%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET630+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 12:41:27 PM UTC 2026
% Result : Theorem 2.95s 1.28s
% Output : Refutation 3.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 67 ( 19 unt; 4 def)
% Number of atoms : 157 ( 2 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 162 ( 72 ~; 65 |; 17 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 5 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 81 ( 0 sgn 76 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : symmetric_difference(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetric_difference_defn) ).
fof(f2,axiom,
! [X0,X1,X2] :
( intersect(X0,union(X1,X2))
<=> ( intersect(X0,X1)
| intersect(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersect_with_union) ).
fof(f3,axiom,
! [X0,X1] : disjoint(intersection(X0,X1),difference(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_and_union_disjoint) ).
fof(f4,axiom,
! [X0,X1,X2] :
( member(X2,intersection(X0,X1))
<=> ( member(X2,X0)
& member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_defn) ).
fof(f5,axiom,
! [X0,X1] :
( intersect(X0,X1)
<=> ? [X2] :
( member(X2,X0)
& member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersect_defn) ).
fof(f6,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> ~ intersect(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjoint_defn) ).
fof(f12,conjecture,
! [X0,X1] : disjoint(intersection(X0,X1),symmetric_difference(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_intersection_and_symmetric_difference_disjoint) ).
fof(f13,negated_conjecture,
~ ! [X0,X1] : disjoint(intersection(X0,X1),symmetric_difference(X0,X1)),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f15,plain,
? [X0,X1] : ~ disjoint(intersection(X0,X1),symmetric_difference(X0,X1)),
inference(ennf_transformation,[],[f13]) ).
fof(f16,plain,
! [X0,X1,X2] :
( ( intersect(X0,union(X1,X2))
| ( ~ intersect(X0,X1)
& ~ intersect(X0,X2) ) )
& ( intersect(X0,X1)
| intersect(X0,X2)
| ~ intersect(X0,union(X1,X2)) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f17,plain,
! [X0,X1,X2] :
( ( intersect(X0,union(X1,X2))
| ( ~ intersect(X0,X1)
& ~ intersect(X0,X2) ) )
& ( intersect(X0,X1)
| intersect(X0,X2)
| ~ intersect(X0,union(X1,X2)) ) ),
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,[],[f4]) ).
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(f20,plain,
! [X0,X1] :
( ( intersect(X0,X1)
| ! [X2] :
( ~ member(X2,X0)
| ~ member(X2,X1) ) )
& ( ? [X2] :
( member(X2,X0)
& member(X2,X1) )
| ~ intersect(X0,X1) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f21,plain,
! [X0,X1] :
( ( intersect(X0,X1)
| ! [X2] :
( ~ member(X2,X0)
| ~ member(X2,X1) ) )
& ( ? [X3] :
( member(X3,X0)
& member(X3,X1) )
| ~ intersect(X0,X1) ) ),
inference(rectify,[],[f20]) ).
fof(f22,plain,
! [X0,X1] :
( ( intersect(X0,X1)
| ! [X2] :
( ~ member(X2,X0)
| ~ member(X2,X1) ) )
& ( ( member(sK0(X0,X1),X0)
& member(sK0(X0,X1),X1) )
| ~ intersect(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1))],[f21]) ).
fof(f23,plain,
! [X0,X1] :
( ( disjoint(X0,X1)
| intersect(X0,X1) )
& ( ~ intersect(X0,X1)
| ~ disjoint(X0,X1) ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f27,plain,
~ disjoint(intersection(sK2,sK3),symmetric_difference(sK2,sK3)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f15]) ).
fof(f28,plain,
! [X0,X1] : symmetric_difference(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
inference(cnf_transformation,[],[f1]) ).
fof(f29,plain,
! [X2,X0,X1] :
( ~ intersect(X0,union(X1,X2))
| intersect(X0,X2)
| intersect(X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f32,plain,
! [X0,X1] : disjoint(intersection(X0,X1),difference(X0,X1)),
inference(cnf_transformation,[],[f3]) ).
fof(f33,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f34,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X0) ),
inference(cnf_transformation,[],[f19]) ).
fof(f35,plain,
! [X2,X0,X1] :
( member(X2,intersection(X0,X1))
| ~ member(X2,X0)
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f36,plain,
! [X0,X1] :
( ~ intersect(X0,X1)
| member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f37,plain,
! [X0,X1] :
( ~ intersect(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f22]) ).
