%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV568+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 : n026.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 4.31s 1.55s
% Output : Refutation 5.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 14
% Syntax : Number of formulae : 96 ( 27 unt; 6 def)
% Number of atoms : 269 ( 61 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 266 ( 93 ~; 149 |; 12 &)
% ( 11 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 11 ( 3 avg)
% Number of predicates : 10 ( 8 usr; 7 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-2 aty)
% Number of variables : 90 ( 0 sgn 88 !; 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(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(a(s(s(n(e))),p(s(n(e)))),u(s(s(n(n(e)))),n(n(n(n(e)))))),u(a(n(s(n(e))),p(s(n(e)))),a(n(s(n(n(e)))),n(n(n(e)))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nsubq_2351_2350) ).
fof(f27,negated_conjecture,
~ ~ subq(u(a(s(s(n(e))),p(s(n(e)))),u(s(s(n(n(e)))),n(n(n(n(e)))))),u(a(n(s(n(e))),p(s(n(e)))),a(n(s(n(n(e)))),n(n(n(e)))))),
inference(negated_conjecture,[status(cth)],[f26]) ).
fof(f28,plain,
subq(u(a(s(s(n(e))),p(s(n(e)))),u(s(s(n(n(e)))),n(n(n(n(e)))))),u(a(n(s(n(e))),p(s(n(e)))),a(n(s(n(n(e)))),n(n(n(e)))))),
inference(flattening,[],[f27]) ).
fof(f30,plain,
! [X0,X1] :
( subq(X0,X1)
<=> ! [X2] :
( mem(X2,X1)
| ~ mem(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
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,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(f35,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,[],[f34]) ).
fof(f39,plain,
! [X0,X1] :
( ( mem(X0,p(X1))
| ~ subq(X0,X1) )
& ( subq(X0,X1)
| ~ mem(X0,p(X1)) ) ),
inference(nnf_transformation,[],[f10]) ).
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,
subq(u(a(s(s(n(e))),p(s(n(e)))),u(s(s(n(n(e)))),n(n(n(n(e)))))),u(a(n(s(n(e))),p(s(n(e)))),a(n(s(n(n(e)))),n(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(f95,plain,
! [X2,X0,X1] :
( ~ mem(X0,u(X1,X2))
| mem(X0,X2)
| mem(X0,X1) ),
inference(cnf_transformation,[],[f35]) ).
fof(f96,plain,
! [X2,X0,X1] :
( mem(X0,u(X1,X2))
| ~ mem(X0,X2) ),
inference(cnf_transformation,[],[f35]) ).
fof(f97,plain,
! [X2,X0,X1] :
( mem(X0,u(X1,X2))
| ~ mem(X0,X1) ),
inference(cnf_transformation,[],[f35]) ).
fof(f98,plain,
! [X0] : n(X0) = a(X0,X0),
inference(cnf_transformation,[],[f9]) ).
fof(f103,plain,
! [X0,X1] :
( mem(X0,p(X1))
| ~ subq(X0,X1) ),
inference(cnf_transformation,[],[f39]) ).
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(f170,plain,
! [X0] : n(X0) = u(X0,s(X0)),
inference(definition_unfolding,[],[f98,f92]) ).
fof(f171,plain,
subq(u(u(s(s(u(e,s(e)))),s(p(s(u(e,s(e)))))),u(s(s(u(u(e,s(e)),s(u(e,s(e)))))),u(u(u(u(e,s(e)),s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(u(u(e,s(e)),s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))))))),u(u(u(s(u(e,s(e))),s(s(u(e,s(e))))),s(p(s(u(e,s(e)))))),u(u(s(u(u(e,s(e)),s(u(e,s(e))))),s(s(u(u(e,s(e)),s(u(e,s(e))))))),s(u(u(u(e,s(e)),s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))))))),
inference(definition_unfolding,[],[f90,f92,f170,f170,f170,f170,f170,f170,f170,f170,f92,f170,f170,f170,f92,f170,f170,f170,f170,f170,f170]) ).
