%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : RNG105+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n015.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 12:36:03 PM UTC 2026
% Result : Theorem 0.16s 0.50s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 14
% Syntax : Number of formulae : 69 ( 17 unt; 4 def)
% Number of atoms : 212 ( 37 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 237 ( 94 ~; 96 |; 36 &)
% ( 8 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 5 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 62 ( 0 sgn 51 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1] :
( ( aElement0(X0)
& aElement0(X1) )
=> aElement0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
fof(f6,axiom,
! [X0,X1] :
( ( aElement0(X0)
& aElement0(X1) )
=> aElement0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f37,axiom,
! [X0] :
( aElement0(X0)
=> ! [X1] :
( X1 = slsdtgt0(X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
<=> ? [X3] :
( aElement0(X3)
& sdtasdt0(X0,X3) = X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefPrIdeal) ).
fof(f38,axiom,
aElement0(xc),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1905) ).
fof(f39,axiom,
( aElementOf0(xx,slsdtgt0(xc))
& aElementOf0(xy,slsdtgt0(xc))
& aElement0(xz) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1933) ).
fof(f40,axiom,
( aElement0(xu)
& sdtasdt0(xc,xu) = xx ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1956) ).
fof(f41,axiom,
( aElement0(xv)
& sdtasdt0(xc,xv) = xy ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1979) ).
fof(f42,axiom,
sdtpldt0(xx,xy) = sdtasdt0(xc,sdtpldt0(xu,xv)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2010) ).
fof(f43,axiom,
sdtasdt0(xz,xx) = sdtasdt0(xc,sdtasdt0(xu,xz)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2043) ).
fof(f44,conjecture,
( aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc))
& aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f45,negated_conjecture,
~ ( aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc))
& aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc)) ),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f56,plain,
! [X0,X1] :
( aElement0(sdtpldt0(X0,X1))
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f57,plain,
! [X0,X1] :
( aElement0(sdtpldt0(X0,X1))
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(flattening,[],[f56]) ).
fof(f58,plain,
! [X0,X1] :
( aElement0(sdtasdt0(X0,X1))
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f59,plain,
! [X0,X1] :
( aElement0(sdtasdt0(X0,X1))
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(flattening,[],[f58]) ).
fof(f102,plain,
! [X0] :
( ! [X1] :
( X1 = slsdtgt0(X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
<=> ? [X3] :
( aElement0(X3)
& sdtasdt0(X0,X3) = X2 ) ) ) )
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f103,plain,
( ~ aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc))
| ~ aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc)) ),
inference(ennf_transformation,[],[f45]) ).
fof(f136,plain,
! [X0] :
( ! [X1] :
( ( X1 = slsdtgt0(X0)
| ~ aSet0(X1)
| ? [X2] :
( ( ! [X3] :
( ~ aElement0(X3)
| sdtasdt0(X0,X3) != X2 )
| ~ aElementOf0(X2,X1) )
& ( ? [X3] :
( aElement0(X3)
& sdtasdt0(X0,X3) = X2 )
| aElementOf0(X2,X1) ) ) )
& ( ( aSet0(X1)
& ! [X2] :
( ( aElementOf0(X2,X1)
| ! [X3] :
( ~ aElement0(X3)
| sdtasdt0(X0,X3) != X2 ) )
& ( ? [X3] :
( aElement0(X3)
& sdtasdt0(X0,X3) = X2 )
| ~ aElementOf0(X2,X1) ) ) )
| slsdtgt0(X0) != X1 ) )
| ~ aElement0(X0) ),
inference(nnf_transformation,[],[f102]) ).
