%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : RNG121+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 : n009.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 12:36:07 PM UTC 2026
% Result : Theorem 0.14s 0.45s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 35 ( 12 unt; 2 def)
% Number of atoms : 113 ( 29 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 104 ( 26 ~; 25 |; 50 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 31 ( 0 sgn 11 !; 20 ?)
% 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(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(f53,conjecture,
( ? [X0,X1] :
( aElementOf0(X0,slsdtgt0(xa))
& aElementOf0(X1,slsdtgt0(xb))
& sdtpldt0(X0,X1) = xb )
| ? [X0,X1] :
( aElementOf0(X0,slsdtgt0(xa))
& aElementOf0(X1,slsdtgt0(xb))
& sdtpldt0(X0,X1) = xb )
| aElementOf0(xb,xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f54,negated_conjecture,
~ ( ? [X0,X1] :
( aElementOf0(X0,slsdtgt0(xa))
& aElementOf0(X1,slsdtgt0(xb))
& sdtpldt0(X0,X1) = xb )
| ? [X0,X1] :
( aElementOf0(X0,slsdtgt0(xa))
& aElementOf0(X1,slsdtgt0(xb))
& sdtpldt0(X0,X1) = xb )
| aElementOf0(xb,xI) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f64,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(f69,plain,
~ ( ? [X0,X1] :
( aElementOf0(X0,slsdtgt0(xa))
& aElementOf0(X1,slsdtgt0(xb))
& sdtpldt0(X0,X1) = xb )
| ? [X2,X3] :
( aElementOf0(X2,slsdtgt0(xa))
& aElementOf0(X3,slsdtgt0(xb))
& xb = sdtpldt0(X2,X3) )
| aElementOf0(xb,xI) ),
inference(rectify,[],[f54]) ).
fof(f80,plain,
! [X0] :
( ( sdtpldt0(X0,sz00) = X0
& X0 = sdtpldt0(sz00,X0) )
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f127,plain,
( ! [X0,X1] :
( ~ aElementOf0(X0,slsdtgt0(xa))
| ~ aElementOf0(X1,slsdtgt0(xb))
| sdtpldt0(X0,X1) != xb )
& ! [X2,X3] :
( ~ aElementOf0(X2,slsdtgt0(xa))
| ~ aElementOf0(X3,slsdtgt0(xb))
| xb != sdtpldt0(X2,X3) )
& ~ aElementOf0(xb,xI) ),
inference(ennf_transformation,[],[f69]) ).
fof(f178,plain,
( aElement0(sK32)
& sz00 = sdtasdt0(xa,sK32)
& aElementOf0(sz00,slsdtgt0(xa))
& aElement0(sK33)
& xa = sdtasdt0(xa,sK33)
& aElementOf0(xa,slsdtgt0(xa))
& aElement0(sK34)
& sz00 = sdtasdt0(xb,sK34)
& aElementOf0(sz00,slsdtgt0(xb))
& aElement0(sK35)
& xb = sdtasdt0(xb,sK35)
& aElementOf0(xb,slsdtgt0(xb)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK32,sK33,sK34,sK35]),skolemize(X0,sK32),skolemize(X1,sK33),skolemize(X2,sK34),skolemize(X3,sK35)],[f64]) ).
fof(f195,plain,
! [X0] :
( ~ aElement0(X0)
| sdtpldt0(sz00,X0) = X0 ),
inference(cnf_transformation,[],[f80]) ).
fof(f279,plain,
aElement0(xb),
inference(cnf_transformation,[],[f39]) ).
fof(f317,plain,
aElementOf0(xb,slsdtgt0(xb)),
inference(cnf_transformation,[],[f178]) ).
fof(f326,plain,
aElementOf0(sz00,slsdtgt0(xa)),
inference(cnf_transformation,[],[f178]) ).
fof(f371,plain,
! [X2,X3] :
( ~ aElementOf0(X2,slsdtgt0(xa))
| ~ aElementOf0(X3,slsdtgt0(xb))
| xb != sdtpldt0(X2,X3) ),
inference(cnf_transformation,[],[f127]) ).
fof(f469,plain,
~ aElementOf0(sz00,slsdtgt0(xa)),
inference(consistent_polarity_flipping,[],[f326]) ).
fof(f472,plain,
~ aElementOf0(xb,slsdtgt0(xb)),
inference(consistent_polarity_flipping,[],[f317]) ).
