%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET594+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 : n001.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 12:41:16 PM UTC 2026
% Result : Theorem 2.73s 1.37s
% Output : Refutation 2.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 46 ( 8 unt; 2 def)
% Number of atoms : 119 ( 5 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 119 ( 46 ~; 47 |; 17 &)
% ( 6 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 64 ( 0 sgn 59 !; 5 ?)
% 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,union(X0,X1))
<=> ( member(X2,X0)
| member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).
fof(f3,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(f9,conjecture,
! [X0,X1,X2] :
( union(intersection(X0,X1),intersection(X0,X2)) = X0
=> subset(X0,union(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th53) ).
fof(f10,negated_conjecture,
~ ! [X0,X1,X2] :
( union(intersection(X0,X1),intersection(X0,X2)) = X0
=> subset(X0,union(X1,X2)) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f11,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f12,plain,
? [X0,X1,X2] :
( ~ subset(X0,union(X1,X2))
& union(intersection(X0,X1),intersection(X0,X2)) = X0 ),
inference(ennf_transformation,[],[f10]) ).
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,[],[f11]) ).
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(f16,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,[],[f2]) ).
fof(f17,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,[],[f16]) ).
fof(f18,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,[],[f3]) ).
fof(f19,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,[],[f18]) ).
fof(f25,plain,
( ~ subset(sK2,union(sK3,sK4))
& sK2 = union(intersection(sK2,sK3),intersection(sK2,sK4)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f12]) ).
fof(f27,plain,
! [X0,X1] :
( member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f28,plain,
! [X0,X1] :
( ~ member(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f29,plain,
! [X2,X0,X1] :
( ~ member(X2,union(X0,X1))
| member(X2,X1)
| member(X2,X0) ),
inference(cnf_transformation,[],[f17]) ).
fof(f30,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| member(X2,union(X0,X1)) ),
inference(cnf_transformation,[],[f17]) ).
fof(f31,plain,
! [X2,X0,X1] :
( ~ member(X2,X0)
| member(X2,union(X0,X1)) ),
inference(cnf_transformation,[],[f17]) ).
fof(f32,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f45,plain,
sK2 = union(intersection(sK2,sK3),intersection(sK2,sK4)),
inference(cnf_transformation,[],[f25]) ).
fof(f46,plain,
~ subset(sK2,union(sK3,sK4)),
inference(cnf_transformation,[],[f25]) ).
fof(f65,plain,
! [X0] :
( ~ member(X0,sK2)
| member(X0,intersection(sK2,sK4))
| member(X0,intersection(sK2,sK3)) ),
inference(superposition,[],[f29,f45]) ).
fof(f68,plain,
! [X0] :
( subset(sK2,X0)
| member(sK0(sK2,X0),intersection(sK2,sK3))
| member(sK0(sK2,X0),intersection(sK2,sK4)) ),
inference(resolution,[],[f65,f27]) ).
fof(f71,plain,
( member(sK0(sK2,union(sK3,sK4)),intersection(sK2,sK3))
| member(sK0(sK2,union(sK3,sK4)),intersection(sK2,sK4)) ),
inference(resolution,[],[f68,f46]) ).
fof(f74,definition,
( spl5_1
<=> member(sK0(sK2,union(sK3,sK4)),intersection(sK2,sK4)) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
fof(f76,plain,
( member(sK0(sK2,union(sK3,sK4)),intersection(sK2,sK4))
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f78,definition,
( spl5_2
<=> member(sK0(sK2,union(sK3,sK4)),intersection(sK2,sK3)) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
fof(f80,plain,
( member(sK0(sK2,union(sK3,sK4)),intersection(sK2,sK3))
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f78]) ).
fof(f81,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f71,f78,f74]) ).
fof(f91,plain,
( member(sK0(sK2,union(sK3,sK4)),sK3)
| ~ spl5_2 ),
inference(resolution,[],[f80,f32]) ).
fof(f111,plain,
( ! [X0] : member(sK0(sK2,union(sK3,sK4)),union(sK3,X0))
| ~ spl5_2 ),
inference(resolution,[],[f91,f31]) ).
fof(f184,plain,
( subset(sK2,union(sK3,sK4))
| ~ spl5_2 ),
inference(resolution,[],[f111,f28]) ).
fof(f192,plain,
( $false
| ~ spl5_2 ),
inference(forward_subsumption_resolution,[],[f184,f46]) ).
fof(f193,plain,
~ spl5_2,
inference(avatar_contradiction_clause,[],[f192]) ).
fof(f227,plain,
( member(sK0(sK2,union(sK3,sK4)),sK4)
| ~ spl5_1 ),
inference(resolution,[],[f76,f32]) ).
