%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET643+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 : 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 12:44:17 PM UTC 2026
% Result : Theorem 0.11s 0.43s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 7
% Syntax : Number of formulae : 56 ( 9 unt; 0 def)
% Number of atoms : 204 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 248 ( 100 ~; 103 |; 20 &)
% ( 8 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 105 ( 101 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ! [X2] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
=> ilf_type(X2,relation_type(X0,X1)) )
& ! [X3] :
( ilf_type(X3,relation_type(X0,X1))
=> ilf_type(X3,subset_type(cross_product(X0,X1))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4) ).
fof(f7,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ilf_type(X1,subset_type(X0))
<=> ilf_type(X1,member_type(power_set(X0))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p7) ).
fof(f11,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( member(X0,power_set(X1))
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X2,X0)
=> member(X2,X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p11) ).
fof(f12,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( ~ empty(power_set(X0))
& ilf_type(power_set(X0),set_type) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12) ).
fof(f13,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ( ~ empty(X1)
& ilf_type(X1,set_type) )
=> ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p13) ).
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)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ilf_type(cross_product(X0,X1),relation_type(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_5) ).
fof(f21,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ilf_type(cross_product(X0,X1),relation_type(X0,X1)) ) ),
inference(negated_conjecture,[status(cth)],[f20]) ).
fof(f26,plain,
! [X0] :
( ! [X1] :
( ( ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X2,subset_type(cross_product(X0,X1))) )
& ! [X3] :
( ilf_type(X3,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X3,relation_type(X0,X1)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f4]) ).
fof(f29,plain,
! [X0] :
( ! [X1] :
( ( ilf_type(X1,subset_type(X0))
<=> ilf_type(X1,member_type(power_set(X0))) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f7]) ).
fof(f34,plain,
! [X0] :
( ! [X1] :
( ( member(X0,power_set(X1))
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f11]) ).
fof(f35,plain,
! [X0] :
( ! [X1] :
( ( member(X0,power_set(X1))
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f34]) ).
fof(f36,plain,
! [X0] :
( ( ~ empty(power_set(X0))
& ilf_type(power_set(X0),set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f12]) ).
fof(f37,plain,
! [X0] :
( ! [X1] :
( ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) )
| empty(X1)
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f13]) ).
fof(f38,plain,
! [X0] :
( ! [X1] :
( ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) )
| empty(X1)
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f37]) ).
fof(f47,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,[],[f21]) ).
fof(f52,plain,
! [X0] :
( ! [X1] :
( ( ( ilf_type(X1,subset_type(X0))
| ~ ilf_type(X1,member_type(power_set(X0))) )
& ( ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,subset_type(X0)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f29]) ).
fof(f57,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,power_set(X1))
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) )
| ~ member(X0,power_set(X1)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f35]) ).
fof(f58,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,power_set(X1))
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type) )
| ~ member(X0,power_set(X1)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f57]) ).
fof(f59,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,power_set(X1))
| ( ~ member(sK5(X0,X1),X1)
& member(sK5(X0,X1),X0)
& ilf_type(sK5(X0,X1),set_type) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type) )
| ~ member(X0,power_set(X1)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X2,sK5(X0,X1))],[f58]) ).
fof(f60,plain,
! [X0] :
( ! [X1] :
( ( ( ilf_type(X0,member_type(X1))
| ~ member(X0,X1) )
& ( member(X0,X1)
| ~ ilf_type(X0,member_type(X1)) ) )
| empty(X1)
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f38]) ).
fof(f68,plain,
( ~ ilf_type(cross_product(sK11,sK12),relation_type(sK11,sK12))
& ilf_type(sK12,set_type)
& ilf_type(sK11,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12]),skolemize(X0,sK11),skolemize(X1,sK12)],[f47]) ).
fof(f78,plain,
! [X2,X0,X1] :
( ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f26]) ).
fof(f82,plain,
! [X0,X1] :
( ilf_type(X1,subset_type(X0))
| ~ ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f52]) ).
fof(f91,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| member(sK5(X0,X1),X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f59]) ).
fof(f92,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| ~ member(sK5(X0,X1),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f59]) ).
fof(f94,plain,
! [X0] :
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f36]) ).
fof(f96,plain,
! [X0,X1] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1)
| empty(X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f60]) ).
fof(f109,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f19]) ).
fof(f112,plain,
~ ilf_type(cross_product(sK11,sK12),relation_type(sK11,sK12)),
inference(cnf_transformation,[],[f68]) ).
fof(f122,plain,
! [X2,X0,X1] :
( ilf_type(X1,set_type)
| ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X2,relation_type(X0,X1))
| ilf_type(X0,set_type) ),
inference(consistent_polarity_flipping,[],[f78]) ).
fof(f126,plain,
! [X0,X1] :
( ilf_type(X1,set_type)
| ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,subset_type(X0))
| ilf_type(X0,set_type) ),
inference(consistent_polarity_flipping,[],[f82]) ).
fof(f134,plain,
! [X0,X1] :
( ilf_type(X1,set_type)
| member(sK5(X0,X1),X1)
| ~ member(X0,power_set(X1))
| ilf_type(X0,set_type) ),
inference(consistent_polarity_flipping,[],[f92]) ).
fof(f135,plain,
! [X0,X1] :
( ilf_type(X1,set_type)
| ~ member(sK5(X0,X1),X0)
| ~ member(X0,power_set(X1))
| ilf_type(X0,set_type) ),
inference(consistent_polarity_flipping,[],[f91]) ).
