%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV566+1 : TPTP v9.3.1. Released v9.1.0.
% 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 12:58:21 PM UTC 2026
% Result : Theorem 4.04s 1.60s
% Output : Refutation 5.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 14
% Syntax : Number of formulae : 107 ( 29 unt; 5 def)
% Number of atoms : 241 ( 16 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 235 ( 101 ~; 105 |; 17 &)
% ( 11 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 6 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 1 con; 0-2 aty)
% Number of variables : 120 ( 0 sgn 118 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subq(X0,X1)
<=> ! [X2] :
( mem(X2,X0)
=> mem(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subq_def) ).
fof(f4,axiom,
! [X0] : ~ mem(X0,e),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_ax) ).
fof(f5,axiom,
! [X0,X1] :
( mem(X0,s(X1))
<=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s_ax) ).
fof(f6,axiom,
! [X0,X1,X2] :
( mem(X0,u(X1,X2))
<=> ( mem(X0,X1)
| mem(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_ax) ).
fof(f7,axiom,
! [X0,X1,X2] :
( mem(X0,m(X1,X2))
<=> ( mem(X0,X1)
& ~ mem(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_ax) ).
fof(f8,axiom,
! [X0,X1] : a(X0,X1) = u(X0,s(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_def) ).
fof(f9,axiom,
! [X0] : n(X0) = a(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n_def) ).
fof(f10,axiom,
! [X0,X1] :
( mem(X0,p(X1))
<=> subq(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p_ax) ).
fof(f26,conjecture,
~ subq(u(m(p(u(n(e),n(s(n(e))))),n(p(s(n(e))))),s(a(s(n(e)),n(n(e))))),u(m(p(u(n(e),n(s(n(e))))),u(s(n(e)),n(p(s(n(e)))))),s(a(s(n(e)),n(n(e)))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nsubq_1242_1240) ).
fof(f27,negated_conjecture,
~ ~ subq(u(m(p(u(n(e),n(s(n(e))))),n(p(s(n(e))))),s(a(s(n(e)),n(n(e))))),u(m(p(u(n(e),n(s(n(e))))),u(s(n(e)),n(p(s(n(e)))))),s(a(s(n(e)),n(n(e)))))),
inference(negated_conjecture,[status(cth)],[f26]) ).
fof(f28,plain,
subq(u(m(p(u(n(e),n(s(n(e))))),n(p(s(n(e))))),s(a(s(n(e)),n(n(e))))),u(m(p(u(n(e),n(s(n(e))))),u(s(n(e)),n(p(s(n(e)))))),s(a(s(n(e)),n(n(e)))))),
inference(flattening,[],[f27]) ).
fof(f29,plain,
! [X0,X1] :
( subq(X0,X1)
<=> ! [X2] :
( mem(X2,X1)
| ~ mem(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f32,plain,
! [X0,X1] :
( ( mem(X0,s(X1))
| X0 != X1 )
& ( X0 = X1
| ~ mem(X0,s(X1)) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f33,plain,
! [X0,X1,X2] :
( ( mem(X0,u(X1,X2))
| ( ~ mem(X0,X1)
& ~ mem(X0,X2) ) )
& ( mem(X0,X1)
| mem(X0,X2)
| ~ mem(X0,u(X1,X2)) ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f34,plain,
! [X0,X1,X2] :
( ( mem(X0,u(X1,X2))
| ( ~ mem(X0,X1)
& ~ mem(X0,X2) ) )
& ( mem(X0,X1)
| mem(X0,X2)
| ~ mem(X0,u(X1,X2)) ) ),
inference(flattening,[],[f33]) ).
fof(f35,plain,
! [X0,X1,X2] :
( ( mem(X0,m(X1,X2))
| ~ mem(X0,X1)
| mem(X0,X2) )
& ( ( mem(X0,X1)
& ~ mem(X0,X2) )
| ~ mem(X0,m(X1,X2)) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f36,plain,
! [X0,X1,X2] :
( ( mem(X0,m(X1,X2))
| ~ mem(X0,X1)
| mem(X0,X2) )
& ( ( mem(X0,X1)
& ~ mem(X0,X2) )
| ~ mem(X0,m(X1,X2)) ) ),
inference(flattening,[],[f35]) ).