fof(f38,plain,
! [X2,X0,X1] :
( intersect(X0,X1)
| ~ member(X2,X0)
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f39,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f40,plain,
! [X0,X1] :
( disjoint(X0,X1)
| intersect(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f49,plain,
~ disjoint(intersection(sK2,sK3),symmetric_difference(sK2,sK3)),
inference(cnf_transformation,[],[f27]) ).
fof(f51,plain,
~ disjoint(intersection(sK2,sK3),union(difference(sK2,sK3),difference(sK3,sK2))),
inference(definition_unfolding,[],[f49,f28]) ).
fof(f62,plain,
intersect(intersection(sK2,sK3),union(difference(sK2,sK3),difference(sK3,sK2))),
inference(resolution,[],[f40,f51]) ).
fof(f64,plain,
! [X0,X1] : ~ intersect(intersection(X0,X1),difference(X0,X1)),
inference(resolution,[],[f32,f39]) ).
fof(f77,plain,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| ~ member(X0,difference(X1,X2)) ),
inference(resolution,[],[f38,f64]) ).
fof(f81,plain,
( intersect(intersection(sK2,sK3),difference(sK3,sK2))
| intersect(intersection(sK2,sK3),difference(sK2,sK3)) ),
inference(resolution,[],[f29,f62]) ).
fof(f87,definition,
( spl5_1
<=> intersect(intersection(sK2,sK3),difference(sK2,sK3)) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
fof(f88,plain,
( intersect(intersection(sK2,sK3),difference(sK2,sK3))
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f87]) ).
fof(f90,definition,
( spl5_2
<=> intersect(intersection(sK2,sK3),difference(sK3,sK2)) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
fof(f91,plain,
( intersect(intersection(sK2,sK3),difference(sK3,sK2))
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f90]) ).
fof(f92,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f81,f90,f87]) ).
fof(f93,plain,
( member(sK0(intersection(sK2,sK3),difference(sK3,sK2)),intersection(sK2,sK3))
| ~ spl5_2 ),
inference(resolution,[],[f91,f37]) ).
fof(f94,plain,
( member(sK0(intersection(sK2,sK3),difference(sK3,sK2)),difference(sK3,sK2))
| ~ spl5_2 ),
inference(resolution,[],[f91,f36]) ).
fof(f95,plain,
( member(sK0(intersection(sK2,sK3),difference(sK3,sK2)),sK2)
| ~ spl5_2 ),
inference(resolution,[],[f93,f34]) ).
fof(f96,plain,
( member(sK0(intersection(sK2,sK3),difference(sK3,sK2)),sK3)
| ~ spl5_2 ),
inference(resolution,[],[f93,f33]) ).
fof(f177,plain,
! [X2,X0,X1] :
( ~ member(X0,difference(X1,X2))
| ~ member(X0,X1)
| ~ member(X0,X2) ),
inference(resolution,[],[f77,f35]) ).
fof(f751,plain,
( ~ member(sK0(intersection(sK2,sK3),difference(sK3,sK2)),sK3)
| ~ member(sK0(intersection(sK2,sK3),difference(sK3,sK2)),sK2)
| ~ spl5_2 ),
inference(resolution,[],[f177,f94]) ).
fof(f755,definition,
( spl5_3
<=> member(sK0(intersection(sK2,sK3),difference(sK3,sK2)),sK2) ),
introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition]) ).
fof(f756,plain,
( ~ member(sK0(intersection(sK2,sK3),difference(sK3,sK2)),sK2)
| spl5_3 ),
inference(avatar_component_clause,[],[f755]) ).
fof(f758,definition,
( spl5_4
<=> member(sK0(intersection(sK2,sK3),difference(sK3,sK2)),sK3) ),
introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition]) ).
fof(f759,plain,
( ~ member(sK0(intersection(sK2,sK3),difference(sK3,sK2)),sK3)
| spl5_4 ),
inference(avatar_component_clause,[],[f758]) ).
fof(f760,plain,
( ~ spl5_3
| ~ spl5_4
| ~ spl5_2 ),
inference(avatar_split_clause,[],[f751,f90,f758,f755]) ).
fof(f768,plain,
( $false
| ~ spl5_2
| spl5_3 ),
inference(resolution,[],[f756,f95]) ).
fof(f770,plain,
( ~ spl5_2
| spl5_3 ),
inference(avatar_contradiction_clause,[],[f768]) ).
fof(f771,plain,
( $false
| ~ spl5_2
| spl5_4 ),
inference(resolution,[],[f759,f96]) ).
