%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET199+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n016.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 12:43:26 PM UTC 2026
% Result : Theorem 0.33s 15.53s
% Output : Refutation 0.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 42 ( 10 unt; 2 def)
% Number of atoms : 104 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 101 ( 39 ~; 35 |; 19 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 50 ( 0 sgn 42 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] :
( member(X2,intersection(X0,X1))
<=> ( member(X2,X0)
& member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_defn) ).
fof(f2,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
fof(f6,conjecture,
! [X0,X1,X2] :
( ( subset(X0,X1)
& subset(X0,X2) )
=> subset(X0,intersection(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_intersection_of_subsets) ).
fof(f7,negated_conjecture,
~ ! [X0,X1,X2] :
( ( subset(X0,X1)
& subset(X0,X2) )
=> subset(X0,intersection(X1,X2)) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f8,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f9,plain,
? [X0,X1,X2] :
( ~ subset(X0,intersection(X1,X2))
& subset(X0,X1)
& subset(X0,X2) ),
inference(ennf_transformation,[],[f7]) ).
fof(f10,plain,
? [X0,X1,X2] :
( ~ subset(X0,intersection(X1,X2))
& subset(X0,X1)
& subset(X0,X2) ),
inference(flattening,[],[f9]) ).
fof(f11,plain,
! [X0,X1,X2] :
( ( member(X2,intersection(X0,X1))
| ~ member(X2,X0)
| ~ member(X2,X1) )
& ( ( member(X2,X0)
& member(X2,X1) )
| ~ member(X2,intersection(X0,X1)) ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f12,plain,
! [X0,X1,X2] :
( ( member(X2,intersection(X0,X1))
| ~ member(X2,X0)
| ~ member(X2,X1) )
& ( ( member(X2,X0)
& member(X2,X1) )
| ~ member(X2,intersection(X0,X1)) ) ),
inference(flattening,[],[f11]) ).
fof(f13,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f14,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f13]) ).
fof(f15,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f14]) ).
fof(f19,plain,
( ~ subset(sK2,intersection(sK3,sK4))
& subset(sK2,sK3)
& subset(sK2,sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f10]) ).
fof(f22,plain,
! [X2,X0,X1] :
( member(X2,intersection(X0,X1))
| ~ member(X2,X0)
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f12]) ).
fof(f23,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f24,plain,
! [X0,X1] :
( member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f25,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f32,plain,
subset(sK2,sK4),
inference(cnf_transformation,[],[f19]) ).
fof(f33,plain,
subset(sK2,sK3),
inference(cnf_transformation,[],[f19]) ).
fof(f34,plain,
~ subset(sK2,intersection(sK3,sK4)),
inference(cnf_transformation,[],[f19]) ).
fof(f43,plain,
~ member(sK0(sK2,intersection(sK3,sK4)),intersection(sK3,sK4)),
inference(resolution,[],[f25,f34]) ).
fof(f44,plain,
! [X0] :
( member(X0,sK4)
| ~ member(X0,sK2) ),
inference(resolution,[],[f23,f32]) ).
fof(f45,plain,
! [X0] :
( member(X0,sK3)
| ~ member(X0,sK2) ),
inference(resolution,[],[f23,f33]) ).
fof(f50,plain,
( ~ member(sK0(sK2,intersection(sK3,sK4)),sK3)
| ~ member(sK0(sK2,intersection(sK3,sK4)),sK4) ),
inference(resolution,[],[f22,f43]) ).
fof(f54,definition,
( spl5_1
<=> member(sK0(sK2,intersection(sK3,sK4)),sK4) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
fof(f56,plain,
( ~ member(sK0(sK2,intersection(sK3,sK4)),sK4)
| spl5_1 ),
inference(avatar_component_clause,[],[f54]) ).
fof(f58,definition,
( spl5_2
<=> member(sK0(sK2,intersection(sK3,sK4)),sK3) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
fof(f60,plain,
( ~ member(sK0(sK2,intersection(sK3,sK4)),sK3)
| spl5_2 ),
inference(avatar_component_clause,[],[f58]) ).
