%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET653+3 : 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 : 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 12:41:33 PM UTC 2026
% Result : Theorem 3.53s 1.48s
% Output : Refutation 3.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 47 ( 11 unt; 2 def)
% Number of atoms : 158 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 189 ( 78 ~; 69 |; 18 &)
% ( 2 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 88 ( 0 sgn 80 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( ( subset(X0,X1)
& subset(X1,X2) )
=> subset(X0,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
fof(f2,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ( subset(domain_of(X2),X0)
& subset(range_of(X2),X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).
fof(f3,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X0,X2))
=> ( subset(domain_of(X3),X1)
=> ilf_type(X3,relation_type(X1,X2)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3) ).
fof(f22,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p22) ).
fof(f23,conjecture,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X0,X2))
=> ( subset(X0,X1)
=> ilf_type(X3,relation_type(X1,X2)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_15) ).
fof(f24,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X0,X2))
=> ( subset(X0,X1)
=> ilf_type(X3,relation_type(X1,X2)) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f23]) ).
fof(f25,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( subset(X0,X2)
| ~ subset(X0,X1)
| ~ subset(X1,X2)
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f1]) ).
fof(f26,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( subset(X0,X2)
| ~ subset(X0,X1)
| ~ subset(X1,X2)
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f25]) ).
fof(f27,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( subset(domain_of(X2),X0)
& subset(range_of(X2),X1) )
| ~ ilf_type(X2,relation_type(X0,X1)) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f2]) ).
fof(f28,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
| ~ subset(domain_of(X3),X1)
| ~ ilf_type(X3,relation_type(X0,X2)) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f3]) ).
fof(f29,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
| ~ subset(domain_of(X3),X1)
| ~ ilf_type(X3,relation_type(X0,X2)) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f28]) ).
fof(f54,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ ilf_type(X3,relation_type(X1,X2))
& subset(X0,X1)
& ilf_type(X3,relation_type(X0,X2)) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f24]) ).
fof(f55,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ ilf_type(X3,relation_type(X1,X2))
& subset(X0,X1)
& ilf_type(X3,relation_type(X0,X2)) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(flattening,[],[f54]) ).
fof(f73,plain,
( ~ ilf_type(sK12,relation_type(sK10,sK11))
& subset(sK9,sK10)
& ilf_type(sK12,relation_type(sK9,sK11))
& ilf_type(sK11,set_type)
& ilf_type(sK10,set_type)
& ilf_type(sK9,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10,sK11,sK12]),skolemize(X0,sK9),skolemize(X1,sK10),skolemize(X2,sK11),skolemize(X3,sK12)],[f55]) ).
fof(f74,plain,
! [X2,X0,X1] :
( subset(X0,X2)
| ~ subset(X0,X1)
| ~ subset(X1,X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f26]) ).
fof(f76,plain,
! [X2,X0,X1] :
( subset(domain_of(X2),X0)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f27]) ).
fof(f77,plain,
! [X2,X3,X0,X1] :
( ilf_type(X3,relation_type(X1,X2))
| ~ subset(domain_of(X3),X1)
| ~ ilf_type(X3,relation_type(X0,X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f29]) ).
fof(f113,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f22]) ).
fof(f117,plain,
ilf_type(sK12,relation_type(sK9,sK11)),
inference(cnf_transformation,[],[f73]) ).
fof(f118,plain,
subset(sK9,sK10),
inference(cnf_transformation,[],[f73]) ).
fof(f119,plain,
~ ilf_type(sK12,relation_type(sK10,sK11)),
inference(cnf_transformation,[],[f73]) ).
fof(f139,plain,
! [X2,X0,X1] :
( subset(domain_of(X2),X0)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f76,f113]) ).
fof(f140,plain,
! [X2,X0,X1] :
( subset(domain_of(X2),X0)
| ~ ilf_type(X2,relation_type(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f139,f113]) ).
