEQ('$i') @ (ap @ X3 @ X2 @ X1 @ X4) @ X5 = $true)) )),
0.20/0.53	  inference(binary_proxy_clausification,[],[f62])).
0.20/0.53	tff(f64,plain,(
0.20/0.53	  ( ! [X4,X2,X5,X3,X1] : (ap @ X3 @ X2 @ X1 @ X4 = X5 | (in @ X4 @ X3 = $false) | (in @ X5 @ X2 = $false) | (in @ (kpair @ X4 @ X5) @ X1 = $false) | (func @ X3 @ X2 @ X1 = $false)) )),
0.20/0.53	  inference(equality_proxy_clausification,[],[f63])).
0.20/0.53	tff(f65,plain,(
0.20/0.53	  ( ! [X1:'$i' -> '$i'] : ((bCOMB @ vPI('$i') @ (bCOMB @ (bCOMB @ vPI('$i')) @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ sCOMB) @ (bCOMB @ (bCOMB @ (bCOMB @ vIMP)) @ (bCOMB @ (bCOMB @ (bCOMB @ vPI('$i'))) @ (bCOMB @ (bCOMB @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ in))))) @ (bCOMB @ cCOMB @ (bCOMB @ in))))))) @ (bCOMB @ (sCOMB @ (bCOMB @ sCOMB @ (cCOMB @ func))) @ (cCOMB @ (bCOMB @ cCOMB @ (cCOMB @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ bCOMB) @ dpsetconstr)) @ (bCOMB @ vEQ('$i'))))))))) @ X1 = $true)) )),
0.20/0.53	  inference(pi_clausification,[],[f34])).
0.20/0.53	tff(f66,plain,(
0.20/0.53	  ( ! [X1:'$i' -> '$i'] : ((vPI('$i') @ (bCOMB @ vPI('$i') @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (bCOMB @ (bCOMB @ vPI('$i')) @ (bCOMB @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ in)))) @ (cCOMB @ (bCOMB @ in @ X1)))))) @ (sCOMB @ (bCOMB @ sCOMB @ (cCOMB @ func)) @ (cCOMB @ (bCOMB @ cCOMB @ (cCOMB @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ bCOMB) @ dpsetconstr)) @ (bCOMB @ vEQ('$i'))))) @ X1)))) = $true)) )),
0.20/0.53	  inference(combinator_demodulation,[],[f65])).
0.20/0.53	tff(f67,plain,(
0.20/0.53	  ( ! [X2,X1:'$i' -> '$i'] : ((bCOMB @ vPI('$i') @ (sCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (bCOMB @ (bCOMB @ vPI('$i')) @ (bCOMB @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ in)))) @ (cCOMB @ (bCOMB @ in @ X1)))))) @ (sCOMB @ (bCOMB @ sCOMB @ (cCOMB @ func)) @ (cCOMB @ (bCOMB @ cCOMB @ (cCOMB @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ bCOMB) @ dpsetconstr)) @ (bCOMB @ vEQ('$i'))))) @ X1))) @ X2 = $true)) )),
0.20/0.53	  inference(pi_clausification,[],[f66])).
0.20/0.53	tff(f68,plain,(
0.20/0.53	  ( ! [X2,X1:'$i' -> '$i'] : ((vPI('$i') @ (sCOMB @ (bCOMB @ vIMP @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ in))) @ (cCOMB @ (bCOMB @ in @ X1) @ X2)))) @ (sCOMB @ (cCOMB @ func @ X2) @ (cCOMB @ (cCOMB @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ bCOMB) @ dpsetconstr)) @ (bCOMB @ vEQ('$i'))) @ X2) @ X1))) = $true)) )),
0.20/0.53	  inference(combinator_demodulation,[],[f67])).
