%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET699+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 : 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 12:41:41 PM UTC 2026
% Result : Theorem 1.61s 1.13s
% Output : Refutation 2.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 8
% Syntax : Number of formulae : 74 ( 5 unt; 4 def)
% Number of atoms : 215 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 223 ( 82 ~; 95 |; 31 &)
% ( 10 <=>; 3 =>; 0 <=; 2 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 80 ( 0 sgn 66 !; 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)),difference(X2,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI33) ).
fof(f13,negated_conjecture,
~ ! [X0,X1,X2] :
( ( subset(X0,X2)
& subset(X1,X2) )
=> ( subset(X0,X1)
<=> subset(intersection(X0,difference(X2,X1)),difference(X2,X0)) ) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f16,plain,
? [X0,X1,X2] :
( ( subset(X0,X1)
<~> subset(intersection(X0,difference(X2,X1)),difference(X2,X0)) )
& subset(X0,X2)
& subset(X1,X2) ),
inference(ennf_transformation,[],[f13]) ).
fof(f17,plain,
? [X0,X1,X2] :
( ( subset(X0,X1)
<~> subset(intersection(X0,difference(X2,X1)),difference(X2,X0)) )
& subset(X0,X2)
& subset(X1,X2) ),
inference(flattening,[],[f16]) ).
fof(f18,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,[],[f14]) ).
fof(f19,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,[],[f18]) ).
fof(f20,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))],[f19]) ).
fof(f22,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(f23,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,[],[f22]) ).
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(f37,plain,
? [X0,X1,X2] :
( ( ~ subset(intersection(X0,difference(X2,X1)),difference(X2,X0))
| ~ subset(X0,X1) )
& ( subset(intersection(X0,difference(X2,X1)),difference(X2,X0))
| subset(X0,X1) )
& subset(X0,X2)
& subset(X1,X2) ),
inference(nnf_transformation,[],[f17]) ).
fof(f38,plain,
? [X0,X1,X2] :
( ( ~ subset(intersection(X0,difference(X2,X1)),difference(X2,X0))
| ~ subset(X0,X1) )
& ( subset(intersection(X0,difference(X2,X1)),difference(X2,X0))
| subset(X0,X1) )
& subset(X0,X2)
& subset(X1,X2) ),
inference(flattening,[],[f37]) ).
fof(f39,plain,
( ( ~ subset(intersection(sK3,difference(sK5,sK4)),difference(sK5,sK3))
| ~ subset(sK3,sK4) )
& ( subset(intersection(sK3,difference(sK5,sK4)),difference(sK5,sK3))
| subset(sK3,sK4) )
& subset(sK3,sK5)
& subset(sK4,sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5)],[f38]) ).
fof(f40,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f41,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f20]) ).
fof(f42,plain,
! [X0,X1] :
( ~ member(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f45,plain,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
inference(cnf_transformation,[],[f23]) ).
fof(f46,plain,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f47,plain,
! [X2,X0,X1] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X1)
| ~ member(X0,X2) ),
inference(cnf_transformation,[],[f23]) ).
fof(f52,plain,
! [X2,X0,X1] :
( ~ member(X0,difference(X2,X1))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f54,plain,
! [X2,X0,X1] :
( member(X0,difference(X2,X1))
| ~ member(X0,X2)
| member(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f67,plain,
subset(sK3,sK5),
inference(cnf_transformation,[],[f39]) ).
fof(f68,plain,
( subset(intersection(sK3,difference(sK5,sK4)),difference(sK5,sK3))
| subset(sK3,sK4) ),
inference(cnf_transformation,[],[f39]) ).
fof(f69,plain,
( ~ subset(intersection(sK3,difference(sK5,sK4)),difference(sK5,sK3))
| ~ subset(sK3,sK4) ),
inference(cnf_transformation,[],[f39]) ).
fof(f74,definition,
( spl6_1
<=> subset(sK3,sK4) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
fof(f75,plain,
( ~ subset(sK3,sK4)
| spl6_1 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f76,plain,
( subset(sK3,sK4)
| ~ spl6_1 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f78,definition,
( spl6_2
<=> subset(intersection(sK3,difference(sK5,sK4)),difference(sK5,sK3)) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
fof(f79,plain,
( ~ subset(intersection(sK3,difference(sK5,sK4)),difference(sK5,sK3))
| spl6_2 ),
inference(avatar_component_clause,[],[f78]) ).
fof(f80,plain,
( subset(intersection(sK3,difference(sK5,sK4)),difference(sK5,sK3))
| ~ spl6_2 ),
inference(avatar_component_clause,[],[f78]) ).
fof(f81,plain,
( spl6_1
| spl6_2 ),
inference(avatar_split_clause,[],[f68,f78,f74]) ).
