%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : RNG109+4 : 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 : n017.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 12:36:04 PM UTC 2026
% Result : Theorem 0.15s 0.47s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 7
% Syntax : Number of formulae : 46 ( 18 unt; 2 def)
% Number of atoms : 199 ( 74 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 215 ( 62 ~; 52 |; 82 &)
% ( 12 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-2 aty)
% Number of variables : 79 ( 0 sgn 48 !; 31 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [X0] :
( aElement0(X0)
=> ( sdtpldt0(X0,sz00) = X0
& X0 = sdtpldt0(sz00,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddZero) ).
fof(f39,axiom,
( aElement0(xa)
& aElement0(xb) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2091) ).
fof(f40,axiom,
( xa != sz00
| xb != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2110) ).
fof(f43,axiom,
( ? [X0] :
( aElement0(X0)
& sdtasdt0(xa,X0) = sz00 )
& aElementOf0(sz00,slsdtgt0(xa))
& ? [X0] :
( aElement0(X0)
& sdtasdt0(xa,X0) = xa )
& aElementOf0(xa,slsdtgt0(xa))
& ? [X0] :
( aElement0(X0)
& sdtasdt0(xb,X0) = sz00 )
& aElementOf0(sz00,slsdtgt0(xb))
& ? [X0] :
( aElement0(X0)
& sdtasdt0(xb,X0) = xb )
& aElementOf0(xb,slsdtgt0(xb)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2203) ).
fof(f44,conjecture,
? [X0] :
( ( ! [X1] :
( aElementOf0(X1,slsdtgt0(xa))
<=> ? [X2] :
( aElement0(X2)
& sdtasdt0(xa,X2) = X1 ) )
=> ( ! [X1] :
( aElementOf0(X1,slsdtgt0(xb))
<=> ? [X2] :
( aElement0(X2)
& sdtasdt0(xb,X2) = X1 ) )
=> ( ? [X1,X2] :
( aElementOf0(X1,slsdtgt0(xa))
& aElementOf0(X2,slsdtgt0(xb))
& sdtpldt0(X1,X2) = X0 )
| aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ) )
& X0 != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f45,negated_conjecture,
~ ? [X0] :
( ( ! [X1] :
( aElementOf0(X1,slsdtgt0(xa))
<=> ? [X2] :
( aElement0(X2)
& sdtasdt0(xa,X2) = X1 ) )
=> ( ! [X1] :
( aElementOf0(X1,slsdtgt0(xb))
<=> ? [X2] :
( aElement0(X2)
& sdtasdt0(xb,X2) = X1 ) )
=> ( ? [X1,X2] :
( aElementOf0(X1,slsdtgt0(xa))
& aElementOf0(X2,slsdtgt0(xb))
& sdtpldt0(X1,X2) = X0 )
| aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ) )
& X0 != sz00 ),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f55,plain,
( ? [X0] :
( aElement0(X0)
& sdtasdt0(xa,X0) = sz00 )
& aElementOf0(sz00,slsdtgt0(xa))
& ? [X1] :
( aElement0(X1)
& xa = sdtasdt0(xa,X1) )
& aElementOf0(xa,slsdtgt0(xa))
& ? [X2] :
( aElement0(X2)
& sz00 = sdtasdt0(xb,X2) )
& aElementOf0(sz00,slsdtgt0(xb))
& ? [X3] :
( aElement0(X3)
& xb = sdtasdt0(xb,X3) )
& aElementOf0(xb,slsdtgt0(xb)) ),
inference(rectify,[],[f43]) ).
fof(f56,plain,
~ ? [X0] :
( ( ! [X1] :
( aElementOf0(X1,slsdtgt0(xa))
<=> ? [X2] :
( aElement0(X2)
& sdtasdt0(xa,X2) = X1 ) )
=> ( ! [X3] :
( aElementOf0(X3,slsdtgt0(xb))
<=> ? [X4] :
( aElement0(X4)
& sdtasdt0(xb,X4) = X3 ) )
=> ( ? [X5,X6] :
( aElementOf0(X5,slsdtgt0(xa))
& aElementOf0(X6,slsdtgt0(xb))
& sdtpldt0(X5,X6) = X0 )
| aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ) )
& X0 != sz00 ),
inference(rectify,[],[f45]) ).
