%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET155-6 : 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 : n005.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 2.98s 1.33s
% Output : Refutation 3.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 16
% Syntax : Number of formulae : 61 ( 11 unt; 7 def)
% Number of atoms : 125 ( 5 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 111 ( 47 ~; 57 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 11 ( 9 usr; 7 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 24 ( 0 sgn 24 !; 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(f7,axiom,
! [X0,X1] :
( ~ subclass(X0,X1)
| ~ subclass(X1,X0)
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_implies_equal) ).
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,
complement(union(x,y)) != intersection(complement(x),complement(y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_demorgans_law1_1) ).
fof(f136,plain,
intersection(complement(x),complement(y)) != complement(complement(intersection(complement(x),complement(y)))),
inference(definition_unfolding,[],[f122,f26]) ).
fof(f180,definition,
! [X0,X1] :
( sQ0_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ0_eqProxy])],[equality_proxy_definition]) ).
fof(f181,plain,
~ sQ0_eqProxy(intersection(complement(x),complement(y)),complement(complement(intersection(complement(x),complement(y))))),
inference(equality_proxy_replacement,[],[f136,f180]) ).
fof(f182,plain,
! [X0,X1] :
( sQ0_eqProxy(X0,X1)
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(equality_proxy_replacement,[],[f7,f180]) ).
fof(f207,plain,
! [X0,X1] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(resolution,[],[f1,f4]) ).
fof(f215,plain,
( ~ subclass(complement(complement(intersection(complement(x),complement(y)))),intersection(complement(x),complement(y)))
| ~ subclass(intersection(complement(x),complement(y)),complement(complement(intersection(complement(x),complement(y))))) ),
inference(resolution,[],[f182,f181]) ).
fof(f218,definition,
( spl1_1
<=> subclass(complement(complement(intersection(complement(x),complement(y)))),intersection(complement(x),complement(y))) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
fof(f219,plain,
( ~ subclass(complement(complement(intersection(complement(x),complement(y)))),intersection(complement(x),complement(y)))
| spl1_1 ),
inference(avatar_component_clause,[],[f218]) ).
fof(f221,definition,
( spl1_2
<=> subclass(intersection(complement(x),complement(y)),complement(complement(intersection(complement(x),complement(y))))) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
fof(f222,plain,
( ~ subclass(intersection(complement(x),complement(y)),complement(complement(intersection(complement(x),complement(y)))))
| spl1_2 ),
inference(avatar_component_clause,[],[f221]) ).
fof(f224,plain,
( ~ spl1_2
| ~ spl1_1 ),
inference(avatar_split_clause,[],[f215,f218,f221]) ).
fof(f225,plain,
( ~ member(not_subclass_element(complement(complement(intersection(complement(x),complement(y)))),intersection(complement(x),complement(y))),intersection(complement(x),complement(y)))
| spl1_1 ),
inference(resolution,[],[f219,f3]) ).
fof(f226,plain,
( member(not_subclass_element(complement(complement(intersection(complement(x),complement(y)))),intersection(complement(x),complement(y))),complement(complement(intersection(complement(x),complement(y)))))
| spl1_1 ),
inference(resolution,[],[f219,f2]) ).
fof(f227,plain,
( ~ member(not_subclass_element(complement(complement(intersection(complement(x),complement(y)))),intersection(complement(x),complement(y))),complement(intersection(complement(x),complement(y))))
| spl1_1 ),
inference(resolution,[],[f226,f24]) ).
fof(f229,plain,
( ~ member(not_subclass_element(complement(complement(intersection(complement(x),complement(y)))),intersection(complement(x),complement(y))),universal_class)
| member(not_subclass_element(complement(complement(intersection(complement(x),complement(y)))),intersection(complement(x),complement(y))),intersection(complement(x),complement(y)))
| spl1_1 ),
inference(resolution,[],[f25,f227]) ).
fof(f231,definition,
( spl1_3
<=> member(not_subclass_element(complement(complement(intersection(complement(x),complement(y)))),intersection(complement(x),complement(y))),intersection(complement(x),complement(y))) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
fof(f232,plain,
( member(not_subclass_element(complement(complement(intersection(complement(x),complement(y)))),intersection(complement(x),complement(y))),intersection(complement(x),complement(y)))
| ~ spl1_3 ),
inference(avatar_component_clause,[],[f231]) ).
fof(f234,definition,
( spl1_4
<=> member(not_subclass_element(complement(complement(intersection(complement(x),complement(y)))),intersection(complement(x),complement(y))),universal_class) ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
fof(f235,plain,
( ~ member(not_subclass_element(complement(complement(intersection(complement(x),complement(y)))),intersection(complement(x),complement(y))),universal_class)
| spl1_4 ),
inference(avatar_component_clause,[],[f234]) ).
fof(f236,plain,
( spl1_3
| ~ spl1_4
| spl1_1 ),
inference(avatar_split_clause,[],[f229,f218,f234,f231]) ).
