%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET642+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n008.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 0.10s 0.45s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 28 ( 7 unt; 0 def)
% Number of atoms : 106 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 128 ( 50 ~; 44 |; 15 &)
% ( 0 <=>; 19 =>; 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 : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 69 ( 61 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,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(X1,X2))
=> ( subset(X0,X3)
=> subset(X0,cross_product(X1,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,set_type)
=> ( subset(X0,cross_product(X1,X2))
=> ilf_type(X0,relation_type(X1,X2)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).
fof(f19,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p19) ).
fof(f20,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(X1,X2))
=> ( subset(X0,X3)
=> ilf_type(X0,relation_type(X1,X2)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_4) ).
fof(f21,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(X1,X2))
=> ( subset(X0,X3)
=> ilf_type(X0,relation_type(X1,X2)) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f20]) ).
fof(f22,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( subset(X0,cross_product(X1,X2))
| ~ subset(X0,X3)
| ~ ilf_type(X3,relation_type(X1,X2)) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f1]) ).
fof(f23,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( subset(X0,cross_product(X1,X2))
| ~ subset(X0,X3)
| ~ ilf_type(X3,relation_type(X1,X2)) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f22]) ).
fof(f24,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ilf_type(X0,relation_type(X1,X2))
| ~ subset(X0,cross_product(X1,X2))
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f2]) ).
fof(f25,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ilf_type(X0,relation_type(X1,X2))
| ~ subset(X0,cross_product(X1,X2))
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f24]) ).
fof(f48,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ ilf_type(X0,relation_type(X1,X2))
& subset(X0,X3)
& ilf_type(X3,relation_type(X1,X2)) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f21]) ).
fof(f49,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ ilf_type(X0,relation_type(X1,X2))
& subset(X0,X3)
& ilf_type(X3,relation_type(X1,X2)) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(flattening,[],[f48]) ).
fof(f67,plain,
( ~ ilf_type(sK9,relation_type(sK10,sK11))
& subset(sK9,sK12)
& ilf_type(sK12,relation_type(sK10,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)],[f49]) ).
fof(f68,plain,
! [X2,X3,X0,X1] :
( subset(X0,cross_product(X1,X2))
| ~ subset(X0,X3)
| ~ ilf_type(X3,relation_type(X1,X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f23]) ).
fof(f69,plain,
! [X2,X0,X1] :
( ilf_type(X0,relation_type(X1,X2))
| ~ subset(X0,cross_product(X1,X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f25]) ).
fof(f103,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f19]) ).
fof(f107,plain,
ilf_type(sK12,relation_type(sK10,sK11)),
inference(cnf_transformation,[],[f67]) ).
fof(f108,plain,
subset(sK9,sK12),
inference(cnf_transformation,[],[f67]) ).
fof(f109,plain,
~ ilf_type(sK9,relation_type(sK10,sK11)),
inference(cnf_transformation,[],[f67]) ).
fof(f228,plain,
! [X2,X0,X1] :
( ilf_type(X0,relation_type(X1,X2))
| ~ subset(X0,cross_product(X1,X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f69,f103]) ).
fof(f229,plain,
! [X2,X0,X1] :
( ilf_type(X0,relation_type(X1,X2))
| ~ subset(X0,cross_product(X1,X2))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f228,f103]) ).
fof(f230,plain,
! [X2,X0,X1] :
( ~ subset(X0,cross_product(X1,X2))
| ilf_type(X0,relation_type(X1,X2)) ),
inference(forward_subsumption_resolution,[],[f229,f103]) ).
fof(f256,plain,
! [X2,X3,X0,X1] :
( subset(X0,cross_product(X1,X2))
| ~ subset(X0,X3)
| ~ ilf_type(X3,relation_type(X1,X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f68,f103]) ).
fof(f257,plain,
! [X2,X3,X0,X1] :
( subset(X0,cross_product(X1,X2))
| ~ subset(X0,X3)
| ~ ilf_type(X3,relation_type(X1,X2))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f256,f103]) ).
fof(f258,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X3,relation_type(X1,X2))
| ~ subset(X0,X3)
| subset(X0,cross_product(X1,X2)) ),
inference(forward_subsumption_resolution,[],[f257,f103]) ).
fof(f261,plain,
! [X0] :
( subset(X0,cross_product(sK10,sK11))
| ~ subset(X0,sK12) ),
inference(resolution,[],[f258,f107]) ).
fof(f264,plain,
! [X0] :
( ilf_type(X0,relation_type(sK10,sK11))
| ~ subset(X0,sK12) ),
inference(resolution,[],[f261,f230]) ).
fof(f268,plain,
~ subset(sK9,sK12),
inference(resolution,[],[f264,f109]) ).
fof(f271,plain,
$false,
inference(forward_subsumption_resolution,[],[f268,f108]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET642+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.37 % Computer : n008.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 28 02:24:39 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.41 Running first-order model finding
% 0.10/0.41 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.45 % (1809666)Will run a generic schedule for satisfiability detection.
% 0.10/0.45 % (1809674)dis+10_1_sil=32000:sp=arity:random_seed=1453447124:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.10/0.45 % (1809674) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1809666-1809674"...
% 0.10/0.45 % (1809672)% WARNING: option uhcvi not known.
% 0.10/0.45 % (1809674)...printing done.
% 0.10/0.45 % (1809674)Refutation found. Thanks to Tanya!
% 0.10/0.45 % SZS status Theorem for theBenchmark
% 0.10/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.45 % (1809674)------------------------------
% 0.10/0.45 % (1809674)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.45 % (1809674)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.45 % (1809674)CaDiCaL version: 2.1.3
% 0.10/0.45 % (1809674)Termination reason: Refutation
% 0.10/0.45 % (1809674)Time elapsed: 0.003 s
% 0.10/0.45 % (1809674)Peak memory usage: 11 MB
% 0.10/0.45 % (1809674)Instructions burned: 7 (million)
% 0.10/0.45 % (1809666)Success in time 0.033 s
% 0.10/0.45 % Vampire exiting
%------------------------------------------------------------------------------