fof(f68,plain,
! [X0] :
( ( sdtpldt0(X0,sz00) = X0
& X0 = sdtpldt0(sz00,X0) )
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f111,plain,
! [X0] :
( ( ! [X5,X6] :
( ~ aElementOf0(X5,slsdtgt0(xa))
| ~ aElementOf0(X6,slsdtgt0(xb))
| sdtpldt0(X5,X6) != X0 )
& ~ aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ! [X3] :
( aElementOf0(X3,slsdtgt0(xb))
<=> ? [X4] :
( aElement0(X4)
& sdtasdt0(xb,X4) = X3 ) )
& ! [X1] :
( aElementOf0(X1,slsdtgt0(xa))
<=> ? [X2] :
( aElement0(X2)
& sdtasdt0(xa,X2) = X1 ) ) )
| sz00 = X0 ),
inference(ennf_transformation,[],[f56]) ).
fof(f112,plain,
! [X0] :
( ( ! [X5,X6] :
( ~ aElementOf0(X5,slsdtgt0(xa))
| ~ aElementOf0(X6,slsdtgt0(xb))
| sdtpldt0(X5,X6) != X0 )
& ~ aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ! [X3] :
( aElementOf0(X3,slsdtgt0(xb))
<=> ? [X4] :
( aElement0(X4)
& sdtasdt0(xb,X4) = X3 ) )
& ! [X1] :
( aElementOf0(X1,slsdtgt0(xa))
<=> ? [X2] :
( aElement0(X2)
& sdtasdt0(xa,X2) = X1 ) ) )
| sz00 = X0 ),
inference(flattening,[],[f111]) ).
fof(f161,plain,
( aElement0(sK31)
& sz00 = sdtasdt0(xa,sK31)
& aElementOf0(sz00,slsdtgt0(xa))
& aElement0(sK32)
& xa = sdtasdt0(xa,sK32)
& aElementOf0(xa,slsdtgt0(xa))
& aElement0(sK33)
& sz00 = sdtasdt0(xb,sK33)
& aElementOf0(sz00,slsdtgt0(xb))
& aElement0(sK34)
& xb = sdtasdt0(xb,sK34)
& aElementOf0(xb,slsdtgt0(xb)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK31,sK32,sK33,sK34]),skolemize(X0,sK31),skolemize(X1,sK32),skolemize(X2,sK33),skolemize(X3,sK34)],[f55]) ).
fof(f162,plain,
! [X0] :
( ( ! [X5,X6] :
( ~ aElementOf0(X5,slsdtgt0(xa))
| ~ aElementOf0(X6,slsdtgt0(xb))
| sdtpldt0(X5,X6) != X0 )
& ~ aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ! [X3] :
( ( aElementOf0(X3,slsdtgt0(xb))
| ! [X4] :
( ~ aElement0(X4)
| sdtasdt0(xb,X4) != X3 ) )
& ( ? [X4] :
( aElement0(X4)
& sdtasdt0(xb,X4) = X3 )
| ~ aElementOf0(X3,slsdtgt0(xb)) ) )
& ! [X1] :
( ( aElementOf0(X1,slsdtgt0(xa))
| ! [X2] :
( ~ aElement0(X2)
| sdtasdt0(xa,X2) != X1 ) )
& ( ? [X2] :
( aElement0(X2)
& sdtasdt0(xa,X2) = X1 )
| ~ aElementOf0(X1,slsdtgt0(xa)) ) ) )
| sz00 = X0 ),
inference(nnf_transformation,[],[f112]) ).