fof(f168,plain,
! [X2,X0,X1] :
( subset(X0,X2)
| ~ subset(X0,X1)
| ~ subset(X1,X2)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f74,f113]) ).
fof(f169,plain,
! [X2,X0,X1] :
( subset(X0,X2)
| ~ subset(X0,X1)
| ~ subset(X1,X2)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f168,f113]) ).
fof(f170,plain,
! [X2,X0,X1] :
( subset(X0,X2)
| ~ subset(X0,X1)
| ~ subset(X1,X2) ),
inference(forward_subsumption_resolution,[],[f169,f113]) ).
fof(f210,plain,
! [X2,X3,X0,X1] :
( ilf_type(X3,relation_type(X1,X2))
| ~ subset(domain_of(X3),X1)
| ~ ilf_type(X3,relation_type(X0,X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(forward_subsumption_resolution,[],[f77,f113]) ).
fof(f211,plain,
! [X2,X3,X0,X1] :
( ilf_type(X3,relation_type(X1,X2))
| ~ subset(domain_of(X3),X1)
| ~ ilf_type(X3,relation_type(X0,X2))
| ~ ilf_type(X2,set_type) ),
inference(forward_subsumption_resolution,[],[f210,f113]) ).
fof(f212,plain,
! [X2,X3,X0,X1] :
( ilf_type(X3,relation_type(X1,X2))
| ~ subset(domain_of(X3),X1)
| ~ ilf_type(X3,relation_type(X0,X2)) ),
inference(forward_subsumption_resolution,[],[f211,f113]) ).
fof(f221,plain,
! [X0] :
( ~ subset(domain_of(sK12),sK10)
| ~ ilf_type(sK12,relation_type(X0,sK11)) ),
inference(resolution,[],[f212,f119]) ).
fof(f223,definition,
( spl13_4
<=> ! [X0] : ~ ilf_type(sK12,relation_type(X0,sK11)) ),
introduced(definition,[new_symbols(definition,[spl13_4])],[avatar_definition]) ).
fof(f224,plain,
( ! [X0] : ~ ilf_type(sK12,relation_type(X0,sK11))
| ~ spl13_4 ),
inference(avatar_component_clause,[],[f223]) ).
fof(f226,definition,
( spl13_5
<=> subset(domain_of(sK12),sK10) ),
introduced(definition,[new_symbols(definition,[spl13_5])],[avatar_definition]) ).
fof(f228,plain,
( ~ subset(domain_of(sK12),sK10)
| spl13_5 ),
inference(avatar_component_clause,[],[f226]) ).
fof(f229,plain,
( spl13_4
| ~ spl13_5 ),
inference(avatar_split_clause,[],[f221,f226,f223]) ).
fof(f231,plain,
( ! [X0] :
( ~ subset(domain_of(sK12),X0)
| ~ subset(X0,sK10) )
| spl13_5 ),
inference(resolution,[],[f228,f170]) ).
fof(f249,plain,
( ! [X0,X1] :
( ~ ilf_type(sK12,relation_type(X0,X1))
| ~ subset(X0,sK10) )
| spl13_5 ),
inference(resolution,[],[f231,f140]) ).
fof(f254,plain,
( ~ subset(sK9,sK10)
| spl13_5 ),
inference(resolution,[],[f249,f117]) ).
fof(f257,plain,
( $false
| spl13_5 ),
inference(forward_subsumption_resolution,[],[f254,f118]) ).
fof(f258,plain,
spl13_5,
inference(avatar_contradiction_clause,[],[f257]) ).
fof(f259,plain,
( $false
| ~ spl13_4 ),
inference(resolution,[],[f224,f117]) ).
fof(f262,plain,
~ spl13_4,
inference(avatar_contradiction_clause,[],[f259]) ).
cnf(s3,plain,
( spl13_4
| ~ spl13_5 ),
inference(sat_conversion,[],[f229]) ).
cnf(s5,plain,
spl13_5,
inference(sat_conversion,[],[f258]) ).
cnf(s6,plain,
~ spl13_4,
inference(sat_conversion,[],[f262]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s3,s5,s6]) ).
fof(f263,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET653+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n026.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Mon Sep 28 02:30:57 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 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
% 3.53/1.48 % (3415056)Detected formulas, will run a generic FOF schedule.
