%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : RNG108+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 : n011.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 0.16s 0.52s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 50 ( 20 unt; 4 def)
% Number of atoms : 142 ( 46 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 158 ( 66 ~; 56 |; 30 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn 22 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aElement0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(f3,axiom,
aElement0(sz10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
fof(f13,axiom,
! [X0] :
( aElement0(X0)
=> ( sdtasdt0(X0,sz10) = X0
& X0 = sdtasdt0(sz10,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulUnit) ).
fof(f16,axiom,
! [X0] :
( aElement0(X0)
=> ( sdtasdt0(X0,sz00) = sz00
& sz00 = sdtasdt0(sz00,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulZero) ).
fof(f39,axiom,
( aElement0(xa)
& aElement0(xb) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2091) ).
fof(f43,conjecture,
( ( ? [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__) ).
fof(f44,negated_conjecture,
~ ( ( ? [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)) ) ),
inference(negated_conjecture,[status(cth)],[f43]) ).
fof(f50,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,[],[f44]) ).
fof(f67,plain,
! [X0] :
( ( sdtasdt0(X0,sz10) = X0
& X0 = sdtasdt0(sz10,X0) )
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f71,plain,
! [X0] :
( ( sdtasdt0(X0,sz00) = sz00
& sz00 = sdtasdt0(sz00,X0) )
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f110,plain,
( ( ! [X0] :
( ~ aElement0(X0)
| sz00 != sdtasdt0(xa,X0) )
& ~ 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(ennf_transformation,[],[f50]) ).
fof(f111,plain,
aElement0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f112,plain,
aElement0(sz10),
inference(cnf_transformation,[],[f3]) ).
fof(f125,plain,
! [X0] :
( ~ aElement0(X0)
| sdtasdt0(X0,sz10) = X0 ),
inference(cnf_transformation,[],[f67]) ).
fof(f131,plain,
! [X0] :
( ~ aElement0(X0)
| sz00 = sdtasdt0(X0,sz00) ),
inference(cnf_transformation,[],[f71]) ).
fof(f200,plain,
aElement0(xb),
inference(cnf_transformation,[],[f39]) ).
fof(f201,plain,
aElement0(xa),
inference(cnf_transformation,[],[f39]) ).
fof(f254,plain,
! [X2,X3,X0,X1] :
( xb != sdtasdt0(xb,X3)
| ~ aElement0(X3)
| sz00 != sdtasdt0(xb,X2)
| ~ aElement0(X2)
| xa != sdtasdt0(xa,X1)
| ~ aElement0(X1)
| sz00 != sdtasdt0(xa,X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f110]) ).
fof(f285,definition,
( spl28_1
<=> ! [X0] :
( sz00 != sdtasdt0(xa,X0)
| ~ aElement0(X0) ) ),
introduced(definition,[new_symbols(definition,[spl28_1])],[avatar_definition]) ).
fof(f286,plain,
( ! [X0] :
( ~ aElement0(X0)
| sz00 != sdtasdt0(xa,X0) )
| ~ spl28_1 ),
inference(avatar_component_clause,[],[f285]) ).
fof(f301,definition,
( spl28_5
<=> ! [X3] :
( xb != sdtasdt0(xb,X3)
| ~ aElement0(X3) ) ),
introduced(definition,[new_symbols(definition,[spl28_5])],[avatar_definition]) ).
fof(f302,plain,
( ! [X3] :
( ~ aElement0(X3)
| xb != sdtasdt0(xb,X3) )
| ~ spl28_5 ),
inference(avatar_component_clause,[],[f301]) ).
fof(f305,definition,
( spl28_6
<=> ! [X2] :
( sz00 != sdtasdt0(xb,X2)
| ~ aElement0(X2) ) ),
introduced(definition,[new_symbols(definition,[spl28_6])],[avatar_definition]) ).
fof(f306,plain,
( ! [X2] :
( ~ aElement0(X2)
| sz00 != sdtasdt0(xb,X2) )
| ~ spl28_6 ),
inference(avatar_component_clause,[],[f305]) ).
fof(f310,definition,
( spl28_7
<=> ! [X1] :
( xa != sdtasdt0(xa,X1)
| ~ aElement0(X1) ) ),
introduced(definition,[new_symbols(definition,[spl28_7])],[avatar_definition]) ).
fof(f311,plain,
( ! [X1] :
( ~ aElement0(X1)
| xa != sdtasdt0(xa,X1) )
| ~ spl28_7 ),
inference(avatar_component_clause,[],[f310]) ).
fof(f313,plain,
( spl28_1
| spl28_7
| spl28_6
| spl28_5 ),
inference(avatar_split_clause,[],[f254,f301,f305,f310,f285]) ).
fof(f343,plain,
( xb != sdtasdt0(xb,sz10)
| ~ spl28_5 ),
inference(resolution,[],[f112,f302]) ).