fof(f237,plain,
( ! [X0] : ~ member(not_subclass_element(complement(complement(intersection(complement(x),complement(y)))),intersection(complement(x),complement(y))),X0)
| spl1_4 ),
inference(resolution,[],[f235,f207]) ).
fof(f238,plain,
( $false
| spl1_1
| spl1_4 ),
inference(resolution,[],[f237,f226]) ).
fof(f245,plain,
( spl1_1
| spl1_4 ),
inference(avatar_contradiction_clause,[],[f238]) ).
fof(f246,plain,
( $false
| spl1_1
| ~ spl1_3 ),
inference(resolution,[],[f232,f225]) ).
fof(f249,plain,
( spl1_1
| ~ spl1_3 ),
inference(avatar_contradiction_clause,[],[f246]) ).
fof(f250,plain,
( ~ member(not_subclass_element(intersection(complement(x),complement(y)),complement(complement(intersection(complement(x),complement(y))))),complement(complement(intersection(complement(x),complement(y)))))
| spl1_2 ),
inference(resolution,[],[f222,f3]) ).
fof(f251,plain,
( member(not_subclass_element(intersection(complement(x),complement(y)),complement(complement(intersection(complement(x),complement(y))))),intersection(complement(x),complement(y)))
| spl1_2 ),
inference(resolution,[],[f222,f2]) ).
fof(f254,plain,
( ~ member(not_subclass_element(intersection(complement(x),complement(y)),complement(complement(intersection(complement(x),complement(y))))),universal_class)
| member(not_subclass_element(intersection(complement(x),complement(y)),complement(complement(intersection(complement(x),complement(y))))),complement(intersection(complement(x),complement(y))))
| spl1_2 ),
inference(resolution,[],[f250,f25]) ).
fof(f256,definition,
( spl1_5
<=> member(not_subclass_element(intersection(complement(x),complement(y)),complement(complement(intersection(complement(x),complement(y))))),complement(intersection(complement(x),complement(y)))) ),
introduced(definition,[new_symbols(definition,[spl1_5])],[avatar_definition]) ).
fof(f257,plain,
( member(not_subclass_element(intersection(complement(x),complement(y)),complement(complement(intersection(complement(x),complement(y))))),complement(intersection(complement(x),complement(y))))
| ~ spl1_5 ),
inference(avatar_component_clause,[],[f256]) ).
fof(f259,definition,
( spl1_6
<=> member(not_subclass_element(intersection(complement(x),complement(y)),complement(complement(intersection(complement(x),complement(y))))),universal_class) ),
introduced(definition,[new_symbols(definition,[spl1_6])],[avatar_definition]) ).
fof(f260,plain,
( ~ member(not_subclass_element(intersection(complement(x),complement(y)),complement(complement(intersection(complement(x),complement(y))))),universal_class)
| spl1_6 ),
inference(avatar_component_clause,[],[f259]) ).
fof(f261,plain,
( spl1_5
| ~ spl1_6
| spl1_2 ),
inference(avatar_split_clause,[],[f254,f221,f259,f256]) ).
fof(f264,plain,
( ! [X0] : ~ member(not_subclass_element(intersection(complement(x),complement(y)),complement(complement(intersection(complement(x),complement(y))))),X0)
| spl1_6 ),
inference(resolution,[],[f260,f207]) ).
fof(f266,plain,
( $false
| spl1_2
| spl1_6 ),
inference(resolution,[],[f264,f251]) ).
fof(f275,plain,
( spl1_2
| spl1_6 ),
inference(avatar_contradiction_clause,[],[f266]) ).
fof(f277,plain,
( ~ member(not_subclass_element(intersection(complement(x),complement(y)),complement(complement(intersection(complement(x),complement(y))))),intersection(complement(x),complement(y)))
| ~ spl1_5 ),
inference(resolution,[],[f257,f24]) ).
fof(f278,plain,
( $false
| spl1_2
| ~ spl1_5 ),
inference(resolution,[],[f277,f251]) ).
fof(f279,plain,
( spl1_2
| ~ spl1_5 ),
inference(avatar_contradiction_clause,[],[f278]) ).
cnf(s2,plain,
( ~ spl1_1
| ~ spl1_2 ),
inference(sat_conversion,[],[f224]) ).
cnf(s3,plain,
( spl1_1
| spl1_3
| ~ spl1_4 ),
inference(sat_conversion,[],[f236]) ).
cnf(s4,plain,
( spl1_1
| spl1_4 ),
inference(sat_conversion,[],[f245]) ).
cnf(s5,plain,
( spl1_1
| ~ spl1_3 ),
inference(sat_conversion,[],[f249]) ).
cnf(s6,plain,
( spl1_2
| spl1_5
| ~ spl1_6 ),
inference(sat_conversion,[],[f261]) ).
cnf(s8,plain,
( spl1_2
| spl1_6 ),
inference(sat_conversion,[],[f275]) ).
cnf(s9,plain,
( spl1_2
| ~ spl1_5 ),
inference(sat_conversion,[],[f279]) ).
