%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET199+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 12:40:29 PM UTC 2026
% Result : Theorem 2.83s 1.37s
% Output : Refutation 2.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 69 ( 5 unt; 3 def)
% Number of atoms : 197 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 210 ( 82 ~; 98 |; 20 &)
% ( 8 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 63 ( 0 sgn 52 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset) ).
fof(f4,axiom,
! [X0,X1,X2] :
( member(X0,intersection(X1,X2))
<=> ( member(X0,X1)
& member(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection) ).
fof(f12,conjecture,
! [X0,X1,X2] :
( ( subset(X0,X1)
& subset(X0,X2) )
<=> subset(X0,intersection(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI46) ).
fof(f13,negated_conjecture,
~ ! [X0,X1,X2] :
( ( subset(X0,X1)
& subset(X0,X2) )
<=> subset(X0,intersection(X1,X2)) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f16,plain,
? [X0,X1,X2] :
( ( subset(X0,X1)
& subset(X0,X2) )
<~> subset(X0,intersection(X1,X2)) ),
inference(ennf_transformation,[],[f13]) ).
fof(f17,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,[],[f14]) ).
fof(f18,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,[],[f17]) ).
fof(f19,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))],[f18]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ( member(X0,intersection(X1,X2))
| ~ member(X0,X1)
| ~ member(X0,X2) )
& ( ( member(X0,X1)
& member(X0,X2) )
| ~ member(X0,intersection(X1,X2)) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ( member(X0,intersection(X1,X2))
| ~ member(X0,X1)
| ~ member(X0,X2) )
& ( ( member(X0,X1)
& member(X0,X2) )
| ~ member(X0,intersection(X1,X2)) ) ),
inference(flattening,[],[f21]) ).
fof(f36,plain,
? [X0,X1,X2] :
( ( ~ subset(X0,intersection(X1,X2))
| ~ subset(X0,X1)
| ~ subset(X0,X2) )
& ( subset(X0,intersection(X1,X2))
| ( subset(X0,X1)
& subset(X0,X2) ) ) ),
inference(nnf_transformation,[],[f16]) ).
fof(f37,plain,
? [X0,X1,X2] :
( ( ~ subset(X0,intersection(X1,X2))
| ~ subset(X0,X1)
| ~ subset(X0,X2) )
& ( subset(X0,intersection(X1,X2))
| ( subset(X0,X1)
& subset(X0,X2) ) ) ),
inference(flattening,[],[f36]) ).
fof(f38,plain,
( ( ~ subset(sK3,intersection(sK4,sK5))
| ~ subset(sK3,sK4)
| ~ subset(sK3,sK5) )
& ( subset(sK3,intersection(sK4,sK5))
| ( subset(sK3,sK4)
& subset(sK3,sK5) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5)],[f37]) ).
fof(f39,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f40,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f19]) ).
fof(f41,plain,
! [X0,X1] :
( ~ member(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f44,plain,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
inference(cnf_transformation,[],[f22]) ).
fof(f45,plain,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f46,plain,
! [X2,X0,X1] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X1)
| ~ member(X0,X2) ),
inference(cnf_transformation,[],[f22]) ).
fof(f65,plain,
( subset(sK3,intersection(sK4,sK5))
| subset(sK3,sK5) ),
inference(cnf_transformation,[],[f38]) ).
fof(f66,plain,
( subset(sK3,intersection(sK4,sK5))
| subset(sK3,sK4) ),
inference(cnf_transformation,[],[f38]) ).
fof(f67,plain,
( ~ subset(sK3,intersection(sK4,sK5))
| ~ subset(sK3,sK4)
| ~ subset(sK3,sK5) ),
inference(cnf_transformation,[],[f38]) ).
fof(f72,definition,
( spl6_1
<=> subset(sK3,sK5) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
fof(f73,plain,
( ~ subset(sK3,sK5)
| spl6_1 ),
inference(avatar_component_clause,[],[f72]) ).
fof(f74,plain,
( subset(sK3,sK5)
| ~ spl6_1 ),
inference(avatar_component_clause,[],[f72]) ).
fof(f76,definition,
( spl6_2
<=> subset(sK3,intersection(sK4,sK5)) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
fof(f77,plain,
( ~ subset(sK3,intersection(sK4,sK5))
| spl6_2 ),
inference(avatar_component_clause,[],[f76]) ).