fof(f82,plain,
( ~ spl6_1
| ~ spl6_2 ),
inference(avatar_split_clause,[],[f69,f78,f74]) ).
fof(f84,plain,
( member(sK0(sK3,sK4),sK3)
| spl6_1 ),
inference(resolution,[],[f41,f75]) ).
fof(f89,plain,
! [X0] :
( member(X0,sK5)
| ~ member(X0,sK3) ),
inference(resolution,[],[f40,f67]) ).
fof(f90,plain,
( ! [X0] :
( ~ member(X0,intersection(sK3,difference(sK5,sK4)))
| member(X0,difference(sK5,sK3)) )
| ~ spl6_2 ),
inference(resolution,[],[f40,f80]) ).
fof(f99,plain,
( ! [X0] :
( member(X0,difference(sK5,sK3))
| ~ member(X0,sK3)
| ~ member(X0,difference(sK5,sK4)) )
| ~ spl6_2 ),
inference(resolution,[],[f90,f47]) ).
fof(f100,plain,
( ! [X0] :
( ~ member(X0,sK3)
| ~ member(X0,difference(sK5,sK4)) )
| ~ spl6_2 ),
inference(forward_subsumption_resolution,[],[f99,f52]) ).
fof(f101,plain,
( ~ member(sK0(sK3,sK4),difference(sK5,sK4))
| spl6_1
| ~ spl6_2 ),
inference(resolution,[],[f100,f84]) ).
fof(f103,plain,
( ~ member(sK0(sK3,sK4),sK5)
| member(sK0(sK3,sK4),sK4)
| spl6_1
| ~ spl6_2 ),
inference(resolution,[],[f101,f54]) ).
fof(f105,definition,
( spl6_3
<=> member(sK0(sK3,sK4),sK4) ),
introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition]) ).
fof(f107,plain,
( member(sK0(sK3,sK4),sK4)
| ~ spl6_3 ),
inference(avatar_component_clause,[],[f105]) ).
fof(f109,definition,
( spl6_4
<=> member(sK0(sK3,sK4),sK5) ),
introduced(definition,[new_symbols(definition,[spl6_4])],[avatar_definition]) ).
fof(f111,plain,
( ~ member(sK0(sK3,sK4),sK5)
| spl6_4 ),
inference(avatar_component_clause,[],[f109]) ).
fof(f112,plain,
( spl6_3
| ~ spl6_4
| spl6_1
| ~ spl6_2 ),
inference(avatar_split_clause,[],[f103,f78,f74,f109,f105]) ).
fof(f113,plain,
( ~ member(sK0(sK3,sK4),sK3)
| spl6_4 ),
inference(resolution,[],[f111,f89]) ).
fof(f114,plain,
( $false
| spl6_1
| spl6_4 ),
inference(forward_subsumption_resolution,[],[f113,f84]) ).
fof(f115,plain,
( spl6_1
| spl6_4 ),
inference(avatar_contradiction_clause,[],[f114]) ).
fof(f116,plain,
( ! [X0] :
( ~ member(X0,sK3)
| member(X0,sK4) )
| ~ spl6_1 ),
inference(resolution,[],[f76,f40]) ).
fof(f117,plain,
( member(sK0(intersection(sK3,difference(sK5,sK4)),difference(sK5,sK3)),intersection(sK3,difference(sK5,sK4)))
| spl6_2 ),
inference(resolution,[],[f79,f41]) ).
fof(f118,plain,
( member(sK0(intersection(sK3,difference(sK5,sK4)),difference(sK5,sK3)),sK3)
| spl6_2 ),
inference(resolution,[],[f117,f46]) ).
fof(f119,plain,
( member(sK0(intersection(sK3,difference(sK5,sK4)),difference(sK5,sK3)),difference(sK5,sK4))
| spl6_2 ),
inference(resolution,[],[f117,f45]) ).
fof(f120,plain,
( member(sK0(intersection(sK3,difference(sK5,sK4)),difference(sK5,sK3)),sK4)
| ~ spl6_1
| spl6_2 ),
inference(resolution,[],[f118,f116]) ).
fof(f124,plain,
( ~ member(sK0(intersection(sK3,difference(sK5,sK4)),difference(sK5,sK3)),sK4)
| spl6_2 ),
inference(resolution,[],[f119,f52]) ).
fof(f125,plain,
( $false
| ~ spl6_1
| spl6_2 ),
inference(forward_subsumption_resolution,[],[f124,f120]) ).
fof(f126,plain,
( ~ spl6_1
| spl6_2 ),
inference(avatar_contradiction_clause,[],[f125]) ).
fof(f129,plain,
( subset(sK3,sK4)
| ~ spl6_3 ),
inference(resolution,[],[f107,f42]) ).