% 3.53/1.48 % (3415073)dis-21_1_sil=8000:lcm=predicate:random_seed=1874568262: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)
% 3.53/1.48 % (3415071)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3630972673:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.53/1.48 % (3415067)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=1782392118:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.53/1.48 % (3415069)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=2341519936:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.53/1.48 % (3415070)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2416139875:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.53/1.48 % (3415068)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=3258299027:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.53/1.48 % (3415072)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1984301724:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.53/1.48 % (3415070)Refutation not found, incomplete strategy
% 3.53/1.48 % (3415070)------------------------------
% 3.53/1.48 % (3415070)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.48 % (3415070)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.48 % (3415070)CaDiCaL version: 2.1.3
% 3.53/1.48 % (3415070)Termination reason: Refutation not found, incomplete strategy
% 3.53/1.48 % (3415070)Time elapsed: 0.001 s
% 3.53/1.48 % (3415070)Peak memory usage: 87 MB
% 3.53/1.48 % (3415071)Refutation not found, incomplete strategy
% 3.53/1.48 % (3415071)------------------------------
% 3.53/1.48 % (3415071)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.48 % (3415071)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.48 % (3415071)CaDiCaL version: 2.1.3
% 3.53/1.48 % (3415071)Termination reason: Refutation not found, incomplete strategy
% 3.53/1.48 % (3415071)Time elapsed: 0.001 s
% 3.53/1.48 % (3415071)Peak memory usage: 87 MB
% 3.53/1.48 % (3415073)Instruction limit reached!
% 3.53/1.48 % (3415073)------------------------------
% 3.53/1.48 % (3415073)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.48 % (3415073)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.48 % (3415073)CaDiCaL version: 2.1.3
% 3.53/1.48 % (3415073)Termination reason: Instruction limit
% 3.53/1.48 % (3415073)Termination phase: Saturation
% 3.53/1.48 % (3415073)Time elapsed: 0.043 s
% 3.53/1.48 % (3415073)Peak memory usage: 90 MB
% 3.53/1.48 % (3415073)Instructions burned: 129 (million)
% 3.53/1.48 % (3415072)First to succeed.
% 3.53/1.48 % (3415072)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3415056"
% 3.53/1.48 % (3415081)lrs+10_1_sil=8000:sp=occurrence:random_seed=1729825584:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.53/1.48 % (3415081)Also succeeded, but the first one will report.
% 3.53/1.48 % (3415070)------------------------------
% 3.53/1.48 % (3415070)------------------------------
% 3.53/1.48 % (3415071)------------------------------
% 3.53/1.48 % (3415071)------------------------------
% 3.53/1.48 % (3415072)Refutation found. Thanks to Tanya!
% 3.53/1.48 % SZS status Theorem for theBenchmark
% 3.53/1.48 % SZS output start Proof for theBenchmark
% See solution above
% 3.53/1.48 % (3415072)------------------------------
% 3.53/1.48 % (3415072)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.48 % (3415072)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.48 % (3415072)CaDiCaL version: 2.1.3
% 3.53/1.48 % (3415072)Termination reason: Refutation
% 3.53/1.48 % (3415072)Time elapsed: 0.007 s
% 3.53/1.48 % (3415072)Peak memory usage: 89 MB
% 3.53/1.48 % (3415072)Instructions burned: 8 (million)
% 3.53/1.48 % (3415072)------------------------------
% 3.53/1.48 % (3415072)------------------------------
% 3.53/1.48 % (3415056)Success in time 0.414 s
% 3.53/1.48 % Vampire exiting
%------------------------------------------------------------------------------