fof(f78,plain,
( subset(sK3,intersection(sK4,sK5))
| ~ spl6_2 ),
inference(avatar_component_clause,[],[f76]) ).
fof(f79,plain,
( spl6_1
| spl6_2 ),
inference(avatar_split_clause,[],[f65,f76,f72]) ).
fof(f81,definition,
( spl6_3
<=> subset(sK3,sK4) ),
introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition]) ).
fof(f82,plain,
( ~ subset(sK3,sK4)
| spl6_3 ),
inference(avatar_component_clause,[],[f81]) ).
fof(f83,plain,
( subset(sK3,sK4)
| ~ spl6_3 ),
inference(avatar_component_clause,[],[f81]) ).
fof(f84,plain,
( spl6_3
| spl6_2 ),
inference(avatar_split_clause,[],[f66,f76,f81]) ).
fof(f85,plain,
( ~ spl6_1
| ~ spl6_3
| ~ spl6_2 ),
inference(avatar_split_clause,[],[f67,f76,f81,f72]) ).
fof(f87,plain,
( member(sK0(sK3,sK4),sK3)
| spl6_3 ),
inference(resolution,[],[f40,f82]) ).
fof(f91,plain,
( ! [X0] :
( ~ member(X0,sK3)
| member(X0,intersection(sK4,sK5)) )
| ~ spl6_2 ),
inference(resolution,[],[f39,f78]) ).
fof(f93,plain,
( member(sK0(sK3,sK4),intersection(sK4,sK5))
| ~ spl6_2
| spl6_3 ),
inference(resolution,[],[f91,f87]) ).
fof(f96,plain,
! [X2,X0,X1] :
( subset(X0,intersection(X1,X2))
| ~ member(sK0(X0,intersection(X1,X2)),X2)
| ~ member(sK0(X0,intersection(X1,X2)),X1) ),
inference(resolution,[],[f46,f41]) ).
fof(f97,plain,
( member(sK0(sK3,sK4),sK4)
| ~ spl6_2
| spl6_3 ),
inference(resolution,[],[f93,f45]) ).
fof(f100,plain,
( subset(sK3,sK4)
| ~ spl6_2
| spl6_3 ),
inference(resolution,[],[f97,f41]) ).
fof(f101,plain,
( $false
| ~ spl6_2
| spl6_3 ),
inference(forward_subsumption_resolution,[],[f100,f82]) ).
fof(f102,plain,
( ~ spl6_2
| spl6_3 ),
inference(avatar_contradiction_clause,[],[f101]) ).
fof(f103,plain,
( member(sK0(sK3,sK5),sK3)
| spl6_1 ),
inference(resolution,[],[f73,f40]) ).
fof(f104,plain,
( ! [X0] :
( member(X0,sK4)
| ~ member(X0,sK3) )
| ~ spl6_3 ),
inference(resolution,[],[f83,f39]) ).
fof(f105,plain,
( member(sK0(sK3,sK5),intersection(sK4,sK5))
| spl6_1
| ~ spl6_2 ),
inference(resolution,[],[f103,f91]) ).
fof(f108,plain,
( member(sK0(sK3,sK5),sK5)
| spl6_1
| ~ spl6_2 ),
inference(resolution,[],[f105,f44]) ).
fof(f109,plain,
( subset(sK3,sK5)
| spl6_1
| ~ spl6_2 ),
inference(resolution,[],[f108,f41]) ).
fof(f110,plain,
( $false
| spl6_1
| ~ spl6_2 ),
inference(forward_subsumption_resolution,[],[f109,f73]) ).
fof(f111,plain,
( spl6_1
| ~ spl6_2 ),
inference(avatar_contradiction_clause,[],[f110]) ).
fof(f112,plain,
( ! [X0] :
( ~ member(X0,sK3)
| member(X0,sK5) )
| ~ spl6_1 ),
inference(resolution,[],[f74,f39]) ).
fof(f113,plain,
( member(sK0(sK3,intersection(sK4,sK5)),sK3)
| spl6_2 ),
inference(resolution,[],[f77,f40]) ).
fof(f114,plain,
( member(sK0(sK3,intersection(sK4,sK5)),sK5)
| ~ spl6_1
| spl6_2 ),
inference(resolution,[],[f113,f112]) ).
fof(f142,plain,
( ~ member(sK0(sK3,intersection(sK4,sK5)),sK5)
| ~ member(sK0(sK3,intersection(sK4,sK5)),sK4)
| spl6_2 ),
inference(resolution,[],[f96,f77]) ).
