%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET154-6 : 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 : n002.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 12:40:19 PM UTC 2026
% Result : Unsatisfiable 3.51s 1.45s
% Output : Refutation 3.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 15
% Syntax : Number of formulae : 48 ( 14 unt; 5 def)
% Number of atoms : 89 ( 6 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 78 ( 37 ~; 36 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 5 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 23 ( 0 sgn 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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,
union(complement(x),x) != universal_class,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_union_with_complement_1) ).
fof(f123,plain,
universal_class != union(complement(x),x),
inference(reorient_equations,[],[f122]) ).
fof(f137,plain,
universal_class != complement(intersection(complement(complement(x)),complement(x))),
inference(definition_unfolding,[],[f123,f26]) ).
fof(f181,definition,
! [X0,X1] :
( sQ0_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ0_eqProxy])],[equality_proxy_definition]) ).
fof(f182,plain,
~ sQ0_eqProxy(universal_class,complement(intersection(complement(complement(x)),complement(x)))),
inference(equality_proxy_replacement,[],[f137,f181]) ).
fof(f183,plain,
! [X0,X1] :
( sQ0_eqProxy(X0,X1)
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(equality_proxy_replacement,[],[f7,f181]) ).
fof(f219,plain,
( ~ subclass(complement(intersection(complement(complement(x)),complement(x))),universal_class)
| ~ subclass(universal_class,complement(intersection(complement(complement(x)),complement(x)))) ),
inference(resolution,[],[f183,f182]) ).
fof(f222,definition,
( spl1_1
<=> subclass(complement(intersection(complement(complement(x)),complement(x))),universal_class) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
fof(f223,plain,
( ~ subclass(complement(intersection(complement(complement(x)),complement(x))),universal_class)
| spl1_1 ),
inference(avatar_component_clause,[],[f222]) ).
fof(f225,definition,
( spl1_2
<=> subclass(universal_class,complement(intersection(complement(complement(x)),complement(x)))) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
fof(f226,plain,
( ~ subclass(universal_class,complement(intersection(complement(complement(x)),complement(x))))
| spl1_2 ),
inference(avatar_component_clause,[],[f225]) ).
fof(f228,plain,
( ~ spl1_2
| ~ spl1_1 ),
inference(avatar_split_clause,[],[f219,f222,f225]) ).
fof(f229,plain,
( $false
| spl1_1 ),
inference(resolution,[],[f223,f4]) ).
fof(f232,plain,
spl1_1,
inference(avatar_contradiction_clause,[],[f229]) ).
fof(f233,plain,
( ~ member(not_subclass_element(universal_class,complement(intersection(complement(complement(x)),complement(x)))),complement(intersection(complement(complement(x)),complement(x))))
| spl1_2 ),
inference(resolution,[],[f226,f3]) ).
fof(f234,plain,
( member(not_subclass_element(universal_class,complement(intersection(complement(complement(x)),complement(x)))),universal_class)
| spl1_2 ),
inference(resolution,[],[f226,f2]) ).
fof(f236,plain,
( ~ member(not_subclass_element(universal_class,complement(intersection(complement(complement(x)),complement(x)))),universal_class)
| member(not_subclass_element(universal_class,complement(intersection(complement(complement(x)),complement(x)))),intersection(complement(complement(x)),complement(x)))
| spl1_2 ),
inference(resolution,[],[f25,f233]) ).
fof(f238,definition,
( spl1_3
<=> member(not_subclass_element(universal_class,complement(intersection(complement(complement(x)),complement(x)))),intersection(complement(complement(x)),complement(x))) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
fof(f239,plain,
( member(not_subclass_element(universal_class,complement(intersection(complement(complement(x)),complement(x)))),intersection(complement(complement(x)),complement(x)))
| ~ spl1_3 ),
inference(avatar_component_clause,[],[f238]) ).
fof(f241,definition,
( spl1_4
<=> member(not_subclass_element(universal_class,complement(intersection(complement(complement(x)),complement(x)))),universal_class) ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
fof(f242,plain,
( ~ member(not_subclass_element(universal_class,complement(intersection(complement(complement(x)),complement(x)))),universal_class)
| spl1_4 ),
inference(avatar_component_clause,[],[f241]) ).
fof(f243,plain,
( spl1_3
| ~ spl1_4
| spl1_2 ),
inference(avatar_split_clause,[],[f236,f225,f241,f238]) ).
fof(f244,plain,
( $false
| spl1_2
| spl1_4 ),
inference(resolution,[],[f242,f234]) ).
fof(f246,plain,
( spl1_2
| spl1_4 ),
inference(avatar_contradiction_clause,[],[f244]) ).
fof(f247,plain,
( member(not_subclass_element(universal_class,complement(intersection(complement(complement(x)),complement(x)))),complement(x))
| ~ spl1_3 ),
inference(resolution,[],[f239,f22]) ).
fof(f248,plain,
( member(not_subclass_element(universal_class,complement(intersection(complement(complement(x)),complement(x)))),complement(complement(x)))
| ~ spl1_3 ),
inference(resolution,[],[f239,f21]) ).
fof(f250,plain,
( ~ member(not_subclass_element(universal_class,complement(intersection(complement(complement(x)),complement(x)))),complement(x))
| ~ spl1_3 ),
inference(resolution,[],[f248,f24]) ).
fof(f251,plain,
( $false
| ~ spl1_3 ),
inference(resolution,[],[f250,f247]) ).
fof(f253,plain,
~ spl1_3,
inference(avatar_contradiction_clause,[],[f251]) ).
