%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET664+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 : n002.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 12:44:21 PM UTC 2026
% Result : Theorem 0.17s 0.48s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 49 ( 10 unt; 0 def)
% Number of atoms : 159 ( 26 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 179 ( 69 ~; 61 |; 24 &)
% ( 2 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 80 ( 74 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( subset(X0,empty_set)
=> X0 = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
fof(f2,axiom,
! [X0] :
( ilf_type(X0,binary_relation_type)
=> ( ( domain_of(X0) = empty_set
| range_of(X0) = empty_set )
=> X0 = empty_set ) ),
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,relation_type(X0,X1))
=> ( subset(domain_of(X2),X0)
& subset(range_of(X2),X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3) ).
fof(f7,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',p6) ).
fof(f14,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( ilf_type(X0,binary_relation_type)
<=> ( relation_like(X0)
& ilf_type(X0,set_type) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p13) ).
fof(f29,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
=> relation_like(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p28) ).
fof(f34,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p33) ).
fof(f35,conjecture,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X1,X0))
=> ( ilf_type(X2,relation_type(X1,empty_set))
=> X2 = empty_set ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_27) ).
fof(f36,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X1,X0))
=> ( ilf_type(X2,relation_type(X1,empty_set))
=> X2 = empty_set ) ) ) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
fof(f38,plain,
! [X0] :
( X0 = empty_set
| ~ subset(X0,empty_set)
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f1]) ).
fof(f39,plain,
! [X0] :
( X0 = empty_set
| ~ subset(X0,empty_set)
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f38]) ).
fof(f40,plain,
! [X0] :
( X0 = empty_set
| ( empty_set != domain_of(X0)
& empty_set != range_of(X0) )
| ~ ilf_type(X0,binary_relation_type) ),
inference(ennf_transformation,[],[f2]) ).
fof(f41,plain,
! [X0] :
( X0 = empty_set
| ( empty_set != domain_of(X0)
& empty_set != range_of(X0) )
| ~ ilf_type(X0,binary_relation_type) ),
inference(flattening,[],[f40]) ).
fof(f42,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,[],[f3]) ).
fof(f44,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,[],[f7]) ).
fof(f51,plain,
! [X0] :
( ( ilf_type(X0,binary_relation_type)
<=> ( relation_like(X0)
& ilf_type(X0,set_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f14]) ).
fof(f72,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( relation_like(X2)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1))) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f29]) ).
fof(f77,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( empty_set != X2
& ilf_type(X2,relation_type(X1,empty_set))
& ilf_type(X2,relation_type(X1,X0)) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f36]) ).
fof(f78,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( empty_set != X2
& ilf_type(X2,relation_type(X1,empty_set))
& ilf_type(X2,relation_type(X1,X0)) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(flattening,[],[f77]) ).
fof(f84,plain,
! [X0] :
( ( ( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type) )
& ( ( relation_like(X0)
& ilf_type(X0,set_type) )
| ~ ilf_type(X0,binary_relation_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f51]) ).
fof(f85,plain,
! [X0] :
( ( ( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type) )
& ( ( relation_like(X0)
& ilf_type(X0,set_type) )
| ~ ilf_type(X0,binary_relation_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f84]) ).
fof(f103,plain,
( empty_set != sK14
& ilf_type(sK14,relation_type(sK13,empty_set))
& ilf_type(sK14,relation_type(sK13,sK12))
& ilf_type(sK13,set_type)
& ilf_type(sK12,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13,sK14]),skolemize(X0,sK12),skolemize(X1,sK13),skolemize(X2,sK14)],[f78]) ).
fof(f104,plain,
! [X0] :
( empty_set = X0
| ~ subset(X0,empty_set)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f39]) ).
fof(f105,plain,
! [X0] :
( empty_set != range_of(X0)
| empty_set = X0
| ~ ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[],[f41]) ).
fof(f107,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,[],[f42]) ).
fof(f111,plain,
! [X3,X0,X1] :
( 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(cnf_transformation,[],[f44]) ).
fof(f126,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f85]) ).
fof(f157,plain,
! [X2,X0,X1] :
( relation_like(X2)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f72]) ).
fof(f162,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f34]) ).
fof(f166,plain,
ilf_type(sK14,relation_type(sK13,empty_set)),
inference(cnf_transformation,[],[f103]) ).
