%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET133-6 : 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 : n011.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 12:43:13 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.45s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 25
% Syntax : Number of formulae : 102 ( 28 unt; 7 def)
% Number of atoms : 199 ( 31 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 158 ( 61 ~; 90 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 12 ( 4 avg)
% Number of predicates : 11 ( 9 usr; 8 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-2 aty)
% Number of variables : 41 ( 0 sgn 41 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( ~ subclass(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',subclass_members) ).
fof(f2,axiom,
! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',not_subclass_members1) ).
fof(f3,axiom,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),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(f8,axiom,
! [X2,X0,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X1
| X0 = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pair_member) ).
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(f23,axiom,
! [X2,X0,X1] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection3) ).
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(f67,axiom,
! [X0] :
( X0 = null_class
| member(regular(X0),X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',regularity1) ).
fof(f68,plain,
! [X0] :
( member(regular(X0),X0)
| null_class = X0 ),
inference(reorient_equations,[],[f67]) ).
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,x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_1_to_member_of_triple_1) ).
fof(f103,negated_conjecture,
member(v,x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_1_to_member_of_triple_2) ).
fof(f104,negated_conjecture,
member(w,x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_1_to_member_of_triple_3) ).
fof(f105,negated_conjecture,
~ subclass(set_builder(u,set_builder(v,set_builder(w,null_class))),x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_1_to_member_of_triple_4) ).
fof(f111,plain,
! [X0,X1] : set_builder(X0,X1) = complement(intersection(complement(unordered_pair(X0,X0)),complement(X1))),
inference(definition_unfolding,[],[f101,f26,f12]) ).
fof(f155,plain,
~ subclass(complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),x),
inference(definition_unfolding,[],[f105,f111,f111,f111]) ).
fof(f162,plain,
! [X0] :
( ~ member(regular(complement(X0)),X0)
| complement(X0) = null_class ),
inference(resolution,[],[f68,f24]) ).
fof(f163,plain,
member(not_subclass_element(complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),x),complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))),
inference(resolution,[],[f2,f155]) ).
fof(f164,plain,
~ member(not_subclass_element(complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),x),x),
inference(resolution,[],[f3,f155]) ).
fof(f165,plain,
~ member(not_subclass_element(complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),x),intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),
inference(resolution,[],[f163,f24]) ).
fof(f168,plain,
! [X0,X1] :
( ~ member(X0,X1)
| member(X0,universal_class) ),
inference(resolution,[],[f1,f4]) ).
fof(f178,plain,
! [X0] :
( member(regular(X0),universal_class)
| null_class = X0 ),
inference(resolution,[],[f168,f68]) ).
fof(f181,plain,
member(not_subclass_element(complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),x),universal_class),
inference(resolution,[],[f168,f163]) ).
fof(f201,plain,
! [X0,X1] :
( ~ member(X0,null_class)
| member(X0,X1)
| null_class = X1 ),
inference(superposition,[],[f21,f70]) ).
fof(f212,plain,
( ~ member(not_subclass_element(complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),x),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))
| ~ member(not_subclass_element(complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),x),complement(unordered_pair(u,u))) ),
inference(resolution,[],[f23,f165]) ).
fof(f216,definition,
( spl0_1
<=> member(not_subclass_element(complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),x),complement(unordered_pair(u,u))) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f218,plain,
( ~ member(not_subclass_element(complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),x),complement(unordered_pair(u,u)))
| spl0_1 ),
inference(avatar_component_clause,[],[f216]) ).
fof(f220,definition,
( spl0_2
<=> member(not_subclass_element(complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),x),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f222,plain,
( ~ member(not_subclass_element(complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),x),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))
| spl0_2 ),
inference(avatar_component_clause,[],[f220]) ).
fof(f223,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f212,f220,f216]) ).
fof(f224,plain,
( ~ member(not_subclass_element(complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),x),universal_class)
| member(not_subclass_element(complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),x),unordered_pair(u,u))
| spl0_1 ),
inference(resolution,[],[f218,f25]) ).
fof(f225,plain,
( member(not_subclass_element(complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),x),unordered_pair(u,u))
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f224,f181]) ).
fof(f232,plain,
( u = not_subclass_element(complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),x)
| u = not_subclass_element(complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),x)
| spl0_1 ),
inference(resolution,[],[f225,f8]) ).
fof(f234,plain,
( u = not_subclass_element(complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),x)
| spl0_1 ),
inference(duplicate_literal_removal,[],[f232]) ).
fof(f236,plain,
( ~ member(u,x)
| spl0_1 ),
inference(superposition,[],[f164,f234]) ).
fof(f241,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f236,f102]) ).
fof(f242,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f241]) ).
fof(f247,plain,
( ~ member(not_subclass_element(complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),x),universal_class)
| member(not_subclass_element(complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),x),complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))
| spl0_2 ),
inference(resolution,[],[f222,f25]) ).
