%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET200-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 12:40:30 PM UTC 2026
% Result : Unsatisfiable 1.55s 1.31s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 19
% Syntax : Number of formulae : 67 ( 18 unt; 6 def)
% Number of atoms : 127 ( 1 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 123 ( 63 ~; 54 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 10 ( 8 usr; 7 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 28 ( 0 sgn 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( ~ subclass(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_members) ).
fof(f2,axiom,
! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_subclass_members1) ).
fof(f3,axiom,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_subclass_members2) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',class_elements_are_sets) ).
fof(f21,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection1) ).
fof(f22,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection2) ).
fof(f23,axiom,
! [X2,X0,X1] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection3) ).
fof(f24,axiom,
! [X0,X1] :
( ~ member(X0,complement(X1))
| ~ member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement1) ).
fof(f25,axiom,
! [X0,X1] :
( member(X0,complement(X1))
| ~ member(X0,universal_class)
| member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement2) ).
fof(f26,axiom,
! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union) ).
fof(f122,negated_conjecture,
subclass(x,y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_union_is_monotonic_1) ).
fof(f123,negated_conjecture,
subclass(z,w),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_union_is_monotonic_2) ).
fof(f124,negated_conjecture,
~ subclass(union(x,z),union(y,w)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_union_is_monotonic_3) ).
fof(f138,plain,
~ subclass(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(w)))),
inference(definition_unfolding,[],[f124,f26,f26]) ).
fof(f205,plain,
member(not_subclass_element(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(w)))),complement(intersection(complement(x),complement(z)))),
inference(resolution,[],[f2,f138]) ).
fof(f206,plain,
~ member(not_subclass_element(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(w)))),complement(intersection(complement(y),complement(w)))),
inference(resolution,[],[f3,f138]) ).
fof(f207,plain,
~ member(not_subclass_element(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(w)))),intersection(complement(x),complement(z))),
inference(resolution,[],[f205,f24]) ).
fof(f208,plain,
! [X0,X1] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(resolution,[],[f1,f4]) ).
fof(f216,plain,
! [X0] :
( member(X0,y)
| ~ member(X0,x) ),
inference(resolution,[],[f1,f122]) ).
fof(f217,plain,
! [X0] :
( member(X0,w)
| ~ member(X0,z) ),
inference(resolution,[],[f1,f123]) ).
fof(f219,plain,
( ~ member(not_subclass_element(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(w)))),universal_class)
| member(not_subclass_element(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(w)))),intersection(complement(y),complement(w))) ),
inference(resolution,[],[f25,f206]) ).
fof(f221,definition,
( spl1_1
<=> member(not_subclass_element(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(w)))),intersection(complement(y),complement(w))) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
fof(f222,plain,
( member(not_subclass_element(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(w)))),intersection(complement(y),complement(w)))
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f221]) ).
fof(f224,definition,
( spl1_2
<=> member(not_subclass_element(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(w)))),universal_class) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
fof(f225,plain,
( ~ member(not_subclass_element(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(w)))),universal_class)
| spl1_2 ),
inference(avatar_component_clause,[],[f224]) ).
fof(f226,plain,
( spl1_1
| ~ spl1_2 ),
inference(avatar_split_clause,[],[f219,f224,f221]) ).
fof(f227,plain,
( ! [X0] : ~ member(not_subclass_element(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(w)))),X0)
| spl1_2 ),
inference(resolution,[],[f225,f208]) ).
fof(f228,plain,
( $false
| spl1_2 ),
inference(resolution,[],[f227,f205]) ).
fof(f236,plain,
spl1_2,
inference(avatar_contradiction_clause,[],[f228]) ).
fof(f237,plain,
( member(not_subclass_element(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(w)))),complement(w))
| ~ spl1_1 ),
inference(resolution,[],[f222,f22]) ).
fof(f238,plain,
( member(not_subclass_element(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(w)))),complement(y))
| ~ spl1_1 ),
inference(resolution,[],[f222,f21]) ).
fof(f239,plain,
( ~ member(not_subclass_element(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(w)))),w)
| ~ spl1_1 ),
inference(resolution,[],[f237,f24]) ).
fof(f240,plain,
( ~ member(not_subclass_element(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(w)))),z)
| ~ spl1_1 ),
inference(resolution,[],[f239,f217]) ).
fof(f241,plain,
( ~ member(not_subclass_element(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(w)))),y)
| ~ spl1_1 ),
inference(resolution,[],[f238,f24]) ).
