%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV561+1 : TPTP v9.3.1. Released v9.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 12:58:20 PM UTC 2026
% Result : Theorem 3.95s 1.61s
% Output : Refutation 5.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 15
% Syntax : Number of formulae : 133 ( 23 unt; 5 def)
% Number of atoms : 332 ( 49 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 346 ( 147 ~; 165 |; 19 &)
% ( 12 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 10 ( 8 usr; 6 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 1 con; 0-2 aty)
% Number of variables : 124 ( 0 sgn 119 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subq(X0,X1)
<=> ! [X2] :
( mem(X2,X0)
=> mem(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subq_def) ).
fof(f2,axiom,
! [X0,X1] :
( subq(X0,X1)
=> ( subq(X1,X0)
=> X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setext) ).
fof(f3,axiom,
! [X0,X1] :
( disj(X0,X1)
<=> ~ ? [X2] :
( mem(X2,X0)
& mem(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',disj_def) ).
fof(f4,axiom,
! [X0] : ~ mem(X0,e),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_ax) ).
fof(f5,axiom,
! [X0,X1] :
( mem(X0,s(X1))
<=> X0 = X1 ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',u_ax) ).
fof(f8,axiom,
! [X0,X1] : a(X0,X1) = u(X0,s(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_def) ).
fof(f9,axiom,
! [X0] : n(X0) = a(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',n_def) ).
fof(f10,axiom,
! [X0,X1] :
( mem(X0,p(X1))
<=> subq(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p_ax) ).
fof(f26,conjecture,
disj(p(s(s(n(e)))),n(a(s(s(n(e))),n(n(e))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',disj_17_4108) ).
fof(f27,negated_conjecture,
~ disj(p(s(s(n(e)))),n(a(s(s(n(e))),n(n(e))))),
inference(negated_conjecture,[status(cth)],[f26]) ).
fof(f28,plain,
~ disj(p(s(s(n(e)))),n(a(s(s(n(e))),n(n(e))))),
inference(flattening,[],[f27]) ).
fof(f29,plain,
! [X0,X1] :
( disj(X0,X1)
<=> ! [X2] :
( ~ mem(X2,X0)
| ~ mem(X2,X1) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f30,plain,
! [X0,X1] :
( subq(X0,X1)
<=> ! [X2] :
( mem(X2,X1)
| ~ mem(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f31,plain,
! [X0,X1] :
( X0 = X1
| ~ subq(X1,X0)
| ~ subq(X0,X1) ),
inference(ennf_transformation,[],[f2]) ).
fof(f32,plain,
! [X0,X1] :
( X0 = X1
| ~ subq(X1,X0)
| ~ subq(X0,X1) ),
inference(flattening,[],[f31]) ).
fof(f33,plain,
! [X0,X1] :
( ( mem(X0,s(X1))
| X0 != X1 )
& ( X0 = X1
| ~ mem(X0,s(X1)) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f34,plain,
! [X0,X1] :
( ( disj(X0,X1)
| ? [X2] :
( mem(X2,X0)
& mem(X2,X1) ) )
& ( ! [X2] :
( ~ mem(X2,X0)
| ~ mem(X2,X1) )
| ~ disj(X0,X1) ) ),
inference(nnf_transformation,[],[f29]) ).
fof(f35,plain,
! [X0,X1] :
( ( disj(X0,X1)
| ? [X2] :
( mem(X2,X0)
& mem(X2,X1) ) )
& ( ! [X3] :
( ~ mem(X3,X0)
| ~ mem(X3,X1) )
| ~ disj(X0,X1) ) ),
inference(rectify,[],[f34]) ).
fof(f36,plain,
! [X0,X1] :
( ( disj(X0,X1)
| ( mem(sK0(X0,X1),X0)
& mem(sK0(X0,X1),X1) ) )
& ( ! [X3] :
( ~ mem(X3,X0)
| ~ mem(X3,X1) )
| ~ disj(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f35]) ).