fof(f37,plain,
! [X0,X1] :
( ( mem(X0,p(X1))
| ~ subq(X0,X1) )
& ( subq(X0,X1)
| ~ mem(X0,p(X1)) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f38,plain,
! [X0,X1] :
( ( subq(X0,X1)
| ? [X2] :
( ~ mem(X2,X1)
& mem(X2,X0) ) )
& ( ! [X2] :
( mem(X2,X1)
| ~ mem(X2,X0) )
| ~ subq(X0,X1) ) ),
inference(nnf_transformation,[],[f29]) ).
fof(f39,plain,
! [X0,X1] :
( ( subq(X0,X1)
| ? [X2] :
( ~ mem(X2,X1)
& mem(X2,X0) ) )
& ( ! [X3] :
( mem(X3,X1)
| ~ mem(X3,X0) )
| ~ subq(X0,X1) ) ),
inference(rectify,[],[f38]) ).
fof(f40,plain,
! [X0,X1] :
( ( subq(X0,X1)
| ( ~ mem(sK0(X0,X1),X1)
& mem(sK0(X0,X1),X0) ) )
& ( ! [X3] :
( mem(X3,X1)
| ~ mem(X3,X0) )
| ~ subq(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f39]) ).
fof(f41,plain,
subq(u(m(p(u(n(e),n(s(n(e))))),n(p(s(n(e))))),s(a(s(n(e)),n(n(e))))),u(m(p(u(n(e),n(s(n(e))))),u(s(n(e)),n(p(s(n(e)))))),s(a(s(n(e)),n(n(e)))))),
inference(cnf_transformation,[],[f28]) ).
fof(f42,plain,
! [X0] : ~ mem(X0,e),
inference(cnf_transformation,[],[f4]) ).
fof(f43,plain,
! [X0,X1] : a(X0,X1) = u(X0,s(X1)),
inference(cnf_transformation,[],[f8]) ).
fof(f44,plain,
! [X0,X1] :
( ~ mem(X0,s(X1))
| X0 = X1 ),
inference(cnf_transformation,[],[f32]) ).
fof(f45,plain,
! [X0,X1] :
( mem(X0,s(X1))
| X0 != X1 ),
inference(cnf_transformation,[],[f32]) ).
fof(f46,plain,
! [X2,X0,X1] :
( ~ mem(X0,u(X1,X2))
| mem(X0,X2)
| mem(X0,X1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f47,plain,
! [X2,X0,X1] :
( mem(X0,u(X1,X2))
| ~ mem(X0,X2) ),
inference(cnf_transformation,[],[f34]) ).
fof(f48,plain,
! [X2,X0,X1] :
( mem(X0,u(X1,X2))
| ~ mem(X0,X1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f49,plain,
! [X2,X0,X1] :
( ~ mem(X0,m(X1,X2))
| ~ mem(X0,X2) ),
inference(cnf_transformation,[],[f36]) ).
fof(f51,plain,
! [X2,X0,X1] :
( mem(X0,m(X1,X2))
| ~ mem(X0,X1)
| mem(X0,X2) ),
inference(cnf_transformation,[],[f36]) ).
fof(f52,plain,
! [X0] : n(X0) = a(X0,X0),
inference(cnf_transformation,[],[f9]) ).
fof(f53,plain,
! [X0,X1] :
( ~ mem(X0,p(X1))
| subq(X0,X1) ),
inference(cnf_transformation,[],[f37]) ).
fof(f54,plain,
! [X0,X1] :
( mem(X0,p(X1))
| ~ subq(X0,X1) ),
inference(cnf_transformation,[],[f37]) ).
fof(f55,plain,
! [X3,X0,X1] :
( ~ mem(X3,X0)
| mem(X3,X1)
| ~ subq(X0,X1) ),
inference(cnf_transformation,[],[f40]) ).
fof(f56,plain,
! [X0,X1] :
( mem(sK0(X0,X1),X0)
| subq(X0,X1) ),
inference(cnf_transformation,[],[f40]) ).
fof(f57,plain,
! [X0,X1] :
( ~ mem(sK0(X0,X1),X1)
| subq(X0,X1) ),
inference(cnf_transformation,[],[f40]) ).
