%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET134-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n019.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 12:43:14 PM UTC 2026
% Result : Unsatisfiable 0.48s 0.47s
% Output : Refutation 0.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 18
% Syntax : Number of formulae : 57 ( 18 unt; 2 def)
% Number of atoms : 109 ( 16 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 99 ( 47 ~; 50 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-2 aty)
% Number of variables : 43 ( 0 sgn 43 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( ~ member(X2,X0)
| ~ subclass(X0,X1)
| member(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',subclass_members) ).
fof(f2,axiom,
! [X0,X1] :
( member(not_subclass_element(X0,X1),X0)
| subclass(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',not_subclass_members1) ).
fof(f3,axiom,
! [X0,X1] :
( ~ member(not_subclass_element(X0,X1),X1)
| subclass(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',not_subclass_members2) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).
fof(f5,axiom,
! [X0,X1] :
( X0 != X1
| subclass(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',equal_implies_subclass1) ).
fof(f9,axiom,
! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pair2) ).
fof(f10,axiom,
! [X0,X1] :
( member(X0,unordered_pair(X1,X0))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pair3) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',singleton_set) ).
fof(f21,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection1) ).
fof(f24,axiom,
! [X0,X1] :
( ~ member(X0,complement(X1))
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement1) ).
fof(f25,axiom,
! [X0,X1] :
( member(X0,complement(X1))
| ~ member(X0,universal_class)
| member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement2) ).
fof(f26,axiom,
! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',union) ).
fof(f69,axiom,
! [X0] :
( X0 = null_class
| intersection(X0,regular(X0)) = null_class ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',regularity2) ).
fof(f70,plain,
! [X0] :
( null_class = intersection(X0,regular(X0))
| null_class = X0 ),
inference(reorient_equations,[],[f69]) ).
fof(f101,axiom,
! [X0,X1] : union(singleton(X0),X1) = set_builder(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_of_set_builder) ).
fof(f102,negated_conjecture,
member(u,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_2_to_member_of_triple_1) ).
fof(f103,negated_conjecture,
set_builder(u,set_builder(y,set_builder(z,null_class))) = null_class,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_2_to_member_of_triple_2) ).
fof(f104,plain,
null_class = set_builder(u,set_builder(y,set_builder(z,null_class))),
inference(reorient_equations,[],[f103]) ).
fof(f110,plain,
! [X0,X1] : set_builder(X0,X1) = complement(intersection(complement(unordered_pair(X0,X0)),complement(X1))),
inference(definition_unfolding,[],[f101,f26,f12]) ).
fof(f154,plain,
null_class = complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(y,y)),complement(complement(intersection(complement(unordered_pair(z,z)),complement(null_class))))))))),
inference(definition_unfolding,[],[f104,f110,f110,f110]) ).
fof(f155,plain,
! [X1] : subclass(X1,X1),
inference(equality_resolution,[],[f5]) ).
fof(f202,plain,
! [X0] :
( ~ subclass(universal_class,X0)
| member(u,X0) ),
inference(resolution,[],[f1,f102]) ).
fof(f252,plain,
! [X0,X1] :
( ~ member(X0,null_class)
| member(X0,X1)
| null_class = X1 ),
inference(superposition,[],[f21,f70]) ).
fof(f282,plain,
! [X0] :
( member(X0,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(y,y)),complement(complement(intersection(complement(unordered_pair(z,z)),complement(null_class)))))))))
| ~ member(X0,universal_class)
| member(X0,null_class) ),
inference(superposition,[],[f25,f154]) ).
fof(f285,plain,
! [X0] :
( member(X0,complement(unordered_pair(u,u)))
| member(X0,null_class)
| ~ member(X0,universal_class) ),
inference(resolution,[],[f282,f21]) ).
fof(f331,plain,
! [X0] :
( ~ member(X0,unordered_pair(u,u))
| ~ member(X0,universal_class)
| member(X0,null_class) ),
inference(resolution,[],[f285,f24]) ).
fof(f333,plain,
! [X0] :
( ~ member(not_subclass_element(X0,complement(unordered_pair(u,u))),universal_class)
| member(not_subclass_element(X0,complement(unordered_pair(u,u))),null_class)
| subclass(X0,complement(unordered_pair(u,u))) ),
inference(resolution,[],[f285,f3]) ).
fof(f337,plain,
( ~ member(u,universal_class)
| member(u,null_class)
| ~ member(u,universal_class) ),
inference(resolution,[],[f331,f10]) ).
fof(f341,plain,
( ~ member(u,universal_class)
| member(u,null_class) ),
inference(duplicate_literal_removal,[],[f337]) ).
fof(f356,plain,
member(u,null_class),
inference(forward_subsumption_resolution,[],[f341,f102]) ).
fof(f385,plain,
( member(not_subclass_element(universal_class,complement(unordered_pair(u,u))),null_class)
| subclass(universal_class,complement(unordered_pair(u,u)))
| subclass(universal_class,complement(unordered_pair(u,u))) ),
inference(resolution,[],[f333,f2]) ).
fof(f386,plain,
( member(not_subclass_element(universal_class,complement(unordered_pair(u,u))),null_class)
| subclass(universal_class,complement(unordered_pair(u,u))) ),
inference(duplicate_literal_removal,[],[f385]) ).
fof(f388,definition,
( spl0_27
<=> subclass(universal_class,complement(unordered_pair(u,u))) ),
introduced(definition,[new_symbols(definition,[spl0_27])],[avatar_definition]) ).
fof(f390,plain,
( subclass(universal_class,complement(unordered_pair(u,u)))
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f388]) ).