fof(f40,plain,
! [X0,X1] :
( ( mem(X0,p(X1))
| ~ subq(X0,X1) )
& ( subq(X0,X1)
| ~ mem(X0,p(X1)) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f43,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(f44,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,[],[f43]) ).
fof(f45,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,[],[f30]) ).
fof(f46,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,[],[f45]) ).
fof(f47,plain,
! [X0,X1] :
( ( subq(X0,X1)
| ( ~ mem(sK2(X0,X1),X1)
& mem(sK2(X0,X1),X0) ) )
& ( ! [X3] :
( mem(X3,X1)
| ~ mem(X3,X0) )
| ~ subq(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f46]) ).
fof(f90,plain,
~ disj(p(s(s(n(e)))),n(a(s(s(n(e))),n(n(e))))),
inference(cnf_transformation,[],[f28]) ).
fof(f91,plain,
! [X0] : ~ mem(X0,e),
inference(cnf_transformation,[],[f4]) ).
fof(f92,plain,
! [X0,X1] : a(X0,X1) = u(X0,s(X1)),
inference(cnf_transformation,[],[f8]) ).
fof(f93,plain,
! [X0,X1] :
( ~ mem(X0,s(X1))
| X0 = X1 ),
inference(cnf_transformation,[],[f33]) ).
fof(f94,plain,
! [X0,X1] :
( mem(X0,s(X1))
| X0 != X1 ),
inference(cnf_transformation,[],[f33]) ).
fof(f96,plain,
! [X0,X1] :
( mem(sK0(X0,X1),X1)
| disj(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f97,plain,
! [X0,X1] :
( mem(sK0(X0,X1),X0)
| disj(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f98,plain,
! [X0] : n(X0) = a(X0,X0),
inference(cnf_transformation,[],[f9]) ).
fof(f102,plain,
! [X0,X1] :
( ~ mem(X0,p(X1))
| subq(X0,X1) ),
inference(cnf_transformation,[],[f40]) ).
fof(f107,plain,
! [X2,X0,X1] :
( ~ mem(X0,u(X1,X2))
| mem(X0,X2)
| mem(X0,X1) ),
inference(cnf_transformation,[],[f44]) ).
fof(f108,plain,
! [X2,X0,X1] :
( mem(X0,u(X1,X2))
| ~ mem(X0,X2) ),
inference(cnf_transformation,[],[f44]) ).
fof(f109,plain,
! [X2,X0,X1] :
( mem(X0,u(X1,X2))
| ~ mem(X0,X1) ),
inference(cnf_transformation,[],[f44]) ).
fof(f110,plain,
! [X3,X0,X1] :
( ~ subq(X0,X1)
| ~ mem(X3,X0)
| mem(X3,X1) ),
inference(cnf_transformation,[],[f47]) ).
fof(f111,plain,
! [X0,X1] :
( mem(sK2(X0,X1),X0)
| subq(X0,X1) ),
inference(cnf_transformation,[],[f47]) ).
fof(f113,plain,
! [X0,X1] :
( ~ subq(X0,X1)
| ~ subq(X1,X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f32]) ).
fof(f170,plain,
! [X0] : n(X0) = u(X0,s(X0)),
inference(definition_unfolding,[],[f98,f92]) ).
fof(f171,plain,
~ disj(p(s(s(u(e,s(e))))),u(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))))),
inference(definition_unfolding,[],[f90,f170,f170,f92,f170,f170,f170]) ).
fof(f172,plain,
! [X1] : mem(X1,s(X1)),
inference(equality_resolution,[],[f94]) ).
fof(f177,plain,
! [X0,X1] :
( subq(sK0(p(X0),X1),X0)
| disj(p(X0),X1) ),
inference(resolution,[],[f102,f97]) ).
fof(f178,plain,
! [X2,X0,X1] :
( mem(sK0(X0,u(X1,X2)),X2)
| mem(sK0(X0,u(X1,X2)),X1)
| disj(X0,u(X1,X2)) ),
inference(resolution,[],[f107,f96]) ).
