%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET695+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 : n017.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 12:41:40 PM UTC 2026
% Result : Theorem 2.53s 1.29s
% Output : Refutation 3.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 9
% Syntax : Number of formulae : 81 ( 7 unt; 6 def)
% Number of atoms : 224 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 225 ( 82 ~; 101 |; 26 &)
% ( 11 <=>; 3 =>; 0 <=; 2 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 7 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 65 ( 0 sgn 51 !; 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(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(difference(X2,X1),difference(X2,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI24) ).
fof(f13,negated_conjecture,
~ ! [X0,X1,X2] :
( ( subset(X0,X2)
& subset(X1,X2) )
=> ( subset(X0,X1)
<=> subset(difference(X2,X1),difference(X2,X0)) ) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
? [X0,X1,X2] :
( ( subset(X0,X1)
<~> subset(difference(X2,X1),difference(X2,X0)) )
& subset(X0,X2)
& subset(X1,X2) ),
inference(ennf_transformation,[],[f13]) ).
fof(f15,plain,
? [X0,X1,X2] :
( ( subset(X0,X1)
<~> subset(difference(X2,X1),difference(X2,X0)) )
& 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(difference(X2,X1),difference(X2,X0))
| ~ subset(X0,X1) )
& ( subset(difference(X2,X1),difference(X2,X0))
| subset(X0,X1) )
& subset(X0,X2)
& subset(X1,X2) ),
inference(nnf_transformation,[],[f15]) ).
fof(f18,plain,
? [X0,X1,X2] :
( ( ~ subset(difference(X2,X1),difference(X2,X0))
| ~ subset(X0,X1) )
& ( subset(difference(X2,X1),difference(X2,X0))
| subset(X0,X1) )
& subset(X0,X2)
& subset(X1,X2) ),
inference(flattening,[],[f17]) ).
fof(f19,plain,
( ( ~ subset(difference(sK2,sK1),difference(sK2,sK0))
| ~ subset(sK0,sK1) )
& ( subset(difference(sK2,sK1),difference(sK2,sK0))
| 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,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(f25,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,[],[f24]) ).
fof(f27,plain,
subset(sK0,sK2),
inference(cnf_transformation,[],[f19]) ).
fof(f28,plain,
( subset(difference(sK2,sK1),difference(sK2,sK0))
| subset(sK0,sK1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f29,plain,
( ~ subset(difference(sK2,sK1),difference(sK2,sK0))
| ~ subset(sK0,sK1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f32,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f33,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK3(X0,X1),X0) ),
inference(cnf_transformation,[],[f23]) ).
fof(f34,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK3(X0,X1),X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f35,plain,
! [X2,X0,X1] :
( ~ member(X0,difference(X2,X1))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f36,plain,
! [X2,X0,X1] :
( ~ member(X0,difference(X2,X1))
| member(X0,X2) ),
inference(cnf_transformation,[],[f25]) ).
fof(f37,plain,
! [X2,X0,X1] :
( member(X0,difference(X2,X1))
| ~ member(X0,X2)
| member(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f39,definition,
( spl4_1
<=> subset(sK0,sK1) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f40,plain,
( subset(sK0,sK1)
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f39]) ).
fof(f42,definition,
( spl4_2
<=> subset(difference(sK2,sK1),difference(sK2,sK0)) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f43,plain,
( subset(difference(sK2,sK1),difference(sK2,sK0))
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f42]) ).
fof(f44,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f28,f42,f39]) ).
fof(f45,plain,
( ~ subset(sK0,sK1)
| spl4_1 ),
inference(avatar_component_clause,[],[f39]) ).
fof(f46,plain,
( ~ subset(difference(sK2,sK1),difference(sK2,sK0))
| spl4_2 ),
inference(avatar_component_clause,[],[f42]) ).
fof(f47,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(avatar_split_clause,[],[f29,f42,f39]) ).
fof(f53,plain,
( member(sK3(sK0,sK1),sK0)
| spl4_1 ),
inference(resolution,[],[f33,f45]) ).
fof(f55,plain,
( ~ member(sK3(sK0,sK1),sK1)
| spl4_1 ),
inference(resolution,[],[f34,f45]) ).
fof(f60,plain,
( ! [X0] :
( ~ member(X0,difference(sK2,sK1))
| member(X0,difference(sK2,sK0)) )
| ~ spl4_2 ),
inference(resolution,[],[f32,f43]) ).
fof(f61,plain,
! [X0] :
( ~ member(X0,sK0)
| member(X0,sK2) ),
inference(resolution,[],[f32,f27]) ).
fof(f65,plain,
( ! [X0] :
( member(X0,difference(sK2,sK0))
| ~ member(X0,sK2)
| member(X0,sK1) )
| ~ spl4_2 ),
inference(resolution,[],[f60,f37]) ).
