%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : RNG091+2 : 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 : n026.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 12:36:00 PM UTC 2026
% Result : Theorem 0.11s 0.46s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 35 ( 14 unt; 2 def)
% Number of atoms : 98 ( 20 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 117 ( 54 ~; 42 |; 19 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 28 ( 0 sgn 16 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f29,axiom,
( aElementOf0(sdtpldt0(xk,xm),xI)
& aElementOf0(sdtpldt0(xl,xn),xJ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__994) ).
fof(f30,axiom,
( aElementOf0(sdtasdt0(xz,xk),xI)
& aElementOf0(sdtasdt0(xz,xl),xJ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1021) ).
fof(f31,axiom,
sdtpldt0(xx,xy) = sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1061) ).
fof(f32,axiom,
sdtasdt0(xz,xx) = sdtpldt0(sdtasdt0(xz,xk),sdtasdt0(xz,xl)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1098) ).
fof(f33,conjecture,
( ( ? [X0,X1] :
( aElementOf0(X0,xI)
& aElementOf0(X1,xJ)
& sdtpldt0(X0,X1) = sdtpldt0(xx,xy) )
| aElementOf0(sdtpldt0(xx,xy),sdtpldt1(xI,xJ)) )
& ( ? [X0,X1] :
( aElementOf0(X0,xI)
& aElementOf0(X1,xJ)
& sdtpldt0(X0,X1) = sdtasdt0(xz,xx) )
| aElementOf0(sdtasdt0(xz,xx),sdtpldt1(xI,xJ)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f34,negated_conjecture,
~ ( ( ? [X0,X1] :
( aElementOf0(X0,xI)
& aElementOf0(X1,xJ)
& sdtpldt0(X0,X1) = sdtpldt0(xx,xy) )
| aElementOf0(sdtpldt0(xx,xy),sdtpldt1(xI,xJ)) )
& ( ? [X0,X1] :
( aElementOf0(X0,xI)
& aElementOf0(X1,xJ)
& sdtpldt0(X0,X1) = sdtasdt0(xz,xx) )
| aElementOf0(sdtasdt0(xz,xx),sdtpldt1(xI,xJ)) ) ),
inference(negated_conjecture,[status(cth)],[f33]) ).
fof(f41,plain,
~ ( ( ? [X0,X1] :
( aElementOf0(X0,xI)
& aElementOf0(X1,xJ)
& sdtpldt0(X0,X1) = sdtpldt0(xx,xy) )
| aElementOf0(sdtpldt0(xx,xy),sdtpldt1(xI,xJ)) )
& ( ? [X2,X3] :
( aElementOf0(X2,xI)
& aElementOf0(X3,xJ)
& sdtasdt0(xz,xx) = sdtpldt0(X2,X3) )
| aElementOf0(sdtasdt0(xz,xx),sdtpldt1(xI,xJ)) ) ),
inference(rectify,[],[f34]) ).
fof(f74,plain,
( ( ! [X0,X1] :
( ~ aElementOf0(X0,xI)
| ~ aElementOf0(X1,xJ)
| sdtpldt0(X0,X1) != sdtpldt0(xx,xy) )
& ~ aElementOf0(sdtpldt0(xx,xy),sdtpldt1(xI,xJ)) )
| ( ! [X2,X3] :
( ~ aElementOf0(X2,xI)
| ~ aElementOf0(X3,xJ)
| sdtasdt0(xz,xx) != sdtpldt0(X2,X3) )
& ~ aElementOf0(sdtasdt0(xz,xx),sdtpldt1(xI,xJ)) ) ),
inference(ennf_transformation,[],[f41]) ).
fof(f163,plain,
aElementOf0(sdtpldt0(xl,xn),xJ),
inference(cnf_transformation,[],[f29]) ).
fof(f164,plain,
aElementOf0(sdtpldt0(xk,xm),xI),
inference(cnf_transformation,[],[f29]) ).
fof(f165,plain,
aElementOf0(sdtasdt0(xz,xl),xJ),
inference(cnf_transformation,[],[f30]) ).
fof(f166,plain,
aElementOf0(sdtasdt0(xz,xk),xI),
inference(cnf_transformation,[],[f30]) ).
fof(f167,plain,
sdtpldt0(xx,xy) = sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)),
inference(cnf_transformation,[],[f31]) ).
fof(f168,plain,
sdtasdt0(xz,xx) = sdtpldt0(sdtasdt0(xz,xk),sdtasdt0(xz,xl)),
inference(cnf_transformation,[],[f32]) ).
fof(f172,plain,
! [X2,X3,X0,X1] :
( ~ aElementOf0(X0,xI)
| ~ aElementOf0(X1,xJ)
| sdtpldt0(X0,X1) != sdtpldt0(xx,xy)
| ~ aElementOf0(X2,xI)
| ~ aElementOf0(X3,xJ)
| sdtasdt0(xz,xx) != sdtpldt0(X2,X3) ),
inference(cnf_transformation,[],[f74]) ).
fof(f189,definition,
( spl14_3
<=> ! [X2,X3] :
( ~ aElementOf0(X2,xI)
| sdtasdt0(xz,xx) != sdtpldt0(X2,X3)
| ~ aElementOf0(X3,xJ) ) ),
introduced(definition,[new_symbols(definition,[spl14_3])],[avatar_definition]) ).