fof(f138,plain,
! [X0] :
( empty(power_set(X0))
| ilf_type(X0,set_type) ),
inference(consistent_polarity_flipping,[],[f94]) ).
fof(f140,plain,
! [X0,X1] :
( ilf_type(X1,set_type)
| member(X0,X1)
| ~ empty(X1)
| ~ ilf_type(X0,member_type(X1))
| ilf_type(X0,set_type) ),
inference(consistent_polarity_flipping,[],[f96]) ).
fof(f154,plain,
! [X0] : ~ ilf_type(X0,set_type),
inference(consistent_polarity_flipping,[],[f109]) ).
fof(f155,plain,
ilf_type(cross_product(sK11,sK12),relation_type(sK11,sK12)),
inference(consistent_polarity_flipping,[],[f112]) ).
fof(f165,plain,
! [X0,X1] :
( ilf_type(X1,set_type)
| ~ ilf_type(X0,subset_type(X1))
| ilf_type(X0,member_type(power_set(X1))) ),
inference(resolution,[],[f126,f154]) ).
fof(f166,plain,
! [X0,X1] :
( ilf_type(X0,member_type(power_set(X1)))
| ~ ilf_type(X0,subset_type(X1)) ),
inference(resolution,[],[f165,f154]) ).
fof(f175,plain,
! [X0,X1] :
( ilf_type(X0,set_type)
| ~ member(X0,power_set(X1))
| member(sK5(X0,X1),X1) ),
inference(resolution,[],[f134,f154]) ).
fof(f176,plain,
! [X0,X1] :
( member(sK5(X0,X1),X1)
| ~ member(X0,power_set(X1)) ),
inference(resolution,[],[f175,f154]) ).
fof(f177,plain,
! [X0,X1] :
( ilf_type(X0,set_type)
| ~ member(X0,power_set(X1))
| ~ member(sK5(X0,X1),X0) ),
inference(resolution,[],[f135,f154]) ).
fof(f178,plain,
! [X0,X1] :
( ~ member(sK5(X0,X1),X0)
| ~ member(X0,power_set(X1)) ),
inference(resolution,[],[f177,f154]) ).
fof(f179,plain,
! [X0] :
( ~ member(X0,power_set(X0))
| ~ member(X0,power_set(X0)) ),
inference(resolution,[],[f178,f176]) ).
fof(f180,plain,
! [X0] : ~ member(X0,power_set(X0)),
inference(duplicate_literal_removal,[],[f179]) ).
fof(f181,plain,
! [X0,X1] :
( ilf_type(X0,set_type)
| ~ empty(X1)
| ~ ilf_type(X0,member_type(X1))
| member(X0,X1) ),
inference(resolution,[],[f140,f154]) ).
fof(f182,plain,
! [X0,X1] :
( member(X1,X0)
| ~ ilf_type(X1,member_type(X0))
| ~ empty(X0) ),
inference(resolution,[],[f181,f154]) ).
fof(f186,plain,
! [X0] :
( ~ ilf_type(X0,member_type(power_set(X0)))
| ~ empty(power_set(X0)) ),
inference(resolution,[],[f182,f180]) ).
fof(f188,plain,
! [X0] :
( ~ ilf_type(X0,subset_type(X0))
| ~ empty(power_set(X0)) ),
inference(resolution,[],[f186,f166]) ).
fof(f214,plain,
! [X2,X0,X1] :
( ilf_type(X1,set_type)
| ~ ilf_type(X0,relation_type(X1,X2))
| ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(resolution,[],[f122,f154]) ).
fof(f219,plain,
! [X2,X0,X1] :
( ilf_type(X0,subset_type(cross_product(X1,X2)))
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[],[f214,f154]) ).
fof(f220,plain,
! [X0,X1] :
( ~ ilf_type(cross_product(X0,X1),relation_type(X0,X1))
| ~ empty(power_set(cross_product(X0,X1))) ),
inference(resolution,[],[f219,f188]) ).
fof(f224,plain,
~ empty(power_set(cross_product(sK11,sK12))),
inference(resolution,[],[f220,f155]) ).
fof(f225,plain,
ilf_type(cross_product(sK11,sK12),set_type),
inference(resolution,[],[f224,f138]) ).
fof(f235,plain,
$false,
inference(resolution,[],[f225,f154]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET643+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n005.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 28 02:23:47 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.40 Running first-order model finding
% 0.11/0.41 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
% 0.11/0.43 % (371017)Will run a generic schedule for satisfiability detection.
% 0.11/0.43 % (371028)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2744039834:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.11/0.43 % (371028) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-371017-371028"...
% 0.11/0.43 % (371023)% WARNING: option uhcvi not known.
% 0.11/0.43 % (371028)...printing done.
% 0.11/0.43 % (371028)Refutation found. Thanks to Tanya!
% 0.11/0.43 % SZS status Theorem for theBenchmark
% 0.11/0.43 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.43 % (371028)------------------------------
% 0.11/0.43 % (371028)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.43 % (371028)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.43 % (371028)CaDiCaL version: 2.1.3
% 0.11/0.43 % (371028)Termination reason: Refutation
% 0.11/0.43 % (371028)Time elapsed: 0.003 s
% 0.11/0.43 % (371028)Peak memory usage: 12 MB
% 0.11/0.43 % (371028)Instructions burned: 7 (million)
% 0.11/0.43 % (371017)Success in time 0.018 s
% 0.11/0.43 % Vampire exiting
%------------------------------------------------------------------------------