%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET190-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 12:40:27 PM UTC 2026
% Result : Unsatisfiable 2.53s 1.26s
% Output : Refutation 2.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 18
% Syntax : Number of formulae : 59 ( 15 unt; 6 def)
% Number of atoms : 115 ( 6 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 110 ( 54 ~; 50 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 10 ( 8 usr; 6 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 27 ( 0 sgn 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( ~ subclass(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_members) ).
fof(f2,axiom,
! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_subclass_members1) ).
fof(f3,axiom,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_subclass_members2) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',class_elements_are_sets) ).
fof(f7,axiom,
! [X0,X1] :
( ~ subclass(X0,X1)
| ~ subclass(X1,X0)
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_implies_equal) ).
fof(f21,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection1) ).
fof(f22,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection2) ).
fof(f24,axiom,
! [X0,X1] :
( ~ member(X0,complement(X1))
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement1) ).
fof(f25,axiom,
! [X0,X1] :
( member(X0,complement(X1))
| ~ member(X0,universal_class)
| member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement2) ).
fof(f26,axiom,
! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union) ).
fof(f122,negated_conjecture,
subclass(x,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_subclass_property7_1) ).
fof(f123,negated_conjecture,
union(complement(x),y) != universal_class,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_subclass_property7_2) ).
fof(f124,plain,
universal_class != union(complement(x),y),
inference(reorient_equations,[],[f123]) ).
fof(f138,plain,
universal_class != complement(intersection(complement(complement(x)),complement(y))),
inference(definition_unfolding,[],[f124,f26]) ).
fof(f182,definition,
! [X0,X1] :
( sQ0_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ0_eqProxy])],[equality_proxy_definition]) ).
fof(f183,plain,
~ sQ0_eqProxy(universal_class,complement(intersection(complement(complement(x)),complement(y)))),
inference(equality_proxy_replacement,[],[f138,f182]) ).
fof(f186,plain,
! [X0,X1] :
( sQ0_eqProxy(X0,X1)
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(equality_proxy_replacement,[],[f7,f182]) ).
fof(f220,plain,
! [X0] :
( member(X0,y)
| ~ member(X0,x) ),
inference(resolution,[],[f1,f122]) ).
fof(f221,plain,
( ~ subclass(complement(intersection(complement(complement(x)),complement(y))),universal_class)
| ~ subclass(universal_class,complement(intersection(complement(complement(x)),complement(y)))) ),
inference(resolution,[],[f186,f183]) ).
fof(f224,definition,
( spl1_1
<=> subclass(complement(intersection(complement(complement(x)),complement(y))),universal_class) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
fof(f225,plain,
( ~ subclass(complement(intersection(complement(complement(x)),complement(y))),universal_class)
| spl1_1 ),
inference(avatar_component_clause,[],[f224]) ).
fof(f227,definition,
( spl1_2
<=> subclass(universal_class,complement(intersection(complement(complement(x)),complement(y)))) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
fof(f228,plain,
( ~ subclass(universal_class,complement(intersection(complement(complement(x)),complement(y))))
| spl1_2 ),
inference(avatar_component_clause,[],[f227]) ).
fof(f230,plain,
( ~ spl1_2
| ~ spl1_1 ),
inference(avatar_split_clause,[],[f221,f224,f227]) ).
fof(f231,plain,
( $false
| spl1_1 ),
inference(resolution,[],[f225,f4]) ).
fof(f234,plain,
spl1_1,
inference(avatar_contradiction_clause,[],[f231]) ).
fof(f235,plain,
( ~ member(not_subclass_element(universal_class,complement(intersection(complement(complement(x)),complement(y)))),complement(intersection(complement(complement(x)),complement(y))))
| spl1_2 ),
inference(resolution,[],[f228,f3]) ).
fof(f236,plain,
( member(not_subclass_element(universal_class,complement(intersection(complement(complement(x)),complement(y)))),universal_class)
| spl1_2 ),
inference(resolution,[],[f228,f2]) ).