fof(f207,plain,
! [X2,X0,X1] :
( mem(sK0(X0,u(X1,s(X2))),X1)
| disj(X0,u(X1,s(X2)))
| sK0(X0,u(X1,s(X2))) = X2 ),
inference(resolution,[],[f178,f93]) ).
fof(f217,plain,
! [X2,X3,X0,X1] :
( mem(sK0(X0,u(u(X1,X2),s(X3))),X2)
| mem(sK0(X0,u(u(X1,X2),s(X3))),X1)
| disj(X0,u(u(X1,X2),s(X3)))
| sK0(X0,u(u(X1,X2),s(X3))) = X3 ),
inference(resolution,[],[f207,f107]) ).
fof(f220,plain,
! [X2,X3,X0,X1] :
( mem(sK0(X0,u(u(X1,s(X2)),s(X3))),X1)
| disj(X0,u(u(X1,s(X2)),s(X3)))
| sK0(X0,u(u(X1,s(X2)),s(X3))) = X3
| sK0(X0,u(u(X1,s(X2)),s(X3))) = X2 ),
inference(resolution,[],[f217,f93]) ).
fof(f243,plain,
! [X0] : subq(e,X0),
inference(resolution,[],[f111,f91]) ).
fof(f300,plain,
! [X2,X3,X0,X1] :
( disj(X0,u(u(s(X1),s(X2)),s(X3)))
| sK0(X0,u(u(s(X1),s(X2)),s(X3))) = X3
| sK0(X0,u(u(s(X1),s(X2)),s(X3))) = X2
| sK0(X0,u(u(s(X1),s(X2)),s(X3))) = X1 ),
inference(resolution,[],[f220,f93]) ).
fof(f308,plain,
( u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))) = sK0(p(s(s(u(e,s(e))))),u(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))))))
| u(u(e,s(e)),s(u(e,s(e)))) = sK0(p(s(s(u(e,s(e))))),u(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))))))
| s(u(e,s(e))) = sK0(p(s(s(u(e,s(e))))),u(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))))) ),
inference(resolution,[],[f300,f171]) ).
fof(f311,definition,
( spl17_1
<=> s(u(e,s(e))) = sK0(p(s(s(u(e,s(e))))),u(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))))) ),
introduced(definition,[new_symbols(definition,[spl17_1])],[avatar_definition]) ).
fof(f312,plain,
( s(u(e,s(e))) = sK0(p(s(s(u(e,s(e))))),u(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))))))
| ~ spl17_1 ),
inference(avatar_component_clause,[],[f311]) ).
fof(f314,definition,
( spl17_2
<=> u(u(e,s(e)),s(u(e,s(e)))) = sK0(p(s(s(u(e,s(e))))),u(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))))) ),
introduced(definition,[new_symbols(definition,[spl17_2])],[avatar_definition]) ).
fof(f315,plain,
( u(u(e,s(e)),s(u(e,s(e)))) = sK0(p(s(s(u(e,s(e))))),u(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))))))
| ~ spl17_2 ),
inference(avatar_component_clause,[],[f314]) ).
fof(f317,definition,
( spl17_3
<=> u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))) = sK0(p(s(s(u(e,s(e))))),u(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))))) ),
introduced(definition,[new_symbols(definition,[spl17_3])],[avatar_definition]) ).
fof(f318,plain,
( u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))) = sK0(p(s(s(u(e,s(e))))),u(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))))))
| ~ spl17_3 ),
inference(avatar_component_clause,[],[f317]) ).
fof(f319,plain,
( spl17_1
| spl17_2
| spl17_3 ),
inference(avatar_split_clause,[],[f308,f317,f314,f311]) ).
fof(f321,plain,
( subq(u(u(e,s(e)),s(u(e,s(e)))),s(s(u(e,s(e)))))
| disj(p(s(s(u(e,s(e))))),u(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))))))
| ~ spl17_2 ),
inference(superposition,[],[f177,f315]) ).
fof(f334,plain,
( subq(u(u(e,s(e)),s(u(e,s(e)))),s(s(u(e,s(e)))))
| ~ spl17_2 ),
inference(forward_subsumption_resolution,[],[f321,f171]) ).
