%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET676+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 12:41:37 PM UTC 2026
% Result : Theorem 2.75s 1.38s
% Output : Refutation 2.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 32 ( 10 unt; 2 def)
% Number of atoms : 71 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 70 ( 31 ~; 26 |; 3 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 21 ( 0 sgn 20 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ilf_type(cross_product(X0,X1),relation_type(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
fof(f4,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ilf_type(X1,identity_relation_of_type(X0))
<=> ilf_type(X1,relation_type(X0,X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4) ).
fof(f19,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p19) ).
fof(f20,conjecture,
! [X0] :
( ilf_type(X0,set_type)
=> ilf_type(cross_product(X0,X0),identity_relation_of_type(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_41) ).
fof(f21,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ilf_type(cross_product(X0,X0),identity_relation_of_type(X0)) ),
inference(negated_conjecture,[status(cth)],[f20]) ).
fof(f22,plain,
! [X0] :
( ! [X1] :
( ilf_type(cross_product(X0,X1),relation_type(X0,X1))
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f1]) ).
fof(f25,plain,
! [X0] :
( ! [X1] :
( ( ilf_type(X1,identity_relation_of_type(X0))
<=> ilf_type(X1,relation_type(X0,X0)) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f4]) ).
fof(f45,plain,
? [X0] :
( ~ ilf_type(cross_product(X0,X0),identity_relation_of_type(X0))
& ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f21]) ).
fof(f49,plain,
! [X0] :
( ! [X1] :
( ( ( ilf_type(X1,identity_relation_of_type(X0))
| ~ ilf_type(X1,relation_type(X0,X0)) )
& ( ilf_type(X1,relation_type(X0,X0))
| ~ ilf_type(X1,identity_relation_of_type(X0)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f25]) ).
fof(f65,plain,
( ~ ilf_type(cross_product(sK11,sK11),identity_relation_of_type(sK11))
& ilf_type(sK11,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X0,sK11)],[f45]) ).
fof(f66,plain,
! [X0,X1] :
( ilf_type(cross_product(X0,X1),relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f22]) ).
fof(f75,plain,
! [X0,X1] :
( ~ ilf_type(X1,relation_type(X0,X0))
| ilf_type(X1,identity_relation_of_type(X0))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f49]) ).
fof(f104,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f19]) ).
fof(f105,plain,
ilf_type(sK11,set_type),
inference(cnf_transformation,[],[f65]) ).
fof(f106,plain,
~ ilf_type(cross_product(sK11,sK11),identity_relation_of_type(sK11)),
inference(cnf_transformation,[],[f65]) ).
fof(f120,plain,
! [X0] :
( ilf_type(cross_product(X0,X0),identity_relation_of_type(X0))
| ~ ilf_type(cross_product(X0,X0),set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[],[f75,f66]) ).
fof(f125,plain,
! [X0] :
( ilf_type(cross_product(X0,X0),identity_relation_of_type(X0))
| ~ ilf_type(cross_product(X0,X0),set_type)
| ~ ilf_type(X0,set_type) ),
inference(duplicate_literal_removal,[],[f120]) ).
fof(f134,plain,
( ~ ilf_type(cross_product(sK11,sK11),set_type)
| ~ ilf_type(sK11,set_type) ),
inference(resolution,[],[f125,f106]) ).
fof(f136,definition,
( spl13_1
<=> ilf_type(sK11,set_type) ),
introduced(definition,[new_symbols(definition,[spl13_1])],[avatar_definition]) ).
fof(f137,plain,
( ~ ilf_type(sK11,set_type)
| spl13_1 ),
inference(avatar_component_clause,[],[f136]) ).
fof(f139,definition,
( spl13_2
<=> ilf_type(cross_product(sK11,sK11),set_type) ),
introduced(definition,[new_symbols(definition,[spl13_2])],[avatar_definition]) ).
fof(f140,plain,
( ~ ilf_type(cross_product(sK11,sK11),set_type)
| spl13_2 ),
inference(avatar_component_clause,[],[f139]) ).
fof(f141,plain,
( ~ spl13_1
| ~ spl13_2 ),
inference(avatar_split_clause,[],[f134,f139,f136]) ).
fof(f142,plain,
( $false
| spl13_1 ),
inference(resolution,[],[f137,f105]) ).
fof(f145,plain,
spl13_1,
inference(avatar_contradiction_clause,[],[f142]) ).
fof(f146,plain,
( $false
| spl13_2 ),
inference(resolution,[],[f140,f104]) ).
fof(f147,plain,
spl13_2,
inference(avatar_contradiction_clause,[],[f146]) ).
cnf(s1,plain,
( ~ spl13_1
| ~ spl13_2 ),
inference(sat_conversion,[],[f141]) ).
cnf(s3,plain,
spl13_1,
inference(sat_conversion,[],[f145]) ).
cnf(s4,plain,
spl13_2,
inference(sat_conversion,[],[f147]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s4,s3]) ).
fof(f148,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET676+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 % Computer : n005.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Mon Sep 28 02:29:17 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.43 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.75/1.38 % (375699)Detected formulas, will run a generic FOF schedule.
% 2.75/1.38 % (375710)dis-21_1_sil=8000:lcm=predicate:random_seed=2298263116: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)
% 2.75/1.38 % (375710)First to succeed.
% 2.75/1.38 % (375710)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-375699"
% 2.75/1.38 % (375709)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1076373810:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.75/1.38 % (375707)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2772593192:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.75/1.38 % (375705)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=3611767870:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.75/1.38 % (375708)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2005673167:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.75/1.38 % (375706)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=1496555008:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.75/1.38 % (375704)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=3289242314:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.75/1.38 % (375707)Refutation not found, incomplete strategy
% 2.75/1.38 % (375707)------------------------------
% 2.75/1.38 % (375707)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.75/1.38 % (375707)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.75/1.38 % (375707)CaDiCaL version: 2.1.3
% 2.75/1.38 % (375707)Termination reason: Refutation not found, incomplete strategy
% 2.75/1.38 % (375707)Time elapsed: 0.001 s
% 2.75/1.38 % (375707)Peak memory usage: 87 MB
% 2.75/1.38 % (375708)Also succeeded, but the first one will report.
% 2.75/1.38 % (375709)Also succeeded, but the first one will report.
% 2.75/1.38 % (375710)Refutation found. Thanks to Tanya!
% 2.75/1.38 % SZS status Theorem for theBenchmark
% 2.75/1.38 % SZS output start Proof for theBenchmark
% See solution above
% 2.75/1.38 % (375710)------------------------------
% 2.75/1.38 % (375710)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.75/1.38 % (375710)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.75/1.38 % (375710)CaDiCaL version: 2.1.3
% 2.75/1.38 % (375710)Termination reason: Refutation
% 2.75/1.38 % (375710)Time elapsed: 0.002 s
% 2.75/1.38 % (375710)Peak memory usage: 89 MB
% 2.75/1.38 % (375710)Instructions burned: 4 (million)
% 2.75/1.38 % (375710)------------------------------
% 2.75/1.38 % (375710)------------------------------
% 2.75/1.38 % (375699)Success in time 0.304 s
% 2.75/1.38 % Vampire exiting
%------------------------------------------------------------------------------