fof(f67,plain,
( ! [X0] :
( member(X0,sK1)
| ~ member(X0,sK2)
| ~ member(X0,sK0) )
| ~ spl4_2 ),
inference(resolution,[],[f65,f35]) ).
fof(f68,plain,
( ~ member(sK3(sK0,sK1),sK2)
| ~ member(sK3(sK0,sK1),sK0)
| spl4_1
| ~ spl4_2 ),
inference(resolution,[],[f67,f55]) ).
fof(f70,definition,
( spl4_3
<=> member(sK3(sK0,sK1),sK0) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
fof(f71,plain,
( ~ member(sK3(sK0,sK1),sK0)
| spl4_3 ),
inference(avatar_component_clause,[],[f70]) ).
fof(f73,definition,
( spl4_4
<=> member(sK3(sK0,sK1),sK2) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
fof(f74,plain,
( ~ member(sK3(sK0,sK1),sK2)
| spl4_4 ),
inference(avatar_component_clause,[],[f73]) ).
fof(f75,plain,
( ~ spl4_3
| ~ spl4_4
| spl4_1
| ~ spl4_2 ),
inference(avatar_split_clause,[],[f68,f42,f39,f73,f70]) ).
fof(f76,plain,
( $false
| spl4_1
| spl4_3 ),
inference(resolution,[],[f71,f53]) ).
fof(f77,plain,
( spl4_1
| spl4_3 ),
inference(avatar_contradiction_clause,[],[f76]) ).
fof(f78,plain,
( ! [X0] :
( member(X0,sK1)
| ~ member(X0,sK0) )
| ~ spl4_1 ),
inference(resolution,[],[f40,f32]) ).
fof(f80,plain,
( ~ member(sK3(difference(sK2,sK1),difference(sK2,sK0)),difference(sK2,sK0))
| spl4_2 ),
inference(resolution,[],[f46,f34]) ).
fof(f81,plain,
( member(sK3(difference(sK2,sK1),difference(sK2,sK0)),difference(sK2,sK1))
| spl4_2 ),
inference(resolution,[],[f46,f33]) ).
fof(f83,plain,
( ~ member(sK3(difference(sK2,sK1),difference(sK2,sK0)),sK2)
| member(sK3(difference(sK2,sK1),difference(sK2,sK0)),sK0)
| spl4_2 ),
inference(resolution,[],[f80,f37]) ).
fof(f85,definition,
( spl4_5
<=> member(sK3(difference(sK2,sK1),difference(sK2,sK0)),sK0) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
fof(f86,plain,
( member(sK3(difference(sK2,sK1),difference(sK2,sK0)),sK0)
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f85]) ).
fof(f88,definition,
( spl4_6
<=> member(sK3(difference(sK2,sK1),difference(sK2,sK0)),sK2) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
fof(f89,plain,
( ~ member(sK3(difference(sK2,sK1),difference(sK2,sK0)),sK2)
| spl4_6 ),
inference(avatar_component_clause,[],[f88]) ).
fof(f90,plain,
( spl4_5
| ~ spl4_6
| spl4_2 ),
inference(avatar_split_clause,[],[f83,f42,f88,f85]) ).
fof(f91,plain,
( member(sK3(difference(sK2,sK1),difference(sK2,sK0)),sK2)
| spl4_2 ),
inference(resolution,[],[f81,f36]) ).
fof(f92,plain,
( ~ member(sK3(difference(sK2,sK1),difference(sK2,sK0)),sK1)
| spl4_2 ),
inference(resolution,[],[f81,f35]) ).
fof(f93,plain,
( $false
| spl4_2
| spl4_6 ),
inference(resolution,[],[f91,f89]) ).
fof(f94,plain,
( spl4_2
| spl4_6 ),
inference(avatar_contradiction_clause,[],[f93]) ).
fof(f95,plain,
( ~ member(sK3(difference(sK2,sK1),difference(sK2,sK0)),sK0)
| ~ spl4_1
| spl4_2 ),
inference(resolution,[],[f92,f78]) ).
fof(f96,plain,
( $false
| ~ spl4_1
| spl4_2
| ~ spl4_5 ),
inference(resolution,[],[f95,f86]) ).
fof(f97,plain,
( ~ spl4_1
| spl4_2
| ~ spl4_5 ),
inference(avatar_contradiction_clause,[],[f96]) ).
fof(f99,plain,
( member(sK3(sK0,sK1),sK0)
| spl4_1 ),
inference(resolution,[],[f45,f33]) ).
fof(f103,plain,
( member(sK3(sK0,sK1),sK2)
| spl4_1 ),
inference(resolution,[],[f99,f61]) ).
fof(f105,plain,
( $false
| spl4_1
| spl4_4 ),
inference(resolution,[],[f74,f103]) ).
fof(f106,plain,
( spl4_1
| spl4_4 ),
inference(avatar_contradiction_clause,[],[f105]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f44]) ).
cnf(s2,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(sat_conversion,[],[f47]) ).
