%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET679+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 : n001.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 12:44:24 PM UTC 2026
% Result : Theorem 0.16s 0.47s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 37 ( 9 unt; 0 def)
% Number of atoms : 112 ( 8 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 134 ( 59 ~; 44 |; 16 &)
% ( 6 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 50 ( 46 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( member(X1,X0)
<=> member(ordered_pair(X1,X1),identity_relation_of(X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
fof(f2,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ~ member(X0,empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).
fof(f8,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( not_equal(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p7) ).
fof(f9,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( empty(X0)
<=> ! [X1] :
( ilf_type(X1,set_type)
=> ~ member(X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p8) ).
fof(f23,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p22) ).
fof(f24,conjecture,
! [X0] :
( ( ~ empty(X0)
& ilf_type(X0,set_type) )
=> not_equal(identity_relation_of(X0),empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_46) ).
fof(f25,negated_conjecture,
~ ! [X0] :
( ( ~ empty(X0)
& ilf_type(X0,set_type) )
=> not_equal(identity_relation_of(X0),empty_set) ),
inference(negated_conjecture,[status(cth)],[f24]) ).
fof(f27,plain,
! [X0] :
( ! [X1] :
( ( member(X1,X0)
<=> member(ordered_pair(X1,X1),identity_relation_of(X0)) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f1]) ).
fof(f28,plain,
! [X0] :
( ~ member(X0,empty_set)
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f2]) ).
fof(f32,plain,
! [X0] :
( ! [X1] :
( ( not_equal(X0,X1)
<=> X0 != X1 )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f8]) ).
fof(f33,plain,
! [X0] :
( ( empty(X0)
<=> ! [X1] :
( ~ member(X1,X0)
| ~ ilf_type(X1,set_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f9]) ).
fof(f51,plain,
? [X0] :
( ~ not_equal(identity_relation_of(X0),empty_set)
& ~ empty(X0)
& ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f25]) ).
fof(f52,plain,
? [X0] :
( ~ not_equal(identity_relation_of(X0),empty_set)
& ~ empty(X0)
& ilf_type(X0,set_type) ),
inference(flattening,[],[f51]) ).
fof(f53,plain,
! [X0] :
( ! [X1] :
( ( ( member(X1,X0)
| ~ member(ordered_pair(X1,X1),identity_relation_of(X0)) )
& ( member(ordered_pair(X1,X1),identity_relation_of(X0))
| ~ member(X1,X0) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f27]) ).
fof(f60,plain,
! [X0] :
( ! [X1] :
( ( ( not_equal(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ not_equal(X0,X1) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f32]) ).
fof(f61,plain,
! [X0] :
( ( ( empty(X0)
| ? [X1] :
( member(X1,X0)
& ilf_type(X1,set_type) ) )
& ( ! [X1] :
( ~ member(X1,X0)
| ~ ilf_type(X1,set_type) )
| ~ empty(X0) ) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f33]) ).
fof(f62,plain,
! [X0] :
( ( ( empty(X0)
| ? [X1] :
( member(X1,X0)
& ilf_type(X1,set_type) ) )
& ( ! [X2] :
( ~ member(X2,X0)
| ~ ilf_type(X2,set_type) )
| ~ empty(X0) ) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f61]) ).
fof(f63,plain,
! [X0] :
( ( ( empty(X0)
| ( member(sK1(X0),X0)
& ilf_type(sK1(X0),set_type) ) )
& ( ! [X2] :
( ~ member(X2,X0)
| ~ ilf_type(X2,set_type) )
| ~ empty(X0) ) )
| ~ ilf_type(X0,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X1,sK1(X0))],[f62]) ).
fof(f77,plain,
( ~ not_equal(identity_relation_of(sK9),empty_set)
& ~ empty(sK9)
& ilf_type(sK9,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X0,sK9)],[f52]) ).
fof(f78,plain,
! [X0,X1] :
( member(ordered_pair(X1,X1),identity_relation_of(X0))
| ~ member(X1,X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f53]) ).
fof(f80,plain,
! [X0] :
( ~ member(X0,empty_set)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f28]) ).
fof(f92,plain,
! [X0,X1] :
( not_equal(X0,X1)
| X0 = X1
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f60]) ).
