%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET700+4 : 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 : n007.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 12:41:41 PM UTC 2026
% Result : Theorem 2.62s 1.31s
% Output : Refutation 2.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 6
% Syntax : Number of formulae : 62 ( 5 unt; 2 def)
% Number of atoms : 190 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 204 ( 76 ~; 84 |; 31 &)
% ( 8 <=>; 3 =>; 0 <=; 2 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 77 ( 0 sgn 63 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset) ).
fof(f4,axiom,
! [X0,X1,X2] :
( member(X0,intersection(X1,X2))
<=> ( member(X0,X1)
& member(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection) ).
fof(f7,axiom,
! [X0,X1,X2] :
( member(X0,difference(X2,X1))
<=> ( member(X0,X2)
& ~ member(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference) ).
fof(f12,conjecture,
! [X0,X1,X2] :
( ( subset(X0,X2)
& subset(X1,X2) )
=> ( subset(X0,X1)
<=> subset(intersection(X0,difference(X2,X1)),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI34) ).
fof(f13,negated_conjecture,
~ ! [X0,X1,X2] :
( ( subset(X0,X2)
& subset(X1,X2) )
=> ( subset(X0,X1)
<=> subset(intersection(X0,difference(X2,X1)),X1) ) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
? [X0,X1,X2] :
( ( subset(X0,X1)
<~> subset(intersection(X0,difference(X2,X1)),X1) )
& subset(X0,X2)
& subset(X1,X2) ),
inference(ennf_transformation,[],[f13]) ).
fof(f15,plain,
? [X0,X1,X2] :
( ( subset(X0,X1)
<~> subset(intersection(X0,difference(X2,X1)),X1) )
& subset(X0,X2)
& subset(X1,X2) ),
inference(flattening,[],[f14]) ).
fof(f16,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f17,plain,
? [X0,X1,X2] :
( ( ~ subset(intersection(X0,difference(X2,X1)),X1)
| ~ subset(X0,X1) )
& ( subset(intersection(X0,difference(X2,X1)),X1)
| subset(X0,X1) )
& subset(X0,X2)
& subset(X1,X2) ),
inference(nnf_transformation,[],[f15]) ).
fof(f18,plain,
? [X0,X1,X2] :
( ( ~ subset(intersection(X0,difference(X2,X1)),X1)
| ~ subset(X0,X1) )
& ( subset(intersection(X0,difference(X2,X1)),X1)
| subset(X0,X1) )
& subset(X0,X2)
& subset(X1,X2) ),
inference(flattening,[],[f17]) ).
fof(f19,plain,
( ( ~ subset(intersection(sK0,difference(sK2,sK1)),sK1)
| ~ subset(sK0,sK1) )
& ( subset(intersection(sK0,difference(sK2,sK1)),sK1)
| subset(sK0,sK1) )
& subset(sK0,sK2)
& subset(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f18]) ).
fof(f21,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,[],[f16]) ).
fof(f22,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,[],[f21]) ).
fof(f23,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK3(X0,X1),X1)
& member(sK3(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X2,sK3(X0,X1))],[f22]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ( member(X0,intersection(X1,X2))
| ~ member(X0,X1)
| ~ member(X0,X2) )
& ( ( member(X0,X1)
& member(X0,X2) )
| ~ member(X0,intersection(X1,X2)) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ( member(X0,intersection(X1,X2))
| ~ member(X0,X1)
| ~ member(X0,X2) )
& ( ( member(X0,X1)
& member(X0,X2) )
| ~ member(X0,intersection(X1,X2)) ) ),
inference(flattening,[],[f24]) ).
fof(f26,plain,
! [X0,X1,X2] :
( ( member(X0,difference(X2,X1))
| ~ member(X0,X2)
| member(X0,X1) )
& ( ( member(X0,X2)
& ~ member(X0,X1) )
| ~ member(X0,difference(X2,X1)) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ( member(X0,difference(X2,X1))
| ~ member(X0,X2)
| member(X0,X1) )
& ( ( member(X0,X2)
& ~ member(X0,X1) )
| ~ member(X0,difference(X2,X1)) ) ),
inference(flattening,[],[f26]) ).
fof(f29,plain,
subset(sK0,sK2),
inference(cnf_transformation,[],[f19]) ).
