%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : RNG088+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 0.10s 0.45s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 33 ( 10 unt; 2 def)
% Number of atoms : 98 ( 2 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 92 ( 27 ~; 24 |; 27 &)
% ( 2 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 3 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 22 ( 0 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f25,axiom,
( aSet0(xI)
& ! [X0] :
( aElementOf0(X0,xI)
=> ( ! [X1] :
( aElementOf0(X1,xI)
=> aElementOf0(sdtpldt0(X0,X1),xI) )
& ! [X1] :
( aElement0(X1)
=> aElementOf0(sdtasdt0(X1,X0),xI) ) ) )
& aIdeal0(xI)
& aSet0(xJ)
& ! [X0] :
( aElementOf0(X0,xJ)
=> ( ! [X1] :
( aElementOf0(X1,xJ)
=> aElementOf0(sdtpldt0(X0,X1),xJ) )
& ! [X1] :
( aElement0(X1)
=> aElementOf0(sdtasdt0(X1,X0),xJ) ) ) )
& aIdeal0(xJ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__870) ).
fof(f27,axiom,
( aElementOf0(xk,xI)
& aElementOf0(xl,xJ)
& xx = sdtpldt0(xk,xl) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__934) ).
fof(f28,axiom,
( aElementOf0(xm,xI)
& aElementOf0(xn,xJ)
& xy = sdtpldt0(xm,xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__967) ).
fof(f29,conjecture,
( aElementOf0(sdtpldt0(xk,xm),xI)
& aElementOf0(sdtpldt0(xl,xn),xJ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f30,negated_conjecture,
~ ( aElementOf0(sdtpldt0(xk,xm),xI)
& aElementOf0(sdtpldt0(xl,xn),xJ) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f33,plain,
( aSet0(xI)
& ! [X0] :
( aElementOf0(X0,xI)
=> ( ! [X1] :
( aElementOf0(X1,xI)
=> aElementOf0(sdtpldt0(X0,X1),xI) )
& ! [X2] :
( aElement0(X2)
=> aElementOf0(sdtasdt0(X2,X0),xI) ) ) )
& aIdeal0(xI)
& aSet0(xJ)
& ! [X3] :
( aElementOf0(X3,xJ)
=> ( ! [X4] :
( aElementOf0(X4,xJ)
=> aElementOf0(sdtpldt0(X3,X4),xJ) )
& ! [X5] :
( aElement0(X5)
=> aElementOf0(sdtasdt0(X5,X3),xJ) ) ) )
& aIdeal0(xJ) ),
inference(rectify,[],[f25]) ).
fof(f68,plain,
( aSet0(xI)
& ! [X0] :
( ( ! [X1] :
( aElementOf0(sdtpldt0(X0,X1),xI)
| ~ aElementOf0(X1,xI) )
& ! [X2] :
( aElementOf0(sdtasdt0(X2,X0),xI)
| ~ aElement0(X2) ) )
| ~ aElementOf0(X0,xI) )
& aIdeal0(xI)
& aSet0(xJ)
& ! [X3] :
( ( ! [X4] :
( aElementOf0(sdtpldt0(X3,X4),xJ)
| ~ aElementOf0(X4,xJ) )
& ! [X5] :
( aElementOf0(sdtasdt0(X5,X3),xJ)
| ~ aElement0(X5) ) )
| ~ aElementOf0(X3,xJ) )
& aIdeal0(xJ) ),
inference(ennf_transformation,[],[f33]) ).
fof(f69,plain,
( ~ aElementOf0(sdtpldt0(xk,xm),xI)
| ~ aElementOf0(sdtpldt0(xl,xn),xJ) ),
inference(ennf_transformation,[],[f30]) ).
fof(f117,plain,
! [X0,X1] :
( aElementOf0(sdtpldt0(X0,X1),xI)
| ~ aElementOf0(X1,xI)
| ~ aElementOf0(X0,xI) ),
inference(cnf_transformation,[],[f68]) ).
fof(f119,plain,
! [X3,X4] :
( aElementOf0(sdtpldt0(X3,X4),xJ)
| ~ aElementOf0(X4,xJ)
| ~ aElementOf0(X3,xJ) ),
inference(cnf_transformation,[],[f68]) ).
fof(f135,plain,
aElementOf0(xl,xJ),
inference(cnf_transformation,[],[f27]) ).