fof(f95,plain,
! [X0] :
( empty(X0)
| member(sK1(X0),X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f63]) ).
fof(f122,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f23]) ).
fof(f124,plain,
~ empty(sK9),
inference(cnf_transformation,[],[f77]) ).
fof(f125,plain,
~ not_equal(identity_relation_of(sK9),empty_set),
inference(cnf_transformation,[],[f77]) ).
fof(f135,plain,
! [X0] : ~ member(X0,empty_set),
inference(forward_subsumption_resolution,[],[f80,f122]) ).
fof(f147,plain,
! [X0] :
( member(sK1(X0),X0)
| empty(X0) ),
inference(forward_subsumption_resolution,[],[f95,f122]) ).
fof(f156,plain,
! [X0,X1] :
( not_equal(X0,X1)
| X0 = X1
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f92,f122]) ).
fof(f157,plain,
! [X0,X1] :
( not_equal(X0,X1)
| X0 = X1 ),
inference(forward_subsumption_resolution,[],[f156,f122]) ).
fof(f158,plain,
empty_set = identity_relation_of(sK9),
inference(resolution,[],[f157,f125]) ).
fof(f167,plain,
! [X0,X1] :
( member(ordered_pair(X1,X1),identity_relation_of(X0))
| ~ member(X1,X0)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f78,f122]) ).
fof(f168,plain,
! [X0,X1] :
( member(ordered_pair(X1,X1),identity_relation_of(X0))
| ~ member(X1,X0) ),
inference(forward_subsumption_resolution,[],[f167,f122]) ).
fof(f170,plain,
! [X0] :
( member(ordered_pair(X0,X0),empty_set)
| ~ member(X0,sK9) ),
inference(superposition,[],[f168,f158]) ).
fof(f171,plain,
! [X0] : ~ member(X0,sK9),
inference(forward_subsumption_resolution,[],[f170,f135]) ).
fof(f172,plain,
empty(sK9),
inference(resolution,[],[f171,f147]) ).
fof(f174,plain,
$false,
inference(forward_subsumption_resolution,[],[f172,f124]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET679+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.38 % Computer : n001.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Mon Sep 28 02:36:02 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.42 Running first-order model finding
% 0.10/0.42 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
% 0.16/0.47 % (4161094)Will run a generic schedule for satisfiability detection.
% 0.16/0.47 % (4161099)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1741601139_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.47 % TRYING [1]
% 0.16/0.47 % TRYING [2]
% 0.16/0.47 % (4161100)% WARNING: option uhcvi not known.
% 0.16/0.47 % TRYING [3]
% 0.16/0.47 % TRYING [4]
% 0.16/0.47 % (4161103)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2699406704:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.47 % (4161100)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1856558532:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.47 % (4161104)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4265293144:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.47 % (4161102)dis+10_1_sil=32000:sp=arity:random_seed=2675996879:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.47 % (4161101)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=820980387:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.47 % (4161105)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4002724878:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.47 % TRYING [5]
% 0.16/0.47 % (4161102) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4161094-4161102"...
% 0.16/0.47 % (4161104) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4161094-4161104"...
% 0.16/0.47 % (4161103) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4161094-4161103"...
% 0.16/0.47 % (4161100) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4161094-4161100"...
% 0.16/0.47 % (4161102)...printing done.
% 0.16/0.47 % (4161104)...printing done.
% 0.16/0.47 % (4161103)...printing done.
% 0.16/0.47 % (4161100)...printing done.
% 0.16/0.47 % (4161102)Refutation found. Thanks to Tanya!
% 0.16/0.47 % SZS status Theorem for theBenchmark
% 0.16/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.47 % (4161102)------------------------------
% 0.16/0.47 % (4161102)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.47 % (4161102)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.47 % (4161102)CaDiCaL version: 2.1.3
% 0.16/0.47 % (4161102)Termination reason: Refutation
% 0.16/0.47 % (4161102)Time elapsed: 0.003 s
% 0.16/0.47 % (4161102)Peak memory usage: 12 MB
% 0.16/0.47 % (4161102)Instructions burned: 4 (million)
% 0.16/0.47 % (4161094)Success in time 0.042 s
% 0.16/0.47 % Vampire exiting
%------------------------------------------------------------------------------