fof(f59,plain,
! [X0] : n(X0) = u(X0,s(X0)),
inference(definition_unfolding,[],[f52,f43]) ).
fof(f60,plain,
subq(u(m(p(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))),u(p(s(u(e,s(e)))),s(p(s(u(e,s(e))))))),s(u(s(u(e,s(e))),s(u(u(e,s(e)),s(u(e,s(e)))))))),u(m(p(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))),u(s(u(e,s(e))),u(p(s(u(e,s(e)))),s(p(s(u(e,s(e)))))))),s(u(s(u(e,s(e))),s(u(u(e,s(e)),s(u(e,s(e))))))))),
inference(definition_unfolding,[],[f41,f59,f59,f59,f59,f59,f43,f59,f59,f59,f59,f59,f59,f59,f59,f59,f43,f59,f59,f59]) ).
fof(f61,plain,
! [X1] : mem(X1,s(X1)),
inference(equality_resolution,[],[f45]) ).
fof(f69,plain,
! [X0] :
( subq(X0,X0)
| subq(X0,X0) ),
inference(resolution,[],[f57,f56]) ).
fof(f71,plain,
! [X2,X0,X1] :
( ~ mem(sK0(X0,u(X1,X2)),X1)
| subq(X0,u(X1,X2)) ),
inference(resolution,[],[f57,f48]) ).
fof(f72,plain,
! [X2,X0,X1] :
( ~ mem(sK0(X0,u(X1,X2)),X2)
| subq(X0,u(X1,X2)) ),
inference(resolution,[],[f57,f47]) ).
fof(f73,plain,
! [X0] : subq(X0,X0),
inference(duplicate_literal_removal,[],[f69]) ).
fof(f74,plain,
! [X0,X1] :
( ~ subq(s(X0),X1)
| mem(X0,X1) ),
inference(resolution,[],[f55,f61]) ).
fof(f76,plain,
! [X2,X3,X0,X1] :
( ~ subq(u(X2,X3),X1)
| mem(X0,X1)
| ~ mem(X0,X2) ),
inference(resolution,[],[f55,f48]) ).
fof(f77,plain,
! [X2,X3,X0,X1] :
( ~ subq(u(X2,X3),X1)
| mem(X0,X1)
| ~ mem(X0,X3) ),
inference(resolution,[],[f55,f47]) ).
fof(f122,plain,
! [X0] :
( mem(X0,u(m(p(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))),u(s(u(e,s(e))),u(p(s(u(e,s(e)))),s(p(s(u(e,s(e)))))))),s(u(s(u(e,s(e))),s(u(u(e,s(e)),s(u(e,s(e)))))))))
| ~ mem(X0,m(p(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))),u(p(s(u(e,s(e)))),s(p(s(u(e,s(e)))))))) ),
inference(resolution,[],[f76,f60]) ).
fof(f123,plain,
! [X0] :
( mem(X0,m(p(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))),u(s(u(e,s(e))),u(p(s(u(e,s(e)))),s(p(s(u(e,s(e)))))))))
| mem(X0,s(u(s(u(e,s(e))),s(u(u(e,s(e)),s(u(e,s(e))))))))
| ~ mem(X0,m(p(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))),u(p(s(u(e,s(e)))),s(p(s(u(e,s(e)))))))) ),
inference(resolution,[],[f122,f46]) ).
fof(f129,plain,
! [X0] :
( ~ mem(X0,m(p(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))),u(p(s(u(e,s(e)))),s(p(s(u(e,s(e))))))))
| mem(X0,s(u(s(u(e,s(e))),s(u(u(e,s(e)),s(u(e,s(e))))))))
| ~ mem(X0,u(s(u(e,s(e))),u(p(s(u(e,s(e)))),s(p(s(u(e,s(e)))))))) ),
inference(resolution,[],[f123,f49]) ).
fof(f147,plain,
! [X0] :
( ~ mem(X0,u(s(u(e,s(e))),u(p(s(u(e,s(e)))),s(p(s(u(e,s(e))))))))
| mem(X0,s(u(s(u(e,s(e))),s(u(u(e,s(e)),s(u(e,s(e))))))))
| ~ mem(X0,p(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))))
| mem(X0,u(p(s(u(e,s(e)))),s(p(s(u(e,s(e))))))) ),
inference(resolution,[],[f129,f51]) ).