fof(f143,plain,
( ~ member(sK0(sK3,intersection(sK4,sK5)),sK4)
| ~ spl6_1
| spl6_2 ),
inference(forward_subsumption_resolution,[],[f142,f114]) ).
fof(f144,plain,
( ~ member(sK0(sK3,intersection(sK4,sK5)),sK3)
| ~ spl6_1
| spl6_2
| ~ spl6_3 ),
inference(resolution,[],[f143,f104]) ).
fof(f145,plain,
( $false
| ~ spl6_1
| spl6_2
| ~ spl6_3 ),
inference(forward_subsumption_resolution,[],[f144,f113]) ).
fof(f146,plain,
( ~ spl6_1
| spl6_2
| ~ spl6_3 ),
inference(avatar_contradiction_clause,[],[f145]) ).
cnf(s1,plain,
( spl6_1
| spl6_2 ),
inference(sat_conversion,[],[f79]) ).
cnf(s2,plain,
( spl6_2
| spl6_3 ),
inference(sat_conversion,[],[f84]) ).
cnf(s3,plain,
( ~ spl6_1
| ~ spl6_2
| ~ spl6_3 ),
inference(sat_conversion,[],[f85]) ).
cnf(s4,plain,
( ~ spl6_2
| spl6_3 ),
inference(sat_conversion,[],[f102]) ).
cnf(s5,plain,
( spl6_1
| ~ spl6_2 ),
inference(sat_conversion,[],[f111]) ).
cnf(s6,plain,
( ~ spl6_1
| spl6_2
| ~ spl6_3 ),
inference(sat_conversion,[],[f146]) ).
cnf(s7,plain,
spl6_1,
inference(rat,[],[s1,s5]) ).
cnf(s8,plain,
spl6_2,
inference(rat,[],[s2,s6,s7]) ).
cnf(s9,plain,
spl6_3,
inference(rat,[],[s4,s8]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s3,s7,s9,s8]) ).
fof(f147,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET199+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n008.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 28 01:05:09 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 2.83/1.37 % (1775617)Detected formulas, will run a generic FOF schedule.
% 2.83/1.37 % (1775728)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=877693996:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.83/1.37 % (1775728)First to succeed.
% 2.83/1.37 % (1775728)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1775617"
% 2.83/1.37 % (1775726)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3948402548:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.83/1.37 % (1775724)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=1364073766:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.83/1.37 % (1775725)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=3991868954:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.83/1.37 % (1775723)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=4268174333:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.83/1.37 % (1775729)dis-21_1_sil=8000:lcm=predicate:random_seed=3924787630: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)
% 2.83/1.37 % (1775726)Refutation not found, incomplete strategy
% 2.83/1.37 % (1775726)------------------------------
% 2.83/1.37 % (1775726)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.83/1.37 % (1775726)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.83/1.37 % (1775726)CaDiCaL version: 2.1.3
% 2.83/1.37 % (1775726)Termination reason: Refutation not found, incomplete strategy
% 2.83/1.37 % (1775726)Time elapsed: 0.001 s
% 2.83/1.37 % (1775726)Peak memory usage: 88 MB
% 2.83/1.37 % (1775729)Also succeeded, but the first one will report.
% 2.83/1.37 % (1775727)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=218278325:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.83/1.37 % (1775727)Also succeeded, but the first one will report.
% 2.83/1.37 % (1775728)Refutation found. Thanks to Tanya!
% 2.83/1.37 % SZS status Theorem for theBenchmark
% 2.83/1.37 % SZS output start Proof for theBenchmark
% See solution above
% 2.83/1.37 % (1775728)------------------------------
% 2.83/1.37 % (1775728)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.83/1.37 % (1775728)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.83/1.37 % (1775728)CaDiCaL version: 2.1.3
% 2.83/1.37 % (1775728)Termination reason: Refutation
% 2.83/1.37 % (1775728)Time elapsed: 0.003 s
% 2.83/1.37 % (1775728)Peak memory usage: 89 MB
% 2.83/1.37 % (1775728)Instructions burned: 6 (million)
% 2.83/1.37 % (1775728)------------------------------
% 2.83/1.37 % (1775728)------------------------------
% 2.83/1.37 % (1775617)Success in time 0.313 s
% 2.83/1.37 % Vampire exiting
%------------------------------------------------------------------------------