fof(f392,definition,
( spl0_28
<=> member(not_subclass_element(universal_class,complement(unordered_pair(u,u))),null_class) ),
introduced(definition,[new_symbols(definition,[spl0_28])],[avatar_definition]) ).
fof(f394,plain,
( member(not_subclass_element(universal_class,complement(unordered_pair(u,u))),null_class)
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f392]) ).
fof(f395,plain,
( spl0_27
| spl0_28 ),
inference(avatar_split_clause,[],[f386,f392,f388]) ).
fof(f396,plain,
( member(u,complement(unordered_pair(u,u)))
| ~ spl0_27 ),
inference(resolution,[],[f390,f202]) ).
fof(f401,plain,
( ~ member(u,unordered_pair(u,u))
| ~ spl0_27 ),
inference(resolution,[],[f396,f24]) ).
fof(f405,plain,
( ~ member(u,universal_class)
| ~ spl0_27 ),
inference(resolution,[],[f401,f9]) ).
fof(f409,plain,
( $false
| ~ spl0_27 ),
inference(forward_subsumption_resolution,[],[f405,f102]) ).
fof(f410,plain,
~ spl0_27,
inference(avatar_contradiction_clause,[],[f409]) ).
fof(f438,plain,
( ! [X0] :
( member(not_subclass_element(universal_class,complement(unordered_pair(u,u))),X0)
| ~ subclass(null_class,X0) )
| ~ spl0_28 ),
inference(resolution,[],[f394,f1]) ).
fof(f450,plain,
( ! [X0] :
( ~ member(not_subclass_element(universal_class,complement(unordered_pair(u,u))),X0)
| ~ subclass(null_class,complement(X0)) )
| ~ spl0_28 ),
inference(resolution,[],[f438,f24]) ).
fof(f472,plain,
( ! [X0] :
( ~ subclass(null_class,complement(X0))
| ~ subclass(null_class,X0) )
| ~ spl0_28 ),
inference(resolution,[],[f450,f438]) ).
fof(f937,plain,
! [X0] :
( member(u,X0)
| null_class = X0 ),
inference(resolution,[],[f252,f356]) ).
fof(f1189,plain,
! [X0] :
( ~ member(u,X0)
| complement(X0) = null_class ),
inference(resolution,[],[f937,f24]) ).
fof(f1230,plain,
null_class = complement(universal_class),
inference(resolution,[],[f1189,f102]) ).
fof(f1300,plain,
( ~ subclass(null_class,null_class)
| ~ subclass(null_class,universal_class)
| ~ spl0_28 ),
inference(superposition,[],[f472,f1230]) ).
fof(f1305,plain,
( ~ subclass(null_class,universal_class)
| ~ spl0_28 ),
inference(forward_subsumption_resolution,[],[f1300,f155]) ).
fof(f1324,plain,
( $false
| ~ spl0_28 ),
inference(forward_subsumption_resolution,[],[f1305,f4]) ).
fof(f1325,plain,
~ spl0_28,
inference(avatar_contradiction_clause,[],[f1324]) ).
cnf(s16,plain,
( spl0_27
| spl0_28 ),
inference(sat_conversion,[],[f395]) ).
cnf(s18,plain,
~ spl0_27,
inference(sat_conversion,[],[f410]) ).
cnf(s101,plain,
~ spl0_28,
inference(sat_conversion,[],[f1325]) ).
cnf(s104,plain,
$false,
inference(rat,[],[s16,s101,s18]) ).
fof(f1326,plain,
$false,
inference(avatar_sat_refutation,[],[s104]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET134-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.35 % Computer : n019.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Mon Sep 28 00:52:19 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.38 Running first-order model finding
% 0.13/0.38 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.48/0.47 % (3561757)Will run a generic schedule for satisfiability detection.
% 0.48/0.47 % (3561767)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3448240434:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.48/0.47 % (3561763)% WARNING: option uhcvi not known.
% 0.48/0.47 % (3561762)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3207764014_2999 on theBenchmark for (2999ds/0Mi)
% 0.48/0.47 % (3561763)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3334836491:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.48/0.47 % (3561764)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1802933639:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.48/0.47 % (3561765)dis+10_1_sil=32000:sp=arity:random_seed=4165058146:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.48/0.47 % (3561766)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2943595076:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.48/0.47 % (3561768)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4269553588:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.48/0.47 % (3561765) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3561757-3561765"...
% 0.48/0.47 % (3561765)...printing done.
% 0.48/0.47 % (3561767)Instruction limit reached!
% 0.48/0.47 % (3561767)------------------------------
% 0.48/0.47 % (3561767)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.47 % (3561767)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.47 % (3561767)CaDiCaL version: 2.1.3
% 0.48/0.47 % (3561767)Termination reason: Instruction limit
% 0.48/0.47 % (3561767)Termination phase: Saturation
% 0.48/0.47 % (3561767)Time elapsed: 0.044 s
% 0.48/0.47 % (3561767)Peak memory usage: 13 MB
% 0.48/0.47 % (3561767)Instructions burned: 132 (million)
% 0.48/0.47 % (3561765)Refutation found. Thanks to Tanya!
% 0.48/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.48/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.48/0.47 % (3561765)------------------------------
% 0.48/0.47 % (3561765)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.47 % (3561765)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.47 % (3561765)CaDiCaL version: 2.1.3
% 0.48/0.47 % (3561765)Termination reason: Refutation
% 0.48/0.47 % (3561765)Time elapsed: 0.036 s
% 0.48/0.47 % (3561765)Peak memory usage: 13 MB
% 0.48/0.47 % (3561765)Instructions burned: 52 (million)
% 0.48/0.47 % (3561757)Success in time 0.071 s
% 0.48/0.47 % Vampire exiting
%------------------------------------------------------------------------------