%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET654+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 : n004.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 12:44:20 PM UTC 2026
% Result : Theorem 0.22s 0.50s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 35 ( 9 unt; 0 def)
% Number of atoms : 134 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 164 ( 65 ~; 59 |; 18 &)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 84 ( 76 !; 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/sandbox2/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/sandbox2/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(X2,X0))
=> ( subset(range_of(X3),X1)
=> ilf_type(X3,relation_type(X2,X1)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3) ).
fof(f22,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox2/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(X2,X0))
=> ( subset(X0,X1)
=> ilf_type(X3,relation_type(X2,X1)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_16) ).
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(X2,X0))
=> ( subset(X0,X1)
=> ilf_type(X3,relation_type(X2,X1)) ) ) ) ) ),
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(X2,X1))
| ~ subset(range_of(X3),X1)
| ~ ilf_type(X3,relation_type(X2,X0)) )
| ~ 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(X2,X1))
| ~ subset(range_of(X3),X1)
| ~ ilf_type(X3,relation_type(X2,X0)) )
| ~ 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(X2,X1))
& subset(X0,X1)
& ilf_type(X3,relation_type(X2,X0)) )
& 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(X2,X1))
& subset(X0,X1)
& ilf_type(X3,relation_type(X2,X0)) )
& 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(sK11,sK10))
& subset(sK9,sK10)
& ilf_type(sK12,relation_type(sK11,sK9))
& 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(f75,plain,
! [X2,X0,X1] :
( subset(range_of(X2),X1)
| ~ 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(X2,X1))
| ~ subset(range_of(X3),X1)
| ~ ilf_type(X3,relation_type(X2,X0))
| ~ 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(sK11,sK9)),
inference(cnf_transformation,[],[f73]) ).
fof(f118,plain,
subset(sK9,sK10),
inference(cnf_transformation,[],[f73]) ).
fof(f119,plain,
~ ilf_type(sK12,relation_type(sK11,sK10)),
inference(cnf_transformation,[],[f73]) ).
fof(f143,plain,
! [X2,X0,X1] :
( subset(range_of(X2),X1)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f75,f113]) ).
fof(f144,plain,
! [X2,X0,X1] :
( ~ ilf_type(X2,relation_type(X0,X1))
| subset(range_of(X2),X1) ),
inference(forward_subsumption_resolution,[],[f143,f113]) ).
fof(f145,plain,
subset(range_of(sK12),sK9),
inference(resolution,[],[f144,f117]) ).
fof(f200,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(f201,plain,
! [X2,X0,X1] :
( subset(X0,X2)
| ~ subset(X0,X1)
| ~ subset(X1,X2)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f200,f113]) ).
fof(f202,plain,
! [X2,X0,X1] :
( ~ subset(X1,X2)
| ~ subset(X0,X1)
| subset(X0,X2) ),
inference(forward_subsumption_resolution,[],[f201,f113]) ).
fof(f219,plain,
! [X0] :
( ~ subset(X0,sK9)
| subset(X0,sK10) ),
inference(resolution,[],[f202,f118]) ).
fof(f223,plain,
subset(range_of(sK12),sK10),
inference(resolution,[],[f219,f145]) ).
fof(f284,plain,
! [X2,X3,X0,X1] :
( ilf_type(X3,relation_type(X2,X1))
| ~ subset(range_of(X3),X1)
| ~ ilf_type(X3,relation_type(X2,X0))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(forward_subsumption_resolution,[],[f77,f113]) ).
fof(f285,plain,
! [X2,X3,X0,X1] :
( ilf_type(X3,relation_type(X2,X1))
| ~ subset(range_of(X3),X1)
| ~ ilf_type(X3,relation_type(X2,X0))
| ~ ilf_type(X2,set_type) ),
inference(forward_subsumption_resolution,[],[f284,f113]) ).
fof(f286,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X3,relation_type(X2,X0))
| ~ subset(range_of(X3),X1)
| ilf_type(X3,relation_type(X2,X1)) ),
inference(forward_subsumption_resolution,[],[f285,f113]) ).
fof(f288,plain,
! [X0] :
( ilf_type(sK12,relation_type(sK11,X0))
| ~ subset(range_of(sK12),X0) ),
inference(resolution,[],[f286,f117]) ).
fof(f291,plain,
~ subset(range_of(sK12),sK10),
inference(resolution,[],[f288,f119]) ).
fof(f296,plain,
$false,
inference(forward_subsumption_resolution,[],[f291,f223]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET654+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.15/0.40 % Computer : n004.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8046.5625MB
% 0.15/0.40 % OS : Linux 6.8.0-71-generic
% 0.15/0.40 % CPULimit : 300
% 0.15/0.40 % WCLimit : 300
% 0.15/0.40 % DateTime : Mon Sep 28 02:28:23 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.41 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.15/0.45 Running first-order model finding
% 0.15/0.45 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
% 0.22/0.50 % (4092784)Will run a generic schedule for satisfiability detection.
% 0.22/0.50 % (4092792)dis+10_1_sil=32000:sp=arity:random_seed=3834676935:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.22/0.50 % (4092792) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4092784-4092792"...
% 0.22/0.50 % (4092790)% WARNING: option uhcvi not known.
% 0.22/0.50 % (4092792)...printing done.
% 0.22/0.50 % (4092792)Refutation found. Thanks to Tanya!
% 0.22/0.50 % SZS status Theorem for theBenchmark
% 0.22/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.50 % (4092792)------------------------------
% 0.22/0.50 % (4092792)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.50 % (4092792)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.50 % (4092792)CaDiCaL version: 2.1.3
% 0.22/0.50 % (4092792)Termination reason: Refutation
% 0.22/0.50 % (4092792)Time elapsed: 0.005 s
% 0.22/0.50 % (4092792)Peak memory usage: 11 MB
% 0.22/0.50 % (4092792)Instructions burned: 8 (million)
% 0.22/0.50 % (4092784)Success in time 0.029 s
% 0.22/0.50 % Vampire exiting
%------------------------------------------------------------------------------