%------------------------------------------------------------------------------
% File : Vampire---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 THM
% Computer : n010.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 2.36s 1.19s
% Output : Refutation 2.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 40 ( 12 unt; 2 def)
% Number of atoms : 134 ( 2 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 130 ( 36 ~; 33 |; 35 &)
% ( 4 <=>; 22 =>; 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 : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 37 ( 0 sgn 37 !; 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,
( 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(f31,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(f36,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(f37,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,[],[f36]) ).
fof(f38,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,[],[f31]) ).
fof(f39,plain,
( ~ aElementOf0(sdtpldt0(xk,xm),xI)
| ~ aElementOf0(sdtpldt0(xl,xn),xJ) ),
inference(ennf_transformation,[],[f30]) ).
fof(f49,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,[],[f37]) ).
fof(f71,plain,
aIdeal0(xJ),
inference(cnf_transformation,[],[f38]) ).
fof(f75,plain,
aIdeal0(xI),
inference(cnf_transformation,[],[f38]) ).
fof(f89,plain,
aElementOf0(xl,xJ),
inference(cnf_transformation,[],[f27]) ).
fof(f90,plain,
aElementOf0(xk,xI),
inference(cnf_transformation,[],[f27]) ).
fof(f92,plain,
aElementOf0(xn,xJ),
inference(cnf_transformation,[],[f28]) ).
fof(f93,plain,
aElementOf0(xm,xI),
inference(cnf_transformation,[],[f28]) ).
fof(f94,plain,
( ~ aElementOf0(sdtpldt0(xk,xm),xI)
| ~ aElementOf0(sdtpldt0(xl,xn),xJ) ),
inference(cnf_transformation,[],[f39]) ).
fof(f104,plain,
! [X2,X0,X1] :
( aElementOf0(sdtpldt0(X1,X2),X0)
| ~ aElementOf0(X2,X0)
| ~ aElementOf0(X1,X0)
| ~ aIdeal0(X0) ),
inference(cnf_transformation,[],[f49]) ).
fof(f128,definition,
( spl14_1
<=> aElementOf0(sdtpldt0(xl,xn),xJ) ),
introduced(definition,[new_symbols(definition,[spl14_1])],[avatar_definition]) ).
fof(f130,plain,
( ~ aElementOf0(sdtpldt0(xl,xn),xJ)
| spl14_1 ),
inference(avatar_component_clause,[],[f128]) ).
fof(f132,definition,
( spl14_2
<=> aElementOf0(sdtpldt0(xk,xm),xI) ),
introduced(definition,[new_symbols(definition,[spl14_2])],[avatar_definition]) ).
fof(f134,plain,
( ~ aElementOf0(sdtpldt0(xk,xm),xI)
| spl14_2 ),
inference(avatar_component_clause,[],[f132]) ).
fof(f135,plain,
( ~ spl14_1
| ~ spl14_2 ),
inference(avatar_split_clause,[],[f94,f132,f128]) ).
fof(f136,plain,
( ~ aElementOf0(xn,xJ)
| ~ aElementOf0(xl,xJ)
| ~ aIdeal0(xJ)
| spl14_1 ),
inference(resolution,[],[f130,f104]) ).
fof(f138,plain,
( ~ aElementOf0(xl,xJ)
| ~ aIdeal0(xJ)
| spl14_1 ),
inference(forward_subsumption_resolution,[],[f136,f92]) ).
fof(f139,plain,
( ~ aIdeal0(xJ)
| spl14_1 ),
inference(forward_subsumption_resolution,[],[f138,f89]) ).
fof(f140,plain,
( $false
| spl14_1 ),
inference(forward_subsumption_resolution,[],[f139,f71]) ).
fof(f141,plain,
spl14_1,
inference(avatar_contradiction_clause,[],[f140]) ).
fof(f144,plain,
( ~ aElementOf0(xm,xI)
| ~ aElementOf0(xk,xI)
| ~ aIdeal0(xI)
| spl14_2 ),
inference(resolution,[],[f134,f104]) ).
fof(f146,plain,
( ~ aElementOf0(xk,xI)
| ~ aIdeal0(xI)
| spl14_2 ),
inference(forward_subsumption_resolution,[],[f144,f93]) ).
fof(f147,plain,
( ~ aIdeal0(xI)
| spl14_2 ),
inference(forward_subsumption_resolution,[],[f146,f90]) ).
fof(f148,plain,
( $false
| spl14_2 ),
inference(forward_subsumption_resolution,[],[f147,f75]) ).
fof(f149,plain,
spl14_2,
inference(avatar_contradiction_clause,[],[f148]) ).
cnf(s1,plain,
( ~ spl14_1
| ~ spl14_2 ),
inference(sat_conversion,[],[f135]) ).
cnf(s2,plain,
spl14_1,
inference(sat_conversion,[],[f141]) ).
cnf(s3,plain,
spl14_2,
inference(sat_conversion,[],[f149]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s3,s2]) ).
fof(f150,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----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 THM
% 0.11/0.36 % Computer : n010.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 27 23:13:02 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 2.36/1.19 % (1411686)Detected formulas, will run a generic FOF schedule.
% 2.36/1.19 % (1411694)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2141328809:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.36/1.19 % (1411694)First to succeed.
% 2.36/1.19 % (1411694)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1411686"
% 2.36/1.19 % (1411696)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=937127059:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.36/1.19 % (1411695)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2880698634:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.36/1.19 % (1411693)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=2145508833:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.36/1.19 % (1411697)dis-21_1_sil=8000:lcm=predicate:random_seed=2145574104: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)
% 2.36/1.19 % (1411691)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=4152000109:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.36/1.19 % (1411692)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=440598879:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.36/1.19 % (1411695)Also succeeded, but the first one will report.
% 2.36/1.19 % (1411697)Also succeeded, but the first one will report.
% 2.36/1.19 % (1411696)Also succeeded, but the first one will report.
% 2.36/1.19 % (1411694)Refutation found. Thanks to Tanya!
% 2.36/1.19 % SZS status Theorem for theBenchmark
% 2.36/1.19 % SZS output start Proof for theBenchmark
% See solution above
% 2.36/1.19 % (1411694)------------------------------
% 2.36/1.19 % (1411694)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.36/1.19 % (1411694)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.36/1.19 % (1411694)CaDiCaL version: 2.1.3
% 2.36/1.19 % (1411694)Termination reason: Refutation
% 2.36/1.19 % (1411694)Time elapsed: 0.003 s
% 2.36/1.19 % (1411694)Peak memory usage: 89 MB
% 2.36/1.19 % (1411694)Instructions burned: 5 (million)
% 2.36/1.19 % (1411694)------------------------------
% 2.36/1.19 % (1411694)------------------------------
% 2.36/1.19 % (1411686)Success in time 0.269 s
% 2.36/1.19 % Vampire exiting
%------------------------------------------------------------------------------