fof(f163,plain,
! [X0] :
( ( ! [X1,X2] :
( ~ aElementOf0(X1,slsdtgt0(xa))
| ~ aElementOf0(X2,slsdtgt0(xb))
| sdtpldt0(X1,X2) != X0 )
& ~ aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ! [X3] :
( ( aElementOf0(X3,slsdtgt0(xb))
| ! [X4] :
( ~ aElement0(X4)
| sdtasdt0(xb,X4) != X3 ) )
& ( ? [X5] :
( aElement0(X5)
& sdtasdt0(xb,X5) = X3 )
| ~ aElementOf0(X3,slsdtgt0(xb)) ) )
& ! [X6] :
( ( aElementOf0(X6,slsdtgt0(xa))
| ! [X7] :
( ~ aElement0(X7)
| sdtasdt0(xa,X7) != X6 ) )
& ( ? [X8] :
( aElement0(X8)
& sdtasdt0(xa,X8) = X6 )
| ~ aElementOf0(X6,slsdtgt0(xa)) ) ) )
| sz00 = X0 ),
inference(rectify,[],[f162]) ).
fof(f164,plain,
! [X0] :
( ( ! [X1,X2] :
( ~ aElementOf0(X1,slsdtgt0(xa))
| ~ aElementOf0(X2,slsdtgt0(xb))
| sdtpldt0(X1,X2) != X0 )
& ~ aElementOf0(X0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ! [X3] :
( ( aElementOf0(X3,slsdtgt0(xb))
| ! [X4] :
( ~ aElement0(X4)
| sdtasdt0(xb,X4) != X3 ) )
& ( ( aElement0(sK35(X3))
& sdtasdt0(xb,sK35(X3)) = X3 )
| ~ aElementOf0(X3,slsdtgt0(xb)) ) )
& ! [X6] :
( ( aElementOf0(X6,slsdtgt0(xa))
| ! [X7] :
( ~ aElement0(X7)
| sdtasdt0(xa,X7) != X6 ) )
& ( ( aElement0(sK36(X6))
& sdtasdt0(xa,sK36(X6)) = X6 )
| ~ aElementOf0(X6,slsdtgt0(xa)) ) ) )
| sz00 = X0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK35,sK36]),skolemize(X5,sK35(X3)),skolemize(X8,sK36(X6))],[f163]) ).
fof(f172,plain,
! [X0] :
( ~ aElement0(X0)
| sdtpldt0(sz00,X0) = X0 ),
inference(cnf_transformation,[],[f68]) ).
fof(f173,plain,
! [X0] :
( ~ aElement0(X0)
| sdtpldt0(X0,sz00) = X0 ),
inference(cnf_transformation,[],[f68]) ).
fof(f255,plain,
aElement0(xb),
inference(cnf_transformation,[],[f39]) ).
fof(f256,plain,
aElement0(xa),
inference(cnf_transformation,[],[f39]) ).
fof(f257,plain,
( sz00 != xa
| sz00 != xb ),
inference(cnf_transformation,[],[f40]) ).
fof(f293,plain,
aElementOf0(xb,slsdtgt0(xb)),
inference(cnf_transformation,[],[f161]) ).
fof(f296,plain,
aElementOf0(sz00,slsdtgt0(xb)),
inference(cnf_transformation,[],[f161]) ).
fof(f299,plain,
aElementOf0(xa,slsdtgt0(xa)),
inference(cnf_transformation,[],[f161]) ).
fof(f302,plain,
aElementOf0(sz00,slsdtgt0(xa)),
inference(cnf_transformation,[],[f161]) ).
fof(f312,plain,
! [X2,X0,X1] :
( ~ aElementOf0(X1,slsdtgt0(xa))
| ~ aElementOf0(X2,slsdtgt0(xb))
| sdtpldt0(X1,X2) != X0
| sz00 = X0 ),
inference(cnf_transformation,[],[f164]) ).
fof(f328,plain,
! [X2,X1] :
( ~ aElementOf0(X2,slsdtgt0(xb))
| ~ aElementOf0(X1,slsdtgt0(xa))
| sz00 = sdtpldt0(X1,X2) ),
inference(equality_resolution,[],[f312]) ).
fof(f361,definition,
( spl37_8
<=> sz00 = xb ),
introduced(definition,[new_symbols(definition,[spl37_8])],[avatar_definition]) ).
fof(f365,definition,
( spl37_9
<=> sz00 = xa ),
introduced(definition,[new_symbols(definition,[spl37_9])],[avatar_definition]) ).