fof(f137,plain,
! [X0] :
( ! [X1] :
( ( X1 = slsdtgt0(X0)
| ~ aSet0(X1)
| ? [X2] :
( ( ! [X3] :
( ~ aElement0(X3)
| sdtasdt0(X0,X3) != X2 )
| ~ aElementOf0(X2,X1) )
& ( ? [X3] :
( aElement0(X3)
& sdtasdt0(X0,X3) = X2 )
| aElementOf0(X2,X1) ) ) )
& ( ( aSet0(X1)
& ! [X2] :
( ( aElementOf0(X2,X1)
| ! [X3] :
( ~ aElement0(X3)
| sdtasdt0(X0,X3) != X2 ) )
& ( ? [X3] :
( aElement0(X3)
& sdtasdt0(X0,X3) = X2 )
| ~ aElementOf0(X2,X1) ) ) )
| slsdtgt0(X0) != X1 ) )
| ~ aElement0(X0) ),
inference(flattening,[],[f136]) ).
fof(f138,plain,
! [X0] :
( ! [X1] :
( ( X1 = slsdtgt0(X0)
| ~ aSet0(X1)
| ? [X2] :
( ( ! [X3] :
( ~ aElement0(X3)
| sdtasdt0(X0,X3) != X2 )
| ~ aElementOf0(X2,X1) )
& ( ? [X4] :
( aElement0(X4)
& sdtasdt0(X0,X4) = X2 )
| aElementOf0(X2,X1) ) ) )
& ( ( aSet0(X1)
& ! [X5] :
( ( aElementOf0(X5,X1)
| ! [X6] :
( ~ aElement0(X6)
| sdtasdt0(X0,X6) != X5 ) )
& ( ? [X7] :
( aElement0(X7)
& sdtasdt0(X0,X7) = X5 )
| ~ aElementOf0(X5,X1) ) ) )
| slsdtgt0(X0) != X1 ) )
| ~ aElement0(X0) ),
inference(rectify,[],[f137]) ).
fof(f139,plain,
! [X0] :
( ! [X1] :
( ( X1 = slsdtgt0(X0)
| ~ aSet0(X1)
| ( ( ! [X3] :
( ~ aElement0(X3)
| sdtasdt0(X0,X3) != sK19(X0,X1) )
| ~ aElementOf0(sK19(X0,X1),X1) )
& ( ( aElement0(sK20(X0,X1))
& sK19(X0,X1) = sdtasdt0(X0,sK20(X0,X1)) )
| aElementOf0(sK19(X0,X1),X1) ) ) )
& ( ( aSet0(X1)
& ! [X5] :
( ( aElementOf0(X5,X1)
| ! [X6] :
( ~ aElement0(X6)
| sdtasdt0(X0,X6) != X5 ) )
& ( ( aElement0(sK21(X0,X5))
& sdtasdt0(X0,sK21(X0,X5)) = X5 )
| ~ aElementOf0(X5,X1) ) ) )
| slsdtgt0(X0) != X1 ) )
| ~ aElement0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19,sK20,sK21]),skolemize(X2,sK19(X0,X1)),skolemize(X4,sK20(X0,X1)),skolemize(X7,sK21(X0,X5))],[f138]) ).
fof(f143,plain,
! [X0,X1] :
( aElement0(sdtpldt0(X0,X1))
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(cnf_transformation,[],[f57]) ).
fof(f144,plain,
! [X0,X1] :
( aElement0(sdtasdt0(X0,X1))
| ~ aElement0(X0)
| ~ aElement0(X1) ),
inference(cnf_transformation,[],[f59]) ).
fof(f224,plain,
! [X0,X1,X6,X5] :
( aElementOf0(X5,X1)
| ~ aElement0(X6)
| sdtasdt0(X0,X6) != X5
| slsdtgt0(X0) != X1
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f139]) ).
fof(f229,plain,
aElement0(xc),
inference(cnf_transformation,[],[f38]) ).
fof(f230,plain,
aElement0(xz),
inference(cnf_transformation,[],[f39]) ).
fof(f234,plain,
aElement0(xu),
inference(cnf_transformation,[],[f40]) ).
fof(f236,plain,
aElement0(xv),
inference(cnf_transformation,[],[f41]) ).
fof(f237,plain,
sdtpldt0(xx,xy) = sdtasdt0(xc,sdtpldt0(xu,xv)),
inference(cnf_transformation,[],[f42]) ).