fof(f360,plain,
( ! [X0] :
( ~ mem(X0,u(u(e,s(e)),s(u(e,s(e)))))
| mem(X0,s(s(u(e,s(e))))) )
| ~ spl17_2 ),
inference(resolution,[],[f334,f110]) ).
fof(f393,plain,
( ! [X0] :
( mem(X0,s(s(u(e,s(e)))))
| ~ mem(X0,s(u(e,s(e)))) )
| ~ spl17_2 ),
inference(resolution,[],[f360,f108]) ).
fof(f482,plain,
( ! [X0] :
( ~ mem(X0,s(u(e,s(e))))
| s(u(e,s(e))) = X0 )
| ~ spl17_2 ),
inference(resolution,[],[f393,f93]) ).
fof(f483,plain,
( u(e,s(e)) = s(u(e,s(e)))
| ~ spl17_2 ),
inference(resolution,[],[f482,f172]) ).
fof(f510,plain,
( mem(u(e,s(e)),u(e,s(e)))
| ~ spl17_2 ),
inference(superposition,[],[f172,f483]) ).
fof(f574,plain,
( mem(u(e,s(e)),s(e))
| mem(u(e,s(e)),e)
| ~ spl17_2 ),
inference(resolution,[],[f510,f107]) ).
fof(f575,plain,
( mem(u(e,s(e)),s(e))
| ~ spl17_2 ),
inference(forward_subsumption_resolution,[],[f574,f91]) ).
fof(f577,plain,
( e = u(e,s(e))
| ~ spl17_2 ),
inference(resolution,[],[f575,f93]) ).
fof(f590,plain,
( mem(e,e)
| ~ spl17_2 ),
inference(superposition,[],[f510,f577]) ).
fof(f607,plain,
( $false
| ~ spl17_2 ),
inference(forward_subsumption_resolution,[],[f590,f91]) ).
fof(f608,plain,
~ spl17_2,
inference(avatar_contradiction_clause,[],[f607]) ).
fof(f634,plain,
( subq(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(s(u(e,s(e)))))
| disj(p(s(s(u(e,s(e))))),u(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))))))
| ~ spl17_3 ),
inference(superposition,[],[f177,f318]) ).
fof(f638,plain,
( mem(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),u(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))))))
| disj(p(s(s(u(e,s(e))))),u(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))))))
| ~ spl17_3 ),
inference(superposition,[],[f96,f318]) ).
fof(f639,plain,
( mem(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),u(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))))))
| ~ spl17_3 ),
inference(forward_subsumption_resolution,[],[f638,f171]) ).
fof(f641,plain,
( subq(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(s(u(e,s(e)))))
| ~ spl17_3 ),
inference(forward_subsumption_resolution,[],[f634,f171]) ).
fof(f644,definition,
( spl17_12
<=> s(s(u(e,s(e)))) = u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))) ),
introduced(definition,[new_symbols(definition,[spl17_12])],[avatar_definition]) ).
fof(f645,plain,
( s(s(u(e,s(e)))) = u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))
| ~ spl17_12 ),
inference(avatar_component_clause,[],[f644]) ).
fof(f647,definition,
( spl17_13
<=> subq(s(s(u(e,s(e)))),u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))) ),
introduced(definition,[new_symbols(definition,[spl17_13])],[avatar_definition]) ).
fof(f648,plain,
( ~ subq(s(s(u(e,s(e)))),u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))))
| spl17_13 ),
inference(avatar_component_clause,[],[f647]) ).
fof(f658,plain,
( ! [X0] :
( ~ mem(X0,u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))))
| mem(X0,s(s(u(e,s(e))))) )
| ~ spl17_3 ),
inference(resolution,[],[f641,f110]) ).
fof(f661,plain,
( ! [X0] :
( ~ mem(X0,s(u(u(e,s(e)),s(u(e,s(e))))))
| mem(X0,s(s(u(e,s(e))))) )
| ~ spl17_3 ),
inference(resolution,[],[f658,f108]) ).
