%------------------------------------------------------------------------------
% File : Vampire---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 THM
% Computer : n020.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 12:41:30 PM UTC 2026
% Result : Theorem 0.15s 1.50s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 4
% Syntax : Number of formulae : 28 ( 7 unt; 0 def)
% Number of atoms : 109 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 134 ( 53 ~; 47 |; 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 : 54 ( 46 !; 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] :
( ~ 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(f23,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,[],[f22]) ).
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(ennf_transformation,[],[f2]) ).
fof(f26,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,[],[f25]) ).
fof(f27,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(f28,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,[],[f27]) ).
fof(f32,plain,
( ~ ilf_type(sK0,relation_type(sK1,sK2))
& subset(sK0,sK3)
& ilf_type(sK3,relation_type(sK1,sK2))
& ilf_type(sK2,set_type)
& ilf_type(sK1,set_type)
& ilf_type(sK0,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f23]) ).
fof(f40,plain,
ilf_type(sK3,relation_type(sK1,sK2)),
inference(cnf_transformation,[],[f32]) ).
fof(f41,plain,
subset(sK0,sK3),
inference(cnf_transformation,[],[f32]) ).
fof(f42,plain,
~ ilf_type(sK0,relation_type(sK1,sK2)),
inference(cnf_transformation,[],[f32]) ).
fof(f43,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f19]) ).
fof(f45,plain,
! [X2,X0,X1] :
( ~ subset(X0,cross_product(X1,X2))
| ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f26]) ).
fof(f46,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X3,relation_type(X1,X2))
| ~ subset(X0,X3)
| subset(X0,cross_product(X1,X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f28]) ).
fof(f52,plain,
! [X0] :
( ~ subset(X0,sK3)
| subset(X0,cross_product(sK1,sK2))
| ~ ilf_type(sK2,set_type)
| ~ ilf_type(sK1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[],[f40,f46]) ).
fof(f53,plain,
! [X0] :
( ~ subset(X0,sK3)
| subset(X0,cross_product(sK1,sK2))
| ~ ilf_type(sK2,set_type)
| ~ ilf_type(sK1,set_type) ),
inference(forward_subsumption_resolution,[],[f52,f43]) ).
fof(f54,plain,
! [X0] :
( ~ subset(X0,sK3)
| subset(X0,cross_product(sK1,sK2))
| ~ ilf_type(sK2,set_type) ),
inference(forward_subsumption_resolution,[],[f53,f43]) ).
fof(f55,plain,
! [X0] :
( subset(X0,cross_product(sK1,sK2))
| ~ subset(X0,sK3) ),
inference(forward_subsumption_resolution,[],[f54,f43]) ).
fof(f56,plain,
! [X0] :
( ~ subset(X0,sK3)
| ilf_type(X0,relation_type(sK1,sK2))
| ~ ilf_type(sK2,set_type)
| ~ ilf_type(sK1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[],[f55,f45]) ).
fof(f57,plain,
! [X0] :
( ~ subset(X0,sK3)
| ilf_type(X0,relation_type(sK1,sK2))
| ~ ilf_type(sK2,set_type)
| ~ ilf_type(sK1,set_type) ),
inference(forward_subsumption_resolution,[],[f56,f43]) ).
fof(f58,plain,
! [X0] :
( ~ subset(X0,sK3)
| ilf_type(X0,relation_type(sK1,sK2))
| ~ ilf_type(sK2,set_type) ),
inference(forward_subsumption_resolution,[],[f57,f43]) ).
fof(f59,plain,
! [X0] :
( ilf_type(X0,relation_type(sK1,sK2))
| ~ subset(X0,sK3) ),
inference(forward_subsumption_resolution,[],[f58,f43]) ).
fof(f61,plain,
~ subset(sK0,sK3),
inference(resolution,[],[f59,f42]) ).
fof(f62,plain,
$false,
inference(forward_subsumption_resolution,[],[f61,f41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % 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 THM
% 0.10/0.37 % Computer : n020.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 02:24:49 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/1.50 % (3976057)Detected formulas, will run a generic FOF schedule.
% 0.15/1.50 % (3976062)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=1753187128:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.15/1.50 % (3976066)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4196848393:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.15/1.50 % (3976064)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=3594387346:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.15/1.50 % (3976067)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1282457630:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.15/1.50 % (3976063)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=1334692017:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.15/1.50 % (3976068)dis-21_1_sil=8000:lcm=predicate:random_seed=63430513: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)
% 0.15/1.50 % (3976065)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4135219208:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.15/1.50 % (3976066)Also succeeded, but the first one will report.
% 0.15/1.50 % (3976065)First to succeed.
% 0.15/1.50 % (3976065)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3976057"
% 0.15/1.50 % (3976067)Also succeeded, but the first one will report.
% 0.15/1.50 % (3976068)Also succeeded, but the first one will report.
% 0.15/1.50 % (3976065)Refutation found. Thanks to Tanya!
% 0.15/1.50 % SZS status Theorem for theBenchmark
% 0.15/1.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/1.50 % (3976065)------------------------------
% 0.15/1.50 % (3976065)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.15/1.50 % (3976065)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/1.50 % (3976065)CaDiCaL version: 2.1.3
% 0.15/1.50 % (3976065)Termination reason: Refutation
% 0.15/1.50 % (3976065)Time elapsed: 0.003 s
% 0.15/1.50 % (3976065)Peak memory usage: 88 MB
% 0.15/1.50 % (3976065)Instructions burned: 2 (million)
% 0.15/1.50 % (3976065)------------------------------
% 0.15/1.50 % (3976065)------------------------------
% 0.15/1.50 % (3976057)Success in time 0.445 s
% 0.15/1.50 % Vampire exiting
%------------------------------------------------------------------------------