fof(f238,plain,
sdtasdt0(xz,xx) = sdtasdt0(xc,sdtasdt0(xu,xz)),
inference(cnf_transformation,[],[f43]) ).
fof(f239,plain,
( ~ aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc))
| ~ aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc)) ),
inference(cnf_transformation,[],[f103]) ).
fof(f248,plain,
! [X0,X1,X6] :
( aElementOf0(sdtasdt0(X0,X6),X1)
| ~ aElement0(X6)
| slsdtgt0(X0) != X1
| ~ aElement0(X0) ),
inference(equality_resolution,[],[f224]) ).
fof(f249,plain,
! [X0,X6] :
( aElementOf0(sdtasdt0(X0,X6),slsdtgt0(X0))
| ~ aElement0(X6)
| ~ aElement0(X0) ),
inference(equality_resolution,[],[f248]) ).
fof(f253,definition,
( spl22_1
<=> aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc)) ),
introduced(definition,[new_symbols(definition,[spl22_1])],[avatar_definition]) ).
fof(f255,plain,
( ~ aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc))
| spl22_1 ),
inference(avatar_component_clause,[],[f253]) ).
fof(f257,definition,
( spl22_2
<=> aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc)) ),
introduced(definition,[new_symbols(definition,[spl22_2])],[avatar_definition]) ).
fof(f260,plain,
( ~ spl22_1
| ~ spl22_2 ),
inference(avatar_split_clause,[],[f239,f257,f253]) ).
fof(f390,definition,
( spl22_6
<=> aElement0(sdtpldt0(xu,xv)) ),
introduced(definition,[new_symbols(definition,[spl22_6])],[avatar_definition]) ).
fof(f391,plain,
( aElement0(sdtpldt0(xu,xv))
| ~ spl22_6 ),
inference(avatar_component_clause,[],[f390]) ).
fof(f392,plain,
( ~ aElement0(sdtpldt0(xu,xv))
| spl22_6 ),
inference(avatar_component_clause,[],[f390]) ).
fof(f398,plain,
( ~ aElement0(xu)
| ~ aElement0(xv)
| spl22_6 ),
inference(resolution,[],[f392,f143]) ).
fof(f399,plain,
( ~ aElement0(xv)
| spl22_6 ),
inference(forward_subsumption_resolution,[],[f398,f234]) ).
fof(f400,plain,
( $false
| spl22_6 ),
inference(forward_subsumption_resolution,[],[f399,f236]) ).
fof(f401,plain,
spl22_6,
inference(avatar_contradiction_clause,[],[f400]) ).
fof(f405,definition,
( spl22_8
<=> aElement0(sdtasdt0(xu,xz)) ),
introduced(definition,[new_symbols(definition,[spl22_8])],[avatar_definition]) ).
fof(f406,plain,
( aElement0(sdtasdt0(xu,xz))
| ~ spl22_8 ),
inference(avatar_component_clause,[],[f405]) ).
fof(f407,plain,
( ~ aElement0(sdtasdt0(xu,xz))
| spl22_8 ),
inference(avatar_component_clause,[],[f405]) ).
fof(f455,plain,
( ~ aElement0(xu)
| ~ aElement0(xz)
| spl22_8 ),
inference(resolution,[],[f407,f144]) ).
fof(f456,plain,
( ~ aElement0(xz)
| spl22_8 ),
inference(forward_subsumption_resolution,[],[f455,f234]) ).
fof(f457,plain,
( $false
| spl22_8 ),
inference(forward_subsumption_resolution,[],[f456,f230]) ).
fof(f458,plain,
spl22_8,
inference(avatar_contradiction_clause,[],[f457]) ).
fof(f482,plain,
( aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc))
| ~ aElement0(sdtpldt0(xu,xv))
| ~ aElement0(xc) ),
inference(superposition,[],[f249,f237]) ).
