%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET753+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 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 12:41:50 PM UTC 2026
% Result : Theorem 2.67s 1.27s
% Output : Refutation 3.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 50 ( 11 unt; 2 def)
% Number of atoms : 139 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 143 ( 54 ~; 49 |; 31 &)
% ( 6 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 3 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 95 ( 0 sgn 80 !; 15 ?)
% 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(f22,axiom,
! [X0,X1,X2] :
( member(X2,image2(X0,X1))
<=> ? [X3] :
( member(X3,X1)
& apply(X0,X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',image2) ).
fof(f29,conjecture,
! [X0,X1,X2,X3,X4] :
( ( maps(X0,X1,X2)
& subset(X3,X1)
& subset(X4,X1) )
=> subset(image2(X0,intersection(X3,X4)),intersection(image2(X0,X3),image2(X0,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIIa03) ).
fof(f30,negated_conjecture,
~ ! [X0,X1,X2,X3,X4] :
( ( maps(X0,X1,X2)
& subset(X3,X1)
& subset(X4,X1) )
=> subset(image2(X0,intersection(X3,X4)),intersection(image2(X0,X3),image2(X0,X4))) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f33,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f41,plain,
? [X0,X1,X2,X3,X4] :
( ~ subset(image2(X0,intersection(X3,X4)),intersection(image2(X0,X3),image2(X0,X4)))
& maps(X0,X1,X2)
& subset(X3,X1)
& subset(X4,X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f42,plain,
? [X0,X1,X2,X3,X4] :
( ~ subset(image2(X0,intersection(X3,X4)),intersection(image2(X0,X3),image2(X0,X4)))
& maps(X0,X1,X2)
& subset(X3,X1)
& subset(X4,X1) ),
inference(flattening,[],[f41]) ).
fof(f43,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,[],[f33]) ).
fof(f44,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,[],[f43]) ).
fof(f45,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))],[f44]) ).
fof(f47,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(f48,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,[],[f47]) ).
fof(f67,plain,
! [X0,X1,X2] :
( ( member(X2,image2(X0,X1))
| ! [X3] :
( ~ member(X3,X1)
| ~ apply(X0,X3,X2) ) )
& ( ? [X3] :
( member(X3,X1)
& apply(X0,X3,X2) )
| ~ member(X2,image2(X0,X1)) ) ),
inference(nnf_transformation,[],[f22]) ).
fof(f68,plain,
! [X0,X1,X2] :
( ( member(X2,image2(X0,X1))
| ! [X3] :
( ~ member(X3,X1)
| ~ apply(X0,X3,X2) ) )
& ( ? [X4] :
( member(X4,X1)
& apply(X0,X4,X2) )
| ~ member(X2,image2(X0,X1)) ) ),
inference(rectify,[],[f67]) ).
fof(f69,plain,
! [X0,X1,X2] :
( ( member(X2,image2(X0,X1))
| ! [X3] :
( ~ member(X3,X1)
| ~ apply(X0,X3,X2) ) )
& ( ( member(sK5(X0,X1,X2),X1)
& apply(X0,sK5(X0,X1,X2),X2) )
| ~ member(X2,image2(X0,X1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X4,sK5(X0,X1,X2))],[f68]) ).
fof(f81,plain,
( ~ subset(image2(sK9,intersection(sK12,sK13)),intersection(image2(sK9,sK12),image2(sK9,sK13)))
& maps(sK9,sK10,sK11)
& subset(sK12,sK10)
& subset(sK13,sK10) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10,sK11,sK12,sK13]),skolemize(X0,sK9),skolemize(X1,sK10),skolemize(X2,sK11),skolemize(X3,sK12),skolemize(X4,sK13)],[f42]) ).
fof(f83,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f45]) ).
fof(f84,plain,
! [X0,X1] :
( ~ member(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f45]) ).
fof(f87,plain,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
inference(cnf_transformation,[],[f48]) ).
fof(f88,plain,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
fof(f89,plain,
! [X2,X0,X1] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X1)
| ~ member(X0,X2) ),
inference(cnf_transformation,[],[f48]) ).
fof(f117,plain,
! [X2,X0,X1] :
( apply(X0,sK5(X0,X1,X2),X2)
| ~ member(X2,image2(X0,X1)) ),
inference(cnf_transformation,[],[f69]) ).
fof(f118,plain,
! [X2,X0,X1] :
( ~ member(X2,image2(X0,X1))
| member(sK5(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f69]) ).
fof(f119,plain,
! [X2,X3,X0,X1] :
( ~ apply(X0,X3,X2)
| ~ member(X3,X1)
| member(X2,image2(X0,X1)) ),
inference(cnf_transformation,[],[f69]) ).