0.20/0.53	tff(f69,plain,(
0.20/0.53	  ( ! [X2,X3,X1:'$i' -> '$i'] : ((sCOMB @ (bCOMB @ vIMP @ (bCOMB @ vPI('$i') @ (cCOMB @ (bCOMB @ sCOMB @ (bCOMB @ (bCOMB @ vIMP) @ (cCOMB @ in))) @ (cCOMB @ (bCOMB @ in @ X1) @ X2)))) @ (sCOMB @ (cCOMB @ func @ X2) @ (cCOMB @ (cCOMB @ (cCOMB @ (bCOMB @ cCOMB @ (bCOMB @ (bCOMB @ bCOMB) @ dpsetconstr)) @ (bCOMB @ vEQ('$i'))) @ X2) @ X1)) @ X3 = $true)) )),
0.20/0.53	  inference(pi_clausification,[],[f68])).
0.20/0.53	tff(f70,plain,(
0.20/0.53	  ( ! [X2,X3,X1:'$i' -> '$i'] : ((vIMP @ (vPI('$i') @ (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ in @ X3)) @ (cCOMB @ (bCOMB @ in @ X1) @ X2))) @ (func @ X3 @ X2 @ (dpsetconstr @ X3 @ X2 @ (bCOMB @ vEQ('$i') @ X1))) = $true)) )),
0.20/0.53	  inference(combinator_demodulation,[],[f69])).
0.20/0.53	tff(f71,plain,(
0.20/0.53	  ( ! [X2,X3,X1:'$i' -> '$i'] : ((vPI('$i') @ (sCOMB @ (bCOMB @ vIMP @ (cCOMB @ in @ X3)) @ (cCOMB @ (bCOMB @ in @ X1) @ X2)) = $false) | (func @ X3 @ X2 @ (dpsetconstr @ X3 @ X2 @ (bCOMB @ vEQ('$i') @ X1)) = $true)) )),
0.20/0.53	  inference(binary_proxy_clausification,[],[f70])).
0.20/0.53	tff(f72,plain,(
0.20/0.53	  ( ! [X2,X3,X1:'$i' -> '$i'] : ((sCOMB @ (bCOMB @ vIMP @ (cCOMB @ in @ X3)) @ (cCOMB @ (bCOMB @ in @ X1) @ X2) @ (sK4 @ X3 @ X2 @ X1) = $false) | (func @ X3 @ X2 @ (dpsetconstr @ X3 @ X2 @ (bCOMB @ vEQ('$i') @ X1)) = $true)) )),
0.20/0.53	  inference(sigma_clausification,[],[f71])).
0.20/0.53	tff(f73,plain,(
0.20/0.53	  ( ! [X2,X3,X1:'$i' -> '$i'] : ((vIMP @ (in @ (sK4 @ X3 @ X2 @ X1) @ X3) @ (in @ (X1 @ (sK4 @ X3 @ X2 @ X1)) @ X2) = $false) | (func @ X3 @ X2 @ (dpsetconstr @ X3 @ X2 @ (bCOMB @ vEQ('$i') @ X1)) = $true)) )),
0.20/0.53	  inference(combinator_demodulation,[],[f72])).
0.20/0.53	tff(f74,plain,(
0.20/0.53	  ( ! [X2,X3,X1:'$i' -> '$i'] : ((func @ X3 @ X2 @ (dpsetconstr @ X3 @ X2 @ (bCOMB @ vEQ('$i') @ X1)) = $true) | (in @ (sK4 @ X3 @ X2 @ X1) @ X3 = $true)) )),
0.20/0.53	  inference(binary_proxy_clausification,[],[f73])).
0.20/0.53	tff(f75,plain,(
0.20/0.53	  ( ! [X2,X3,X1:'$i' -> '$i'] : ((func @ X3 @ X2 @ (dpsetconstr @ X3 @ X2 @ (bCOMB @ vEQ('$i') @ X1)) = $true) | (in @ (X1 @ (sK4 @ X3 @ X2 @ X1)) @ X2 = $false)) )),
0.20/0.53	  inference(binary_proxy_clausification,[],[f73])).