fof(f715,plain,
( mem(u(u(e,s(e)),s(u(e,s(e)))),s(s(u(e,s(e)))))
| ~ spl17_3 ),
inference(resolution,[],[f661,f172]) ).
fof(f915,plain,
( subq(s(u(e,s(e))),s(s(u(e,s(e)))))
| disj(p(s(s(u(e,s(e))))),u(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))))))
| ~ spl17_1 ),
inference(superposition,[],[f177,f312]) ).
fof(f929,plain,
( subq(s(u(e,s(e))),s(s(u(e,s(e)))))
| ~ spl17_1 ),
inference(forward_subsumption_resolution,[],[f915,f171]) ).
fof(f1380,plain,
( s(u(e,s(e))) = u(u(e,s(e)),s(u(e,s(e))))
| ~ spl17_3 ),
inference(resolution,[],[f715,f93]) ).
fof(f1401,plain,
( ! [X0] :
( mem(X0,s(u(e,s(e))))
| ~ mem(X0,u(e,s(e))) )
| ~ spl17_3 ),
inference(superposition,[],[f109,f1380]) ).
fof(f1439,plain,
( ~ subq(s(s(u(e,s(e)))),u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))))
| s(s(u(e,s(e)))) = u(s(s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))
| ~ spl17_3 ),
inference(resolution,[],[f641,f113]) ).
fof(f1451,plain,
( ! [X0] :
( ~ mem(X0,u(e,s(e)))
| u(e,s(e)) = X0 )
| ~ spl17_3 ),
inference(resolution,[],[f1401,f93]) ).
fof(f1453,plain,
( ! [X0] :
( ~ mem(X0,s(e))
| u(e,s(e)) = X0 )
| ~ spl17_3 ),
inference(resolution,[],[f1451,f108]) ).
fof(f1470,plain,
( e = u(e,s(e))
| ~ spl17_3 ),
inference(resolution,[],[f1453,f172]) ).
fof(f1490,plain,
( mem(u(s(s(e)),s(u(e,s(e)))),u(u(s(s(e)),s(u(e,s(e)))),s(u(s(s(e)),s(u(e,s(e)))))))
| ~ spl17_3 ),
inference(superposition,[],[f639,f1470]) ).
fof(f1493,plain,
( s(s(e)) = u(s(s(e)),s(u(e,s(e))))
| ~ spl17_3
| ~ spl17_12 ),
inference(superposition,[],[f645,f1470]) ).
fof(f1501,plain,
( s(e) = u(e,s(e))
| ~ spl17_3 ),
inference(superposition,[],[f1380,f1470]) ).
fof(f1520,plain,
( e = s(e)
| ~ spl17_3 ),
inference(forward_demodulation,[],[f1501,f1470]) ).
fof(f1524,plain,
( s(s(e)) = u(s(s(e)),s(e))
| ~ spl17_3
| ~ spl17_12 ),
inference(forward_demodulation,[],[f1493,f1470]) ).
fof(f1527,plain,
( mem(u(s(s(e)),s(e)),u(u(s(s(e)),s(e)),s(u(s(s(e)),s(e)))))
| ~ spl17_3 ),
inference(forward_demodulation,[],[f1490,f1470]) ).
fof(f1533,plain,
( s(e) = u(s(e),e)
| ~ spl17_3
| ~ spl17_12 ),
inference(forward_demodulation,[],[f1524,f1520]) ).
fof(f1536,plain,
( mem(u(s(e),e),u(u(s(e),e),s(u(s(e),e))))
| ~ spl17_3 ),
inference(forward_demodulation,[],[f1527,f1520]) ).
fof(f1540,plain,
( e = u(e,e)
| ~ spl17_3
| ~ spl17_12 ),
inference(forward_demodulation,[],[f1533,f1520]) ).
fof(f1543,plain,
( mem(u(e,e),u(u(e,e),s(u(e,e))))
| ~ spl17_3 ),
inference(forward_demodulation,[],[f1536,f1520]) ).
fof(f1549,plain,
( mem(e,u(e,s(e)))
| ~ spl17_3
| ~ spl17_12 ),
inference(forward_demodulation,[],[f1543,f1540]) ).