fof(f134,plain,
~ subset(image2(sK9,intersection(sK12,sK13)),intersection(image2(sK9,sK12),image2(sK9,sK13))),
inference(cnf_transformation,[],[f81]) ).
fof(f139,plain,
member(sK0(image2(sK9,intersection(sK12,sK13)),intersection(image2(sK9,sK12),image2(sK9,sK13))),image2(sK9,intersection(sK12,sK13))),
inference(resolution,[],[f83,f134]) ).
fof(f148,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,[],[f89,f84]) ).
fof(f149,plain,
member(sK5(sK9,intersection(sK12,sK13),sK0(image2(sK9,intersection(sK12,sK13)),intersection(image2(sK9,sK12),image2(sK9,sK13)))),intersection(sK12,sK13)),
inference(resolution,[],[f118,f139]) ).
fof(f150,plain,
member(sK5(sK9,intersection(sK12,sK13),sK0(image2(sK9,intersection(sK12,sK13)),intersection(image2(sK9,sK12),image2(sK9,sK13)))),sK12),
inference(resolution,[],[f149,f88]) ).
fof(f151,plain,
member(sK5(sK9,intersection(sK12,sK13),sK0(image2(sK9,intersection(sK12,sK13)),intersection(image2(sK9,sK12),image2(sK9,sK13)))),sK13),
inference(resolution,[],[f149,f87]) ).
fof(f153,plain,
! [X2,X3,X0,X1] :
( ~ member(X2,image2(X0,X1))
| member(X2,image2(X0,X3))
| ~ member(sK5(X0,X1,X2),X3) ),
inference(resolution,[],[f119,f117]) ).
fof(f262,plain,
! [X0] :
( member(sK0(image2(sK9,intersection(sK12,sK13)),intersection(image2(sK9,sK12),image2(sK9,sK13))),image2(sK9,X0))
| ~ member(sK5(sK9,intersection(sK12,sK13),sK0(image2(sK9,intersection(sK12,sK13)),intersection(image2(sK9,sK12),image2(sK9,sK13)))),X0) ),
inference(resolution,[],[f153,f139]) ).
fof(f282,plain,
( ~ member(sK0(image2(sK9,intersection(sK12,sK13)),intersection(image2(sK9,sK12),image2(sK9,sK13))),image2(sK9,sK13))
| ~ member(sK0(image2(sK9,intersection(sK12,sK13)),intersection(image2(sK9,sK12),image2(sK9,sK13))),image2(sK9,sK12)) ),
inference(resolution,[],[f148,f134]) ).
fof(f285,definition,
( spl14_3
<=> member(sK0(image2(sK9,intersection(sK12,sK13)),intersection(image2(sK9,sK12),image2(sK9,sK13))),image2(sK9,sK12)) ),
introduced(definition,[new_symbols(definition,[spl14_3])],[avatar_definition]) ).
fof(f287,plain,
( ~ member(sK0(image2(sK9,intersection(sK12,sK13)),intersection(image2(sK9,sK12),image2(sK9,sK13))),image2(sK9,sK12))
| spl14_3 ),
inference(avatar_component_clause,[],[f285]) ).
fof(f289,definition,
( spl14_4
<=> member(sK0(image2(sK9,intersection(sK12,sK13)),intersection(image2(sK9,sK12),image2(sK9,sK13))),image2(sK9,sK13)) ),
introduced(definition,[new_symbols(definition,[spl14_4])],[avatar_definition]) ).
fof(f291,plain,
( ~ member(sK0(image2(sK9,intersection(sK12,sK13)),intersection(image2(sK9,sK12),image2(sK9,sK13))),image2(sK9,sK13))
| spl14_4 ),
inference(avatar_component_clause,[],[f289]) ).
fof(f292,plain,
( ~ spl14_3
| ~ spl14_4 ),
inference(avatar_split_clause,[],[f282,f289,f285]) ).
fof(f320,plain,
( ~ member(sK5(sK9,intersection(sK12,sK13),sK0(image2(sK9,intersection(sK12,sK13)),intersection(image2(sK9,sK12),image2(sK9,sK13)))),sK12)
| spl14_3 ),
inference(resolution,[],[f262,f287]) ).
fof(f324,plain,
( $false
| spl14_3 ),
inference(forward_subsumption_resolution,[],[f320,f150]) ).
fof(f325,plain,
spl14_3,
inference(avatar_contradiction_clause,[],[f324]) ).
fof(f329,plain,
( ~ member(sK5(sK9,intersection(sK12,sK13),sK0(image2(sK9,intersection(sK12,sK13)),intersection(image2(sK9,sK12),image2(sK9,sK13)))),sK13)
| spl14_4 ),
inference(resolution,[],[f291,f262]) ).