cnf(s2,plain,
( ~ spl1_1
| ~ spl1_2 ),
inference(sat_conversion,[],[f228]) ).
cnf(s3,plain,
spl1_1,
inference(sat_conversion,[],[f232]) ).
cnf(s4,plain,
( spl1_2
| spl1_3
| ~ spl1_4 ),
inference(sat_conversion,[],[f243]) ).
cnf(s5,plain,
( spl1_2
| spl1_4 ),
inference(sat_conversion,[],[f246]) ).
cnf(s6,plain,
~ spl1_3,
inference(sat_conversion,[],[f253]) ).
cnf(s8,plain,
( spl1_2
| ~ spl1_4 ),
inference(rat,[],[s4,s6]) ).
cnf(s9,plain,
~ spl1_2,
inference(rat,[],[s2,s3]) ).
cnf(s10,plain,
spl1_4,
inference(rat,[],[s5,s9]) ).
cnf(s11,plain,
$false,
inference(rat,[],[s8,s10,s9]) ).
fof(f258,plain,
$false,
inference(avatar_sat_refutation,[],[s11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET154-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n002.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 00:58:22 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 3.51/1.45 % (4060748)Input is clausal, will run a generic CNF schedule.
% 3.51/1.45 % (4060757)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=358838346:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.51/1.45 % (4060757)Instruction limit reached!
% 3.51/1.45 % (4060757)------------------------------
% 3.51/1.45 % (4060757)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.51/1.45 % (4060757)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.51/1.45 % (4060757)CaDiCaL version: 2.1.3
% 3.51/1.45 % (4060757)Termination reason: Instruction limit
% 3.51/1.45 % (4060757)Termination phase: Saturation
% 3.51/1.45 % (4060757)Time elapsed: 0.038 s
% 3.51/1.45 % (4060757)Peak memory usage: 89 MB
% 3.51/1.45 % (4060757)Instructions burned: 115 (million)
% 3.51/1.45 % (4060756)lrs+10_1_sil=8000:sp=occurrence:random_seed=418369760:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.51/1.45 % (4060758)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=173917472:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.51/1.45 % (4060754)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=275962443:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.51/1.45 % (4060753)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=3777625397:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.51/1.45 % (4060755)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=390040000:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.51/1.45 % (4060756)Refutation not found, incomplete strategy
% 3.51/1.45 % (4060756)------------------------------
% 3.51/1.45 % (4060756)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.51/1.45 % (4060756)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.51/1.45 % (4060756)CaDiCaL version: 2.1.3
% 3.51/1.45 % (4060756)Termination reason: Refutation not found, incomplete strategy
% 3.51/1.45 % (4060756)Time elapsed: 0.002 s
% 3.51/1.45 % (4060756)Peak memory usage: 88 MB
% 3.51/1.45 % (4060756)Instructions burned: 1 (million)
% 3.51/1.45 % (4060759)dis-21_1_sil=8000:lcm=predicate:random_seed=3177079079: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)
% 3.51/1.45 % (4060759)First to succeed.
% 3.51/1.45 % (4060759)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4060748"
% 3.51/1.45 % (4060766)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=1370655735:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 3.51/1.45 % (4060766)Refutation not found, incomplete strategy
% 3.51/1.45 % (4060766)------------------------------
% 3.51/1.45 % (4060766)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.51/1.45 % (4060766)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.51/1.45 % (4060766)CaDiCaL version: 2.1.3
% 3.51/1.45 % (4060766)Termination reason: Refutation not found, incomplete strategy
% 3.51/1.45 % (4060766)Time elapsed: 0.001 s
% 3.51/1.45 % (4060766)Peak memory usage: 88 MB
% 3.51/1.45 % (4060766)Instructions burned: 3 (million)
% 3.51/1.45 % (4060758)Instruction limit reached!
% 3.51/1.45 % (4060758)------------------------------
% 3.51/1.45 % (4060758)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.51/1.45 % (4060758)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.51/1.45 % (4060758)CaDiCaL version: 2.1.3
% 3.51/1.45 % (4060758)Termination reason: Instruction limit
% 3.51/1.45 % (4060758)Termination phase: Saturation
% 3.51/1.45 % (4060758)Time elapsed: 0.140 s
% 3.51/1.45 % (4060758)Peak memory usage: 90 MB
% 3.51/1.45 % (4060758)Instructions burned: 180 (million)
% 3.51/1.45 % (4060766)------------------------------
% 3.51/1.45 % (4060766)------------------------------
% 3.51/1.45 % (4060756)------------------------------
% 3.51/1.45 % (4060756)------------------------------
% 3.51/1.45 % (4060759)Refutation found. Thanks to Tanya!
% 3.51/1.45 % SZS status Unsatisfiable for theBenchmark
% 3.51/1.45 % SZS output start Proof for theBenchmark
% See solution above
% 3.51/1.45 % (4060759)------------------------------
% 3.51/1.45 % (4060759)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.51/1.45 % (4060759)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.51/1.45 % (4060759)CaDiCaL version: 2.1.3
% 3.51/1.45 % (4060759)Termination reason: Refutation
% 3.51/1.45 % (4060759)Time elapsed: 0.006 s
% 3.51/1.45 % (4060759)Peak memory usage: 89 MB
% 3.51/1.45 % (4060759)Instructions burned: 8 (million)
% 3.51/1.45 % (4060759)------------------------------
% 3.51/1.45 % (4060759)------------------------------
% 3.51/1.45 % (4060748)Success in time 0.416 s
% 3.51/1.45 % Vampire exiting
%------------------------------------------------------------------------------