%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET173-6 : 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 : n014.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 12:40:24 PM UTC 2026
% Result : Unsatisfiable 0.62s 0.94s
% Output : Refutation 2.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 18
% Syntax : Number of formulae : 64 ( 15 unt; 7 def)
% Number of atoms : 126 ( 6 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 114 ( 52 ~; 55 |; 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 : 29 ( 0 sgn 29 !; 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(f21,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection1) ).
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,
intersection(x,union(x,y)) != x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_absorbtion_for_intersection_1) ).
fof(f123,plain,
x != intersection(x,union(x,y)),
inference(reorient_equations,[],[f122]) ).
fof(f136,plain,
x != intersection(x,complement(intersection(complement(x),complement(y)))),
inference(definition_unfolding,[],[f123,f26]) ).
fof(f178,definition,
! [X0,X1] :
( sQ0_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ0_eqProxy])],[equality_proxy_definition]) ).
fof(f179,plain,
~ sQ0_eqProxy(x,intersection(x,complement(intersection(complement(x),complement(y))))),
inference(equality_proxy_replacement,[],[f136,f178]) ).
fof(f180,plain,
! [X0,X1] :
( sQ0_eqProxy(X0,X1)
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(equality_proxy_replacement,[],[f7,f178]) ).
fof(f203,plain,
! [X0,X1] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(resolution,[],[f1,f4]) ).
fof(f210,plain,
( ~ subclass(intersection(x,complement(intersection(complement(x),complement(y)))),x)
| ~ subclass(x,intersection(x,complement(intersection(complement(x),complement(y))))) ),
inference(resolution,[],[f180,f179]) ).
fof(f213,definition,
( spl1_1
<=> subclass(intersection(x,complement(intersection(complement(x),complement(y)))),x) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
fof(f214,plain,
( ~ subclass(intersection(x,complement(intersection(complement(x),complement(y)))),x)
| spl1_1 ),
inference(avatar_component_clause,[],[f213]) ).
fof(f216,definition,
( spl1_2
<=> subclass(x,intersection(x,complement(intersection(complement(x),complement(y))))) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
fof(f217,plain,
( ~ subclass(x,intersection(x,complement(intersection(complement(x),complement(y)))))
| spl1_2 ),
inference(avatar_component_clause,[],[f216]) ).
fof(f219,plain,
( ~ spl1_2
| ~ spl1_1 ),
inference(avatar_split_clause,[],[f210,f213,f216]) ).
fof(f220,plain,
( ~ member(not_subclass_element(intersection(x,complement(intersection(complement(x),complement(y)))),x),x)
| spl1_1 ),
inference(resolution,[],[f214,f3]) ).
fof(f221,plain,
( member(not_subclass_element(intersection(x,complement(intersection(complement(x),complement(y)))),x),intersection(x,complement(intersection(complement(x),complement(y)))))
| spl1_1 ),
inference(resolution,[],[f214,f2]) ).
fof(f223,plain,
( member(not_subclass_element(intersection(x,complement(intersection(complement(x),complement(y)))),x),x)
| spl1_1 ),
inference(resolution,[],[f221,f21]) ).
fof(f224,plain,
( $false
| spl1_1 ),
inference(resolution,[],[f223,f220]) ).
fof(f225,plain,
spl1_1,
inference(avatar_contradiction_clause,[],[f224]) ).
fof(f226,plain,
( ~ member(not_subclass_element(x,intersection(x,complement(intersection(complement(x),complement(y))))),intersection(x,complement(intersection(complement(x),complement(y)))))
| spl1_2 ),
inference(resolution,[],[f217,f3]) ).
fof(f227,plain,
( member(not_subclass_element(x,intersection(x,complement(intersection(complement(x),complement(y))))),x)
| spl1_2 ),
inference(resolution,[],[f217,f2]) ).
fof(f233,plain,
( ~ member(not_subclass_element(x,intersection(x,complement(intersection(complement(x),complement(y))))),complement(intersection(complement(x),complement(y))))
| ~ member(not_subclass_element(x,intersection(x,complement(intersection(complement(x),complement(y))))),x)
| spl1_2 ),
inference(resolution,[],[f23,f226]) ).