fof(f330,plain,
( $false
| spl14_4 ),
inference(forward_subsumption_resolution,[],[f329,f151]) ).
fof(f331,plain,
spl14_4,
inference(avatar_contradiction_clause,[],[f330]) ).
cnf(s2,plain,
( ~ spl14_3
| ~ spl14_4 ),
inference(sat_conversion,[],[f292]) ).
cnf(s3,plain,
spl14_3,
inference(sat_conversion,[],[f325]) ).
cnf(s4,plain,
spl14_4,
inference(sat_conversion,[],[f331]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s2,s4,s3]) ).
fof(f332,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET753+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n016.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 02:48:48 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 2.67/1.27 % (3208609)Detected formulas, will run a generic FOF schedule.
% 2.67/1.27 % (3208615)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=2083456734:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.67/1.27 % (3208618)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3706132608:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.67/1.27 % (3208614)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=2724810472:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.67/1.27 % (3208620)dis-21_1_sil=8000:lcm=predicate:random_seed=1211054670: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)
% 2.67/1.27 % (3208616)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=3731752166:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.67/1.27 % (3208617)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3842017843:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.67/1.27 % (3208619)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=86826678:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.67/1.27 % (3208617)Refutation not found, incomplete strategy
% 2.67/1.27 % (3208617)------------------------------
% 2.67/1.27 % (3208617)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.67/1.27 % (3208617)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.67/1.27 % (3208617)CaDiCaL version: 2.1.3
% 2.67/1.27 % (3208617)Termination reason: Refutation not found, incomplete strategy
% 2.67/1.27 % (3208617)Time elapsed: 0.003 s
% 2.67/1.27 % (3208617)Peak memory usage: 88 MB
% 2.67/1.27 % (3208617)Instructions burned: 3 (million)
% 2.67/1.27 % (3208619)First to succeed.
% 2.67/1.27 % (3208619)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3208609"
% 2.67/1.27 % (3208618)Instruction limit reached!
% 2.67/1.27 % (3208618)------------------------------
% 2.67/1.27 % (3208618)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.67/1.27 % (3208618)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.67/1.27 % (3208618)CaDiCaL version: 2.1.3
% 2.67/1.27 % (3208618)Termination reason: Instruction limit
% 2.67/1.27 % (3208618)Termination phase: Saturation
% 2.67/1.27 % (3208618)Time elapsed: 0.071 s
% 2.67/1.27 % (3208618)Peak memory usage: 88 MB
% 2.67/1.27 % (3208618)Instructions burned: 119 (million)
% 2.67/1.27 % (3208620)Instruction limit reached!
% 2.67/1.27 % (3208620)------------------------------
% 2.67/1.27 % (3208620)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.67/1.27 % (3208620)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.67/1.27 % (3208620)CaDiCaL version: 2.1.3
% 2.67/1.27 % (3208620)Termination reason: Instruction limit
% 2.67/1.27 % (3208620)Termination phase: Saturation
% 2.67/1.27 % (3208620)Time elapsed: 0.083 s
% 2.67/1.27 % (3208620)Peak memory usage: 89 MB
% 2.67/1.27 % (3208620)Instructions burned: 130 (million)
% 2.67/1.27 % (3208628)lrs+10_1_sil=8000:sp=occurrence:random_seed=1275238876:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.67/1.27 % (3208629)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3632986109:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.67/1.27 % (3208629)Also succeeded, but the first one will report.
% 2.67/1.27 % (3208617)------------------------------
% 2.67/1.27 % (3208617)------------------------------
% 2.67/1.27 % (3208619)Refutation found. Thanks to Tanya!
% 2.67/1.27 % SZS status Theorem for theBenchmark
% 2.67/1.27 % SZS output start Proof for theBenchmark
% See solution above
% 3.56/1.47 % (3208619)------------------------------
% 3.56/1.47 % (3208619)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.56/1.47 % (3208619)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.56/1.47 % (3208619)CaDiCaL version: 2.1.3
% 3.56/1.47 % (3208619)Termination reason: Refutation
% 3.56/1.47 % (3208619)Time elapsed: 0.015 s
% 3.56/1.47 % (3208619)Peak memory usage: 89 MB
% 3.56/1.47 % (3208619)Instructions burned: 19 (million)
% 3.56/1.47 % (3208619)------------------------------
% 3.56/1.47 % (3208619)------------------------------
% 3.56/1.47 % (3208609)Success in time 0.421 s
% 3.56/1.47 % Vampire exiting
%------------------------------------------------------------------------------