fof(f367,plain,
( sz00 != xa
| spl37_9 ),
inference(avatar_component_clause,[],[f365]) ).
fof(f368,plain,
( ~ spl37_8
| ~ spl37_9 ),
inference(avatar_split_clause,[],[f257,f365,f361]) ).
fof(f868,plain,
! [X0] :
( ~ aElementOf0(X0,slsdtgt0(xa))
| sz00 = sdtpldt0(X0,xb) ),
inference(resolution,[],[f293,f328]) ).
fof(f872,plain,
! [X0] :
( ~ aElementOf0(X0,slsdtgt0(xa))
| sz00 = sdtpldt0(X0,sz00) ),
inference(resolution,[],[f296,f328]) ).
fof(f895,plain,
sz00 = sdtpldt0(sz00,xb),
inference(resolution,[],[f868,f302]) ).
fof(f919,plain,
sz00 = sdtpldt0(xa,sz00),
inference(resolution,[],[f872,f299]) ).
fof(f947,plain,
xb = sdtpldt0(sz00,xb),
inference(resolution,[],[f172,f255]) ).
fof(f969,plain,
sz00 = xb,
inference(forward_demodulation,[],[f947,f895]) ).
fof(f970,plain,
spl37_8,
inference(avatar_split_clause,[],[f969,f361]) ).
fof(f1009,plain,
xa = sdtpldt0(xa,sz00),
inference(resolution,[],[f173,f256]) ).
fof(f1039,plain,
sz00 = xa,
inference(forward_demodulation,[],[f1009,f919]) ).
fof(f1040,plain,
( $false
| spl37_9 ),
inference(forward_subsumption_resolution,[],[f1039,f367]) ).
fof(f1041,plain,
spl37_9,
inference(avatar_contradiction_clause,[],[f1040]) ).
cnf(s9,plain,
( ~ spl37_8
| ~ spl37_9 ),
inference(sat_conversion,[],[f368]) ).
cnf(s97,plain,
spl37_8,
inference(sat_conversion,[],[f970]) ).
cnf(s98,plain,
spl37_9,
inference(sat_conversion,[],[f1041]) ).
cnf(s126,plain,
$false,
inference(rat,[],[s9,s98,s97]) ).
fof(f1042,plain,
$false,
inference(avatar_sat_refutation,[],[s126]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG109+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.37 % Computer : n017.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 23:14:06 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.41 Running first-order model finding
% 0.10/0.41 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
% 0.15/0.47 % (3061375)Will run a generic schedule for satisfiability detection.
% 0.15/0.47 % (3061384)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1876061260:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.15/0.47 % (3061381)% WARNING: option uhcvi not known.
% 0.15/0.47 % (3061380)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3159419852_2999 on theBenchmark for (2999ds/0Mi)
% 0.15/0.47 % (3061382)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=568501524:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.15/0.47 % (3061381)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=141241473:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.15/0.47 % (3061383)dis+10_1_sil=32000:sp=arity:random_seed=999909130:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.15/0.47 % (3061386)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4123617875:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.15/0.47 % (3061385)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=806709838:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.15/0.47 % TRYING [1]
% 0.15/0.47 % TRYING [2]
% 0.15/0.47 % (3061383) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3061375-3061383"...
% 0.15/0.47 % TRYING [3]
% 0.15/0.47 % (3061383)...printing done.
% 0.15/0.47 % (3061383)Refutation found. Thanks to Tanya!
% 0.15/0.47 % SZS status Theorem for theBenchmark
% 0.15/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.47 % (3061383)------------------------------
% 0.15/0.47 % (3061383)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.47 % (3061383)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.47 % (3061383)CaDiCaL version: 2.1.3
% 0.15/0.47 % (3061383)Termination reason: Refutation
% 0.15/0.47 % (3061383)Time elapsed: 0.017 s
% 0.15/0.47 % (3061383)Peak memory usage: 13 MB
% 0.15/0.47 % (3061383)Instructions burned: 23 (million)
% 0.15/0.47 % (3061375)Success in time 0.051 s
% 0.15/0.47 % Vampire exiting
%------------------------------------------------------------------------------