fof(f235,definition,
( spl1_3
<=> member(not_subclass_element(x,intersection(x,complement(intersection(complement(x),complement(y))))),x) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
fof(f236,plain,
( ~ member(not_subclass_element(x,intersection(x,complement(intersection(complement(x),complement(y))))),x)
| spl1_3 ),
inference(avatar_component_clause,[],[f235]) ).
fof(f238,definition,
( spl1_4
<=> member(not_subclass_element(x,intersection(x,complement(intersection(complement(x),complement(y))))),complement(intersection(complement(x),complement(y)))) ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
fof(f239,plain,
( ~ member(not_subclass_element(x,intersection(x,complement(intersection(complement(x),complement(y))))),complement(intersection(complement(x),complement(y))))
| spl1_4 ),
inference(avatar_component_clause,[],[f238]) ).
fof(f240,plain,
( ~ spl1_3
| ~ spl1_4
| spl1_2 ),
inference(avatar_split_clause,[],[f233,f216,f238,f235]) ).
fof(f241,plain,
( $false
| spl1_2
| spl1_3 ),
inference(resolution,[],[f236,f227]) ).
fof(f242,plain,
( spl1_2
| spl1_3 ),
inference(avatar_contradiction_clause,[],[f241]) ).
fof(f243,plain,
( ~ member(not_subclass_element(x,intersection(x,complement(intersection(complement(x),complement(y))))),universal_class)
| member(not_subclass_element(x,intersection(x,complement(intersection(complement(x),complement(y))))),intersection(complement(x),complement(y)))
| spl1_4 ),
inference(resolution,[],[f239,f25]) ).
fof(f245,definition,
( spl1_5
<=> member(not_subclass_element(x,intersection(x,complement(intersection(complement(x),complement(y))))),intersection(complement(x),complement(y))) ),
introduced(definition,[new_symbols(definition,[spl1_5])],[avatar_definition]) ).
fof(f246,plain,
( member(not_subclass_element(x,intersection(x,complement(intersection(complement(x),complement(y))))),intersection(complement(x),complement(y)))
| ~ spl1_5 ),
inference(avatar_component_clause,[],[f245]) ).
fof(f248,definition,
( spl1_6
<=> member(not_subclass_element(x,intersection(x,complement(intersection(complement(x),complement(y))))),universal_class) ),
introduced(definition,[new_symbols(definition,[spl1_6])],[avatar_definition]) ).
fof(f249,plain,
( ~ member(not_subclass_element(x,intersection(x,complement(intersection(complement(x),complement(y))))),universal_class)
| spl1_6 ),
inference(avatar_component_clause,[],[f248]) ).
fof(f250,plain,
( spl1_5
| ~ spl1_6
| spl1_4 ),
inference(avatar_split_clause,[],[f243,f238,f248,f245]) ).
fof(f251,plain,
( ! [X0] : ~ member(not_subclass_element(x,intersection(x,complement(intersection(complement(x),complement(y))))),X0)
| spl1_6 ),
inference(resolution,[],[f249,f203]) ).
fof(f252,plain,
( $false
| spl1_2
| spl1_6 ),
inference(resolution,[],[f251,f227]) ).
fof(f260,plain,
( spl1_2
| spl1_6 ),
inference(avatar_contradiction_clause,[],[f252]) ).
fof(f262,plain,
( member(not_subclass_element(x,intersection(x,complement(intersection(complement(x),complement(y))))),complement(x))
| ~ spl1_5 ),
inference(resolution,[],[f246,f21]) ).
fof(f264,plain,
( ~ member(not_subclass_element(x,intersection(x,complement(intersection(complement(x),complement(y))))),x)
| ~ spl1_5 ),
inference(resolution,[],[f262,f24]) ).
fof(f265,plain,
( ~ spl1_3
| ~ spl1_5 ),
inference(avatar_split_clause,[],[f264,f245,f235]) ).
cnf(s2,plain,
( ~ spl1_1
| ~ spl1_2 ),
inference(sat_conversion,[],[f219]) ).
cnf(s3,plain,
spl1_1,
inference(sat_conversion,[],[f225]) ).
cnf(s4,plain,
( spl1_2
| ~ spl1_3
| ~ spl1_4 ),
inference(sat_conversion,[],[f240]) ).