fof(f132,plain,
( $false
| spl6_1
| ~ spl6_3 ),
inference(forward_subsumption_resolution,[],[f129,f75]) ).
fof(f133,plain,
( spl6_1
| ~ spl6_3 ),
inference(avatar_contradiction_clause,[],[f132]) ).
cnf(s1,plain,
( spl6_1
| spl6_2 ),
inference(sat_conversion,[],[f81]) ).
cnf(s2,plain,
( ~ spl6_1
| ~ spl6_2 ),
inference(sat_conversion,[],[f82]) ).
cnf(s3,plain,
( spl6_1
| ~ spl6_2
| spl6_3
| ~ spl6_4 ),
inference(sat_conversion,[],[f112]) ).
cnf(s4,plain,
( spl6_1
| spl6_4 ),
inference(sat_conversion,[],[f115]) ).
cnf(s5,plain,
( ~ spl6_1
| spl6_2 ),
inference(sat_conversion,[],[f126]) ).
cnf(s7,plain,
( spl6_1
| ~ spl6_3 ),
inference(sat_conversion,[],[f133]) ).
cnf(s8,plain,
( spl6_1
| ~ spl6_4
| spl6_3 ),
inference(rat,[],[s1,s3]) ).
cnf(s9,plain,
spl6_1,
inference(rat,[],[s8,s4,s7]) ).
cnf(s10,plain,
spl6_2,
inference(rat,[],[s5,s9]) ).
cnf(s11,plain,
$false,
inference(rat,[],[s2,s10,s9]) ).
fof(f134,plain,
$false,
inference(avatar_sat_refutation,[],[s11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET699+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n010.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 28 02:33:32 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 1.61/1.13 % (1508097)Detected formulas, will run a generic FOF schedule.
% 1.61/1.13 % (1508107)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=489506573:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 1.61/1.13 % (1508107)First to succeed.
% 1.61/1.13 % (1508107)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1508097"
% 1.61/1.13 % (1508106)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4003978552:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 1.61/1.13 % (1508104)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=106452092:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 1.61/1.13 % (1508105)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3161375685:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 1.61/1.13 % (1508102)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=621493588:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 1.61/1.13 % (1508103)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=3149531887:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 1.61/1.13 % (1508105)Refutation not found, incomplete strategy
% 1.61/1.13 % (1508105)------------------------------
% 1.61/1.13 % (1508105)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.61/1.13 % (1508105)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.61/1.13 % (1508105)CaDiCaL version: 2.1.3
% 1.61/1.13 % (1508105)Termination reason: Refutation not found, incomplete strategy
% 1.61/1.13 % (1508105)Time elapsed: 0.001 s
% 1.61/1.13 % (1508105)Peak memory usage: 88 MB
% 1.61/1.13 % (1508105)Instructions burned: 1 (million)
% 1.61/1.13 % (1508108)dis-21_1_sil=8000:lcm=predicate:random_seed=1134859124: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)
% 1.61/1.13 % (1508108)Also succeeded, but the first one will report.
% 1.61/1.13 % (1508106)Instruction limit reached!
% 1.61/1.13 % (1508106)------------------------------
% 1.61/1.13 % (1508106)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.61/1.13 % (1508106)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.61/1.13 % (1508106)CaDiCaL version: 2.1.3
% 1.61/1.13 % (1508106)Termination reason: Instruction limit
% 1.61/1.13 % (1508106)Termination phase: Saturation
% 1.61/1.13 % (1508106)Time elapsed: 0.075 s
% 1.61/1.13 % (1508106)Peak memory usage: 89 MB
% 1.61/1.13 % (1508106)Instructions burned: 119 (million)
% 1.61/1.13 % (1508107)Refutation found. Thanks to Tanya!
% 1.61/1.13 % SZS status Theorem for theBenchmark
% 1.61/1.13 % SZS output start Proof for theBenchmark
% See solution above
% 2.52/1.32 % (1508107)------------------------------
% 2.52/1.32 % (1508107)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.52/1.32 % (1508107)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.52/1.32 % (1508107)CaDiCaL version: 2.1.3
% 2.52/1.32 % (1508107)Termination reason: Refutation
% 2.52/1.32 % (1508107)Time elapsed: 0.003 s
% 2.52/1.32 % (1508107)Peak memory usage: 89 MB
% 2.52/1.32 % (1508107)Instructions burned: 6 (million)
% 2.52/1.32 % (1508107)------------------------------
% 2.52/1.32 % (1508107)------------------------------
% 2.52/1.32 % (1508097)Success in time 0.275 s
% 2.52/1.32 % Vampire exiting
%------------------------------------------------------------------------------