fof(f180,plain,
! [X0,X1] :
( subq(X0,u(X0,X1))
| subq(X0,u(X0,X1)) ),
inference(resolution,[],[f71,f56]) ).
fof(f192,plain,
! [X0,X1] : subq(X0,u(X0,X1)),
inference(duplicate_literal_removal,[],[f180]) ).
fof(f198,plain,
! [X0,X1] :
( subq(X0,u(X1,X0))
| subq(X0,u(X1,X0)) ),
inference(resolution,[],[f72,f56]) ).
fof(f210,plain,
! [X0,X1] : subq(X0,u(X1,X0)),
inference(duplicate_literal_removal,[],[f198]) ).
fof(f212,plain,
! [X0,X1] : mem(X0,u(s(X0),X1)),
inference(resolution,[],[f192,f74]) ).
fof(f222,plain,
! [X0,X1] : mem(X0,u(X1,s(X0))),
inference(resolution,[],[f210,f74]) ).
fof(f313,plain,
( mem(u(e,s(e)),s(u(s(u(e,s(e))),s(u(u(e,s(e)),s(u(e,s(e))))))))
| ~ mem(u(e,s(e)),p(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))))
| mem(u(e,s(e)),u(p(s(u(e,s(e)))),s(p(s(u(e,s(e))))))) ),
inference(resolution,[],[f147,f212]) ).
fof(f323,definition,
( spl1_3
<=> mem(u(e,s(e)),u(p(s(u(e,s(e)))),s(p(s(u(e,s(e))))))) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
fof(f325,plain,
( mem(u(e,s(e)),u(p(s(u(e,s(e)))),s(p(s(u(e,s(e)))))))
| ~ spl1_3 ),
inference(avatar_component_clause,[],[f323]) ).
fof(f327,definition,
( spl1_4
<=> mem(u(e,s(e)),p(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))))) ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
fof(f329,plain,
( ~ mem(u(e,s(e)),p(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))))
| spl1_4 ),
inference(avatar_component_clause,[],[f327]) ).
fof(f331,definition,
( spl1_5
<=> mem(u(e,s(e)),s(u(s(u(e,s(e))),s(u(u(e,s(e)),s(u(e,s(e)))))))) ),
introduced(definition,[new_symbols(definition,[spl1_5])],[avatar_definition]) ).
fof(f333,plain,
( mem(u(e,s(e)),s(u(s(u(e,s(e))),s(u(u(e,s(e)),s(u(e,s(e))))))))
| ~ spl1_5 ),
inference(avatar_component_clause,[],[f331]) ).
fof(f334,plain,
( spl1_3
| ~ spl1_4
| spl1_5 ),
inference(avatar_split_clause,[],[f313,f331,f327,f323]) ).
fof(f343,plain,
( ~ subq(u(e,s(e)),u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))))
| spl1_4 ),
inference(resolution,[],[f329,f54]) ).
fof(f345,plain,
( $false
| spl1_4 ),
inference(forward_subsumption_resolution,[],[f343,f192]) ).
fof(f346,plain,
spl1_4,
inference(avatar_contradiction_clause,[],[f345]) ).
fof(f356,plain,
( mem(u(e,s(e)),s(p(s(u(e,s(e))))))
| mem(u(e,s(e)),p(s(u(e,s(e)))))
| ~ spl1_3 ),
inference(resolution,[],[f325,f46]) ).
fof(f359,definition,
( spl1_6
<=> mem(u(e,s(e)),p(s(u(e,s(e))))) ),
introduced(definition,[new_symbols(definition,[spl1_6])],[avatar_definition]) ).
fof(f361,plain,
( mem(u(e,s(e)),p(s(u(e,s(e)))))
| ~ spl1_6 ),
inference(avatar_component_clause,[],[f359]) ).
fof(f363,definition,
( spl1_7
<=> mem(u(e,s(e)),s(p(s(u(e,s(e)))))) ),
introduced(definition,[new_symbols(definition,[spl1_7])],[avatar_definition]) ).
