%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : RNG099+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:36:02 PM UTC 2026
% Result : Theorem 0.18s 0.46s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 13
% Syntax : Number of formulae : 63 ( 24 unt; 3 def)
% Number of atoms : 166 ( 3 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 158 ( 55 ~; 52 |; 32 &)
% ( 3 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 4 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 44 ( 0 sgn 42 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1] :
( ( aElement0(X0)
& aElement0(X1) )
=> aElement0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
fof(f6,axiom,
! [X0,X1] :
( ( aElement0(X0)
& aElement0(X1) )
=> aElement0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f20,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
fof(f28,axiom,
( aSet0(xI)
& ! [X0] :
( aElementOf0(X0,xI)
=> ( ! [X1] :
( aElementOf0(X1,xI)
=> aElementOf0(sdtpldt0(X0,X1),xI) )
& ! [X1] :
( aElement0(X1)
=> aElementOf0(sdtasdt0(X1,X0),xI) ) ) )
& aIdeal0(xI)
& aSet0(xJ)
& ! [X0] :
( aElementOf0(X0,xJ)
=> ( ! [X1] :
( aElementOf0(X1,xJ)
=> aElementOf0(sdtpldt0(X0,X1),xJ) )
& ! [X1] :
( aElement0(X1)
=> aElementOf0(sdtasdt0(X1,X0),xJ) ) ) )
& aIdeal0(xJ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1205) ).
fof(f30,axiom,
( aElement0(xx)
& aElement0(xy) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1217) ).
fof(f31,axiom,
( aElementOf0(xa,xI)
& aElementOf0(xb,xJ)
& sdtpldt0(xa,xb) = sz10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1294) ).
fof(f32,axiom,
xw = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1319) ).
fof(f33,axiom,
aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1332) ).
fof(f34,axiom,
aElementOf0(sdtpldt0(xw,smndt0(xy)),xJ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1409) ).
fof(f35,conjecture,
? [X0] :
( aElement0(X0)
& ( aElementOf0(sdtpldt0(X0,smndt0(xx)),xI)
| sdteqdtlpzmzozddtrp0(X0,xx,xI) )
& ( aElementOf0(sdtpldt0(X0,smndt0(xy)),xJ)
| sdteqdtlpzmzozddtrp0(X0,xy,xJ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f36,negated_conjecture,
~ ? [X0] :
( aElement0(X0)
& ( aElementOf0(sdtpldt0(X0,smndt0(xx)),xI)
| sdteqdtlpzmzozddtrp0(X0,xx,xI) )
& ( aElementOf0(sdtpldt0(X0,smndt0(xy)),xJ)
| sdteqdtlpzmzozddtrp0(X0,xy,xJ) ) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
fof(f41,plain,
( aSet0(xI)
& ! [X0] :
( aElementOf0(X0,xI)
=> ( ! [X1] :
( aElementOf0(X1,xI)
=> aElementOf0(sdtpldt0(X0,X1),xI) )
& ! [X2] :
( aElement0(X2)
=> aElementOf0(sdtasdt0(X2,X0),xI) ) ) )
& aIdeal0(xI)
& aSet0(xJ)
& ! [X3] :
( aElementOf0(X3,xJ)
=> ( ! [X4] :
( aElementOf0(X4,xJ)
=> aElementOf0(sdtpldt0(X3,X4),xJ) )
& ! [X5] :
( aElement0(X5)
=> aElementOf0(sdtasdt0(X5,X3),xJ) ) ) )
& aIdeal0(xJ) ),
inference(rectify,[],[f28]) ).
fof(f43,plain,
! [X0,X1] :
( aElement0(sdtpldt0(X0,X1))
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f44,plain,
! [X0,X1] :
( aElement0(sdtpldt0(X0,X1))
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(flattening,[],[f43]) ).
fof(f45,plain,
! [X0,X1] :
( aElement0(sdtasdt0(X0,X1))
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f46,plain,
! [X0,X1] :
( aElement0(sdtasdt0(X0,X1))
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(flattening,[],[f45]) ).