fof(f167,plain,
empty_set != sK14,
inference(cnf_transformation,[],[f103]) ).
fof(f172,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type) ),
inference(duplicate_literal_removal,[],[f126]) ).
fof(f183,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0) ),
inference(forward_subsumption_resolution,[],[f172,f162]) ).
fof(f185,plain,
! [X0] :
( ~ subset(X0,empty_set)
| empty_set = X0 ),
inference(forward_subsumption_resolution,[],[f104,f162]) ).
fof(f209,plain,
! [X2,X0,X1] :
( relation_like(X2)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f157,f162]) ).
fof(f210,plain,
! [X2,X0,X1] :
( ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| relation_like(X2) ),
inference(forward_subsumption_resolution,[],[f209,f162]) ).
fof(f212,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,[],[f107,f162]) ).
fof(f213,plain,
! [X2,X0,X1] :
( ~ ilf_type(X2,relation_type(X0,X1))
| subset(range_of(X2),X1) ),
inference(forward_subsumption_resolution,[],[f212,f162]) ).
fof(f215,plain,
subset(range_of(sK14),empty_set),
inference(resolution,[],[f213,f166]) ).
fof(f219,plain,
empty_set = range_of(sK14),
inference(resolution,[],[f215,f185]) ).
fof(f227,plain,
( empty_set != empty_set
| empty_set = sK14
| ~ ilf_type(sK14,binary_relation_type) ),
inference(superposition,[],[f105,f219]) ).
fof(f228,plain,
( empty_set = sK14
| ~ ilf_type(sK14,binary_relation_type) ),
inference(trivial_inequality_removal,[],[f227]) ).
fof(f229,plain,
~ ilf_type(sK14,binary_relation_type),
inference(forward_subsumption_resolution,[],[f228,f167]) ).
fof(f232,plain,
~ relation_like(sK14),
inference(resolution,[],[f229,f183]) ).
fof(f273,plain,
! [X3,X0,X1] :
( ilf_type(X3,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X3,relation_type(X0,X1))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f111,f162]) ).
fof(f274,plain,
! [X3,X0,X1] :
( ilf_type(X3,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X3,relation_type(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f273,f162]) ).
fof(f276,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,relation_type(X1,X2))
| relation_like(X0) ),
inference(resolution,[],[f274,f210]) ).
fof(f282,plain,
relation_like(sK14),
inference(resolution,[],[f276,f166]) ).
fof(f284,plain,
$false,
inference(forward_subsumption_resolution,[],[f282,f232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET664+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.39 % Computer : n002.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Mon Sep 28 02:31:37 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.42 Running first-order model finding
% 0.11/0.42 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
% 0.17/0.48 % (4096766)Will run a generic schedule for satisfiability detection.
% 0.17/0.48 % (4096775)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2102251304:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.48 % (4096772)% WARNING: option uhcvi not known.
% 0.17/0.48 % (4096771)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2884667365_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.48 % (4096772)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=562955928:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.48 % (4096773)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2114139154:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.48 % (4096774)dis+10_1_sil=32000:sp=arity:random_seed=491672712:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.48 % (4096776)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1678069147:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.48 % (4096777)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=14677082:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.48 % (4096774) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4096766-4096774"...
% 0.17/0.48 % (4096776) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4096766-4096776"...
% 0.17/0.48 % TRYING [1]
% 0.17/0.48 % (4096774)...printing done.
% 0.17/0.48 % TRYING [2]
% 0.17/0.48 % (4096772) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4096766-4096772"...
% 0.17/0.48 % (4096776)...printing done.
% 0.17/0.48 % (4096774)Refutation found. Thanks to Tanya!
% 0.17/0.48 % SZS status Theorem for theBenchmark
% 0.17/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.48 % (4096774)------------------------------
% 0.17/0.48 % (4096774)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.48 % (4096774)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.48 % (4096774)CaDiCaL version: 2.1.3
% 0.17/0.48 % (4096774)Termination reason: Refutation
% 0.17/0.48 % (4096774)Time elapsed: 0.006 s
% 0.17/0.48 % (4096774)Peak memory usage: 11 MB
% 0.17/0.48 % (4096774)Instructions burned: 7 (million)
% 0.17/0.48 % (4096766)Success in time 0.045 s
% 0.17/0.48 % Vampire exiting
%------------------------------------------------------------------------------