fof(f238,plain,
( ~ member(not_subclass_element(universal_class,complement(intersection(complement(complement(x)),complement(y)))),universal_class)
| member(not_subclass_element(universal_class,complement(intersection(complement(complement(x)),complement(y)))),intersection(complement(complement(x)),complement(y)))
| spl1_2 ),
inference(resolution,[],[f25,f235]) ).
fof(f240,definition,
( spl1_3
<=> member(not_subclass_element(universal_class,complement(intersection(complement(complement(x)),complement(y)))),intersection(complement(complement(x)),complement(y))) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
fof(f241,plain,
( member(not_subclass_element(universal_class,complement(intersection(complement(complement(x)),complement(y)))),intersection(complement(complement(x)),complement(y)))
| ~ spl1_3 ),
inference(avatar_component_clause,[],[f240]) ).
fof(f243,definition,
( spl1_4
<=> member(not_subclass_element(universal_class,complement(intersection(complement(complement(x)),complement(y)))),universal_class) ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
fof(f244,plain,
( ~ member(not_subclass_element(universal_class,complement(intersection(complement(complement(x)),complement(y)))),universal_class)
| spl1_4 ),
inference(avatar_component_clause,[],[f243]) ).
fof(f245,plain,
( spl1_3
| ~ spl1_4
| spl1_2 ),
inference(avatar_split_clause,[],[f238,f227,f243,f240]) ).
fof(f246,plain,
( $false
| spl1_2
| spl1_4 ),
inference(resolution,[],[f244,f236]) ).
fof(f248,plain,
( spl1_2
| spl1_4 ),
inference(avatar_contradiction_clause,[],[f246]) ).
fof(f249,plain,
( member(not_subclass_element(universal_class,complement(intersection(complement(complement(x)),complement(y)))),complement(y))
| ~ spl1_3 ),
inference(resolution,[],[f241,f22]) ).
fof(f250,plain,
( member(not_subclass_element(universal_class,complement(intersection(complement(complement(x)),complement(y)))),complement(complement(x)))
| ~ spl1_3 ),
inference(resolution,[],[f241,f21]) ).
fof(f251,plain,
( ~ member(not_subclass_element(universal_class,complement(intersection(complement(complement(x)),complement(y)))),y)
| ~ spl1_3 ),
inference(resolution,[],[f249,f24]) ).
fof(f252,plain,
( ~ member(not_subclass_element(universal_class,complement(intersection(complement(complement(x)),complement(y)))),complement(x))
| ~ spl1_3 ),
inference(resolution,[],[f250,f24]) ).
fof(f253,plain,
( ~ member(not_subclass_element(universal_class,complement(intersection(complement(complement(x)),complement(y)))),x)
| ~ spl1_3 ),
inference(resolution,[],[f251,f220]) ).
fof(f254,plain,
( ~ member(not_subclass_element(universal_class,complement(intersection(complement(complement(x)),complement(y)))),universal_class)
| member(not_subclass_element(universal_class,complement(intersection(complement(complement(x)),complement(y)))),x)
| ~ spl1_3 ),
inference(resolution,[],[f252,f25]) ).
fof(f256,definition,
( spl1_5
<=> member(not_subclass_element(universal_class,complement(intersection(complement(complement(x)),complement(y)))),x) ),
introduced(definition,[new_symbols(definition,[spl1_5])],[avatar_definition]) ).
fof(f257,plain,
( member(not_subclass_element(universal_class,complement(intersection(complement(complement(x)),complement(y)))),x)
| ~ spl1_5 ),
inference(avatar_component_clause,[],[f256]) ).
fof(f258,plain,
( spl1_5
| ~ spl1_4
| ~ spl1_3 ),
inference(avatar_split_clause,[],[f254,f240,f243,f256]) ).
fof(f259,plain,
( $false
| ~ spl1_3
| ~ spl1_5 ),
inference(resolution,[],[f257,f253]) ).
fof(f260,plain,
( ~ spl1_3
| ~ spl1_5 ),
inference(avatar_contradiction_clause,[],[f259]) ).
cnf(s2,plain,
( ~ spl1_1
| ~ spl1_2 ),
inference(sat_conversion,[],[f230]) ).
