%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET591+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 : n010.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 12:41:15 PM UTC 2026
% Result : Theorem 0.19s 1.40s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 46 ( 12 unt; 3 def)
% Number of atoms : 115 ( 12 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 119 ( 50 ~; 41 |; 18 &)
% ( 7 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 57 ( 0 sgn 53 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
fof(f2,axiom,
! [X0,X1,X2] :
( member(X2,difference(X0,X1))
<=> ( member(X2,X0)
& ~ member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_defn) ).
fof(f3,axiom,
! [X0] : ~ member(X0,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_defn) ).
fof(f4,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
fof(f7,conjecture,
! [X0,X1] :
( subset(X0,difference(X1,X0))
=> X0 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th50) ).
fof(f8,negated_conjecture,
~ ! [X0,X1] :
( subset(X0,difference(X1,X0))
=> X0 = empty_set ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f10,plain,
? [X0,X1] :
( empty_set != X0
& subset(X0,difference(X1,X0)) ),
inference(ennf_transformation,[],[f8]) ).
fof(f11,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,[],[f9]) ).
fof(f12,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,[],[f11]) ).
fof(f13,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))],[f12]) ).
fof(f14,plain,
! [X0,X1,X2] :
( ( member(X2,difference(X0,X1))
| ~ member(X2,X0)
| member(X2,X1) )
& ( ( member(X2,X0)
& ~ member(X2,X1) )
| ~ member(X2,difference(X0,X1)) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f15,plain,
! [X0,X1,X2] :
( ( member(X2,difference(X0,X1))
| ~ member(X2,X0)
| member(X2,X1) )
& ( ( member(X2,X0)
& ~ member(X2,X1) )
| ~ member(X2,difference(X0,X1)) ) ),
inference(flattening,[],[f14]) ).
fof(f16,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f17,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(flattening,[],[f16]) ).
fof(f18,plain,
( empty_set != sK1
& subset(sK1,difference(sK2,sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X0,sK1),skolemize(X1,sK2)],[f10]) ).
fof(f19,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f13]) ).
fof(f20,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f13]) ).
fof(f22,plain,
! [X2,X0,X1] :
( ~ member(X2,difference(X0,X1))
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f25,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f3]) ).
fof(f28,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(cnf_transformation,[],[f17]) ).
fof(f30,plain,
subset(sK1,difference(sK2,sK1)),
inference(cnf_transformation,[],[f18]) ).
fof(f31,plain,
empty_set != sK1,
inference(cnf_transformation,[],[f18]) ).
fof(f34,definition,
! [X0,X1] :
( sQ3_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ3_eqProxy])],[equality_proxy_definition]) ).
fof(f35,plain,
! [X0,X1] :
( sQ3_eqProxy(X0,X1)
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(equality_proxy_replacement,[],[f28,f34]) ).
fof(f36,plain,
~ sQ3_eqProxy(empty_set,sK1),
inference(equality_proxy_replacement,[],[f31,f34]) ).
fof(f41,plain,
! [X0] :
( member(X0,difference(sK2,sK1))
| ~ member(X0,sK1) ),
inference(resolution,[],[f19,f30]) ).
fof(f46,plain,
! [X0] :
( ~ member(X0,sK1)
| ~ member(X0,sK1) ),
inference(resolution,[],[f41,f22]) ).
fof(f47,plain,
! [X0] : ~ member(X0,sK1),
inference(duplicate_literal_removal,[],[f46]) ).
fof(f48,plain,
( ~ subset(empty_set,sK1)
| ~ subset(sK1,empty_set) ),
inference(resolution,[],[f35,f36]) ).
fof(f51,definition,
( spl4_1
<=> subset(empty_set,sK1) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f52,plain,
( ~ subset(empty_set,sK1)
| spl4_1 ),
inference(avatar_component_clause,[],[f51]) ).
fof(f54,definition,
( spl4_2
<=> subset(sK1,empty_set) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f55,plain,
( ~ subset(sK1,empty_set)
| spl4_2 ),
inference(avatar_component_clause,[],[f54]) ).
fof(f57,plain,
( ~ spl4_2
| ~ spl4_1 ),
inference(avatar_split_clause,[],[f48,f51,f54]) ).
fof(f59,plain,
( member(sK0(empty_set,sK1),empty_set)
| spl4_1 ),
inference(resolution,[],[f52,f20]) ).
fof(f60,plain,
( $false
| spl4_1 ),
inference(resolution,[],[f59,f25]) ).
fof(f61,plain,
spl4_1,
inference(avatar_contradiction_clause,[],[f60]) ).
fof(f63,plain,
( member(sK0(sK1,empty_set),sK1)
| spl4_2 ),
inference(resolution,[],[f55,f20]) ).
fof(f64,plain,
( $false
| spl4_2 ),
inference(resolution,[],[f63,f47]) ).
fof(f65,plain,
spl4_2,
inference(avatar_contradiction_clause,[],[f64]) ).
cnf(s2,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(sat_conversion,[],[f57]) ).
cnf(s3,plain,
spl4_1,
inference(sat_conversion,[],[f61]) ).
cnf(s4,plain,
spl4_2,
inference(sat_conversion,[],[f65]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s2,s4,s3]) ).
fof(f66,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET591+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.39 % Computer : n010.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Mon Sep 28 02:17:09 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.43 Running first-order theorem proving
% 0.14/0.43 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
% 0.19/1.40 % (1501917)Detected formulas, will run a generic FOF schedule.
% 0.19/1.40 % (1501986)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=3426461133:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.19/1.40 % (1501987)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=549460526:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.19/1.40 % (1501991)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=237887234:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.19/1.40 % (1501992)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1894661792:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.19/1.40 % (1501990)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=975627518:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.19/1.40 % (1501993)dis-21_1_sil=8000:lcm=predicate:random_seed=3812688090: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)
% 0.19/1.40 % (1501989)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=3039806455:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.19/1.40 % (1501990)Refutation not found, incomplete strategy
% 0.19/1.40 % (1501990)------------------------------
% 0.19/1.40 % (1501990)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.40 % (1501990)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.40 % (1501990)CaDiCaL version: 2.1.3
% 0.19/1.40 % (1501990)Termination reason: Refutation not found, incomplete strategy
% 0.19/1.40 % (1501990)Time elapsed: 0.001 s
% 0.19/1.40 % (1501990)Peak memory usage: 88 MB
% 0.19/1.40 % (1501993)First to succeed.
% 0.19/1.40 % (1501991)Also succeeded, but the first one will report.
% 0.19/1.40 % (1501993)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1501917"
% 0.19/1.40 % (1501992)Also succeeded, but the first one will report.
% 0.19/1.40 % (1501990)------------------------------
% 0.19/1.40 % (1501990)------------------------------
% 0.19/1.40 % (1501993)Refutation found. Thanks to Tanya!
% 0.19/1.40 % SZS status Theorem for theBenchmark
% 0.19/1.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/1.40 % (1501993)------------------------------
% 0.19/1.40 % (1501993)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.40 % (1501993)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.40 % (1501993)CaDiCaL version: 2.1.3
% 0.19/1.40 % (1501993)Termination reason: Refutation
% 0.19/1.40 % (1501993)Time elapsed: 0.003 s
% 0.19/1.40 % (1501993)Peak memory usage: 89 MB
% 0.19/1.40 % (1501993)Instructions burned: 2 (million)
% 0.19/1.40 % (1501993)------------------------------
% 0.19/1.40 % (1501993)------------------------------
% 0.19/1.40 % (1501917)Success in time 0.418 s
% 0.19/1.40 % Vampire exiting
%------------------------------------------------------------------------------