fof(f172,plain,
! [X1] : mem(X1,s(X1)),
inference(equality_resolution,[],[f94]) ).
fof(f174,plain,
! [X0] :
( ~ mem(X0,u(u(s(s(u(e,s(e)))),s(p(s(u(e,s(e)))))),u(s(s(u(u(e,s(e)),s(u(e,s(e)))))),u(u(u(u(e,s(e)),s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(u(u(e,s(e)),s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))))))))
| mem(X0,u(u(u(s(u(e,s(e))),s(s(u(e,s(e))))),s(p(s(u(e,s(e)))))),u(u(s(u(u(e,s(e)),s(u(e,s(e))))),s(s(u(u(e,s(e)),s(u(e,s(e))))))),s(u(u(u(e,s(e)),s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))))))) ),
inference(resolution,[],[f110,f171]) ).
fof(f175,plain,
! [X0] :
( mem(X0,u(u(u(s(u(e,s(e))),s(s(u(e,s(e))))),s(p(s(u(e,s(e)))))),u(u(s(u(u(e,s(e)),s(u(e,s(e))))),s(s(u(u(e,s(e)),s(u(e,s(e))))))),s(u(u(u(e,s(e)),s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))))))
| ~ mem(X0,u(s(s(u(u(e,s(e)),s(u(e,s(e)))))),u(u(u(u(e,s(e)),s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(u(u(e,s(e)),s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))))))) ),
inference(resolution,[],[f174,f96]) ).
fof(f179,plain,
! [X0] :
( ~ mem(X0,u(s(s(u(u(e,s(e)),s(u(e,s(e)))))),u(u(u(u(e,s(e)),s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(u(u(e,s(e)),s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))))))
| mem(X0,u(u(s(u(e,s(e))),s(s(u(e,s(e))))),s(p(s(u(e,s(e)))))))
| mem(X0,u(u(s(u(u(e,s(e)),s(u(e,s(e))))),s(s(u(u(e,s(e)),s(u(e,s(e))))))),s(u(u(u(e,s(e)),s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))))) ),
inference(resolution,[],[f95,f175]) ).
fof(f181,plain,
! [X0] :
( mem(X0,u(u(s(u(u(e,s(e)),s(u(e,s(e))))),s(s(u(u(e,s(e)),s(u(e,s(e))))))),s(u(u(u(e,s(e)),s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))))))
| mem(X0,u(u(s(u(e,s(e))),s(s(u(e,s(e))))),s(p(s(u(e,s(e)))))))
| ~ mem(X0,u(u(u(u(e,s(e)),s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(u(u(e,s(e)),s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))))) ),
inference(resolution,[],[f179,f96]) ).
fof(f182,plain,
! [X0] :
( ~ mem(X0,u(u(u(u(e,s(e)),s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))),s(u(u(u(e,s(e)),s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))))))
| mem(X0,u(u(s(u(e,s(e))),s(s(u(e,s(e))))),s(p(s(u(e,s(e)))))))
| mem(X0,s(u(u(u(e,s(e)),s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))))
| mem(X0,u(s(u(u(e,s(e)),s(u(e,s(e))))),s(s(u(u(e,s(e)),s(u(e,s(e)))))))) ),
inference(resolution,[],[f181,f95]) ).
fof(f192,plain,
! [X0] :
( mem(X0,u(s(u(u(e,s(e)),s(u(e,s(e))))),s(s(u(u(e,s(e)),s(u(e,s(e))))))))
| mem(X0,s(u(u(u(e,s(e)),s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))))
| mem(X0,u(u(s(u(e,s(e))),s(s(u(e,s(e))))),s(p(s(u(e,s(e)))))))
| ~ mem(X0,u(u(u(e,s(e)),s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))) ),
inference(resolution,[],[f182,f97]) ).