fof(f30,plain,
( subset(intersection(sK0,difference(sK2,sK1)),sK1)
| subset(sK0,sK1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f31,plain,
( ~ subset(intersection(sK0,difference(sK2,sK1)),sK1)
| ~ subset(sK0,sK1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f34,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f35,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK3(X0,X1),X0) ),
inference(cnf_transformation,[],[f23]) ).
fof(f36,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK3(X0,X1),X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f38,plain,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f39,plain,
! [X2,X0,X1] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X1)
| ~ member(X0,X2) ),
inference(cnf_transformation,[],[f25]) ).
fof(f42,plain,
! [X2,X0,X1] :
( member(X0,difference(X2,X1))
| ~ member(X0,X2)
| member(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f44,definition,
( spl4_1
<=> subset(sK0,sK1) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f45,plain,
( subset(sK0,sK1)
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f44]) ).
fof(f47,definition,
( spl4_2
<=> subset(intersection(sK0,difference(sK2,sK1)),sK1) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f48,plain,
( subset(intersection(sK0,difference(sK2,sK1)),sK1)
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f47]) ).
fof(f49,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f30,f47,f44]) ).
fof(f50,plain,
( ~ subset(sK0,sK1)
| spl4_1 ),
inference(avatar_component_clause,[],[f44]) ).
fof(f51,plain,
( ~ subset(intersection(sK0,difference(sK2,sK1)),sK1)
| spl4_2 ),
inference(avatar_component_clause,[],[f47]) ).
fof(f52,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(avatar_split_clause,[],[f31,f47,f44]) ).
fof(f58,plain,
( member(sK3(sK0,sK1),sK0)
| spl4_1 ),
inference(resolution,[],[f35,f50]) ).
fof(f60,plain,
( ~ member(sK3(sK0,sK1),sK1)
| spl4_1 ),
inference(resolution,[],[f36,f50]) ).
fof(f65,plain,
( ! [X0] :
( ~ member(X0,intersection(sK0,difference(sK2,sK1)))
| member(X0,sK1) )
| ~ spl4_2 ),
inference(resolution,[],[f34,f48]) ).
fof(f66,plain,
! [X0] :
( member(X0,sK2)
| ~ member(X0,sK0) ),
inference(resolution,[],[f34,f29]) ).
fof(f70,plain,
( ! [X0] :
( ~ member(X0,difference(sK2,sK1))
| ~ member(X0,sK0)
| member(X0,sK1) )
| ~ spl4_2 ),
inference(resolution,[],[f39,f65]) ).
fof(f73,plain,
( ! [X0] :
( ~ member(X0,sK2)
| member(X0,sK1)
| ~ member(X0,sK0)
| member(X0,sK1) )
| ~ spl4_2 ),
inference(resolution,[],[f42,f70]) ).
fof(f74,plain,
( ! [X0] :
( ~ member(X0,sK2)
| member(X0,sK1)
| ~ member(X0,sK0) )
| ~ spl4_2 ),
inference(duplicate_literal_removal,[],[f73]) ).
fof(f75,plain,
( ! [X0] :
( member(X0,sK1)
| ~ member(X0,sK0)
| ~ member(X0,sK0) )
| ~ spl4_2 ),
inference(resolution,[],[f74,f66]) ).
fof(f76,plain,
( ! [X0] :
( ~ member(X0,sK0)
| member(X0,sK1) )
| ~ spl4_2 ),
inference(duplicate_literal_removal,[],[f75]) ).
fof(f77,plain,
( member(sK3(sK0,sK1),sK1)
| spl4_1
| ~ spl4_2 ),
inference(resolution,[],[f76,f58]) ).
fof(f78,plain,
( $false
| spl4_1
| ~ spl4_2 ),
inference(resolution,[],[f77,f60]) ).
fof(f79,plain,
( spl4_1
| ~ spl4_2 ),
inference(avatar_contradiction_clause,[],[f78]) ).
fof(f80,plain,
( ! [X0] :
( ~ member(X0,sK0)
| member(X0,sK1) )
| ~ spl4_1 ),
inference(resolution,[],[f45,f34]) ).
fof(f82,plain,
( ~ member(sK3(intersection(sK0,difference(sK2,sK1)),sK1),sK1)
| spl4_2 ),
inference(resolution,[],[f51,f36]) ).