fof(f242,plain,
( ~ member(not_subclass_element(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(w)))),x)
| ~ spl1_1 ),
inference(resolution,[],[f241,f216]) ).
fof(f247,plain,
( ~ member(not_subclass_element(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(w)))),complement(z))
| ~ member(not_subclass_element(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(w)))),complement(x)) ),
inference(resolution,[],[f23,f207]) ).
fof(f249,definition,
( spl1_3
<=> member(not_subclass_element(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(w)))),complement(x)) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
fof(f250,plain,
( ~ member(not_subclass_element(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(w)))),complement(x))
| spl1_3 ),
inference(avatar_component_clause,[],[f249]) ).
fof(f252,definition,
( spl1_4
<=> member(not_subclass_element(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(w)))),complement(z)) ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
fof(f253,plain,
( ~ member(not_subclass_element(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(w)))),complement(z))
| spl1_4 ),
inference(avatar_component_clause,[],[f252]) ).
fof(f254,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_split_clause,[],[f247,f252,f249]) ).
fof(f255,plain,
( ~ member(not_subclass_element(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(w)))),universal_class)
| member(not_subclass_element(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(w)))),x)
| spl1_3 ),
inference(resolution,[],[f250,f25]) ).
fof(f257,definition,
( spl1_5
<=> member(not_subclass_element(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(w)))),x) ),
introduced(definition,[new_symbols(definition,[spl1_5])],[avatar_definition]) ).
fof(f258,plain,
( member(not_subclass_element(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(w)))),x)
| ~ spl1_5 ),
inference(avatar_component_clause,[],[f257]) ).
fof(f259,plain,
( spl1_5
| ~ spl1_2
| spl1_3 ),
inference(avatar_split_clause,[],[f255,f249,f224,f257]) ).
fof(f260,plain,
( ~ member(not_subclass_element(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(w)))),universal_class)
| member(not_subclass_element(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(w)))),z)
| spl1_4 ),
inference(resolution,[],[f253,f25]) ).
fof(f262,definition,
( spl1_6
<=> member(not_subclass_element(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(w)))),z) ),
introduced(definition,[new_symbols(definition,[spl1_6])],[avatar_definition]) ).
fof(f263,plain,
( member(not_subclass_element(complement(intersection(complement(x),complement(z))),complement(intersection(complement(y),complement(w)))),z)
| ~ spl1_6 ),
inference(avatar_component_clause,[],[f262]) ).
fof(f264,plain,
( spl1_6
| ~ spl1_2
| spl1_4 ),
inference(avatar_split_clause,[],[f260,f252,f224,f262]) ).
fof(f265,plain,
( $false
| ~ spl1_1
| ~ spl1_6 ),
inference(resolution,[],[f263,f240]) ).
fof(f266,plain,
( ~ spl1_1
| ~ spl1_6 ),
inference(avatar_contradiction_clause,[],[f265]) ).
fof(f267,plain,
( $false
| ~ spl1_1
| ~ spl1_5 ),
inference(resolution,[],[f258,f242]) ).
fof(f268,plain,
( ~ spl1_1
| ~ spl1_5 ),
inference(avatar_contradiction_clause,[],[f267]) ).
cnf(s1,plain,
( spl1_1
| ~ spl1_2 ),
inference(sat_conversion,[],[f226]) ).
cnf(s2,plain,
spl1_2,
inference(sat_conversion,[],[f236]) ).
cnf(s3,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(sat_conversion,[],[f254]) ).
cnf(s4,plain,
( ~ spl1_2
| spl1_3
| spl1_5 ),
inference(sat_conversion,[],[f259]) ).
cnf(s5,plain,
( ~ spl1_2
| spl1_4
| spl1_6 ),
inference(sat_conversion,[],[f264]) ).
cnf(s6,plain,
( ~ spl1_1
| ~ spl1_6 ),
inference(sat_conversion,[],[f266]) ).
cnf(s7,plain,
( ~ spl1_1
| ~ spl1_5 ),
inference(sat_conversion,[],[f268]) ).
cnf(s8,plain,
spl1_1,
inference(rat,[],[s1,s2]) ).
cnf(s9,plain,
~ spl1_5,
inference(rat,[],[s7,s8]) ).
cnf(s10,plain,
~ spl1_6,
inference(rat,[],[s6,s8]) ).
cnf(s11,plain,
spl1_3,
inference(rat,[],[s4,s2,s9]) ).
cnf(s12,plain,
spl1_4,
inference(rat,[],[s5,s2,s10]) ).
cnf(s13,plain,
$false,
inference(rat,[],[s3,s12,s11]) ).
fof(f269,plain,
$false,
inference(avatar_sat_refutation,[],[s13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET200-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n003.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Mon Sep 28 01:06:45 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 1.55/1.31 % (1095419)Input is clausal, will run a generic CNF schedule.