fof(f390,plain,
xa = sdtasdt0(xa,sz10),
inference(resolution,[],[f125,f201]) ).
fof(f391,plain,
xb = sdtasdt0(xb,sz10),
inference(resolution,[],[f125,f200]) ).
fof(f395,plain,
( $false
| ~ spl28_5 ),
inference(forward_subsumption_resolution,[],[f391,f343]) ).
fof(f396,plain,
~ spl28_5,
inference(avatar_contradiction_clause,[],[f395]) ).
fof(f397,plain,
( sz00 != sdtasdt0(xb,sz00)
| ~ spl28_6 ),
inference(resolution,[],[f306,f111]) ).
fof(f417,plain,
sz00 = sdtasdt0(xa,sz00),
inference(resolution,[],[f131,f201]) ).
fof(f418,plain,
sz00 = sdtasdt0(xb,sz00),
inference(resolution,[],[f131,f200]) ).
fof(f422,plain,
( $false
| ~ spl28_6 ),
inference(forward_subsumption_resolution,[],[f418,f397]) ).
fof(f423,plain,
~ spl28_6,
inference(avatar_contradiction_clause,[],[f422]) ).
fof(f425,plain,
( xa != sdtasdt0(xa,sz10)
| ~ spl28_7 ),
inference(resolution,[],[f311,f112]) ).
fof(f432,plain,
( $false
| ~ spl28_7 ),
inference(forward_subsumption_resolution,[],[f425,f390]) ).
fof(f433,plain,
~ spl28_7,
inference(avatar_contradiction_clause,[],[f432]) ).
fof(f436,plain,
( sz00 != sdtasdt0(xa,sz00)
| ~ spl28_1 ),
inference(resolution,[],[f286,f111]) ).
fof(f445,plain,
( $false
| ~ spl28_1 ),
inference(forward_subsumption_resolution,[],[f436,f417]) ).
fof(f446,plain,
~ spl28_1,
inference(avatar_contradiction_clause,[],[f445]) ).
cnf(s6,plain,
( spl28_1
| spl28_5
| spl28_6
| spl28_7 ),
inference(sat_conversion,[],[f313]) ).
cnf(s18,plain,
~ spl28_5,
inference(sat_conversion,[],[f396]) ).
cnf(s19,plain,
~ spl28_6,
inference(sat_conversion,[],[f423]) ).
cnf(s20,plain,
~ spl28_7,
inference(sat_conversion,[],[f433]) ).
cnf(s22,plain,
~ spl28_1,
inference(sat_conversion,[],[f446]) ).
cnf(s31,plain,
$false,
inference(rat,[],[s6,s20,s19,s18,s22]) ).
fof(f448,plain,
$false,
inference(avatar_sat_refutation,[],[s31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : RNG108+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.43 % Computer : n011.cluster.edu
% 0.12/0.43 % Model : x86_64 x86_64
% 0.12/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.43 % Memory : 8046.5625MB
% 0.12/0.43 % OS : Linux 6.8.0-71-generic
% 0.12/0.43 % CPULimit : 300
% 0.12/0.43 % WCLimit : 300
% 0.12/0.43 % DateTime : Sun Sep 27 23:19:01 UTC 2026
% 0.12/0.43 % CPUTime :
% 0.12/0.43 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.16/0.47 Running first-order model finding
% 0.16/0.47 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
% 0.16/0.52 % (2872966)Will run a generic schedule for satisfiability detection.
% 0.16/0.52 % (2872975)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1028095952:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.52 % (2872972)% WARNING: option uhcvi not known.
% 0.16/0.52 % (2872976)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1453207335:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.52 % (2872971)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2443776133_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.52 % (2872973)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=680251598:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.52 % (2872974)dis+10_1_sil=32000:sp=arity:random_seed=1864255488:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.52 % (2872972)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4273586663:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.52 % (2872975) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2872966-2872975"...
% 0.16/0.52 % (2872977)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4268169777:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.52 % (2872975)...printing done.
% 0.16/0.52 % (2872975)Refutation found. Thanks to Tanya!
% 0.16/0.52 % SZS status Theorem for theBenchmark
% 0.16/0.52 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.52 % (2872975)------------------------------
% 0.16/0.52 % (2872975)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.52 % (2872975)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.52 % (2872975)CaDiCaL version: 2.1.3
% 0.16/0.52 % (2872975)Termination reason: Refutation
% 0.16/0.52 % (2872975)Time elapsed: 0.007 s
% 0.16/0.52 % (2872975)Peak memory usage: 13 MB
% 0.16/0.52 % (2872975)Instructions burned: 20 (million)
% 0.16/0.52 % (2872966)Success in time 0.04 s
% 0.16/0.52 % Vampire exiting
%------------------------------------------------------------------------------