cnf(s10,plain,
spl1_1,
inference(rat,[],[s3,s4,s5]) ).
cnf(s11,plain,
~ spl1_2,
inference(rat,[],[s2,s10]) ).
cnf(s12,plain,
~ spl1_5,
inference(rat,[],[s9,s11]) ).
cnf(s13,plain,
spl1_6,
inference(rat,[],[s8,s11]) ).
cnf(s14,plain,
$false,
inference(rat,[],[s6,s12,s13,s11]) ).
fof(f280,plain,
$false,
inference(avatar_sat_refutation,[],[s14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET155-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 % Computer : n005.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Mon Sep 28 00:55:47 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.44 Running first-order theorem proving
% 0.13/0.44 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
% 2.98/1.33 % (336569)Input is clausal, will run a generic CNF schedule.
% 2.98/1.33 % (336577)lrs+10_1_sil=8000:sp=occurrence:random_seed=592494657:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.98/1.33 % (336577)Refutation not found, incomplete strategy
% 2.98/1.33 % (336577)------------------------------
% 2.98/1.33 % (336577)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.98/1.33 % (336577)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.98/1.33 % (336577)CaDiCaL version: 2.1.3
% 2.98/1.33 % (336577)Termination reason: Refutation not found, incomplete strategy
% 2.98/1.33 % (336577)Time elapsed: 0.001 s
% 2.98/1.33 % (336577)Peak memory usage: 88 MB
% 2.98/1.33 % (336577)Instructions burned: 1 (million)
% 2.98/1.33 % (336575)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3299956915:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.98/1.33 % (336576)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1010462813:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.98/1.33 % (336574)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=3262276418:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.98/1.33 % (336580)dis-21_1_sil=8000:lcm=predicate:random_seed=1449066196: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)
% 2.98/1.33 % (336578)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1735070127:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.98/1.33 % (336579)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3902630896:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.98/1.33 % (336580)First to succeed.
% 2.98/1.33 % (336580)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-336569"
% 2.98/1.33 % (336578)Instruction limit reached!
% 2.98/1.33 % (336578)------------------------------
% 2.98/1.33 % (336578)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.98/1.33 % (336578)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.98/1.33 % (336578)CaDiCaL version: 2.1.3
% 2.98/1.33 % (336578)Termination reason: Instruction limit
% 2.98/1.33 % (336578)Termination phase: Saturation
% 2.98/1.33 % (336578)Time elapsed: 0.069 s
% 2.98/1.33 % (336578)Peak memory usage: 89 MB
% 2.98/1.33 % (336578)Instructions burned: 114 (million)
% 2.98/1.33 % (336577)------------------------------
% 2.98/1.33 % (336577)------------------------------
% 2.98/1.33 % (336579)Instruction limit reached!
% 2.98/1.33 % (336579)------------------------------
% 2.98/1.33 % (336579)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.98/1.33 % (336579)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.98/1.33 % (336579)CaDiCaL version: 2.1.3
% 2.98/1.33 % (336579)Termination reason: Instruction limit
% 2.98/1.33 % (336579)Termination phase: Saturation
% 2.98/1.33 % (336579)Time elapsed: 0.132 s
% 2.98/1.33 % (336579)Peak memory usage: 90 MB
% 2.98/1.33 % (336579)Instructions burned: 181 (million)
% 2.98/1.33 % (336588)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=1976522271:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 2.98/1.33 % (336588)Refutation not found, incomplete strategy
% 2.98/1.33 % (336588)------------------------------
% 2.98/1.33 % (336588)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.98/1.33 % (336588)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.98/1.33 % (336588)CaDiCaL version: 2.1.3
% 2.98/1.33 % (336588)Termination reason: Refutation not found, incomplete strategy
% 2.98/1.33 % (336588)Time elapsed: 0.002 s
% 2.98/1.33 % (336588)Peak memory usage: 88 MB
% 2.98/1.33 % (336588)Instructions burned: 3 (million)
% 2.98/1.33 % (336580)Refutation found. Thanks to Tanya!
% 2.98/1.33 % SZS status Unsatisfiable for theBenchmark
% 2.98/1.33 % SZS output start Proof for theBenchmark
% See solution above
% 3.79/1.53 % (336580)------------------------------
% 3.79/1.53 % (336580)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.79/1.53 % (336580)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.79/1.53 % (336580)CaDiCaL version: 2.1.3
% 3.79/1.53 % (336580)Termination reason: Refutation
% 3.79/1.53 % (336580)Time elapsed: 0.006 s
% 3.79/1.53 % (336580)Peak memory usage: 89 MB
% 3.79/1.53 % (336580)Instructions burned: 9 (million)
% 3.79/1.53 % (336580)------------------------------
% 3.79/1.53 % (336580)------------------------------
% 3.79/1.53 % (336569)Success in time 0.443 s
% 3.79/1.53 % Vampire exiting
%------------------------------------------------------------------------------