fof(f1553,plain,
( mem(e,e)
| ~ spl17_3
| ~ spl17_12 ),
inference(forward_demodulation,[],[f1549,f1470]) ).
fof(f1557,plain,
( $false
| ~ spl17_3
| ~ spl17_12 ),
inference(forward_subsumption_resolution,[],[f1553,f91]) ).
fof(f1558,plain,
( ~ spl17_3
| ~ spl17_12 ),
inference(avatar_contradiction_clause,[],[f1557]) ).
fof(f1579,plain,
( ! [X0] :
( mem(X0,s(s(u(e,s(e)))))
| ~ mem(X0,s(u(e,s(e)))) )
| ~ spl17_1 ),
inference(resolution,[],[f929,f110]) ).
fof(f1587,plain,
( ! [X0] :
( ~ mem(X0,s(u(e,s(e))))
| s(u(e,s(e))) = X0 )
| ~ spl17_1 ),
inference(resolution,[],[f1579,f93]) ).
fof(f1606,plain,
( u(e,s(e)) = s(u(e,s(e)))
| ~ spl17_1 ),
inference(resolution,[],[f1587,f172]) ).
fof(f1634,plain,
( mem(u(e,s(e)),u(e,s(e)))
| ~ spl17_1 ),
inference(superposition,[],[f172,f1606]) ).
fof(f1720,plain,
( mem(u(e,s(e)),s(e))
| mem(u(e,s(e)),e)
| ~ spl17_1 ),
inference(resolution,[],[f1634,f107]) ).
fof(f1721,plain,
( mem(u(e,s(e)),s(e))
| ~ spl17_1 ),
inference(forward_subsumption_resolution,[],[f1720,f91]) ).
fof(f1723,plain,
( e = u(e,s(e))
| ~ spl17_1 ),
inference(resolution,[],[f1721,f93]) ).
fof(f1737,plain,
( mem(e,e)
| ~ spl17_1 ),
inference(superposition,[],[f1634,f1723]) ).
fof(f1758,plain,
( $false
| ~ spl17_1 ),
inference(forward_subsumption_resolution,[],[f1737,f91]) ).
fof(f1759,plain,
~ spl17_1,
inference(avatar_contradiction_clause,[],[f1758]) ).
fof(f1795,plain,
( spl17_12
| ~ spl17_13
| ~ spl17_3 ),
inference(avatar_split_clause,[],[f1439,f317,f647,f644]) ).
fof(f1812,plain,
( ~ subq(s(s(u(e,s(e)))),u(s(s(u(e,s(e)))),s(s(u(e,s(e))))))
| ~ spl17_3
| spl17_13 ),
inference(forward_demodulation,[],[f648,f1380]) ).
fof(f1817,plain,
( ~ subq(s(s(e)),u(s(s(e)),s(s(e))))
| ~ spl17_3
| spl17_13 ),
inference(forward_demodulation,[],[f1812,f1470]) ).
fof(f1822,plain,
( ~ subq(s(e),u(s(e),s(e)))
| ~ spl17_3
| spl17_13 ),
inference(forward_demodulation,[],[f1817,f1520]) ).
fof(f1825,plain,
( ~ subq(e,u(e,e))
| ~ spl17_3
| spl17_13 ),
inference(forward_demodulation,[],[f1822,f1520]) ).
fof(f1828,plain,
( $false
| ~ spl17_3
| spl17_13 ),
inference(forward_subsumption_resolution,[],[f1825,f243]) ).
fof(f1829,plain,
( ~ spl17_3
| spl17_13 ),
inference(avatar_contradiction_clause,[],[f1828]) ).
cnf(s1,plain,
( spl17_1
| spl17_2
| spl17_3 ),
inference(sat_conversion,[],[f319]) ).
cnf(s8,plain,
~ spl17_2,
inference(sat_conversion,[],[f608]) ).
cnf(s21,plain,
( ~ spl17_3
| ~ spl17_12 ),
inference(sat_conversion,[],[f1558]) ).