fof(f483,plain,
( aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc))
| ~ aElement0(sdtasdt0(xu,xz))
| ~ aElement0(xc) ),
inference(superposition,[],[f249,f238]) ).
fof(f494,plain,
( ~ aElement0(sdtasdt0(xu,xz))
| ~ aElement0(xc)
| spl22_1 ),
inference(forward_subsumption_resolution,[],[f483,f255]) ).
fof(f495,plain,
( aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc))
| ~ aElement0(xc)
| ~ spl22_6 ),
inference(forward_subsumption_resolution,[],[f482,f391]) ).
fof(f501,plain,
( ~ aElement0(xc)
| spl22_1
| ~ spl22_8 ),
inference(forward_subsumption_resolution,[],[f494,f406]) ).
fof(f502,plain,
( aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc))
| ~ spl22_6 ),
inference(forward_subsumption_resolution,[],[f495,f229]) ).
fof(f504,plain,
( $false
| spl22_1
| ~ spl22_8 ),
inference(forward_subsumption_resolution,[],[f501,f229]) ).
fof(f505,plain,
( spl22_1
| ~ spl22_8 ),
inference(avatar_contradiction_clause,[],[f504]) ).
fof(f506,plain,
( spl22_2
| ~ spl22_6 ),
inference(avatar_split_clause,[],[f502,f390,f257]) ).
cnf(s1,plain,
( ~ spl22_1
| ~ spl22_2 ),
inference(sat_conversion,[],[f260]) ).
cnf(s6,plain,
spl22_6,
inference(sat_conversion,[],[f401]) ).
cnf(s8,plain,
spl22_8,
inference(sat_conversion,[],[f458]) ).
cnf(s9,plain,
( spl22_1
| ~ spl22_8 ),
inference(sat_conversion,[],[f505]) ).
cnf(s10,plain,
( spl22_2
| ~ spl22_6 ),
inference(sat_conversion,[],[f506]) ).
cnf(s11,plain,
spl22_1,
inference(rat,[],[s9,s8]) ).
cnf(s13,plain,
spl22_2,
inference(rat,[],[s10,s6]) ).
cnf(s17,plain,
$false,
inference(rat,[],[s1,s13,s11]) ).
fof(f507,plain,
$false,
inference(avatar_sat_refutation,[],[s17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG105+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 % Computer : n015.cluster.edu
% 0.11/0.41 % Model : x86_64 x86_64
% 0.11/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.41 % Memory : 8046.5625MB
% 0.11/0.41 % OS : Linux 6.8.0-71-generic
% 0.11/0.41 % CPULimit : 300
% 0.11/0.41 % WCLimit : 300
% 0.11/0.41 % DateTime : Sun Sep 27 23:20:57 UTC 2026
% 0.11/0.42 % CPUTime :
% 0.11/0.42 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.45 Running first-order model finding
% 0.11/0.45 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.50 % (2123653)Will run a generic schedule for satisfiability detection.
% 0.16/0.50 % (2123661)dis+10_1_sil=32000:sp=arity:random_seed=1513022524:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.50 % (2123659)% WARNING: option uhcvi not known.
% 0.16/0.50 % (2123661) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2123653-2123661"...
% 0.16/0.50 % (2123661)...printing done.
% 0.16/0.50 % (2123661)Refutation found. Thanks to Tanya!
% 0.16/0.50 % SZS status Theorem for theBenchmark
% 0.16/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.50 % (2123661)------------------------------
% 0.16/0.50 % (2123661)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.50 % (2123661)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.50 % (2123661)CaDiCaL version: 2.1.3
% 0.16/0.50 % (2123661)Termination reason: Refutation
% 0.16/0.50 % (2123661)Time elapsed: 0.005 s
% 0.16/0.50 % (2123661)Peak memory usage: 12 MB
% 0.16/0.50 % (2123661)Instructions burned: 13 (million)
% 0.16/0.50 % (2123653)Success in time 0.039 s
% 0.16/0.50 % Vampire exiting
%------------------------------------------------------------------------------