fof(f248,plain,
( member(not_subclass_element(complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),x),complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f247,f181]) ).
fof(f250,plain,
( ~ member(not_subclass_element(complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),x),intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))
| spl0_2 ),
inference(resolution,[],[f248,f24]) ).
fof(f252,plain,
( ~ member(not_subclass_element(complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),x),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))
| ~ member(not_subclass_element(complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),x),complement(unordered_pair(v,v)))
| spl0_2 ),
inference(resolution,[],[f250,f23]) ).
fof(f254,definition,
( spl0_3
<=> member(not_subclass_element(complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),x),complement(unordered_pair(v,v))) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f256,plain,
( ~ member(not_subclass_element(complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),x),complement(unordered_pair(v,v)))
| spl0_3 ),
inference(avatar_component_clause,[],[f254]) ).
fof(f258,definition,
( spl0_4
<=> member(not_subclass_element(complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),x),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f260,plain,
( ~ member(not_subclass_element(complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),x),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))
| spl0_4 ),
inference(avatar_component_clause,[],[f258]) ).
fof(f261,plain,
( ~ spl0_3
| ~ spl0_4
| spl0_2 ),
inference(avatar_split_clause,[],[f252,f220,f258,f254]) ).
fof(f262,plain,
( ~ member(not_subclass_element(complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),x),universal_class)
| member(not_subclass_element(complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),x),unordered_pair(v,v))
| spl0_3 ),
inference(resolution,[],[f256,f25]) ).
fof(f263,plain,
( member(not_subclass_element(complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),x),unordered_pair(v,v))
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f262,f181]) ).
fof(f266,plain,
( v = not_subclass_element(complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),x)
| v = not_subclass_element(complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),x)
| spl0_3 ),
inference(resolution,[],[f263,f8]) ).
fof(f268,plain,
( v = not_subclass_element(complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),x)
| spl0_3 ),
inference(duplicate_literal_removal,[],[f266]) ).
fof(f272,plain,
( ~ member(v,x)
| spl0_3 ),
inference(superposition,[],[f164,f268]) ).
fof(f282,plain,
( $false
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f272,f103]) ).
fof(f283,plain,
spl0_3,
inference(avatar_contradiction_clause,[],[f282]) ).
fof(f291,plain,
( ~ member(not_subclass_element(complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),x),universal_class)
| member(not_subclass_element(complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),x),complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))
| spl0_4 ),
inference(resolution,[],[f260,f25]) ).
fof(f292,plain,
( member(not_subclass_element(complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),x),complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))
| spl0_4 ),
inference(forward_subsumption_resolution,[],[f291,f181]) ).
fof(f296,plain,
( ~ member(not_subclass_element(complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),x),intersection(complement(unordered_pair(w,w)),complement(null_class)))
| spl0_4 ),
inference(resolution,[],[f292,f24]) ).
fof(f302,plain,
( ~ member(not_subclass_element(complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),x),complement(null_class))
| ~ member(not_subclass_element(complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),x),complement(unordered_pair(w,w)))
| spl0_4 ),
inference(resolution,[],[f296,f23]) ).
fof(f304,definition,
( spl0_5
<=> member(not_subclass_element(complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),x),complement(unordered_pair(w,w))) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f306,plain,
( ~ member(not_subclass_element(complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),x),complement(unordered_pair(w,w)))
| spl0_5 ),
inference(avatar_component_clause,[],[f304]) ).
fof(f308,definition,
( spl0_6
<=> member(not_subclass_element(complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),x),complement(null_class)) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f310,plain,
( ~ member(not_subclass_element(complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),x),complement(null_class))
| spl0_6 ),
inference(avatar_component_clause,[],[f308]) ).
fof(f311,plain,
( ~ spl0_5
| ~ spl0_6
| spl0_4 ),
inference(avatar_split_clause,[],[f302,f258,f308,f304]) ).
fof(f314,plain,
( ~ member(not_subclass_element(complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),x),universal_class)
| member(not_subclass_element(complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),x),unordered_pair(w,w))
| spl0_5 ),
inference(resolution,[],[f306,f25]) ).
fof(f315,plain,
( member(not_subclass_element(complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),x),unordered_pair(w,w))
| spl0_5 ),
inference(forward_subsumption_resolution,[],[f314,f181]) ).
fof(f316,plain,
( w = not_subclass_element(complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),x)
| w = not_subclass_element(complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),x)
| spl0_5 ),
inference(resolution,[],[f315,f8]) ).
fof(f318,plain,
( w = not_subclass_element(complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),x)
| spl0_5 ),
inference(duplicate_literal_removal,[],[f316]) ).
fof(f320,plain,
( ~ member(w,x)
| spl0_5 ),
inference(superposition,[],[f164,f318]) ).
fof(f335,plain,
( $false
| spl0_5 ),
inference(forward_subsumption_resolution,[],[f320,f104]) ).