cnf(s28,plain,
~ spl17_1,
inference(sat_conversion,[],[f1759]) ).
cnf(s36,plain,
( ~ spl17_3
| spl17_12
| ~ spl17_13 ),
inference(sat_conversion,[],[f1795]) ).
cnf(s37,plain,
( ~ spl17_3
| spl17_13 ),
inference(sat_conversion,[],[f1829]) ).
cnf(s39,plain,
spl17_3,
inference(rat,[],[s1,s8,s28]) ).
cnf(s41,plain,
spl17_13,
inference(rat,[],[s37,s39]) ).
cnf(s42,plain,
spl17_12,
inference(rat,[],[s36,s41,s39]) ).
cnf(s44,plain,
$false,
inference(rat,[],[s21,s42,s39]) ).
fof(f1832,plain,
$false,
inference(avatar_sat_refutation,[],[s44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV561+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n020.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 28 06:37:19 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.95/1.61 % (4191228)Detected formulas, will run a generic FOF schedule.
% 3.95/1.61 % (4191234)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=1785180067:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.95/1.61 % (4191238)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=278856270:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.95/1.61 % (4191239)dis-21_1_sil=8000:lcm=predicate:random_seed=2556416610: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)
% 3.95/1.61 % (4191233)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=3224274790:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.95/1.61 % (4191237)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1863941308:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.95/1.61 % (4191235)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=1087045186:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.95/1.61 % (4191236)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1899924118:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.95/1.61 % (4191236)Refutation not found, incomplete strategy
% 3.95/1.61 % (4191236)------------------------------
% 3.95/1.61 % (4191236)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.95/1.61 % (4191236)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.95/1.61 % (4191236)CaDiCaL version: 2.1.3
% 3.95/1.61 % (4191236)Termination reason: Refutation not found, incomplete strategy
% 3.95/1.61 % (4191236)Time elapsed: 0.001 s
% 3.95/1.61 % (4191236)Peak memory usage: 88 MB
% 3.95/1.61 % (4191237)Instruction limit reached!
% 3.95/1.61 % (4191237)------------------------------
% 3.95/1.61 % (4191237)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.95/1.61 % (4191237)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.95/1.61 % (4191237)CaDiCaL version: 2.1.3
% 3.95/1.61 % (4191237)Termination reason: Instruction limit
% 3.95/1.61 % (4191237)Termination phase: Saturation
% 3.95/1.61 % (4191237)Time elapsed: 0.051 s
% 3.95/1.61 % (4191237)Peak memory usage: 87 MB
% 3.95/1.61 % (4191237)Instructions burned: 119 (million)
% 3.95/1.61 % (4191239)Instruction limit reached!
% 3.95/1.61 % (4191239)------------------------------
% 3.95/1.61 % (4191239)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.95/1.61 % (4191239)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.95/1.61 % (4191239)CaDiCaL version: 2.1.3
% 3.95/1.61 % (4191239)Termination reason: Instruction limit
% 3.95/1.61 % (4191239)Termination phase: Saturation
% 3.95/1.61 % (4191239)Time elapsed: 0.074 s
% 3.95/1.61 % (4191239)Peak memory usage: 89 MB
% 3.95/1.61 % (4191239)Instructions burned: 130 (million)
% 3.95/1.61 % (4191238)Instruction limit reached!