fof(f190,plain,
( ! [X2,X3] :
( sdtasdt0(xz,xx) != sdtpldt0(X2,X3)
| ~ aElementOf0(X2,xI)
| ~ aElementOf0(X3,xJ) )
| ~ spl14_3 ),
inference(avatar_component_clause,[],[f189]) ).
fof(f193,definition,
( spl14_4
<=> ! [X0,X1] :
( ~ aElementOf0(X0,xI)
| sdtpldt0(X0,X1) != sdtpldt0(xx,xy)
| ~ aElementOf0(X1,xJ) ) ),
introduced(definition,[new_symbols(definition,[spl14_4])],[avatar_definition]) ).
fof(f194,plain,
( ! [X0,X1] :
( sdtpldt0(X0,X1) != sdtpldt0(xx,xy)
| ~ aElementOf0(X0,xI)
| ~ aElementOf0(X1,xJ) )
| ~ spl14_4 ),
inference(avatar_component_clause,[],[f193]) ).
fof(f196,plain,
( spl14_3
| spl14_4 ),
inference(avatar_split_clause,[],[f172,f193,f189]) ).
fof(f592,plain,
( sdtasdt0(xz,xx) != sdtasdt0(xz,xx)
| ~ aElementOf0(sdtasdt0(xz,xk),xI)
| ~ aElementOf0(sdtasdt0(xz,xl),xJ)
| ~ spl14_3 ),
inference(superposition,[],[f190,f168]) ).
fof(f593,plain,
( ~ aElementOf0(sdtasdt0(xz,xk),xI)
| ~ aElementOf0(sdtasdt0(xz,xl),xJ)
| ~ spl14_3 ),
inference(trivial_inequality_removal,[],[f592]) ).
fof(f594,plain,
( ~ aElementOf0(sdtasdt0(xz,xl),xJ)
| ~ spl14_3 ),
inference(forward_subsumption_resolution,[],[f593,f166]) ).
fof(f610,plain,
( $false
| ~ spl14_3 ),
inference(forward_subsumption_resolution,[],[f594,f165]) ).
fof(f611,plain,
~ spl14_3,
inference(avatar_contradiction_clause,[],[f610]) ).
fof(f630,plain,
( sdtpldt0(xx,xy) != sdtpldt0(xx,xy)
| ~ aElementOf0(sdtpldt0(xk,xm),xI)
| ~ aElementOf0(sdtpldt0(xl,xn),xJ)
| ~ spl14_4 ),
inference(superposition,[],[f194,f167]) ).
fof(f638,plain,
( ~ aElementOf0(sdtpldt0(xk,xm),xI)
| ~ aElementOf0(sdtpldt0(xl,xn),xJ)
| ~ spl14_4 ),
inference(trivial_inequality_removal,[],[f630]) ).
fof(f650,plain,
( ~ aElementOf0(sdtpldt0(xl,xn),xJ)
| ~ spl14_4 ),
inference(forward_subsumption_resolution,[],[f638,f164]) ).
fof(f656,plain,
( $false
| ~ spl14_4 ),
inference(forward_subsumption_resolution,[],[f650,f163]) ).
fof(f657,plain,
~ spl14_4,
inference(avatar_contradiction_clause,[],[f656]) ).
cnf(s4,plain,
( spl14_3
| spl14_4 ),
inference(sat_conversion,[],[f196]) ).
cnf(s33,plain,
~ spl14_3,
inference(sat_conversion,[],[f611]) ).
cnf(s38,plain,
~ spl14_4,
inference(sat_conversion,[],[f657]) ).
cnf(s40,plain,
$false,
inference(rat,[],[s4,s38,s33]) ).
fof(f658,plain,
$false,
inference(avatar_sat_refutation,[],[s40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG091+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n026.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 23:15:57 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.40 Running first-order model finding
% 0.11/0.40 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
% 0.11/0.46 % (3320007)Will run a generic schedule for satisfiability detection.
% 0.11/0.46 % (3320015)dis+10_1_sil=32000:sp=arity:random_seed=525684146:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.11/0.46 % (3320013)% WARNING: option uhcvi not known.
% 0.11/0.46 % (3320015) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3320007-3320015"...
% 0.11/0.46 % (3320015)...printing done.
% 0.11/0.46 % (3320014)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2456981985:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.11/0.46 % (3320012)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2670386674_2999 on theBenchmark for (2999ds/0Mi)
% 0.11/0.46 % (3320013)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=726002163:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.11/0.46 % (3320016)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1239490327:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.11/0.46 % (3320018)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=98151103:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.11/0.46 % (3320017)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=911047960:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.11/0.46 % (3320015)Refutation found. Thanks to Tanya!
% 0.11/0.46 % SZS status Theorem for theBenchmark
% 0.11/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.46 % (3320015)------------------------------
% 0.11/0.46 % (3320015)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.46 % (3320015)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.46 % (3320015)CaDiCaL version: 2.1.3
% 0.11/0.46 % (3320015)Termination reason: Refutation
% 0.11/0.46 % (3320015)Time elapsed: 0.006 s
% 0.11/0.46 % (3320015)Peak memory usage: 12 MB
% 0.11/0.46 % (3320015)Instructions burned: 14 (million)
% 0.11/0.46 % (3320007)Success in time 0.044 s
% 0.11/0.46 % Vampire exiting
%------------------------------------------------------------------------------