fof(f365,plain,
( mem(u(e,s(e)),s(p(s(u(e,s(e))))))
| ~ spl1_7 ),
inference(avatar_component_clause,[],[f363]) ).
fof(f366,plain,
( spl1_6
| spl1_7
| ~ spl1_3 ),
inference(avatar_split_clause,[],[f356,f323,f363,f359]) ).
fof(f578,plain,
( subq(u(e,s(e)),s(u(e,s(e))))
| ~ spl1_6 ),
inference(resolution,[],[f361,f53]) ).
fof(f595,plain,
( ! [X0] :
( mem(X0,s(u(e,s(e))))
| ~ mem(X0,s(e)) )
| ~ spl1_6 ),
inference(resolution,[],[f578,f77]) ).
fof(f845,plain,
( ! [X0] :
( ~ mem(X0,s(e))
| u(e,s(e)) = X0 )
| ~ spl1_6 ),
inference(resolution,[],[f595,f44]) ).
fof(f878,plain,
( e = u(e,s(e))
| ~ spl1_6 ),
inference(resolution,[],[f845,f61]) ).
fof(f942,plain,
( mem(e,e)
| ~ spl1_6 ),
inference(superposition,[],[f222,f878]) ).
fof(f962,plain,
( $false
| ~ spl1_6 ),
inference(forward_subsumption_resolution,[],[f942,f42]) ).
fof(f963,plain,
~ spl1_6,
inference(avatar_contradiction_clause,[],[f962]) ).
fof(f1051,plain,
( u(e,s(e)) = p(s(u(e,s(e))))
| ~ spl1_7 ),
inference(resolution,[],[f365,f44]) ).
fof(f1099,plain,
( ! [X0] :
( ~ subq(X0,s(u(e,s(e))))
| mem(X0,u(e,s(e))) )
| ~ spl1_7 ),
inference(superposition,[],[f54,f1051]) ).
fof(f1273,plain,
( mem(s(u(e,s(e))),u(e,s(e)))
| ~ spl1_7 ),
inference(resolution,[],[f1099,f73]) ).
fof(f1322,plain,
( mem(s(u(e,s(e))),s(e))
| mem(s(u(e,s(e))),e)
| ~ spl1_7 ),
inference(resolution,[],[f1273,f46]) ).
fof(f1324,plain,
( mem(s(u(e,s(e))),s(e))
| ~ spl1_7 ),
inference(forward_subsumption_resolution,[],[f1322,f42]) ).
fof(f1357,plain,
( e = s(u(e,s(e)))
| ~ spl1_7 ),
inference(resolution,[],[f1324,f44]) ).
fof(f1416,plain,
( mem(u(e,s(e)),e)
| ~ spl1_7 ),
inference(superposition,[],[f61,f1357]) ).
fof(f1426,plain,
( $false
| ~ spl1_7 ),
inference(forward_subsumption_resolution,[],[f1416,f42]) ).
fof(f1427,plain,
~ spl1_7,
inference(avatar_contradiction_clause,[],[f1426]) ).
fof(f1925,plain,
( u(e,s(e)) = u(s(u(e,s(e))),s(u(u(e,s(e)),s(u(e,s(e))))))
| ~ spl1_5 ),
inference(resolution,[],[f333,f44]) ).
fof(f1997,plain,
( mem(u(e,s(e)),u(e,s(e)))
| ~ spl1_5 ),
inference(superposition,[],[f212,f1925]) ).
fof(f2170,plain,
( mem(u(e,s(e)),s(e))
| mem(u(e,s(e)),e)
| ~ spl1_5 ),
inference(resolution,[],[f1997,f46]) ).
fof(f2172,plain,
( mem(u(e,s(e)),s(e))
| ~ spl1_5 ),
inference(forward_subsumption_resolution,[],[f2170,f42]) ).
fof(f2246,plain,
( e = u(e,s(e))
| ~ spl1_5 ),
inference(resolution,[],[f2172,f44]) ).
fof(f2310,plain,
( mem(e,e)
| ~ spl1_5 ),
inference(superposition,[],[f1997,f2246]) ).