0.20/0.53	tff(f76,plain,(
0.20/0.53	  sK2 @ sK3 != ap @ sK0 @ sK1 @ (dpsetconstr @ sK0 @ sK1 @ (bCOMB @ vEQ('$i') @ sK2)) @ sK3),
0.20/0.53	  inference(combinator_demodulation,[],[f33])).
0.20/0.53	tff(f81,plain,(
0.20/0.53	  ( ! [X0] : (sK2 @ sK3 != X0 | (in @ sK3 @ sK0 = $false) | (in @ X0 @ sK1 = $false) | (in @ (kpair @ sK3 @ X0) @ (dpsetconstr @ sK0 @ sK1 @ (bCOMB @ vEQ('$i') @ sK2)) = $false) | (func @ sK0 @ sK1 @ (dpsetconstr @ sK0 @ sK1 @ (bCOMB @ vEQ('$i') @ sK2)) = $false)) )),
0.20/0.53	  inference(superposition,[],[f76,f64])).
0.20/0.53	tff(f83,plain,(
0.20/0.53	  ( ! [X0] : (($false = $true) | sK2 @ sK3 != X0 | (in @ X0 @ sK1 = $false) | (in @ (kpair @ sK3 @ X0) @ (dpsetconstr @ sK0 @ sK1 @ (bCOMB @ vEQ('$i') @ sK2)) = $false) | (func @ sK0 @ sK1 @ (dpsetconstr @ sK0 @ sK1 @ (bCOMB @ vEQ('$i') @ sK2)) = $false)) )),
0.20/0.53	  inference(forward_demodulation,[],[f81,f27])).
0.20/0.53	tff(f84,plain,(
0.20/0.53	  ( ! [X0] : ((in @ (kpair @ sK3 @ X0) @ (dpsetconstr @ sK0 @ sK1 @ (bCOMB @ vEQ('$i') @ sK2)) = $false) | (in @ X0 @ sK1 = $false) | sK2 @ sK3 != X0 | (func @ sK0 @ sK1 @ (dpsetconstr @ sK0 @ sK1 @ (bCOMB @ vEQ('$i') @ sK2)) = $false)) )),
0.20/0.53	  inference(trivial_inequality_removal,[],[f83])).
0.20/0.53	tff(f107,plain,(
0.20/0.53	  ( ! [X2] : (($false = $true) | (in @ X2 @ sK1 = $false) | sK2 @ sK3 != X2 | (func @ sK0 @ sK1 @ (dpsetconstr @ sK0 @ sK1 @ (bCOMB @ vEQ('$i') @ sK2)) = $false) | (in @ X2 @ sK1 = $false) | (bCOMB @ vEQ('$i') @ sK2 @ sK3 @ X2 = $false) | (in @ sK3 @ sK0 = $false)) )),
0.20/0.53	  inference(superposition,[],[f84,f49])).
0.20/0.53	tff(f114,plain,(
0.20/0.53	  ( ! [X2] : (($false = $true) | (in @ X2 @ sK1 = $false) | sK2 @ sK3 != X2 | (func @ sK0 @ sK1 @ (dpsetconstr @ sK0 @ sK1 @ (bCOMB @ vEQ('$i') @ sK2)) = $false) | (bCOMB @ vEQ('$i') @ sK2 @ sK3 @ X2 = $false) | (in @ sK3 @ sK0 = $false)) )),
0.20/0.53	  inference(duplicate_literal_removal,[],[f107])).
0.20/0.53	tff(f115,plain,(
0.20/0.53	  ( ! [X2] : ((in @ X2 @ sK1 = $false) | sK2 @ sK3 != X2 | (func @ sK0 @ sK1 @ (dpsetconstr @ sK0 @ sK1 @ (bCOMB @ vEQ('$i') @ sK2)) = $false) | (bCOMB @ vEQ('$i') @ sK2 @ sK3 @ X2 = $false) | (in @ sK3 @ sK0 = $false)) )),
0.20/0.53	  inference(trivial_inequality_removal,[],[f114])).
