TSTP Solution File: NUM561+2 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUM561+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 14:33:25 EDT 2024
% Result : Theorem 0.20s 0.39s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 22
% Syntax : Number of formulae : 62 ( 27 unt; 0 def)
% Number of atoms : 124 ( 25 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 112 ( 50 ~; 31 |; 15 &)
% ( 14 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 13 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 32 ( 25 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f494,plain,
$false,
inference(avatar_sat_refutation,[],[f438,f443,f448,f453,f458,f463,f467,f473,f477,f482,f487,f492,f493]) ).
fof(f493,plain,
( ~ spl26_10
| ~ spl26_7 ),
inference(avatar_split_clause,[],[f468,f465,f479]) ).
fof(f479,plain,
( spl26_10
<=> aElementOf0(xx,szDzozmdt0(xF)) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_10])]) ).
fof(f465,plain,
( spl26_7
<=> ! [X0] :
( sdtlpdtrp0(xF,X0) != sdtlpdtrp0(xF,xx)
| ~ aElementOf0(X0,szDzozmdt0(xF)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_7])]) ).
fof(f468,plain,
( ~ aElementOf0(xx,szDzozmdt0(xF))
| ~ spl26_7 ),
inference(equality_resolution,[],[f466]) ).
fof(f466,plain,
( ! [X0] :
( sdtlpdtrp0(xF,X0) != sdtlpdtrp0(xF,xx)
| ~ aElementOf0(X0,szDzozmdt0(xF)) )
| ~ spl26_7 ),
inference(avatar_component_clause,[],[f465]) ).
fof(f492,plain,
( ~ spl26_6
| ~ spl26_12 ),
inference(avatar_split_clause,[],[f413,f489,f460]) ).
fof(f460,plain,
( spl26_6
<=> aSet0(slcrc0) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_6])]) ).
fof(f489,plain,
( spl26_12
<=> isCountable0(slcrc0) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_12])]) ).
fof(f413,plain,
( ~ isCountable0(slcrc0)
| ~ aSet0(slcrc0) ),
inference(equality_resolution,[],[f328]) ).
fof(f328,plain,
! [X0] :
( slcrc0 != X0
| ~ isCountable0(X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f122]) ).
fof(f122,plain,
! [X0] :
( slcrc0 != X0
| ~ isCountable0(X0)
| ~ aSet0(X0) ),
inference(flattening,[],[f121]) ).
fof(f121,plain,
! [X0] :
( slcrc0 != X0
| ~ isCountable0(X0)
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0] :
( ( isCountable0(X0)
& aSet0(X0) )
=> slcrc0 != X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCountNFin_01) ).
fof(f487,plain,
spl26_11,
inference(avatar_split_clause,[],[f271,f484]) ).
fof(f484,plain,
( spl26_11
<=> slcrc0 = slbdtrb0(sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_11])]) ).
fof(f271,plain,
slcrc0 = slbdtrb0(sz00),
inference(cnf_transformation,[],[f52]) ).
fof(f52,axiom,
slcrc0 = slbdtrb0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSegZero) ).
fof(f482,plain,
spl26_10,
inference(avatar_split_clause,[],[f268,f479]) ).
fof(f268,plain,
aElementOf0(xx,szDzozmdt0(xF)),
inference(cnf_transformation,[],[f70]) ).
fof(f70,axiom,
aElementOf0(xx,szDzozmdt0(xF)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2911_02) ).
fof(f477,plain,
spl26_9,
inference(avatar_split_clause,[],[f418,f475]) ).
fof(f475,plain,
( spl26_9
<=> ! [X2] : ~ aElementOf0(X2,slcrc0) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_9])]) ).
fof(f418,plain,
! [X2] : ~ aElementOf0(X2,slcrc0),
inference(equality_resolution,[],[f344]) ).
fof(f344,plain,
! [X2,X0] :
( ~ aElementOf0(X2,X0)
| slcrc0 != X0 ),
inference(cnf_transformation,[],[f230]) ).
fof(f230,plain,
! [X0] :
( ( slcrc0 = X0
| aElementOf0(sK19(X0),X0)
| ~ aSet0(X0) )
& ( ( ! [X2] : ~ aElementOf0(X2,X0)
& aSet0(X0) )
| slcrc0 != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f228,f229]) ).
fof(f229,plain,
! [X0] :
( ? [X1] : aElementOf0(X1,X0)
=> aElementOf0(sK19(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f228,plain,
! [X0] :
( ( slcrc0 = X0
| ? [X1] : aElementOf0(X1,X0)
| ~ aSet0(X0) )
& ( ( ! [X2] : ~ aElementOf0(X2,X0)
& aSet0(X0) )
| slcrc0 != X0 ) ),
inference(rectify,[],[f227]) ).
fof(f227,plain,
! [X0] :
( ( slcrc0 = X0
| ? [X1] : aElementOf0(X1,X0)
| ~ aSet0(X0) )
& ( ( ! [X1] : ~ aElementOf0(X1,X0)
& aSet0(X0) )
| slcrc0 != X0 ) ),
inference(flattening,[],[f226]) ).
fof(f226,plain,
! [X0] :
( ( slcrc0 = X0
| ? [X1] : aElementOf0(X1,X0)
| ~ aSet0(X0) )
& ( ( ! [X1] : ~ aElementOf0(X1,X0)
& aSet0(X0) )
| slcrc0 != X0 ) ),
inference(nnf_transformation,[],[f137]) ).
fof(f137,plain,
! [X0] :
( slcrc0 = X0
<=> ( ! [X1] : ~ aElementOf0(X1,X0)
& aSet0(X0) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0] :
( slcrc0 = X0
<=> ( ~ ? [X1] : aElementOf0(X1,X0)
& aSet0(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefEmp) ).
