%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET146+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 : n015.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 12:40:17 PM UTC 2026
% Result : Theorem 3.36s 1.34s
% Output : Refutation 3.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 42 ( 14 unt; 3 def)
% Number of atoms : 104 ( 12 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 104 ( 42 ~; 38 |; 16 &)
% ( 7 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 48 ( 0 sgn 45 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] :
( member(X2,intersection(X0,X1))
<=> ( member(X2,X0)
& member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_defn) ).
fof(f2,axiom,
! [X0] : ~ member(X0,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_defn) ).
fof(f3,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
fof(f5,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
fof(f9,conjecture,
! [X0] : intersection(X0,empty_set) = empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th61) ).
fof(f10,negated_conjecture,
~ ! [X0] : intersection(X0,empty_set) = empty_set,
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f11,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f12,plain,
? [X0] : empty_set != intersection(X0,empty_set),
inference(ennf_transformation,[],[f10]) ).
fof(f13,plain,
! [X0,X1,X2] :
( ( member(X2,intersection(X0,X1))
| ~ member(X2,X0)
| ~ member(X2,X1) )
& ( ( member(X2,X0)
& member(X2,X1) )
| ~ member(X2,intersection(X0,X1)) ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f14,plain,
! [X0,X1,X2] :
( ( member(X2,intersection(X0,X1))
| ~ member(X2,X0)
| ~ member(X2,X1) )
& ( ( member(X2,X0)
& member(X2,X1) )
| ~ member(X2,intersection(X0,X1)) ) ),
inference(flattening,[],[f13]) ).
fof(f15,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f16,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(flattening,[],[f15]) ).
fof(f17,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f18,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f18]) ).
fof(f23,plain,
empty_set != intersection(sK2,empty_set),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X0,sK2)],[f12]) ).
fof(f24,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X1) ),
inference(cnf_transformation,[],[f14]) ).
fof(f27,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f2]) ).
fof(f30,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(cnf_transformation,[],[f16]) ).
fof(f33,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f19]) ).
fof(f40,plain,
empty_set != intersection(sK2,empty_set),
inference(cnf_transformation,[],[f23]) ).
fof(f45,definition,
! [X0,X1] :
( sQ3_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ3_eqProxy])],[equality_proxy_definition]) ).
fof(f46,plain,
! [X0,X1] :
( sQ3_eqProxy(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(equality_proxy_replacement,[],[f30,f45]) ).
fof(f50,plain,
~ sQ3_eqProxy(empty_set,intersection(sK2,empty_set)),
inference(equality_proxy_replacement,[],[f40,f45]) ).
fof(f58,plain,
( ~ subset(empty_set,intersection(sK2,empty_set))
| ~ subset(intersection(sK2,empty_set),empty_set) ),
inference(resolution,[],[f46,f50]) ).
fof(f61,definition,
( spl4_1
<=> subset(empty_set,intersection(sK2,empty_set)) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f62,plain,
( ~ subset(empty_set,intersection(sK2,empty_set))
| spl4_1 ),
inference(avatar_component_clause,[],[f61]) ).
fof(f64,definition,
( spl4_2
<=> subset(intersection(sK2,empty_set),empty_set) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f65,plain,
( ~ subset(intersection(sK2,empty_set),empty_set)
| spl4_2 ),
inference(avatar_component_clause,[],[f64]) ).
fof(f67,plain,
( ~ spl4_2
| ~ spl4_1 ),
inference(avatar_split_clause,[],[f58,f61,f64]) ).
fof(f69,plain,
( member(sK0(empty_set,intersection(sK2,empty_set)),empty_set)
| spl4_1 ),
inference(resolution,[],[f62,f33]) ).
fof(f70,plain,
( $false
| spl4_1 ),
inference(resolution,[],[f69,f27]) ).
fof(f71,plain,
spl4_1,
inference(avatar_contradiction_clause,[],[f70]) ).
fof(f75,plain,
( member(sK0(intersection(sK2,empty_set),empty_set),intersection(sK2,empty_set))
| spl4_2 ),
inference(resolution,[],[f65,f33]) ).
fof(f77,plain,
( member(sK0(intersection(sK2,empty_set),empty_set),empty_set)
| spl4_2 ),
inference(resolution,[],[f75,f24]) ).
fof(f78,plain,
( $false
| spl4_2 ),
inference(resolution,[],[f77,f27]) ).
fof(f79,plain,
spl4_2,
inference(avatar_contradiction_clause,[],[f78]) ).
cnf(s2,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(sat_conversion,[],[f67]) ).
cnf(s3,plain,
spl4_1,
inference(sat_conversion,[],[f71]) ).
cnf(s4,plain,
spl4_2,
inference(sat_conversion,[],[f79]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s2,s4,s3]) ).
fof(f80,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET146+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n015.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 28 00:57:46 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 3.36/1.34 % (2167449)Detected formulas, will run a generic FOF schedule.
% 3.36/1.34 % (2167456)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=3623837890:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.36/1.34 % (2167459)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3429779010:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.36/1.34 % (2167460)dis-21_1_sil=8000:lcm=predicate:random_seed=3087447737: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)
% 3.36/1.34 % (2167457)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=133705858:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.36/1.34 % (2167458)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4164852130:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.36/1.34 % (2167455)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=1668206254:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.36/1.34 % (2167454)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=2897445134:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.36/1.34 % (2167457)Refutation not found, incomplete strategy
% 3.36/1.34 % (2167457)------------------------------
% 3.36/1.34 % (2167457)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.36/1.34 % (2167457)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.36/1.34 % (2167457)CaDiCaL version: 2.1.3
% 3.36/1.34 % (2167457)Termination reason: Refutation not found, incomplete strategy
% 3.36/1.34 % (2167457)Time elapsed: 0.001 s
% 3.36/1.34 % (2167457)Peak memory usage: 88 MB
% 3.36/1.34 % (2167460)First to succeed.
% 3.36/1.34 % (2167458)Also succeeded, but the first one will report.
% 3.36/1.34 % (2167460)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2167449"
% 3.36/1.34 % (2167459)Also succeeded, but the first one will report.
% 3.36/1.34 % (2167457)------------------------------
% 3.36/1.34 % (2167457)------------------------------
% 3.36/1.34 % (2167460)Refutation found. Thanks to Tanya!
% 3.36/1.34 % SZS status Theorem for theBenchmark
% 3.36/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 3.36/1.34 % (2167460)------------------------------
% 3.36/1.34 % (2167460)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.36/1.34 % (2167460)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.36/1.34 % (2167460)CaDiCaL version: 2.1.3
% 3.36/1.34 % (2167460)Termination reason: Refutation
% 3.36/1.34 % (2167460)Time elapsed: 0.003 s
% 3.36/1.34 % (2167460)Peak memory usage: 89 MB
% 3.36/1.34 % (2167460)Instructions burned: 2 (million)
% 3.36/1.34 % (2167460)------------------------------
% 3.36/1.34 % (2167460)------------------------------
% 3.36/1.34 % (2167449)Success in time 0.404 s
% 3.36/1.34 % Vampire exiting
%------------------------------------------------------------------------------