fof(f136,plain,
aElementOf0(xk,xI),
inference(cnf_transformation,[],[f27]) ).
fof(f138,plain,
aElementOf0(xn,xJ),
inference(cnf_transformation,[],[f28]) ).
fof(f139,plain,
aElementOf0(xm,xI),
inference(cnf_transformation,[],[f28]) ).
fof(f140,plain,
( ~ aElementOf0(sdtpldt0(xl,xn),xJ)
| ~ aElementOf0(sdtpldt0(xk,xm),xI) ),
inference(cnf_transformation,[],[f69]) ).
fof(f152,definition,
( spl12_1
<=> aElementOf0(sdtpldt0(xk,xm),xI) ),
introduced(definition,[new_symbols(definition,[spl12_1])],[avatar_definition]) ).
fof(f154,plain,
( ~ aElementOf0(sdtpldt0(xk,xm),xI)
| spl12_1 ),
inference(avatar_component_clause,[],[f152]) ).
fof(f156,definition,
( spl12_2
<=> aElementOf0(sdtpldt0(xl,xn),xJ) ),
introduced(definition,[new_symbols(definition,[spl12_2])],[avatar_definition]) ).
fof(f158,plain,
( ~ aElementOf0(sdtpldt0(xl,xn),xJ)
| spl12_2 ),
inference(avatar_component_clause,[],[f156]) ).
fof(f159,plain,
( ~ spl12_1
| ~ spl12_2 ),
inference(avatar_split_clause,[],[f140,f156,f152]) ).
fof(f314,plain,
( ~ aElementOf0(xm,xI)
| ~ aElementOf0(xk,xI)
| spl12_1 ),
inference(resolution,[],[f117,f154]) ).
fof(f329,plain,
( ~ aElementOf0(xk,xI)
| spl12_1 ),
inference(forward_subsumption_resolution,[],[f314,f139]) ).
fof(f358,plain,
( $false
| spl12_1 ),
inference(forward_subsumption_resolution,[],[f329,f136]) ).
fof(f359,plain,
spl12_1,
inference(avatar_contradiction_clause,[],[f358]) ).
fof(f360,plain,
( ~ aElementOf0(xn,xJ)
| ~ aElementOf0(xl,xJ)
| spl12_2 ),
inference(resolution,[],[f119,f158]) ).
fof(f375,plain,
( ~ aElementOf0(xl,xJ)
| spl12_2 ),
inference(forward_subsumption_resolution,[],[f360,f138]) ).
fof(f404,plain,
( $false
| spl12_2 ),
inference(forward_subsumption_resolution,[],[f375,f135]) ).
fof(f405,plain,
spl12_2,
inference(avatar_contradiction_clause,[],[f404]) ).
cnf(s1,plain,
( ~ spl12_1
| ~ spl12_2 ),
inference(sat_conversion,[],[f159]) ).
cnf(s10,plain,
spl12_1,
inference(sat_conversion,[],[f359]) ).
cnf(s15,plain,
spl12_2,
inference(sat_conversion,[],[f405]) ).
cnf(s16,plain,
$false,
inference(rat,[],[s1,s15,s10]) ).
fof(f406,plain,
$false,
inference(avatar_sat_refutation,[],[s16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG088+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.38 % Computer : n026.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 23:15:26 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
% 0.10/0.45 % (3319217)Will run a generic schedule for satisfiability detection.
% 0.10/0.45 % (3319226)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2879073813:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.10/0.45 % (3319223)% WARNING: option uhcvi not known.
% 0.10/0.45 % (3319226) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3319217-3319226"...
% 0.10/0.45 % (3319226)...printing done.
% 0.10/0.45 % (3319226)Refutation found. Thanks to Tanya!
% 0.10/0.45 % SZS status Theorem for theBenchmark
% 0.10/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.45 % (3319226)------------------------------
% 0.10/0.45 % (3319226)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.45 % (3319226)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.45 % (3319226)CaDiCaL version: 2.1.3
% 0.10/0.45 % (3319226)Termination reason: Refutation
% 0.10/0.45 % (3319226)Time elapsed: 0.005 s
% 0.10/0.45 % (3319226)Peak memory usage: 12 MB
% 0.10/0.45 % (3319226)Instructions burned: 12 (million)
% 0.10/0.45 % (3319217)Success in time 0.031 s
% 0.10/0.45 % Vampire exiting
%------------------------------------------------------------------------------