fof(f473,plain,
spl26_8,
inference(avatar_split_clause,[],[f270,f470]) ).
fof(f470,plain,
( spl26_8
<=> aElementOf0(sz00,szNzAzT0) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_8])]) ).
fof(f270,plain,
aElementOf0(sz00,szNzAzT0),
inference(cnf_transformation,[],[f24]) ).
fof(f24,axiom,
aElementOf0(sz00,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroNum) ).
fof(f467,plain,
spl26_7,
inference(avatar_split_clause,[],[f265,f465]) ).
fof(f265,plain,
! [X0] :
( sdtlpdtrp0(xF,X0) != sdtlpdtrp0(xF,xx)
| ~ aElementOf0(X0,szDzozmdt0(xF)) ),
inference(cnf_transformation,[],[f81]) ).
fof(f81,plain,
( ~ aElementOf0(sdtlpdtrp0(xF,xx),sdtlcdtrc0(xF,szDzozmdt0(xF)))
& ! [X0] :
( sdtlpdtrp0(xF,X0) != sdtlpdtrp0(xF,xx)
| ~ aElementOf0(X0,szDzozmdt0(xF)) ) ),
inference(ennf_transformation,[],[f72]) ).
fof(f72,negated_conjecture,
~ ( aElementOf0(sdtlpdtrp0(xF,xx),sdtlcdtrc0(xF,szDzozmdt0(xF)))
| ? [X0] :
( sdtlpdtrp0(xF,X0) = sdtlpdtrp0(xF,xx)
& aElementOf0(X0,szDzozmdt0(xF)) ) ),
inference(negated_conjecture,[],[f71]) ).
fof(f71,conjecture,
( aElementOf0(sdtlpdtrp0(xF,xx),sdtlcdtrc0(xF,szDzozmdt0(xF)))
| ? [X0] :
( sdtlpdtrp0(xF,X0) = sdtlpdtrp0(xF,xx)
& aElementOf0(X0,szDzozmdt0(xF)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f463,plain,
spl26_6,
inference(avatar_split_clause,[],[f419,f460]) ).
fof(f419,plain,
aSet0(slcrc0),
inference(equality_resolution,[],[f343]) ).
fof(f343,plain,
! [X0] :
( aSet0(X0)
| slcrc0 != X0 ),
inference(cnf_transformation,[],[f230]) ).
fof(f458,plain,
spl26_5,
inference(avatar_split_clause,[],[f273,f455]) ).
fof(f455,plain,
( spl26_5
<=> isCountable0(szNzAzT0) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_5])]) ).
fof(f273,plain,
isCountable0(szNzAzT0),
inference(cnf_transformation,[],[f23]) ).
fof(f23,axiom,
( isCountable0(szNzAzT0)
& aSet0(szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNATSet) ).
fof(f453,plain,
spl26_4,
inference(avatar_split_clause,[],[f272,f450]) ).
fof(f450,plain,
( spl26_4
<=> aSet0(szNzAzT0) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_4])]) ).
fof(f272,plain,
aSet0(szNzAzT0),
inference(cnf_transformation,[],[f23]) ).
fof(f448,plain,
spl26_3,
inference(avatar_split_clause,[],[f269,f445]) ).
fof(f445,plain,
( spl26_3
<=> isFinite0(slcrc0) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_3])]) ).
fof(f269,plain,
isFinite0(slcrc0),
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
isFinite0(slcrc0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEmpFin) ).
fof(f443,plain,
spl26_2,
inference(avatar_split_clause,[],[f267,f440]) ).
fof(f440,plain,
( spl26_2
<=> aFunction0(xF) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_2])]) ).
fof(f267,plain,
aFunction0(xF),
inference(cnf_transformation,[],[f69]) ).
fof(f69,axiom,
aFunction0(xF),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2911) ).
fof(f438,plain,
~ spl26_1,
inference(avatar_split_clause,[],[f266,f435]) ).
fof(f435,plain,
( spl26_1
<=> aElementOf0(sdtlpdtrp0(xF,xx),sdtlcdtrc0(xF,szDzozmdt0(xF))) ),
introduced(avatar_definition,[new_symbols(naming,[spl26_1])]) ).
fof(f266,plain,
~ aElementOf0(sdtlpdtrp0(xF,xx),sdtlcdtrc0(xF,szDzozmdt0(xF))),
inference(cnf_transformation,[],[f81]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUM561+2 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36 % Computer : n020.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Mon Apr 29 23:42:47 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (17088)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38 % (17091)WARNING: value z3 for option sas not known
% 0.14/0.38 % (17093)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.38 % (17095)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.14/0.38 % (17090)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.38 % (17091)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.38 % (17094)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.38 % (17092)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.20/0.39 % (17089)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.20/0.39 % (17093)First to succeed.
% 0.20/0.39 % (17094)Also succeeded, but the first one will report.
% 0.20/0.39 % (17093)Refutation found. Thanks to Tanya!
% 0.20/0.39 % SZS status Theorem for theBenchmark
% 0.20/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.39 % (17093)------------------------------
% 0.20/0.39 % (17093)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.20/0.39 % (17093)Termination reason: Refutation
% 0.20/0.39
% 0.20/0.39 % (17093)Memory used [KB]: 1032
% 0.20/0.39 % (17093)Time elapsed: 0.008 s
% 0.20/0.39 % (17093)Instructions burned: 13 (million)
% 0.20/0.39 % (17093)------------------------------
% 0.20/0.39 % (17093)------------------------------
% 0.20/0.39 % (17088)Success in time 0.024 s
%------------------------------------------------------------------------------