% 1.55/1.31 % (1095424)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=1186718668:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 1.55/1.31 % (1095430)dis-21_1_sil=8000:lcm=predicate:random_seed=1122057909: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)
% 1.55/1.31 % (1095426)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3715137279:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 1.55/1.31 % (1095425)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3877700338:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 1.55/1.31 % (1095428)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1087518790:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 1.55/1.31 % (1095429)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1929606665:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 1.55/1.31 % (1095427)lrs+10_1_sil=8000:sp=occurrence:random_seed=4195081151:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 1.55/1.31 % (1095430)First to succeed.
% 1.55/1.31 % (1095430)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1095419"
% 1.55/1.31 % (1095427)Refutation not found, incomplete strategy
% 1.55/1.31 % (1095427)------------------------------
% 1.55/1.31 % (1095427)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.55/1.31 % (1095427)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.55/1.31 % (1095427)CaDiCaL version: 2.1.3
% 1.55/1.31 % (1095427)Termination reason: Refutation not found, incomplete strategy
% 1.55/1.31 % (1095427)Time elapsed: 0.028 s
% 1.55/1.31 % (1095427)Peak memory usage: 89 MB
% 1.55/1.31 % (1095427)Instructions burned: 40 (million)
% 1.55/1.31 % (1095428)Instruction limit reached!
% 1.55/1.31 % (1095428)------------------------------
% 1.55/1.31 % (1095428)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.55/1.31 % (1095428)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.55/1.31 % (1095428)CaDiCaL version: 2.1.3
% 1.55/1.31 % (1095428)Termination reason: Instruction limit
% 1.55/1.31 % (1095428)Termination phase: Saturation
% 1.55/1.31 % (1095428)Time elapsed: 0.069 s
% 1.55/1.31 % (1095428)Peak memory usage: 89 MB
% 1.55/1.31 % (1095428)Instructions burned: 114 (million)
% 1.55/1.31 % (1095429)Instruction limit reached!
% 1.55/1.31 % (1095429)------------------------------
% 1.55/1.31 % (1095429)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.55/1.31 % (1095429)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.55/1.31 % (1095429)CaDiCaL version: 2.1.3
% 1.55/1.31 % (1095429)Termination reason: Instruction limit
% 1.55/1.31 % (1095429)Termination phase: Saturation
% 1.55/1.31 % (1095429)Time elapsed: 0.135 s
% 1.55/1.31 % (1095429)Peak memory usage: 90 MB
% 1.55/1.31 % (1095429)Instructions burned: 180 (million)
% 1.55/1.31 % (1095438)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=2426185114:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 1.55/1.31 % (1095438)Refutation not found, incomplete strategy
% 1.55/1.31 % (1095438)------------------------------
% 1.55/1.31 % (1095438)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.55/1.31 % (1095438)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.55/1.31 % (1095438)CaDiCaL version: 2.1.3
% 1.55/1.31 % (1095438)Termination reason: Refutation not found, incomplete strategy
% 1.55/1.31 % (1095438)Time elapsed: 0.003 s
% 1.55/1.31 % (1095438)Peak memory usage: 88 MB
% 1.55/1.31 % (1095438)Instructions burned: 2 (million)
% 1.55/1.31 % (1095430)Refutation found. Thanks to Tanya!
% 1.55/1.31 % SZS status Unsatisfiable for theBenchmark
% 1.55/1.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/1.40 % (1095430)------------------------------
% 0.17/1.40 % (1095430)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.40 % (1095430)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.40 % (1095430)CaDiCaL version: 2.1.3
% 0.17/1.40 % (1095430)Termination reason: Refutation
% 0.17/1.40 % (1095430)Time elapsed: 0.006 s
% 0.17/1.40 % (1095430)Peak memory usage: 89 MB
% 0.17/1.40 % (1095430)Instructions burned: 9 (million)
% 0.17/1.40 % (1095430)------------------------------
% 0.17/1.40 % (1095430)------------------------------
% 0.17/1.40 % (1095419)Success in time 0.44 s
% 0.17/1.40 % Vampire exiting
%------------------------------------------------------------------------------