fof(f83,plain,
( member(sK3(intersection(sK0,difference(sK2,sK1)),sK1),intersection(sK0,difference(sK2,sK1)))
| spl4_2 ),
inference(resolution,[],[f51,f35]) ).
fof(f85,plain,
( member(sK3(intersection(sK0,difference(sK2,sK1)),sK1),sK0)
| spl4_2 ),
inference(resolution,[],[f83,f38]) ).
fof(f87,plain,
( member(sK3(intersection(sK0,difference(sK2,sK1)),sK1),sK1)
| ~ spl4_1
| spl4_2 ),
inference(resolution,[],[f85,f80]) ).
fof(f90,plain,
( $false
| ~ spl4_1
| spl4_2 ),
inference(resolution,[],[f87,f82]) ).
fof(f91,plain,
( ~ spl4_1
| spl4_2 ),
inference(avatar_contradiction_clause,[],[f90]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f49]) ).
cnf(s2,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(sat_conversion,[],[f52]) ).
cnf(s3,plain,
( spl4_1
| ~ spl4_2 ),
inference(sat_conversion,[],[f79]) ).
cnf(s4,plain,
( ~ spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f91]) ).
cnf(s5,plain,
spl4_1,
inference(rat,[],[s1,s3]) ).
cnf(s6,plain,
spl4_2,
inference(rat,[],[s4,s5]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s2,s6,s5]) ).
fof(f92,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET700+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.35 % Computer : n007.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 28 02:32:25 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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
% 2.62/1.31 % (1973609)Detected formulas, will run a generic FOF schedule.
% 2.62/1.31 % (1973620)dis-21_1_sil=8000:lcm=predicate:random_seed=2033579270: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)
% 2.62/1.31 % (1973620)First to succeed.
% 2.62/1.31 % (1973620)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1973609"
% 2.62/1.31 % (1973619)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3310278532:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.62/1.31 % (1973615)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=2059501391:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.62/1.31 % (1973618)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1109870659:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.62/1.31 % (1973617)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1363474929:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.62/1.31 % (1973614)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=588358722:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.62/1.31 % (1973616)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=3297004800:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.62/1.31 % (1973617)Refutation not found, incomplete strategy
% 2.62/1.31 % (1973617)------------------------------
% 2.62/1.31 % (1973617)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.62/1.31 % (1973617)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/1.31 % (1973617)CaDiCaL version: 2.1.3
% 2.62/1.31 % (1973617)Termination reason: Refutation not found, incomplete strategy
% 2.62/1.31 % (1973617)Time elapsed: 0.001 s
% 2.62/1.31 % (1973617)Peak memory usage: 88 MB
% 2.62/1.31 % (1973617)Instructions burned: 1 (million)
% 2.62/1.31 % (1973619)Also succeeded, but the first one will report.
% 2.62/1.31 % (1973618)Instruction limit reached!
% 2.62/1.31 % (1973618)------------------------------
% 2.62/1.31 % (1973618)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.62/1.31 % (1973618)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/1.31 % (1973618)CaDiCaL version: 2.1.3
% 2.62/1.31 % (1973618)Termination reason: Instruction limit
% 2.62/1.31 % (1973618)Termination phase: Saturation
% 2.62/1.31 % (1973618)Time elapsed: 0.071 s
% 2.62/1.31 % (1973618)Peak memory usage: 89 MB
% 2.62/1.31 % (1973618)Instructions burned: 120 (million)
% 2.62/1.31 % (1973620)Refutation found. Thanks to Tanya!
% 2.62/1.31 % SZS status Theorem for theBenchmark
% 2.62/1.31 % SZS output start Proof for theBenchmark
% See solution above
% 2.62/1.31 % (1973620)------------------------------
% 2.62/1.31 % (1973620)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.62/1.31 % (1973620)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/1.31 % (1973620)CaDiCaL version: 2.1.3
% 2.62/1.31 % (1973620)Termination reason: Refutation
% 2.62/1.31 % (1973620)Time elapsed: 0.002 s
% 2.62/1.31 % (1973620)Peak memory usage: 89 MB
% 2.62/1.31 % (1973620)Instructions burned: 3 (million)
% 2.62/1.31 % (1973620)------------------------------
% 2.62/1.31 % (1973620)------------------------------
% 2.62/1.31 % (1973609)Success in time 0.286 s
% 2.62/1.31 % Vampire exiting
%------------------------------------------------------------------------------