%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET014+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 : n026.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 12:39:31 PM UTC 2026
% Result : Theorem 3.51s 1.48s
% Output : Refutation 3.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 41 ( 11 unt; 2 def)
% Number of atoms : 101 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 98 ( 38 ~; 34 |; 18 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 50 ( 0 sgn 42 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] :
( member(X2,union(X0,X1))
<=> ( member(X2,X0)
| member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).
fof(f2,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
fof(f6,conjecture,
! [X0,X1,X2] :
( ( subset(X0,X1)
& subset(X2,X1) )
=> subset(union(X0,X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_union_subset) ).
fof(f7,negated_conjecture,
~ ! [X0,X1,X2] :
( ( subset(X0,X1)
& subset(X2,X1) )
=> subset(union(X0,X2),X1) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f8,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f9,plain,
? [X0,X1,X2] :
( ~ subset(union(X0,X2),X1)
& subset(X0,X1)
& subset(X2,X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f10,plain,
? [X0,X1,X2] :
( ~ subset(union(X0,X2),X1)
& subset(X0,X1)
& subset(X2,X1) ),
inference(flattening,[],[f9]) ).
fof(f11,plain,
! [X0,X1,X2] :
( ( member(X2,union(X0,X1))
| ( ~ member(X2,X0)
& ~ member(X2,X1) ) )
& ( member(X2,X0)
| member(X2,X1)
| ~ member(X2,union(X0,X1)) ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f12,plain,
! [X0,X1,X2] :
( ( member(X2,union(X0,X1))
| ( ~ member(X2,X0)
& ~ member(X2,X1) ) )
& ( member(X2,X0)
| member(X2,X1)
| ~ member(X2,union(X0,X1)) ) ),
inference(flattening,[],[f11]) ).
fof(f13,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,[],[f8]) ).
fof(f14,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,[],[f13]) ).
fof(f15,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))],[f14]) ).
fof(f19,plain,
( ~ subset(union(sK2,sK4),sK3)
& subset(sK2,sK3)
& subset(sK4,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f10]) ).
fof(f20,plain,
! [X2,X0,X1] :
( ~ member(X2,union(X0,X1))
| member(X2,X1)
| member(X2,X0) ),
inference(cnf_transformation,[],[f12]) ).
fof(f23,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f24,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f15]) ).
fof(f25,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f32,plain,
subset(sK4,sK3),
inference(cnf_transformation,[],[f19]) ).
fof(f33,plain,
subset(sK2,sK3),
inference(cnf_transformation,[],[f19]) ).
fof(f34,plain,
~ subset(union(sK2,sK4),sK3),
inference(cnf_transformation,[],[f19]) ).
fof(f43,plain,
member(sK0(union(sK2,sK4),sK3),union(sK2,sK4)),
inference(resolution,[],[f24,f34]) ).
fof(f44,plain,
~ member(sK0(union(sK2,sK4),sK3),sK3),
inference(resolution,[],[f25,f34]) ).
fof(f45,plain,
! [X0] :
( ~ member(X0,sK4)
| member(X0,sK3) ),
inference(resolution,[],[f23,f32]) ).
fof(f46,plain,
! [X0] :
( ~ member(X0,sK2)
| member(X0,sK3) ),
inference(resolution,[],[f23,f33]) ).
fof(f52,plain,
( member(sK0(union(sK2,sK4),sK3),sK4)
| member(sK0(union(sK2,sK4),sK3),sK2) ),
inference(resolution,[],[f20,f43]) ).
fof(f54,definition,
( spl6_1
<=> member(sK0(union(sK2,sK4),sK3),sK2) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
fof(f55,plain,
( member(sK0(union(sK2,sK4),sK3),sK2)
| ~ spl6_1 ),
inference(avatar_component_clause,[],[f54]) ).
fof(f57,definition,
( spl6_2
<=> member(sK0(union(sK2,sK4),sK3),sK4) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
fof(f58,plain,
( member(sK0(union(sK2,sK4),sK3),sK4)
| ~ spl6_2 ),
inference(avatar_component_clause,[],[f57]) ).