fof(f2360,plain,
( $false
| ~ spl1_5 ),
inference(forward_subsumption_resolution,[],[f2310,f42]) ).
fof(f2361,plain,
~ spl1_5,
inference(avatar_contradiction_clause,[],[f2360]) ).
cnf(s2,plain,
( spl1_3
| ~ spl1_4
| spl1_5 ),
inference(sat_conversion,[],[f334]) ).
cnf(s3,plain,
spl1_4,
inference(sat_conversion,[],[f346]) ).
cnf(s4,plain,
( ~ spl1_3
| spl1_6
| spl1_7 ),
inference(sat_conversion,[],[f366]) ).
cnf(s17,plain,
~ spl1_6,
inference(sat_conversion,[],[f963]) ).
cnf(s21,plain,
~ spl1_7,
inference(sat_conversion,[],[f1427]) ).
cnf(s34,plain,
~ spl1_5,
inference(sat_conversion,[],[f2361]) ).
cnf(s41,plain,
~ spl1_3,
inference(rat,[],[s4,s21,s17]) ).
cnf(s42,plain,
$false,
inference(rat,[],[s2,s34,s3,s41]) ).
fof(f2382,plain,
$false,
inference(avatar_sat_refutation,[],[s42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV566+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n005.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 28 06:35:31 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 4.04/1.60 % (595962)Detected formulas, will run a generic FOF schedule.
% 4.04/1.60 % (595969)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=2146615611:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.04/1.60 % (595970)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1472907197:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.04/1.60 % (595971)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=163068493:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.04/1.60 % (595967)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=3707324029:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.04/1.60 % (595968)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3007516966:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.04/1.60 % (595972)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1865690077:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.04/1.60 % (595970)Refutation not found, incomplete strategy
% 4.04/1.60 % (595970)------------------------------
% 4.04/1.60 % (595970)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.04/1.60 % (595970)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.04/1.60 % (595970)CaDiCaL version: 2.1.3
% 4.04/1.60 % (595970)Termination reason: Refutation not found, incomplete strategy
% 4.04/1.60 % (595970)Time elapsed: 0.002 s
% 4.04/1.60 % (595970)Peak memory usage: 88 MB
% 4.04/1.60 % (595970)Instructions burned: 1 (million)
% 4.04/1.60 % (595973)dis-21_1_sil=8000:lcm=predicate:random_seed=3066546289:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 4.04/1.60 % (595971)Instruction limit reached!
% 4.04/1.60 % (595971)------------------------------
% 4.04/1.60 % (595971)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.04/1.60 % (595971)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.04/1.60 % (595971)CaDiCaL version: 2.1.3
% 4.04/1.60 % (595971)Termination reason: Instruction limit
% 4.04/1.60 % (595971)Termination phase: Saturation
% 4.04/1.60 % (595971)Time elapsed: 0.075 s
% 4.04/1.60 % (595971)Peak memory usage: 88 MB
% 4.04/1.60 % (595971)Instructions burned: 120 (million)
% 4.04/1.60 % (595973)Instruction limit reached!
% 4.04/1.60 % (595973)------------------------------
% 4.04/1.60 % (595973)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.04/1.60 % (595973)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.04/1.60 % (595973)CaDiCaL version: 2.1.3
% 4.04/1.60 % (595973)Termination reason: Instruction limit
% 4.04/1.60 % (595973)Termination phase: Saturation
% 4.04/1.60 % (595973)Time elapsed: 0.070 s
% 4.04/1.60 % (595973)Peak memory usage: 89 MB
% 4.04/1.60 % (595973)Instructions burned: 129 (million)
% 4.04/1.60 % (595972)Instruction limit reached!