cnf(s3,plain,
spl1_1,
inference(sat_conversion,[],[f234]) ).
cnf(s4,plain,
( spl1_2
| spl1_3
| ~ spl1_4 ),
inference(sat_conversion,[],[f245]) ).
cnf(s5,plain,
( spl1_2
| spl1_4 ),
inference(sat_conversion,[],[f248]) ).
cnf(s6,plain,
( ~ spl1_3
| ~ spl1_4
| spl1_5 ),
inference(sat_conversion,[],[f258]) ).
cnf(s7,plain,
( ~ spl1_3
| ~ spl1_5 ),
inference(sat_conversion,[],[f260]) ).
cnf(s8,plain,
~ spl1_2,
inference(rat,[],[s2,s3]) ).
cnf(s9,plain,
spl1_4,
inference(rat,[],[s5,s8]) ).
cnf(s10,plain,
spl1_3,
inference(rat,[],[s4,s9,s8]) ).
cnf(s11,plain,
~ spl1_5,
inference(rat,[],[s7,s10]) ).
cnf(s12,plain,
$false,
inference(rat,[],[s6,s9,s11,s10]) ).
fof(f261,plain,
$false,
inference(avatar_sat_refutation,[],[s12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET190-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n013.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 01:02:37 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 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
% 2.53/1.26 % (713728)Input is clausal, will run a generic CNF schedule.
% 2.53/1.26 % (713739)dis-21_1_sil=8000:lcm=predicate:random_seed=924932534:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 2.53/1.26 % (713739)First to succeed.
% 2.53/1.26 % (713739)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-713728"
% 2.53/1.26 % (713736)lrs+10_1_sil=8000:sp=occurrence:random_seed=2324144524:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.53/1.26 % (713734)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1534558376:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.53/1.26 % (713733)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=3533216387:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.53/1.26 % (713737)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1735629605:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.53/1.26 % (713735)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2856839938:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.53/1.26 % (713738)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3322451274:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.53/1.26 % (713736)Instruction limit reached!
% 2.53/1.26 % (713736)------------------------------
% 2.53/1.26 % (713736)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.53/1.26 % (713736)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.53/1.26 % (713736)CaDiCaL version: 2.1.3
% 2.53/1.26 % (713736)Termination reason: Instruction limit
% 2.53/1.26 % (713736)Termination phase: Saturation
% 2.53/1.26 % (713736)Time elapsed: 0.042 s
% 2.53/1.26 % (713736)Peak memory usage: 88 MB
% 2.53/1.26 % (713736)Instructions burned: 109 (million)
% 2.53/1.26 % (713737)Instruction limit reached!
% 2.53/1.26 % (713737)------------------------------
% 2.53/1.26 % (713737)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.53/1.26 % (713737)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.53/1.26 % (713737)CaDiCaL version: 2.1.3
% 2.53/1.26 % (713737)Termination reason: Instruction limit
% 2.53/1.26 % (713737)Termination phase: Saturation
% 2.53/1.26 % (713737)Time elapsed: 0.070 s
% 2.53/1.26 % (713737)Peak memory usage: 89 MB
% 2.53/1.26 % (713737)Instructions burned: 115 (million)
% 2.53/1.26 % (713739)Refutation found. Thanks to Tanya!
% 2.53/1.26 % SZS status Unsatisfiable for theBenchmark
% 2.53/1.26 % SZS output start Proof for theBenchmark
% See solution above
% 2.53/1.26 % (713739)------------------------------
% 2.53/1.26 % (713739)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.53/1.26 % (713739)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.53/1.26 % (713739)CaDiCaL version: 2.1.3
% 2.53/1.26 % (713739)Termination reason: Refutation
% 2.53/1.26 % (713739)Time elapsed: 0.003 s
% 2.53/1.26 % (713739)Peak memory usage: 89 MB
% 2.53/1.26 % (713739)Instructions burned: 8 (million)
% 2.53/1.26 % (713739)------------------------------
% 2.53/1.26 % (713739)------------------------------
% 2.53/1.26 % (713728)Success in time 0.289 s
% 2.53/1.26 % Vampire exiting
%------------------------------------------------------------------------------