fof(f64,plain,
! [X0] :
( ! [X1] :
( aElement0(X1)
| ~ aElementOf0(X1,X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f78,plain,
( aSet0(xI)
& ! [X0] :
( ( ! [X1] :
( aElementOf0(sdtpldt0(X0,X1),xI)
| ~ aElementOf0(X1,xI) )
& ! [X2] :
( aElementOf0(sdtasdt0(X2,X0),xI)
| ~ aElement0(X2) ) )
| ~ aElementOf0(X0,xI) )
& aIdeal0(xI)
& aSet0(xJ)
& ! [X3] :
( ( ! [X4] :
( aElementOf0(sdtpldt0(X3,X4),xJ)
| ~ aElementOf0(X4,xJ) )
& ! [X5] :
( aElementOf0(sdtasdt0(X5,X3),xJ)
| ~ aElement0(X5) ) )
| ~ aElementOf0(X3,xJ) )
& aIdeal0(xJ) ),
inference(ennf_transformation,[],[f41]) ).
fof(f80,plain,
! [X0] :
( ~ aElement0(X0)
| ( ~ aElementOf0(sdtpldt0(X0,smndt0(xx)),xI)
& ~ sdteqdtlpzmzozddtrp0(X0,xx,xI) )
| ( ~ aElementOf0(sdtpldt0(X0,smndt0(xy)),xJ)
& ~ sdteqdtlpzmzozddtrp0(X0,xy,xJ) ) ),
inference(ennf_transformation,[],[f36]) ).
fof(f104,plain,
! [X0,X1] :
( aElement0(sdtpldt0(X0,X1))
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(cnf_transformation,[],[f44]) ).
fof(f105,plain,
! [X0,X1] :
( aElement0(sdtasdt0(X0,X1))
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(cnf_transformation,[],[f46]) ).
fof(f124,plain,
! [X0,X1] :
( ~ aElementOf0(X1,X0)
| aElement0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f163,plain,
aSet0(xJ),
inference(cnf_transformation,[],[f78]) ).
fof(f167,plain,
aSet0(xI),
inference(cnf_transformation,[],[f78]) ).
fof(f172,plain,
aElement0(xy),
inference(cnf_transformation,[],[f30]) ).
fof(f173,plain,
aElement0(xx),
inference(cnf_transformation,[],[f30]) ).
fof(f175,plain,
aElementOf0(xb,xJ),
inference(cnf_transformation,[],[f31]) ).
fof(f176,plain,
aElementOf0(xa,xI),
inference(cnf_transformation,[],[f31]) ).
fof(f177,plain,
xw = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),
inference(cnf_transformation,[],[f32]) ).
fof(f178,plain,
aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
inference(cnf_transformation,[],[f33]) ).
fof(f179,plain,
aElementOf0(sdtpldt0(xw,smndt0(xy)),xJ),
inference(cnf_transformation,[],[f34]) ).
fof(f183,plain,
! [X0] :
( ~ aElementOf0(sdtpldt0(X0,smndt0(xy)),xJ)
| ~ aElementOf0(sdtpldt0(X0,smndt0(xx)),xI)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f198,definition,
( spl15_2
<=> aElement0(xw) ),
introduced(definition,[new_symbols(definition,[spl15_2])],[avatar_definition]) ).
fof(f200,plain,
( ~ aElement0(xw)
| spl15_2 ),
inference(avatar_component_clause,[],[f198]) ).
fof(f202,plain,
( ~ aElementOf0(sdtpldt0(xw,smndt0(xx)),xI)
| ~ aElement0(xw) ),
inference(resolution,[],[f179,f183]) ).
fof(f209,plain,
~ aElement0(xw),
inference(forward_subsumption_resolution,[],[f202,f178]) ).
fof(f210,plain,
~ spl15_2,
inference(avatar_split_clause,[],[f209,f198]) ).
fof(f244,plain,
( aElement0(xa)
| ~ aSet0(xI) ),
inference(resolution,[],[f124,f176]) ).
fof(f245,plain,
( aElement0(xb)
| ~ aSet0(xJ) ),
inference(resolution,[],[f124,f175]) ).
fof(f250,plain,
aElement0(xb),
inference(forward_subsumption_resolution,[],[f245,f163]) ).
fof(f251,plain,
aElement0(xa),
inference(forward_subsumption_resolution,[],[f244,f167]) ).
fof(f340,plain,
( aElement0(xw)
| ~ aElement0(sdtasdt0(xy,xa))
| ~ aElement0(sdtasdt0(xx,xb)) ),
inference(superposition,[],[f104,f177]) ).
fof(f341,plain,
( ~ aElement0(sdtasdt0(xy,xa))
| ~ aElement0(sdtasdt0(xx,xb))
| spl15_2 ),
inference(forward_subsumption_resolution,[],[f340,f200]) ).