fof(f248,plain,
( ! [X0] : member(sK0(sK2,union(sK3,sK4)),union(X0,sK4))
| ~ spl5_1 ),
inference(resolution,[],[f227,f30]) ).
fof(f315,plain,
( subset(sK2,union(sK3,sK4))
| ~ spl5_1 ),
inference(resolution,[],[f248,f28]) ).
fof(f323,plain,
( $false
| ~ spl5_1 ),
inference(forward_subsumption_resolution,[],[f315,f46]) ).
fof(f324,plain,
~ spl5_1,
inference(avatar_contradiction_clause,[],[f323]) ).
cnf(s1,plain,
( spl5_1
| spl5_2 ),
inference(sat_conversion,[],[f81]) ).
cnf(s2,plain,
~ spl5_2,
inference(sat_conversion,[],[f193]) ).
cnf(s6,plain,
~ spl5_1,
inference(sat_conversion,[],[f324]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s1,s2,s6]) ).
fof(f325,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET594+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 % Computer : n001.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Mon Sep 28 02:22:47 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.42 Running first-order theorem proving
% 0.17/0.42 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
% 2.73/1.37 % (4153774)Detected formulas, will run a generic FOF schedule.
% 2.73/1.37 % (4153784)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1305579694:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.73/1.37 % (4153784)First to succeed.
% 2.73/1.37 % (4153784)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4153774"
% 2.73/1.37 % (4153781)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=1383359743:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.73/1.37 % (4153782)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4019320531:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.73/1.37 % (4153779)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=3255218995:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.73/1.37 % (4153785)dis-21_1_sil=8000:lcm=predicate:random_seed=1009449116: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)
% 2.73/1.37 % (4153780)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=1862584258:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.73/1.37 % (4153783)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2510604902:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.73/1.37 % (4153782)Instruction limit reached!
% 2.73/1.37 % (4153782)------------------------------
% 2.73/1.37 % (4153782)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.73/1.37 % (4153782)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.73/1.37 % (4153782)CaDiCaL version: 2.1.3
% 2.73/1.37 % (4153782)Termination reason: Instruction limit
% 2.73/1.37 % (4153782)Termination phase: Saturation
% 2.73/1.37 % (4153782)Time elapsed: 0.069 s
% 2.73/1.37 % (4153782)Peak memory usage: 89 MB
% 2.73/1.37 % (4153782)Instructions burned: 110 (million)
% 2.73/1.37 % (4153785)Instruction limit reached!
% 2.73/1.37 % (4153785)------------------------------
% 2.73/1.37 % (4153785)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.73/1.37 % (4153785)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.73/1.37 % (4153785)CaDiCaL version: 2.1.3
% 2.73/1.37 % (4153785)Termination reason: Instruction limit
% 2.73/1.37 % (4153785)Termination phase: Saturation
% 2.73/1.37 % (4153785)Time elapsed: 0.074 s
% 2.73/1.37 % (4153785)Peak memory usage: 89 MB
% 2.73/1.37 % (4153785)Instructions burned: 130 (million)
% 2.73/1.37 % (4153783)Instruction limit reached!
% 2.73/1.37 % (4153783)------------------------------
% 2.73/1.37 % (4153783)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.73/1.37 % (4153783)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.73/1.37 % (4153783)CaDiCaL version: 2.1.3
% 2.73/1.37 % (4153783)Termination reason: Instruction limit
% 2.73/1.37 % (4153783)Termination phase: Saturation
% 2.73/1.37 % (4153783)Time elapsed: 0.076 s
% 2.73/1.37 % (4153783)Peak memory usage: 89 MB
% 2.73/1.37 % (4153783)Instructions burned: 121 (million)
% 2.73/1.37 % (4153784)Refutation found. Thanks to Tanya!
% 2.73/1.37 % SZS status Theorem for theBenchmark
% 2.73/1.37 % SZS output start Proof for theBenchmark
% See solution above
% 2.73/1.37 % (4153784)------------------------------
% 2.73/1.37 % (4153784)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.73/1.37 % (4153784)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.73/1.37 % (4153784)CaDiCaL version: 2.1.3
% 2.73/1.37 % (4153784)Termination reason: Refutation
% 2.73/1.37 % (4153784)Time elapsed: 0.007 s
% 2.73/1.37 % (4153784)Peak memory usage: 90 MB
% 2.73/1.37 % (4153784)Instructions burned: 15 (million)
% 2.73/1.37 % (4153784)------------------------------
% 2.73/1.37 % (4153784)------------------------------
% 2.73/1.37 % (4153774)Success in time 0.299 s
% 2.73/1.37 % Vampire exiting
%------------------------------------------------------------------------------