%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : RNG089+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 12:36:00 PM UTC 2026
% Result : Theorem 0.11s 0.45s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 34 ( 9 unt; 2 def)
% Number of atoms : 121 ( 7 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 114 ( 27 ~; 24 |; 49 &)
% ( 2 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 3 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 11 con; 0-2 aty)
% Number of variables : 30 ( 0 sgn 22 !; 8 ?)
% 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/sandbox2/benchmark/theBenchmark.p',m__870) ).
fof(f26,axiom,
( ? [X0,X1] :
( aElementOf0(X0,xI)
& aElementOf0(X1,xJ)
& sdtpldt0(X0,X1) = xx )
& aElementOf0(xx,sdtpldt1(xI,xJ))
& ? [X0,X1] :
( aElementOf0(X0,xI)
& aElementOf0(X1,xJ)
& sdtpldt0(X0,X1) = xy )
& aElementOf0(xy,sdtpldt1(xI,xJ))
& aElement0(xz) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__901) ).
fof(f27,axiom,
( aElementOf0(xk,xI)
& aElementOf0(xl,xJ)
& xx = sdtpldt0(xk,xl) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__934) ).
fof(f30,conjecture,
( aElementOf0(sdtasdt0(xz,xk),xI)
& aElementOf0(sdtasdt0(xz,xl),xJ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f31,negated_conjecture,
~ ( aElementOf0(sdtasdt0(xz,xk),xI)
& aElementOf0(sdtasdt0(xz,xl),xJ) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
fof(f36,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(f37,plain,
( ? [X0,X1] :
( aElementOf0(X0,xI)
& aElementOf0(X1,xJ)
& sdtpldt0(X0,X1) = xx )
& aElementOf0(xx,sdtpldt1(xI,xJ))
& ? [X2,X3] :
( aElementOf0(X2,xI)
& aElementOf0(X3,xJ)
& xy = sdtpldt0(X2,X3) )
& aElementOf0(xy,sdtpldt1(xI,xJ))
& aElement0(xz) ),
inference(rectify,[],[f26]) ).
fof(f69,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,[],[f36]) ).
fof(f70,plain,
( ~ aElementOf0(sdtasdt0(xz,xk),xI)
| ~ aElementOf0(sdtasdt0(xz,xl),xJ) ),
inference(ennf_transformation,[],[f31]) ).
fof(f85,plain,
( aElementOf0(sK10,xI)
& aElementOf0(sK11,xJ)
& xx = sdtpldt0(sK10,sK11)
& aElementOf0(xx,sdtpldt1(xI,xJ))
& aElementOf0(sK12,xI)
& aElementOf0(sK13,xJ)
& xy = sdtpldt0(sK12,sK13)
& aElementOf0(xy,sdtpldt1(xI,xJ))
& aElement0(xz) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11,sK12,sK13]),skolemize(X0,sK10),skolemize(X1,sK11),skolemize(X2,sK12),skolemize(X3,sK13)],[f37]) ).
fof(f137,plain,
! [X3,X5] :
( aElementOf0(sdtasdt0(X5,X3),xJ)
| ~ aElement0(X5)
| ~ aElementOf0(X3,xJ) ),
inference(cnf_transformation,[],[f69]) ).
fof(f141,plain,
! [X2,X0] :
( aElementOf0(sdtasdt0(X2,X0),xI)
| ~ aElement0(X2)
| ~ aElementOf0(X0,xI) ),
inference(cnf_transformation,[],[f69]) ).
fof(f144,plain,
aElement0(xz),
inference(cnf_transformation,[],[f85]) ).
fof(f154,plain,
aElementOf0(xl,xJ),
inference(cnf_transformation,[],[f27]) ).
fof(f155,plain,
aElementOf0(xk,xI),
inference(cnf_transformation,[],[f27]) ).
fof(f161,plain,
( ~ aElementOf0(sdtasdt0(xz,xk),xI)
| ~ aElementOf0(sdtasdt0(xz,xl),xJ) ),
inference(cnf_transformation,[],[f70]) ).