fof(f343,definition,
( spl15_4
<=> aElement0(sdtasdt0(xx,xb)) ),
introduced(definition,[new_symbols(definition,[spl15_4])],[avatar_definition]) ).
fof(f345,plain,
( ~ aElement0(sdtasdt0(xx,xb))
| spl15_4 ),
inference(avatar_component_clause,[],[f343]) ).
fof(f347,definition,
( spl15_5
<=> aElement0(sdtasdt0(xy,xa)) ),
introduced(definition,[new_symbols(definition,[spl15_5])],[avatar_definition]) ).
fof(f349,plain,
( ~ aElement0(sdtasdt0(xy,xa))
| spl15_5 ),
inference(avatar_component_clause,[],[f347]) ).
fof(f350,plain,
( ~ spl15_4
| ~ spl15_5
| spl15_2 ),
inference(avatar_split_clause,[],[f341,f198,f347,f343]) ).
fof(f351,plain,
( ~ aElement0(xx)
| ~ aElement0(xb)
| spl15_4 ),
inference(resolution,[],[f345,f105]) ).
fof(f352,plain,
( ~ aElement0(xb)
| spl15_4 ),
inference(forward_subsumption_resolution,[],[f351,f173]) ).
fof(f353,plain,
( $false
| spl15_4 ),
inference(forward_subsumption_resolution,[],[f352,f250]) ).
fof(f354,plain,
spl15_4,
inference(avatar_contradiction_clause,[],[f353]) ).
fof(f388,plain,
( ~ aElement0(xy)
| ~ aElement0(xa)
| spl15_5 ),
inference(resolution,[],[f349,f105]) ).
fof(f389,plain,
( ~ aElement0(xa)
| spl15_5 ),
inference(forward_subsumption_resolution,[],[f388,f172]) ).
fof(f390,plain,
( $false
| spl15_5 ),
inference(forward_subsumption_resolution,[],[f389,f251]) ).
fof(f391,plain,
spl15_5,
inference(avatar_contradiction_clause,[],[f390]) ).
cnf(s3,plain,
~ spl15_2,
inference(sat_conversion,[],[f210]) ).
cnf(s4,plain,
( spl15_2
| ~ spl15_4
| ~ spl15_5 ),
inference(sat_conversion,[],[f350]) ).
cnf(s5,plain,
spl15_4,
inference(sat_conversion,[],[f354]) ).
cnf(s6,plain,
spl15_5,
inference(sat_conversion,[],[f391]) ).
cnf(s7,plain,
spl15_2,
inference(rat,[],[s4,s6,s5]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s3,s7]) ).
fof(f392,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG099+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.37 % Computer : n001.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 23:21:17 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.41 Running first-order model finding
% 0.10/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.46 % (4079847)Will run a generic schedule for satisfiability detection.
% 0.18/0.46 % (4079852)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1625531360_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.46 % (4079853)% WARNING: option uhcvi not known.
% 0.18/0.46 % TRYING [1]
% 0.18/0.46 % TRYING [2]
% 0.18/0.46 % TRYING [3]
% 0.18/0.46 % (4079853)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3098542577:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.46 % (4079854)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3112683781:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.46 % (4079855)dis+10_1_sil=32000:sp=arity:random_seed=524134622:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.46 % (4079856)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=962616089:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.46 % (4079858)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=331884345:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.46 % (4079857)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=602222617:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.46 % TRYING [4]
% 0.18/0.46 % (4079855) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4079847-4079855"...
% 0.18/0.46 % (4079855)...printing done.
% 0.18/0.46 % (4079853) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4079847-4079853"...
% 0.18/0.46 % (4079855)Refutation found. Thanks to Tanya!
% 0.18/0.46 % SZS status Theorem for theBenchmark
% 0.18/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.46 % (4079855)------------------------------
% 0.18/0.46 % (4079855)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.46 % (4079855)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.46 % (4079855)CaDiCaL version: 2.1.3
% 0.18/0.46 % (4079855)Termination reason: Refutation
% 0.18/0.46 % (4079855)Time elapsed: 0.008 s
% 0.18/0.46 % (4079855)Peak memory usage: 12 MB
% 0.18/0.46 % (4079855)Instructions burned: 11 (million)
% 0.18/0.46 % (4079847)Success in time 0.046 s
% 0.18/0.46 % Vampire exiting
%------------------------------------------------------------------------------