fof(f773,plain,
( ~ spl5_2
| spl5_4 ),
inference(avatar_contradiction_clause,[],[f771]) ).
fof(f774,plain,
( $false
| ~ spl5_1 ),
inference(resolution,[],[f88,f64]) ).
fof(f801,plain,
~ spl5_1,
inference(avatar_contradiction_clause,[],[f774]) ).
cnf(s1,plain,
( spl5_1
| spl5_2 ),
inference(sat_conversion,[],[f92]) ).
cnf(s2,plain,
( ~ spl5_2
| ~ spl5_3
| ~ spl5_4 ),
inference(sat_conversion,[],[f760]) ).
cnf(s4,plain,
( ~ spl5_2
| spl5_3 ),
inference(sat_conversion,[],[f770]) ).
cnf(s5,plain,
( ~ spl5_2
| spl5_4 ),
inference(sat_conversion,[],[f773]) ).
cnf(s6,plain,
~ spl5_1,
inference(sat_conversion,[],[f801]) ).
cnf(s7,plain,
spl5_2,
inference(rat,[],[s1,s6]) ).
cnf(s8,plain,
spl5_4,
inference(rat,[],[s5,s7]) ).
cnf(s9,plain,
spl5_3,
inference(rat,[],[s4,s7]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s2,s8,s9,s7]) ).
fof(f802,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET630+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n006.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 28 02:22:40 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.95/1.28 % (3529829)Detected formulas, will run a generic FOF schedule.
% 2.95/1.28 % (3529836)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=4293624068:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.95/1.28 % (3529834)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=4231452992:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.95/1.28 % (3529837)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3863017447:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.95/1.28 % (3529840)dis-21_1_sil=8000:lcm=predicate:random_seed=1041606158: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)
% 2.95/1.28 % (3529835)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=300678726:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.95/1.28 % (3529838)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1226211655:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.95/1.28 % (3529839)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=534531470:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.95/1.28 % (3529837)Refutation not found, incomplete strategy
% 2.95/1.28 % (3529837)------------------------------
% 2.95/1.28 % (3529837)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.95/1.28 % (3529837)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.95/1.28 % (3529837)CaDiCaL version: 2.1.3
% 2.95/1.28 % (3529837)Termination reason: Refutation not found, incomplete strategy
% 2.95/1.28 % (3529837)Time elapsed: 0.001 s
% 2.95/1.28 % (3529837)Peak memory usage: 88 MB
% 2.95/1.28 % (3529838)Refutation not found, incomplete strategy
% 2.95/1.28 % (3529838)------------------------------
% 2.95/1.28 % (3529838)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.95/1.28 % (3529838)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.95/1.28 % (3529838)CaDiCaL version: 2.1.3
% 2.95/1.28 % (3529838)Termination reason: Refutation not found, incomplete strategy
% 2.95/1.28 % (3529838)Time elapsed: 0.001 s
% 2.95/1.28 % (3529838)Peak memory usage: 88 MB
% 2.95/1.28 % (3529840)First to succeed.
% 2.95/1.28 % (3529840)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3529829"
% 2.95/1.28 % (3529839)Also succeeded, but the first one will report.
% 2.95/1.28 % (3529837)------------------------------
% 2.95/1.28 % (3529837)------------------------------
% 2.95/1.28 % (3529838)------------------------------
% 2.95/1.28 % (3529838)------------------------------
% 2.95/1.28 % (3529840)Refutation found. Thanks to Tanya!
% 2.95/1.28 % SZS status Theorem for theBenchmark
% 2.95/1.28 % SZS output start Proof for theBenchmark
% See solution above
% 3.69/1.48 % (3529840)------------------------------
% 3.69/1.48 % (3529840)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.69/1.48 % (3529840)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.69/1.48 % (3529840)CaDiCaL version: 2.1.3
% 3.69/1.48 % (3529840)Termination reason: Refutation
% 3.69/1.48 % (3529840)Time elapsed: 0.017 s
% 3.69/1.48 % (3529840)Peak memory usage: 89 MB
% 3.69/1.48 % (3529840)Instructions burned: 26 (million)
% 3.69/1.48 % (3529840)------------------------------
% 3.69/1.48 % (3529840)------------------------------
% 3.69/1.48 % (3529829)Success in time 0.442 s
% 3.69/1.48 % Vampire exiting
%------------------------------------------------------------------------------