0.20/0.53	tff(f116,plain,(
0.20/0.53	  ( ! [X2] : ((in @ X2 @ sK1 = $false) | sK2 @ sK3 != X2 | (func @ sK0 @ sK1 @ (dpsetconstr @ sK0 @ sK1 @ (bCOMB @ vEQ('$i') @ sK2)) = $false) | (vEQ('$i') @ (sK2 @ sK3) @ X2 = $false) | (in @ sK3 @ sK0 = $false)) )),
0.20/0.53	  inference(combinator_demodulation,[],[f115])).
0.20/0.53	tff(f117,plain,(
0.20/0.53	  ( ! [X2] : ((in @ X2 @ sK1 = $false) | sK2 @ sK3 != X2 | (func @ sK0 @ sK1 @ (dpsetconstr @ sK0 @ sK1 @ (bCOMB @ vEQ('$i') @ sK2)) = $false) | sK2 @ sK3 != X2 | (in @ sK3 @ sK0 = $false)) )),
0.20/0.53	  inference(equality_proxy_clausification,[],[f116])).
0.20/0.53	tff(f118,plain,(
0.20/0.53	  ( ! [X2] : ((in @ X2 @ sK1 = $false) | sK2 @ sK3 != X2 | (func @ sK0 @ sK1 @ (dpsetconstr @ sK0 @ sK1 @ (bCOMB @ vEQ('$i') @ sK2)) = $false) | (in @ sK3 @ sK0 = $false)) )),
0.20/0.53	  inference(duplicate_literal_removal,[],[f117])).
0.20/0.53	tff(f119,plain,(
0.20/0.53	  ( ! [X2] : (($false = $true) | (in @ X2 @ sK1 = $false) | sK2 @ sK3 != X2 | (func @ sK0 @ sK1 @ (dpsetconstr @ sK0 @ sK1 @ (bCOMB @ vEQ('$i') @ sK2)) = $false)) )),
0.20/0.53	  inference(forward_demodulation,[],[f118,f27])).
0.20/0.53	tff(f120,plain,(
0.20/0.53	  ( ! [X2] : ((func @ sK0 @ sK1 @ (dpsetconstr @ sK0 @ sK1 @ (bCOMB @ vEQ('$i') @ sK2)) = $false) | sK2 @ sK3 != X2 | (in @ X2 @ sK1 = $false)) )),
0.20/0.53	  inference(trivial_inequality_removal,[],[f119])).
0.20/0.53	tff(f121,plain,(
0.20/0.53	  ( ! [X0:'$i' -> '$i',X1] : (($false = $true) | sK2 @ sK3 != X1 | (in @ X1 @ sK1 = $false) | (in @ (X0 @ (sK4 @ sK0 @ sK1 @ X0)) @ sK1 = $false) | bCOMB @ vEQ('$i') @ sK2 != bCOMB @ vEQ('$i') @ X0) )),
0.20/0.53	  inference(superposition,[],[f120,f75])).
0.20/0.53	tff(f122,plain,(
0.20/0.53	  ( ! [X2:'$i' -> '$i',X3] : (($false = $true) | sK2 @ sK3 != X3 | (in @ X3 @ sK1 = $false) | (in @ (sK4 @ sK0 @ sK1 @ X2) @ sK0 = $true) | bCOMB @ vEQ('$i') @ sK2 != bCOMB @ vEQ('$i') @ X2) )),
0.20/0.53	  inference(superposition,[],[f120,f74])).
0.20/0.53	tff(f127,plain,(
0.20/0.53	  ( ! [X2:'$i' -> '$i',X3] : (bCOMB @ vEQ('$i') @ sK2 != bCOMB @ vEQ('$i') @ X2 | (in @ X3 @ sK1 = $false) | (in @ (sK4 @ sK0 @ sK1 @ X2) @ sK0 = $true) | sK2 @ sK3 != X3) )),
0.20/0.53	  inference(trivial_inequality_removal,[],[f122])).