% 3.95/1.61 % (4191238)------------------------------
% 3.95/1.61 % (4191238)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.95/1.61 % (4191238)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.95/1.61 % (4191238)CaDiCaL version: 2.1.3
% 3.95/1.61 % (4191238)Termination reason: Instruction limit
% 3.95/1.61 % (4191238)Termination phase: Saturation
% 3.95/1.61 % (4191238)Time elapsed: 0.091 s
% 3.95/1.61 % (4191238)Peak memory usage: 89 MB
% 3.95/1.61 % (4191238)Instructions burned: 140 (million)
% 3.95/1.61 % (4191247)lrs+10_1_sil=8000:sp=occurrence:random_seed=872621467:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.95/1.61 % (4191248)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1240912934:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.95/1.61 % (4191248)Refutation not found, incomplete strategy
% 3.95/1.61 % (4191248)------------------------------
% 3.95/1.61 % (4191248)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.95/1.61 % (4191248)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.95/1.61 % (4191248)CaDiCaL version: 2.1.3
% 3.95/1.61 % (4191248)Termination reason: Refutation not found, incomplete strategy
% 3.95/1.61 % (4191248)Time elapsed: 0.002 s
% 3.95/1.61 % (4191248)Peak memory usage: 89 MB
% 3.95/1.61 % (4191248)Instructions burned: 1 (million)
% 3.95/1.61 % (4191236)------------------------------
% 3.95/1.61 % (4191236)------------------------------
% 3.95/1.61 % (4191249)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1796020073:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 3.95/1.61 % (4191249)Refutation not found, incomplete strategy
% 3.95/1.61 % (4191249)------------------------------
% 3.95/1.61 % (4191249)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.95/1.61 % (4191249)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.95/1.61 % (4191249)CaDiCaL version: 2.1.3
% 3.95/1.61 % (4191249)Termination reason: Refutation not found, incomplete strategy
% 3.95/1.61 % (4191249)Time elapsed: 0.002 s
% 3.95/1.61 % (4191249)Peak memory usage: 88 MB
% 3.95/1.61 % (4191249)Instructions burned: 1 (million)
% 3.95/1.61 % (4191247)Instruction limit reached!
% 3.95/1.61 % (4191247)------------------------------
% 3.95/1.61 % (4191247)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.95/1.61 % (4191247)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.95/1.61 % (4191247)CaDiCaL version: 2.1.3
% 3.95/1.61 % (4191247)Termination reason: Instruction limit
% 3.95/1.61 % (4191247)Termination phase: Saturation
% 3.95/1.61 % (4191247)Time elapsed: 0.183 s
% 3.95/1.61 % (4191247)Peak memory usage: 92 MB
% 3.95/1.61 % (4191247)Instructions burned: 285 (million)
% 3.95/1.61 % (4191234)First to succeed.
% 3.95/1.61 % (4191234)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4191228"
% 3.95/1.61 % (4191253)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=3200688962:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 3.95/1.61 % (4191248)------------------------------
% 3.95/1.61 % (4191248)------------------------------
% 3.95/1.61 % (4191249)------------------------------
% 3.95/1.61 % (4191249)------------------------------
% 3.95/1.61 % (4191253)Instruction limit reached!
% 3.95/1.61 % (4191253)------------------------------
% 3.95/1.61 % (4191253)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.95/1.61 % (4191253)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.95/1.61 % (4191253)CaDiCaL version: 2.1.3
% 3.95/1.61 % (4191253)Termination reason: Instruction limit
% 3.95/1.61 % (4191253)Termination phase: Saturation
% 3.95/1.61 % (4191253)Time elapsed: 0.140 s
% 3.95/1.61 % (4191253)Peak memory usage: 92 MB
% 3.95/1.61 % (4191253)Instructions burned: 250 (million)
% 3.95/1.61 % (4191234)Refutation found. Thanks to Tanya!
% 3.95/1.61 % SZS status Theorem for theBenchmark
% 3.95/1.61 % SZS output start Proof for theBenchmark
% See solution above
% 5.83/1.71 % (4191234)------------------------------
% 5.83/1.71 % (4191234)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.83/1.71 % (4191234)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.83/1.71 % (4191234)CaDiCaL version: 2.1.3
% 5.83/1.71 % (4191234)Termination reason: Refutation
% 5.83/1.71 % (4191234)Time elapsed: 0.445 s
% 5.83/1.71 % (4191234)Peak memory usage: 132 MB
% 5.83/1.71 % (4191234)Instructions burned: 1205 (million)
% 5.83/1.71 % (4191234)------------------------------
% 5.83/1.71 % (4191234)------------------------------
% 5.83/1.71 % (4191228)Success in time 0.752 s
% 5.83/1.71 % Vampire exiting
%------------------------------------------------------------------------------