fof(f61,plain,
( ~ spl5_1
| ~ spl5_2 ),
inference(avatar_split_clause,[],[f50,f58,f54]) ).
fof(f62,plain,
( ~ member(sK0(sK2,intersection(sK3,sK4)),sK2)
| spl5_1 ),
inference(resolution,[],[f56,f44]) ).
fof(f63,plain,
( ~ member(sK0(sK2,intersection(sK3,sK4)),sK2)
| spl5_2 ),
inference(resolution,[],[f60,f45]) ).
fof(f64,plain,
( subset(sK2,intersection(sK3,sK4))
| spl5_1 ),
inference(resolution,[],[f62,f24]) ).
fof(f65,plain,
( $false
| spl5_1 ),
inference(resolution,[],[f64,f34]) ).
fof(f67,plain,
spl5_1,
inference(avatar_contradiction_clause,[],[f65]) ).
fof(f70,plain,
( subset(sK2,intersection(sK3,sK4))
| spl5_2 ),
inference(resolution,[],[f63,f24]) ).
fof(f71,plain,
( $false
| spl5_2 ),
inference(resolution,[],[f70,f34]) ).
fof(f73,plain,
spl5_2,
inference(avatar_contradiction_clause,[],[f71]) ).
cnf(s1,plain,
( ~ spl5_1
| ~ spl5_2 ),
inference(sat_conversion,[],[f61]) ).
cnf(s2,plain,
spl5_1,
inference(sat_conversion,[],[f67]) ).
cnf(s3,plain,
spl5_2,
inference(sat_conversion,[],[f73]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s3,s2]) ).
fof(f74,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET199+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.42 % Computer : n016.cluster.edu
% 0.13/0.42 % Model : x86_64 x86_64
% 0.13/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.42 % Memory : 8046.5625MB
% 0.13/0.42 % OS : Linux 6.8.0-71-generic
% 0.09/15.44 % CPULimit : 300
% 0.09/15.44 % WCLimit : 300
% 0.09/15.44 % DateTime : Mon Sep 28 01:05:31 UTC 2026
% 0.09/15.45 % CPUTime :
% 0.09/15.45 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/15.48 Running first-order model finding
% 0.09/15.48 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
% 0.33/15.53 % (1472515)Will run a generic schedule for satisfiability detection.
% 0.33/15.53 % (1472525)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=287025213:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.33/15.53 % (1472521)% WARNING: option uhcvi not known.
% 0.33/15.53 % (1472521)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2222641274:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.33/15.53 % (1472520)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=72851922_2999 on theBenchmark for (2999ds/0Mi)
% 0.33/15.53 % (1472522)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1778660751:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.33/15.53 % (1472524)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2905987695:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.33/15.53 % (1472523)dis+10_1_sil=32000:sp=arity:random_seed=3555219913:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.33/15.53 % (1472526)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1564246701:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.33/15.53 % TRYING [1]
% 0.33/15.53 % TRYING [2]
% 0.33/15.53 % TRYING [3]
% 0.33/15.53 % TRYING [4]
% 0.33/15.53 % (1472526) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1472515-1472526"...
% 0.33/15.53 % (1472524) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1472515-1472524"...
% 0.33/15.53 % (1472526)...printing done.
% 0.33/15.53 % (1472524)...printing done.
% 0.33/15.53 % (1472526)Refutation found. Thanks to Tanya!
% 0.33/15.53 % SZS status Theorem for theBenchmark
% 0.33/15.53 % SZS output start Proof for theBenchmark
% See solution above
% 0.33/15.53 % (1472526)------------------------------
% 0.33/15.53 % (1472526)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.33/15.53 % (1472526)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.33/15.53 % (1472526)CaDiCaL version: 2.1.3
% 0.33/15.53 % (1472526)Termination reason: Refutation
% 0.33/15.53 % (1472526)Time elapsed: 0.003 s
% 0.33/15.53 % (1472526)Peak memory usage: 12 MB
% 0.33/15.53 % (1472526)Instructions burned: 3 (million)
% 0.33/15.53 % (1472515)Success in time 0.036 s
% 0.33/15.53 % Vampire exiting
%------------------------------------------------------------------------------