%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG088+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 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 12:35:27 PM UTC 2026
% Result : Theorem 2.76s 1.37s
% Output : Refutation 2.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 38 ( 12 unt; 2 def)
% Number of atoms : 90 ( 2 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 78 ( 26 ~; 23 |; 15 &)
% ( 4 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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 : 25 ( 0 sgn 25 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f24,axiom,
! [X0] :
( aIdeal0(X0)
<=> ( aSet0(X0)
& ! [X1] :
( aElementOf0(X1,X0)
=> ( ! [X2] :
( aElementOf0(X2,X0)
=> aElementOf0(sdtpldt0(X1,X2),X0) )
& ! [X2] :
( aElement0(X2)
=> aElementOf0(sdtasdt0(X2,X1),X0) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefIdeal) ).
fof(f25,axiom,
( aIdeal0(xI)
& 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(f34,plain,
! [X0] :
( aIdeal0(X0)
<=> ( aSet0(X0)
& ! [X1] :
( aElementOf0(X1,X0)
=> ( ! [X2] :
( aElementOf0(X2,X0)
=> aElementOf0(sdtpldt0(X1,X2),X0) )
& ! [X3] :
( aElement0(X3)
=> aElementOf0(sdtasdt0(X3,X1),X0) ) ) ) ) ),
inference(rectify,[],[f24]) ).
fof(f35,plain,
! [X0] :
( aIdeal0(X0)
=> ( aSet0(X0)
& ! [X1] :
( aElementOf0(X1,X0)
=> ( ! [X2] :
( aElementOf0(X2,X0)
=> aElementOf0(sdtpldt0(X1,X2),X0) )
& ! [X3] :
( aElement0(X3)
=> aElementOf0(sdtasdt0(X3,X1),X0) ) ) ) ) ),
inference(unused_predicate_definition_removal,[],[f34]) ).
fof(f65,plain,
! [X0] :
( ( aSet0(X0)
& ! [X1] :
( ( ! [X2] :
( aElementOf0(sdtpldt0(X1,X2),X0)
| ~ aElementOf0(X2,X0) )
& ! [X3] :
( aElementOf0(sdtasdt0(X3,X1),X0)
| ~ aElement0(X3) ) )
| ~ aElementOf0(X1,X0) ) )
| ~ aIdeal0(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f66,plain,
( ~ aElementOf0(sdtpldt0(xk,xm),xI)
| ~ aElementOf0(sdtpldt0(xl,xn),xJ) ),
inference(ennf_transformation,[],[f30]) ).
fof(f129,plain,
! [X2,X0,X1] :
( ~ aIdeal0(X0)
| ~ aElementOf0(X2,X0)
| ~ aElementOf0(X1,X0)
| aElementOf0(sdtpldt0(X1,X2),X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f131,plain,
aIdeal0(xJ),
inference(cnf_transformation,[],[f25]) ).
fof(f132,plain,
aIdeal0(xI),
inference(cnf_transformation,[],[f25]) ).
fof(f137,plain,
aElementOf0(xl,xJ),
inference(cnf_transformation,[],[f27]) ).
fof(f138,plain,
aElementOf0(xk,xI),
inference(cnf_transformation,[],[f27]) ).
fof(f140,plain,
aElementOf0(xn,xJ),
inference(cnf_transformation,[],[f28]) ).
fof(f141,plain,
aElementOf0(xm,xI),
inference(cnf_transformation,[],[f28]) ).
fof(f142,plain,
( ~ aElementOf0(sdtpldt0(xk,xm),xI)
| ~ aElementOf0(sdtpldt0(xl,xn),xJ) ),
inference(cnf_transformation,[],[f66]) ).
fof(f150,definition,
( spl10_1
<=> aElementOf0(sdtpldt0(xl,xn),xJ) ),
introduced(definition,[new_symbols(definition,[spl10_1])],[avatar_definition]) ).
fof(f152,plain,
( ~ aElementOf0(sdtpldt0(xl,xn),xJ)
| spl10_1 ),
inference(avatar_component_clause,[],[f150]) ).
fof(f154,definition,
( spl10_2
<=> aElementOf0(sdtpldt0(xk,xm),xI) ),
introduced(definition,[new_symbols(definition,[spl10_2])],[avatar_definition]) ).
fof(f156,plain,
( ~ aElementOf0(sdtpldt0(xk,xm),xI)
| spl10_2 ),
inference(avatar_component_clause,[],[f154]) ).
fof(f157,plain,
( ~ spl10_1
| ~ spl10_2 ),
inference(avatar_split_clause,[],[f142,f154,f150]) ).