cnf(s3,plain,
( spl4_1
| ~ spl4_2
| ~ spl4_3
| ~ spl4_4 ),
inference(sat_conversion,[],[f75]) ).
cnf(s4,plain,
( spl4_1
| spl4_3 ),
inference(sat_conversion,[],[f77]) ).
cnf(s5,plain,
( spl4_2
| spl4_5
| ~ spl4_6 ),
inference(sat_conversion,[],[f90]) ).
cnf(s6,plain,
( spl4_2
| spl4_6 ),
inference(sat_conversion,[],[f94]) ).
cnf(s7,plain,
( ~ spl4_1
| spl4_2
| ~ spl4_5 ),
inference(sat_conversion,[],[f97]) ).
cnf(s8,plain,
( spl4_1
| spl4_4 ),
inference(sat_conversion,[],[f106]) ).
cnf(s9,plain,
( spl4_1
| ~ spl4_4
| ~ spl4_3 ),
inference(rat,[],[s1,s3]) ).
cnf(s10,plain,
spl4_1,
inference(rat,[],[s9,s4,s8]) ).
cnf(s11,plain,
~ spl4_2,
inference(rat,[],[s2,s10]) ).
cnf(s12,plain,
~ spl4_5,
inference(rat,[],[s7,s10,s11]) ).
cnf(s13,plain,
spl4_6,
inference(rat,[],[s6,s11]) ).
cnf(s14,plain,
$false,
inference(rat,[],[s5,s13,s12,s11]) ).
fof(f107,plain,
$false,
inference(avatar_sat_refutation,[],[s14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET695+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n017.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Mon Sep 28 02:29:05 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 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
% 2.53/1.29 % (3157271)Detected formulas, will run a generic FOF schedule.
% 2.53/1.29 % (3157279)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2543368222:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.53/1.29 % (3157279)Refutation not found, incomplete strategy
% 2.53/1.29 % (3157279)------------------------------
% 2.53/1.29 % (3157279)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.53/1.29 % (3157279)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.53/1.29 % (3157279)CaDiCaL version: 2.1.3
% 2.53/1.29 % (3157279)Termination reason: Refutation not found, incomplete strategy
% 2.53/1.29 % (3157279)Time elapsed: 0.001 s
% 2.53/1.29 % (3157279)Peak memory usage: 88 MB
% 2.53/1.29 % (3157282)dis-21_1_sil=8000:lcm=predicate:random_seed=1198472819: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)
% 2.53/1.29 % (3157280)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3958938432:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.53/1.29 % (3157276)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=284097039:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.53/1.29 % (3157277)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=673513725:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.53/1.29 % (3157278)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=625428520:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.53/1.29 % (3157281)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3485234411:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.53/1.29 % (3157282)First to succeed.
% 2.53/1.29 % (3157282)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3157271"
% 2.53/1.29 % (3157281)Also succeeded, but the first one will report.
% 2.53/1.29 % (3157280)Instruction limit reached!
% 2.53/1.29 % (3157280)------------------------------
% 2.53/1.29 % (3157280)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.53/1.29 % (3157280)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.53/1.29 % (3157280)CaDiCaL version: 2.1.3
% 2.53/1.29 % (3157280)Termination reason: Instruction limit
% 2.53/1.29 % (3157280)Termination phase: Saturation
% 2.53/1.29 % (3157280)Time elapsed: 0.074 s
% 2.53/1.29 % (3157280)Peak memory usage: 88 MB
% 2.53/1.29 % (3157280)Instructions burned: 119 (million)
% 2.53/1.29 % (3157279)------------------------------
% 2.53/1.29 % (3157279)------------------------------
% 2.53/1.29 % (3157291)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3156398275:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.53/1.29 % (3157291)Also succeeded, but the first one will report.
% 2.53/1.29 % (3157290)lrs+10_1_sil=8000:sp=occurrence:random_seed=2820169746:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.53/1.29 % (3157282)Refutation found. Thanks to Tanya!
% 2.53/1.29 % SZS status Theorem for theBenchmark
% 2.53/1.29 % SZS output start Proof for theBenchmark
% See solution above
% 3.48/1.44 % (3157282)------------------------------
% 3.48/1.44 % (3157282)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.48/1.44 % (3157282)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/1.44 % (3157282)CaDiCaL version: 2.1.3
% 3.48/1.44 % (3157282)Termination reason: Refutation
% 3.48/1.44 % (3157282)Time elapsed: 0.004 s
% 3.48/1.44 % (3157282)Peak memory usage: 89 MB
% 3.48/1.44 % (3157282)Instructions burned: 3 (million)
% 3.48/1.44 % (3157282)------------------------------
% 3.48/1.44 % (3157282)------------------------------
% 3.48/1.44 % (3157271)Success in time 0.418 s
% 3.48/1.44 % Vampire exiting
%------------------------------------------------------------------------------