cnf(s5,plain,
( spl1_2
| spl1_3 ),
inference(sat_conversion,[],[f242]) ).
cnf(s6,plain,
( spl1_4
| spl1_5
| ~ spl1_6 ),
inference(sat_conversion,[],[f250]) ).
cnf(s7,plain,
( spl1_2
| spl1_6 ),
inference(sat_conversion,[],[f260]) ).
cnf(s8,plain,
( ~ spl1_3
| ~ spl1_5 ),
inference(sat_conversion,[],[f265]) ).
cnf(s9,plain,
~ spl1_2,
inference(rat,[],[s2,s3]) ).
cnf(s10,plain,
spl1_6,
inference(rat,[],[s7,s9]) ).
cnf(s11,plain,
spl1_3,
inference(rat,[],[s5,s9]) ).
cnf(s12,plain,
~ spl1_5,
inference(rat,[],[s8,s11]) ).
cnf(s13,plain,
~ spl1_4,
inference(rat,[],[s4,s9,s11]) ).
cnf(s14,plain,
$false,
inference(rat,[],[s6,s10,s12,s13]) ).
fof(f266,plain,
$false,
inference(avatar_sat_refutation,[],[s14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET173-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 % Computer : n014.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8046.5625MB
% 0.12/0.40 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Mon Sep 28 01:00:31 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 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
% 0.62/0.94 % (1333105)Input is clausal, will run a generic CNF schedule.
% 0.62/0.94 % (1333150)dis-21_1_sil=8000:lcm=predicate:random_seed=3684571159: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)
% 0.62/0.94 % (1333150)First to succeed.
% 0.62/0.94 % (1333150)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1333105"
% 0.62/0.94 % (1333146)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3129618324:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.62/0.94 % (1333149)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2338601943:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.62/0.94 % (1333145)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=4104260788:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.62/0.94 % (1333144)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=2867472303:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.62/0.94 % (1333147)lrs+10_1_sil=8000:sp=occurrence:random_seed=1084942180:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.62/0.94 % (1333148)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2204838456:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.62/0.94 % (1333147)Refutation not found, incomplete strategy
% 0.62/0.94 % (1333147)------------------------------
% 0.62/0.94 % (1333147)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.62/0.94 % (1333147)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.62/0.94 % (1333147)CaDiCaL version: 2.1.3
% 0.62/0.94 % (1333147)Termination reason: Refutation not found, incomplete strategy
% 0.62/0.94 % (1333147)Time elapsed: 0.005 s
% 0.62/0.94 % (1333147)Peak memory usage: 88 MB
% 0.62/0.94 % (1333147)Instructions burned: 4 (million)
% 0.62/0.94 % (1333148)Instruction limit reached!
% 0.62/0.94 % (1333148)------------------------------
% 0.62/0.94 % (1333148)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.62/0.94 % (1333148)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.62/0.94 % (1333148)CaDiCaL version: 2.1.3
% 0.62/0.94 % (1333148)Termination reason: Instruction limit
% 0.62/0.94 % (1333148)Termination phase: Saturation
% 0.62/0.94 % (1333148)Time elapsed: 0.072 s
% 0.62/0.94 % (1333148)Peak memory usage: 89 MB
% 0.62/0.94 % (1333148)Instructions burned: 115 (million)
% 0.62/0.94 % (1333150)Refutation found. Thanks to Tanya!
% 0.62/0.94 % SZS status Unsatisfiable for theBenchmark
% 0.62/0.94 % SZS output start Proof for theBenchmark
% See solution above
% 2.38/1.04 % (1333150)------------------------------
% 2.38/1.04 % (1333150)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.38/1.04 % (1333150)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.38/1.04 % (1333150)CaDiCaL version: 2.1.3
% 2.38/1.04 % (1333150)Termination reason: Refutation
% 2.38/1.04 % (1333150)Time elapsed: 0.004 s
% 2.38/1.04 % (1333150)Peak memory usage: 89 MB
% 2.38/1.04 % (1333150)Instructions burned: 8 (million)
% 2.38/1.04 % (1333150)------------------------------
% 2.38/1.04 % (1333150)------------------------------
% 2.38/1.04 % (1333105)Success in time 0.285 s
% 2.38/1.04 % Vampire exiting
%------------------------------------------------------------------------------