%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET663+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 12:41:34 PM UTC 2026
% Result : Theorem 3.17s 1.42s
% Output : Refutation 4.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 49 ( 10 unt; 0 def)
% Number of atoms : 159 ( 27 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 181 ( 71 ~; 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 : 83 ( 77 !; 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(X0,X1))
=> ( ilf_type(X2,relation_type(empty_set,X1))
=> X2 = empty_set ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_26) ).
fof(f36,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ( ilf_type(X2,relation_type(empty_set,X1))
=> 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(empty_set,X1))
& ilf_type(X2,relation_type(X0,X1)) )
& 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(empty_set,X1))
& ilf_type(X2,relation_type(X0,X1)) )
& 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(empty_set,sK13))
& ilf_type(sK14,relation_type(sK12,sK13))
& 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(f106,plain,
! [X0] :
( empty_set != domain_of(X0)
| empty_set = X0
| ~ ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[],[f41]) ).
fof(f108,plain,
! [X2,X0,X1] :
( subset(domain_of(X2),X0)
| ~ 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(empty_set,sK13)),
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(f181,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0) ),
inference(forward_subsumption_resolution,[],[f172,f162]) ).
fof(f182,plain,
! [X0] :
( ~ subset(X0,empty_set)
| empty_set = X0 ),
inference(forward_subsumption_resolution,[],[f104,f162]) ).
fof(f198,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(f199,plain,
! [X2,X0,X1] :
( relation_like(X2)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1))) ),
inference(forward_subsumption_resolution,[],[f198,f162]) ).
fof(f208,plain,
! [X2,X0,X1] :
( subset(domain_of(X2),X0)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[],[f108,f162]) ).
fof(f209,plain,
! [X2,X0,X1] :
( subset(domain_of(X2),X0)
| ~ ilf_type(X2,relation_type(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f208,f162]) ).
fof(f212,plain,
! [X0,X1] :
( ~ ilf_type(X0,relation_type(empty_set,X1))
| empty_set = domain_of(X0) ),
inference(resolution,[],[f209,f182]) ).
fof(f219,plain,
empty_set = domain_of(sK14),
inference(resolution,[],[f212,f166]) ).
fof(f224,plain,
( empty_set != empty_set
| empty_set = sK14
| ~ ilf_type(sK14,binary_relation_type) ),
inference(superposition,[],[f106,f219]) ).
fof(f225,plain,
( empty_set = sK14
| ~ ilf_type(sK14,binary_relation_type) ),
inference(trivial_inequality_removal,[],[f224]) ).
fof(f226,plain,
~ ilf_type(sK14,binary_relation_type),
inference(forward_subsumption_resolution,[],[f225,f167]) ).
fof(f227,plain,
~ relation_like(sK14),
inference(resolution,[],[f226,f181]) ).
fof(f228,plain,
! [X0,X1] : ~ ilf_type(sK14,subset_type(cross_product(X0,X1))),
inference(resolution,[],[f227,f199]) ).
fof(f261,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(f262,plain,
! [X3,X0,X1] :
( ilf_type(X3,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X3,relation_type(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f261,f162]) ).
fof(f265,plain,
! [X0,X1] : ~ ilf_type(sK14,relation_type(X0,X1)),
inference(resolution,[],[f262,f228]) ).
fof(f267,plain,
$false,
inference(resolution,[],[f265,f166]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET663+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 % Computer : n019.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Mon Sep 28 02:28:48 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.43 Running first-order theorem proving
% 0.13/0.43 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.17/1.42 % (3605012)Detected formulas, will run a generic FOF schedule.
% 3.17/1.42 % (3605042)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3931573689:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.17/1.42 % (3605043)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3885220014:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.17/1.42 % (3605047)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1712074408:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.17/1.42 % (3605045)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1180631056:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.17/1.42 % (3605048)dis-21_1_sil=8000:lcm=predicate:random_seed=3131094778:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 3.17/1.42 % (3605044)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=2763209801:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.17/1.42 % (3605045)Refutation not found, incomplete strategy
% 3.17/1.42 % (3605045)------------------------------
% 3.17/1.42 % (3605045)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.17/1.42 % (3605045)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.17/1.42 % (3605045)CaDiCaL version: 2.1.3
% 3.17/1.42 % (3605045)Termination reason: Refutation not found, incomplete strategy
% 3.17/1.42 % (3605045)Time elapsed: 0.002 s
% 3.17/1.42 % (3605045)Peak memory usage: 88 MB
% 3.17/1.42 % (3605047)First to succeed.
% 3.17/1.42 % (3605047)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3605012"
% 3.17/1.42 % (3605048)Also succeeded, but the first one will report.
% 3.17/1.42 % (3605046)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3422581113:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.17/1.42 % (3605046)Refutation not found, incomplete strategy
% 3.17/1.42 % (3605046)------------------------------
% 3.17/1.42 % (3605046)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.17/1.42 % (3605046)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.17/1.42 % (3605046)CaDiCaL version: 2.1.3
% 3.17/1.42 % (3605046)Termination reason: Refutation not found, incomplete strategy
% 3.17/1.42 % (3605046)Time elapsed: 0.002 s
% 3.17/1.42 % (3605046)Peak memory usage: 88 MB
% 3.17/1.42 % (3605045)------------------------------
% 3.17/1.42 % (3605045)------------------------------
% 3.17/1.42 % (3605047)Refutation found. Thanks to Tanya!
% 3.17/1.42 % SZS status Theorem for theBenchmark
% 3.17/1.42 % SZS output start Proof for theBenchmark
% See solution above
% 4.50/1.61 % (3605047)------------------------------
% 4.50/1.61 % (3605047)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.50/1.61 % (3605047)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.50/1.61 % (3605047)CaDiCaL version: 2.1.3
% 4.50/1.61 % (3605047)Termination reason: Refutation
% 4.50/1.61 % (3605047)Time elapsed: 0.010 s
% 4.50/1.61 % (3605047)Peak memory usage: 89 MB
% 4.50/1.61 % (3605047)Instructions burned: 8 (million)
% 4.50/1.61 % (3605047)------------------------------
% 4.50/1.61 % (3605047)------------------------------
% 4.50/1.61 % (3605012)Success in time 0.538 s
% 4.50/1.61 % Vampire exiting
%------------------------------------------------------------------------------