fof(f169,definition,
( spl14_1
<=> aElementOf0(sdtasdt0(xz,xl),xJ) ),
introduced(definition,[new_symbols(definition,[spl14_1])],[avatar_definition]) ).
fof(f171,plain,
( ~ aElementOf0(sdtasdt0(xz,xl),xJ)
| spl14_1 ),
inference(avatar_component_clause,[],[f169]) ).
fof(f173,definition,
( spl14_2
<=> aElementOf0(sdtasdt0(xz,xk),xI) ),
introduced(definition,[new_symbols(definition,[spl14_2])],[avatar_definition]) ).
fof(f175,plain,
( ~ aElementOf0(sdtasdt0(xz,xk),xI)
| spl14_2 ),
inference(avatar_component_clause,[],[f173]) ).
fof(f176,plain,
( ~ spl14_1
| ~ spl14_2 ),
inference(avatar_split_clause,[],[f161,f173,f169]) ).
fof(f361,plain,
( ~ aElement0(xz)
| ~ aElementOf0(xl,xJ)
| spl14_1 ),
inference(resolution,[],[f137,f171]) ).
fof(f369,plain,
( ~ aElementOf0(xl,xJ)
| spl14_1 ),
inference(forward_subsumption_resolution,[],[f361,f144]) ).
fof(f384,plain,
( $false
| spl14_1 ),
inference(forward_subsumption_resolution,[],[f369,f154]) ).
fof(f385,plain,
spl14_1,
inference(avatar_contradiction_clause,[],[f384]) ).
fof(f398,plain,
( ~ aElement0(xz)
| ~ aElementOf0(xk,xI)
| spl14_2 ),
inference(resolution,[],[f141,f175]) ).
fof(f406,plain,
( ~ aElementOf0(xk,xI)
| spl14_2 ),
inference(forward_subsumption_resolution,[],[f398,f144]) ).
fof(f421,plain,
( $false
| spl14_2 ),
inference(forward_subsumption_resolution,[],[f406,f155]) ).
fof(f422,plain,
spl14_2,
inference(avatar_contradiction_clause,[],[f421]) ).
cnf(s1,plain,
( ~ spl14_1
| ~ spl14_2 ),
inference(sat_conversion,[],[f176]) ).
cnf(s16,plain,
spl14_1,
inference(sat_conversion,[],[f385]) ).
cnf(s19,plain,
spl14_2,
inference(sat_conversion,[],[f422]) ).
cnf(s21,plain,
$false,
inference(rat,[],[s1,s19,s16]) ).
fof(f423,plain,
$false,
inference(avatar_sat_refutation,[],[s21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG089+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n009.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 23:13:00 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.40 Running first-order model finding
% 0.11/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.45 % (2515110)Will run a generic schedule for satisfiability detection.
% 0.11/0.45 % (2515118)dis+10_1_sil=32000:sp=arity:random_seed=4231426396:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.11/0.45 % (2515116)% WARNING: option uhcvi not known.
% 0.11/0.45 % (2515118) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2515110-2515118"...
% 0.11/0.45 % (2515118)...printing done.
% 0.11/0.45 % (2515118)Refutation found. Thanks to Tanya!
% 0.11/0.45 % SZS status Theorem for theBenchmark
% 0.11/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.45 % (2515118)------------------------------
% 0.11/0.45 % (2515118)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.45 % (2515118)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.45 % (2515118)CaDiCaL version: 2.1.3
% 0.11/0.45 % (2515118)Termination reason: Refutation
% 0.11/0.45 % (2515118)Time elapsed: 0.004 s
% 0.11/0.45 % (2515118)Peak memory usage: 12 MB
% 0.11/0.45 % (2515118)Instructions burned: 10 (million)
% 0.11/0.45 % (2515110)Success in time 0.034 s
% 0.11/0.45 % Vampire exiting
%------------------------------------------------------------------------------