fof(f336,plain,
spl0_5,
inference(avatar_contradiction_clause,[],[f335]) ).
fof(f337,plain,
( ~ member(not_subclass_element(complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),x),universal_class)
| member(not_subclass_element(complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),x),null_class)
| spl0_6 ),
inference(resolution,[],[f310,f25]) ).
fof(f338,plain,
( member(not_subclass_element(complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),x),null_class)
| spl0_6 ),
inference(forward_subsumption_resolution,[],[f337,f181]) ).
fof(f532,plain,
( null_class = complement(universal_class)
| null_class = complement(universal_class) ),
inference(resolution,[],[f162,f178]) ).
fof(f542,plain,
null_class = complement(universal_class),
inference(duplicate_literal_removal,[],[f532]) ).
fof(f582,definition,
( spl0_22
<=> null_class = complement(universal_class) ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
fof(f584,plain,
( null_class = complement(universal_class)
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f582]) ).
fof(f586,plain,
spl0_22,
inference(avatar_split_clause,[],[f542,f582]) ).
fof(f590,plain,
( ! [X0] :
( ~ member(X0,null_class)
| ~ member(X0,universal_class) )
| ~ spl0_22 ),
inference(superposition,[],[f24,f584]) ).
fof(f591,plain,
( ! [X0] : ~ member(X0,null_class)
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f590,f168]) ).
fof(f610,plain,
( ! [X0] :
( member(not_subclass_element(complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),x),X0)
| null_class = X0 )
| spl0_6 ),
inference(resolution,[],[f201,f338]) ).
fof(f659,plain,
( null_class = x
| spl0_6 ),
inference(resolution,[],[f610,f164]) ).
fof(f728,plain,
( member(u,null_class)
| spl0_6 ),
inference(superposition,[],[f102,f659]) ).
fof(f775,plain,
( $false
| spl0_6
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f728,f591]) ).
fof(f776,plain,
( spl0_6
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f775]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f223]) ).
cnf(s2,plain,
spl0_1,
inference(sat_conversion,[],[f242]) ).
cnf(s3,plain,
( spl0_2
| ~ spl0_3
| ~ spl0_4 ),
inference(sat_conversion,[],[f261]) ).
cnf(s4,plain,
spl0_3,
inference(sat_conversion,[],[f283]) ).
cnf(s5,plain,
( spl0_4
| ~ spl0_5
| ~ spl0_6 ),
inference(sat_conversion,[],[f311]) ).
cnf(s6,plain,
spl0_5,
inference(sat_conversion,[],[f336]) ).
cnf(s18,plain,
spl0_22,
inference(sat_conversion,[],[f586]) ).
cnf(s27,plain,
( spl0_6
| ~ spl0_22 ),
inference(sat_conversion,[],[f776]) ).
cnf(s35,plain,
spl0_6,
inference(rat,[],[s27,s18]) ).
cnf(s36,plain,
spl0_4,
inference(rat,[],[s5,s35,s6]) ).
cnf(s37,plain,
spl0_2,
inference(rat,[],[s3,s36,s4]) ).
cnf(s38,plain,
$false,
inference(rat,[],[s1,s37,s2]) ).
fof(f872,plain,
$false,
inference(avatar_sat_refutation,[],[s38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET133-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.36 % Computer : n011.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 28 00:51:46 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.40 Running first-order model finding
% 0.10/0.40 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
% 0.10/0.45 % (2919858)Will run a generic schedule for satisfiability detection.
% 0.10/0.45 % (2919867)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4147208207:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.10/0.45 % (2919863)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=360478978_2999 on theBenchmark for (2999ds/0Mi)
% 0.10/0.45 % (2919868)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1963559946:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.10/0.45 % (2919865)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4255069458:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.10/0.45 % (2919866)dis+10_1_sil=32000:sp=arity:random_seed=379819282:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.10/0.45 % (2919869)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3536213132:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.10/0.45 % (2919864)% WARNING: option uhcvi not known.
% 0.10/0.45 % (2919864)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1319388725:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.10/0.45 % (2919867) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2919858-2919867"...
% 0.10/0.45 % (2919867)...printing done.
% 0.10/0.45 % (2919867)Refutation found. Thanks to Tanya!
% 0.10/0.45 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.45 % (2919867)------------------------------
% 0.10/0.45 % (2919867)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.45 % (2919867)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.45 % (2919867)CaDiCaL version: 2.1.3
% 0.10/0.45 % (2919867)Termination reason: Refutation
% 0.10/0.45 % (2919867)Time elapsed: 0.019 s
% 0.10/0.45 % (2919867)Peak memory usage: 13 MB
% 0.10/0.45 % (2919867)Instructions burned: 58 (million)
% 0.10/0.45 % (2919858)Success in time 0.047 s
% 0.10/0.45 % Vampire exiting
%------------------------------------------------------------------------------