% 4.04/1.60 % (595972)------------------------------
% 4.04/1.60 % (595972)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.04/1.60 % (595972)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.04/1.60 % (595972)CaDiCaL version: 2.1.3
% 4.04/1.60 % (595972)Termination reason: Instruction limit
% 4.04/1.60 % (595972)Termination phase: Saturation
% 4.04/1.60 % (595972)Time elapsed: 0.089 s
% 4.04/1.60 % (595972)Peak memory usage: 89 MB
% 4.04/1.60 % (595972)Instructions burned: 140 (million)
% 4.04/1.60 % (595981)lrs+10_1_sil=8000:sp=occurrence:random_seed=1209964616:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 4.04/1.60 % (595970)------------------------------
% 4.04/1.60 % (595970)------------------------------
% 4.04/1.60 % (595982)lrs+10_1_sil=32000:urr=on:br=off:random_seed=4088540994:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.04/1.60 % (595983)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2968850985:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.04/1.60 % (595981)First to succeed.
% 4.04/1.60 % (595981)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-595962"
% 4.04/1.60 % (595982)Instruction limit reached!
% 4.04/1.60 % (595982)------------------------------
% 4.04/1.60 % (595982)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.04/1.60 % (595982)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.04/1.60 % (595982)CaDiCaL version: 2.1.3
% 4.04/1.60 % (595982)Termination reason: Instruction limit
% 4.04/1.60 % (595982)Termination phase: Saturation
% 4.04/1.60 % (595982)Time elapsed: 0.083 s
% 4.04/1.60 % (595982)Peak memory usage: 90 MB
% 4.04/1.60 % (595982)Instructions burned: 159 (million)
% 4.04/1.60 % (595985)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=1727045833:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 4.04/1.60 % (595983)Instruction limit reached!
% 4.04/1.60 % (595983)------------------------------
% 4.04/1.60 % (595983)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.04/1.60 % (595983)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.04/1.60 % (595983)CaDiCaL version: 2.1.3
% 4.04/1.60 % (595983)Termination reason: Instruction limit
% 4.04/1.60 % (595983)Termination phase: Saturation
% 4.04/1.60 % (595983)Time elapsed: 0.189 s
% 4.04/1.60 % (595983)Peak memory usage: 90 MB
% 4.04/1.60 % (595983)Instructions burned: 326 (million)
% 4.04/1.60 % (595985)Instruction limit reached!
% 4.04/1.60 % (595985)------------------------------
% 4.04/1.60 % (595985)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.04/1.60 % (595985)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.04/1.60 % (595985)CaDiCaL version: 2.1.3
% 4.04/1.60 % (595985)Termination reason: Instruction limit
% 4.04/1.60 % (595985)Termination phase: Saturation
% 4.04/1.60 % (595985)Time elapsed: 0.075 s
% 4.04/1.60 % (595985)Peak memory usage: 91 MB
% 4.04/1.60 % (595985)Instructions burned: 250 (million)
% 4.04/1.60 % (595988)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=293910062:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2994 on theBenchmark for (2994ds/294Mi)
% 4.04/1.60 % (595988)Refutation not found, incomplete strategy
% 4.04/1.60 % (595988)------------------------------
% 4.04/1.60 % (595988)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.04/1.60 % (595988)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.04/1.60 % (595988)CaDiCaL version: 2.1.3
% 4.04/1.60 % (595988)Termination reason: Refutation not found, incomplete strategy
% 4.04/1.60 % (595988)Time elapsed: 0.002 s
% 4.04/1.60 % (595988)Peak memory usage: 88 MB
% 4.04/1.60 % (595988)Instructions burned: 1 (million)
% 4.04/1.60 % (595991)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3914510428:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 4.04/1.60 % (595981)Refutation found. Thanks to Tanya!
% 4.04/1.60 % SZS status Theorem for theBenchmark
% 4.04/1.60 % SZS output start Proof for theBenchmark
% See solution above
% 5.86/1.80 % (595981)------------------------------
% 5.86/1.80 % (595981)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.86/1.80 % (595981)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.86/1.80 % (595981)CaDiCaL version: 2.1.3
% 5.86/1.80 % (595981)Termination reason: Refutation
% 5.86/1.80 % (595981)Time elapsed: 0.082 s
% 5.86/1.80 % (595981)Peak memory usage: 91 MB
% 5.86/1.80 % (595981)Instructions burned: 125 (million)
% 5.86/1.80 % (595981)------------------------------
% 5.86/1.80 % (595981)------------------------------
% 5.86/1.80 % (595962)Success in time 0.75 s
% 5.86/1.80 % Vampire exiting
%------------------------------------------------------------------------------