fof(f238,plain,
! [X0,X1] :
( ~ aElementOf0(X0,xJ)
| ~ aElementOf0(X1,xJ)
| aElementOf0(sdtpldt0(X1,X0),xJ) ),
inference(resolution,[],[f129,f131]) ).
fof(f239,plain,
! [X0,X1] :
( ~ aElementOf0(X0,xI)
| ~ aElementOf0(X1,xI)
| aElementOf0(sdtpldt0(X1,X0),xI) ),
inference(resolution,[],[f129,f132]) ).
fof(f464,plain,
! [X0] :
( aElementOf0(sdtpldt0(X0,xn),xJ)
| ~ aElementOf0(X0,xJ) ),
inference(resolution,[],[f238,f140]) ).
fof(f502,plain,
! [X0] :
( aElementOf0(sdtpldt0(X0,xm),xI)
| ~ aElementOf0(X0,xI) ),
inference(resolution,[],[f239,f141]) ).
fof(f751,plain,
( ~ aElementOf0(xl,xJ)
| spl10_1 ),
inference(resolution,[],[f464,f152]) ).
fof(f767,plain,
( $false
| spl10_1 ),
inference(forward_subsumption_resolution,[],[f751,f137]) ).
fof(f768,plain,
spl10_1,
inference(avatar_contradiction_clause,[],[f767]) ).
fof(f1334,plain,
( ~ aElementOf0(xk,xI)
| spl10_2 ),
inference(resolution,[],[f502,f156]) ).
fof(f1341,plain,
( $false
| spl10_2 ),
inference(forward_subsumption_resolution,[],[f1334,f138]) ).
fof(f1342,plain,
spl10_2,
inference(avatar_contradiction_clause,[],[f1341]) ).
cnf(s1,plain,
( ~ spl10_1
| ~ spl10_2 ),
inference(sat_conversion,[],[f157]) ).
cnf(s42,plain,
spl10_1,
inference(sat_conversion,[],[f768]) ).
cnf(s48,plain,
spl10_2,
inference(sat_conversion,[],[f1342]) ).
cnf(s76,plain,
$false,
inference(rat,[],[s1,s48,s42]) ).
fof(f1353,plain,
$false,
inference(avatar_sat_refutation,[],[s76]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG088+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.38 % Computer : n026.cluster.edu
% 0.14/0.38 % Model : x86_64 x86_64
% 0.14/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.38 % Memory : 8046.5625MB
% 0.14/0.38 % OS : Linux 6.8.0-71-generic
% 0.14/0.38 % CPULimit : 300
% 0.14/0.38 % WCLimit : 300
% 0.14/0.38 % DateTime : Sun Sep 27 23:15:42 UTC 2026
% 0.14/0.39 % CPUTime :
% 0.14/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.42 Running first-order theorem proving
% 0.14/0.42 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.76/1.37 % (3319609)Detected formulas, will run a generic FOF schedule.
% 2.76/1.37 % (3319619)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=490843072:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.76/1.37 % (3319619)First to succeed.
% 2.76/1.37 % (3319619)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3319609"
% 2.76/1.37 % (3319614)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=939683220:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.76/1.37 % (3319616)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=3125193498:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.76/1.37 % (3319615)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2353991373:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.76/1.37 % (3319617)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=386764555:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.76/1.37 % (3319618)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1004729390:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.76/1.37 % (3319617)Also succeeded, but the first one will report.
% 2.76/1.37 % (3319618)Also succeeded, but the first one will report.
% 2.76/1.37 % (3319620)dis-21_1_sil=8000:lcm=predicate:random_seed=121690591:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.76/1.37 % (3319620)Also succeeded, but the first one will report.
% 2.76/1.37 % (3319619)Refutation found. Thanks to Tanya!
% 2.76/1.37 % SZS status Theorem for theBenchmark
% 2.76/1.37 % SZS output start Proof for theBenchmark
% See solution above
% 2.76/1.37 % (3319619)------------------------------
% 2.76/1.37 % (3319619)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.76/1.37 % (3319619)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.76/1.37 % (3319619)CaDiCaL version: 2.1.3
% 2.76/1.37 % (3319619)Termination reason: Refutation
% 2.76/1.37 % (3319619)Time elapsed: 0.021 s
% 2.76/1.37 % (3319619)Peak memory usage: 90 MB
% 2.76/1.37 % (3319619)Instructions burned: 52 (million)
% 2.76/1.37 % (3319619)------------------------------
% 2.76/1.37 % (3319619)------------------------------
% 2.76/1.37 % (3319609)Success in time 0.305 s
% 2.76/1.37 % Vampire exiting
%------------------------------------------------------------------------------