fof(f493,plain,
! [X2,X3] :
( xb != sdtpldt0(X2,X3)
| aElementOf0(X3,slsdtgt0(xb))
| aElementOf0(X2,slsdtgt0(xa)) ),
inference(consistent_polarity_flipping,[],[f371]) ).
fof(f615,plain,
xb = sdtpldt0(sz00,xb),
inference(resolution,[],[f195,f279]) ).
fof(f634,plain,
( xb != xb
| aElementOf0(xb,slsdtgt0(xb))
| aElementOf0(sz00,slsdtgt0(xa)) ),
inference(superposition,[],[f493,f615]) ).
fof(f635,plain,
( aElementOf0(xb,slsdtgt0(xb))
| aElementOf0(sz00,slsdtgt0(xa)) ),
inference(trivial_inequality_removal,[],[f634]) ).
fof(f637,definition,
( spl48_22
<=> aElementOf0(sz00,slsdtgt0(xa)) ),
introduced(definition,[new_symbols(definition,[spl48_22])],[avatar_definition]) ).
fof(f639,plain,
( aElementOf0(sz00,slsdtgt0(xa))
| ~ spl48_22 ),
inference(avatar_component_clause,[],[f637]) ).
fof(f641,definition,
( spl48_23
<=> aElementOf0(xb,slsdtgt0(xb)) ),
introduced(definition,[new_symbols(definition,[spl48_23])],[avatar_definition]) ).
fof(f643,plain,
( aElementOf0(xb,slsdtgt0(xb))
| ~ spl48_23 ),
inference(avatar_component_clause,[],[f641]) ).
fof(f644,plain,
( spl48_22
| spl48_23 ),
inference(avatar_split_clause,[],[f635,f641,f637]) ).
fof(f645,plain,
( $false
| ~ spl48_22 ),
inference(resolution,[],[f639,f469]) ).
fof(f646,plain,
~ spl48_22,
inference(avatar_contradiction_clause,[],[f645]) ).
fof(f647,plain,
( $false
| ~ spl48_23 ),
inference(resolution,[],[f643,f472]) ).
fof(f648,plain,
~ spl48_23,
inference(avatar_contradiction_clause,[],[f647]) ).
cnf(s16,plain,
( spl48_22
| spl48_23 ),
inference(sat_conversion,[],[f644]) ).
cnf(s17,plain,
~ spl48_22,
inference(sat_conversion,[],[f646]) ).
cnf(s18,plain,
~ spl48_23,
inference(sat_conversion,[],[f648]) ).
cnf(s19,plain,
$false,
inference(rat,[],[s16,s18,s17]) ).
fof(f649,plain,
$false,
inference(avatar_sat_refutation,[],[s19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG121+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.36 % Computer : n009.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 23:22:00 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.14/0.39 Running first-order model finding
% 0.14/0.39 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
% 0.14/0.45 % (2519698)Will run a generic schedule for satisfiability detection.
% 0.14/0.45 % (2519704)% WARNING: option uhcvi not known.
% 0.14/0.45 % (2519703)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1344599868_2999 on theBenchmark for (2999ds/0Mi)
% 0.14/0.45 % (2519704)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=892238168:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.14/0.45 % (2519709)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3931321049:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.14/0.45 % (2519705)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1404367232:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.14/0.45 % (2519706)dis+10_1_sil=32000:sp=arity:random_seed=2693674210:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.14/0.45 % (2519707)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=72067295:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.14/0.45 % (2519708)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1851072049:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.14/0.45 % (2519709) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2519698-2519709"...
% 0.14/0.45 % (2519708) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2519698-2519708"...
% 0.14/0.45 % (2519709)...printing done.
% 0.14/0.45 % (2519705) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2519698-2519705"...
% 0.14/0.45 % TRYING [1]
% 0.14/0.45 % (2519708)...printing done.
% 0.14/0.45 % (2519709)Refutation found. Thanks to Tanya!
% 0.14/0.45 % SZS status Theorem for theBenchmark
% 0.14/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.45 % (2519709)------------------------------
% 0.14/0.45 % (2519709)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.14/0.45 % (2519709)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.14/0.45 % (2519709)CaDiCaL version: 2.1.3
% 0.14/0.45 % (2519709)Termination reason: Refutation
% 0.14/0.45 % (2519709)Time elapsed: 0.011 s
% 0.14/0.45 % (2519709)Peak memory usage: 13 MB
% 0.14/0.45 % (2519709)Instructions burned: 15 (million)
% 0.14/0.45 % (2519698)Success in time 0.046 s
% 0.14/0.45 % Vampire exiting
%------------------------------------------------------------------------------