fof(f59,plain,
( spl6_1
| spl6_2 ),
inference(avatar_split_clause,[],[f52,f57,f54]) ).
fof(f60,plain,
( member(sK0(union(sK2,sK4),sK3),sK3)
| ~ spl6_2 ),
inference(resolution,[],[f58,f45]) ).
fof(f61,plain,
( $false
| ~ spl6_2 ),
inference(resolution,[],[f60,f44]) ).
fof(f62,plain,
~ spl6_2,
inference(avatar_contradiction_clause,[],[f61]) ).
fof(f63,plain,
( member(sK0(union(sK2,sK4),sK3),sK3)
| ~ spl6_1 ),
inference(resolution,[],[f55,f46]) ).
fof(f64,plain,
( $false
| ~ spl6_1 ),
inference(resolution,[],[f63,f44]) ).
fof(f65,plain,
~ spl6_1,
inference(avatar_contradiction_clause,[],[f64]) ).
cnf(s1,plain,
( spl6_1
| spl6_2 ),
inference(sat_conversion,[],[f59]) ).
cnf(s2,plain,
~ spl6_2,
inference(sat_conversion,[],[f62]) ).
cnf(s3,plain,
~ spl6_1,
inference(sat_conversion,[],[f65]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
fof(f66,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET014+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n026.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 28 00:06:41 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 3.51/1.48 % (3352539)Detected formulas, will run a generic FOF schedule.
% 3.51/1.48 % (3352645)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3179637236:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.51/1.48 % (3352645)Refutation not found, incomplete strategy
% 3.51/1.48 % (3352645)------------------------------
% 3.51/1.48 % (3352645)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.51/1.48 % (3352645)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.51/1.48 % (3352645)CaDiCaL version: 2.1.3
% 3.51/1.48 % (3352645)Termination reason: Refutation not found, incomplete strategy
% 3.51/1.48 % (3352645)Time elapsed: 0.001 s
% 3.51/1.48 % (3352645)Peak memory usage: 88 MB
% 3.51/1.48 % (3352644)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=3763412001:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.51/1.48 % (3352642)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=3148145994:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.51/1.48 % (3352646)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2225659625:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.51/1.48 % (3352648)dis-21_1_sil=8000:lcm=predicate:random_seed=9579324: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)
% 3.51/1.48 % (3352648)First to succeed.
% 3.51/1.48 % (3352648)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3352539"
% 3.51/1.48 % (3352646)Also succeeded, but the first one will report.
% 3.51/1.48 % (3352643)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=1919119153:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.51/1.48 % (3352647)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4134713843:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.51/1.48 % (3352645)------------------------------
% 3.51/1.48 % (3352645)------------------------------
% 3.51/1.48 % (3352647)Also succeeded, but the first one will report.
% 3.51/1.48 % (3352684)lrs+10_1_sil=8000:sp=occurrence:random_seed=2491999606:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.51/1.48 % (3352648)Refutation found. Thanks to Tanya!
% 3.51/1.48 % SZS status Theorem for theBenchmark
% 3.51/1.48 % SZS output start Proof for theBenchmark
% See solution above
% 3.51/1.48 % (3352648)------------------------------
% 3.51/1.48 % (3352648)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.51/1.48 % (3352648)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.51/1.48 % (3352648)CaDiCaL version: 2.1.3
% 3.51/1.48 % (3352648)Termination reason: Refutation
% 3.51/1.48 % (3352648)Time elapsed: 0.004 s
% 3.51/1.48 % (3352648)Peak memory usage: 89 MB
% 3.51/1.48 % (3352648)Instructions burned: 2 (million)
% 3.51/1.48 % (3352648)------------------------------
% 3.51/1.48 % (3352648)------------------------------
% 3.51/1.48 % (3352539)Success in time 0.414 s
% 3.51/1.48 % Vampire exiting
%------------------------------------------------------------------------------