0.20/0.53	tff(f128,plain,(
0.20/0.53	  ( ! [X0:'$i' -> '$i',X1] : (bCOMB @ vEQ('$i') @ sK2 != bCOMB @ vEQ('$i') @ X0 | (in @ X1 @ sK1 = $false) | (in @ (X0 @ (sK4 @ sK0 @ sK1 @ X0)) @ sK1 = $false) | sK2 @ sK3 != X1) )),
0.20/0.53	  inference(trivial_inequality_removal,[],[f121])).
0.20/0.53	tff(f130,plain,(
0.20/0.53	  ( ! [X0] : ((in @ (sK4 @ sK0 @ sK1 @ sK2) @ sK0 = $true) | (in @ X0 @ sK1 = $false) | sK2 @ sK3 != X0) )),
0.20/0.53	  inference(equality_resolution,[],[f127])).
0.20/0.53	tff(f133,plain,(
0.20/0.53	  ( ! [X0] : ((in @ (sK2 @ (sK4 @ sK0 @ sK1 @ sK2)) @ sK1 = $false) | (in @ X0 @ sK1 = $false) | sK2 @ sK3 != X0) )),
0.20/0.53	  inference(equality_resolution,[],[f128])).
0.20/0.53	tff(f136,plain,(
0.20/0.53	  ( ! [X0] : (($false = $true) | (in @ X0 @ sK1 = $false) | sK2 @ sK3 != X0 | (in @ (sK4 @ sK0 @ sK1 @ sK2) @ sK0 != $true)) )),
0.20/0.53	  inference(superposition,[],[f133,f26])).
0.20/0.53	tff(f141,plain,(
0.20/0.53	  ( ! [X0] : ((in @ X0 @ sK1 = $false) | sK2 @ sK3 != X0 | (in @ (sK4 @ sK0 @ sK1 @ sK2) @ sK0 != $true)) )),
0.20/0.53	  inference(trivial_inequality_removal,[],[f136])).
0.20/0.53	tff(f142,plain,(
0.20/0.53	  ( ! [X0] : ((in @ X0 @ sK1 = $false) | sK2 @ sK3 != X0) )),
0.20/0.53	  inference(subsumption_resolution,[],[f141,f130])).
0.20/0.53	tff(f171,plain,(
0.20/0.53	  ( ! [X0] : (($false = $true) | sK2 @ sK3 != sK2 @ X0 | (in @ X0 @ sK0 != $true)) )),
0.20/0.53	  inference(superposition,[],[f142,f26])).
0.20/0.53	tff(f174,plain,(
0.20/0.53	  ( ! [X0] : ((in @ X0 @ sK0 != $true) | sK2 @ sK3 != sK2 @ X0) )),
0.20/0.53	  inference(trivial_inequality_removal,[],[f171])).
0.20/0.53	tff(f176,plain,(
0.20/0.53	  ($true != $true) | sK2 @ sK3 != sK2 @ sK3),
0.20/0.53	  inference(superposition,[],[f174,f27])).
0.20/0.53	tff(f181,plain,(
0.20/0.53	  $false),
0.20/0.53	  inference(trivial_inequality_removal,[],[f176])).
0.20/0.53	% SZS output end Proof for theBenchmark
0.20/0.53	% (22593)------------------------------
0.20/0.53	% (22593)Version: Vampire 4.5.0 (commit 7ae30c7f on 2020-06-30 15:57:20 +0100)
0.20/0.53	% (22593)Termination reason: Refutation
0.20/0.53	
0.20/0.53	% (22593)Memory used [KB]: 1279
0.20/0.53	% (22593)Time elapsed: 0.135 s
0.20/0.53	% (22593)------------------------------
0.20/0.53	% (22593)------------------------------
0.20/0.53	% (22592)Success in time 0.171 s
0.20/0.53	EOF