fof(f194,plain,
! [X0] :
( mem(X0,s(u(u(u(e,s(e)),s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))))
| mem(X0,u(u(s(u(e,s(e))),s(s(u(e,s(e))))),s(p(s(u(e,s(e)))))))
| ~ mem(X0,u(u(u(e,s(e)),s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))))
| mem(X0,s(s(u(u(e,s(e)),s(u(e,s(e)))))))
| mem(X0,s(u(u(e,s(e)),s(u(e,s(e)))))) ),
inference(resolution,[],[f192,f95]) ).
fof(f195,plain,
! [X0] :
( ~ mem(X0,u(u(u(e,s(e)),s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))))
| mem(X0,u(u(s(u(e,s(e))),s(s(u(e,s(e))))),s(p(s(u(e,s(e)))))))
| mem(X0,s(s(u(u(e,s(e)),s(u(e,s(e)))))))
| mem(X0,s(u(u(e,s(e)),s(u(e,s(e))))))
| u(u(u(e,s(e)),s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))) = X0 ),
inference(resolution,[],[f194,f93]) ).
fof(f196,plain,
! [X0] :
( mem(X0,u(u(s(u(e,s(e))),s(s(u(e,s(e))))),s(p(s(u(e,s(e)))))))
| mem(X0,s(s(u(u(e,s(e)),s(u(e,s(e)))))))
| mem(X0,s(u(u(e,s(e)),s(u(e,s(e))))))
| u(u(u(e,s(e)),s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))) = X0
| ~ mem(X0,u(u(e,s(e)),s(u(e,s(e))))) ),
inference(resolution,[],[f195,f97]) ).
fof(f198,plain,
! [X0] :
( mem(X0,u(s(u(e,s(e))),s(s(u(e,s(e))))))
| mem(X0,s(u(u(e,s(e)),s(u(e,s(e))))))
| u(u(u(e,s(e)),s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))) = X0
| ~ mem(X0,u(u(e,s(e)),s(u(e,s(e)))))
| mem(X0,s(p(s(u(e,s(e))))))
| mem(X0,s(s(u(u(e,s(e)),s(u(e,s(e))))))) ),
inference(resolution,[],[f196,f95]) ).
fof(f199,plain,
! [X0] :
( mem(X0,s(s(u(u(e,s(e)),s(u(e,s(e)))))))
| u(u(u(e,s(e)),s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))) = X0
| ~ mem(X0,u(u(e,s(e)),s(u(e,s(e)))))
| mem(X0,s(p(s(u(e,s(e))))))
| mem(X0,s(u(u(e,s(e)),s(u(e,s(e))))))
| mem(X0,s(s(u(e,s(e)))))
| mem(X0,s(u(e,s(e)))) ),
inference(resolution,[],[f198,f95]) ).
fof(f200,plain,
! [X0] :
( mem(X0,s(u(u(e,s(e)),s(u(e,s(e))))))
| ~ mem(X0,u(u(e,s(e)),s(u(e,s(e)))))
| mem(X0,s(p(s(u(e,s(e))))))
| u(u(u(e,s(e)),s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))) = X0
| mem(X0,s(s(u(e,s(e)))))
| mem(X0,s(u(e,s(e))))
| s(u(u(e,s(e)),s(u(e,s(e))))) = X0 ),
inference(resolution,[],[f199,f93]) ).
fof(f201,plain,
! [X0] :
( ~ mem(X0,u(u(e,s(e)),s(u(e,s(e)))))
| mem(X0,s(p(s(u(e,s(e))))))
| u(u(u(e,s(e)),s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))) = X0
| mem(X0,s(s(u(e,s(e)))))
| mem(X0,s(u(e,s(e))))
| s(u(u(e,s(e)),s(u(e,s(e))))) = X0
| u(u(e,s(e)),s(u(e,s(e)))) = X0 ),
inference(resolution,[],[f200,f93]) ).
fof(f202,plain,
! [X0] :
( mem(X0,s(p(s(u(e,s(e))))))
| u(u(u(e,s(e)),s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))) = X0
| mem(X0,s(s(u(e,s(e)))))
| mem(X0,s(u(e,s(e))))
| s(u(u(e,s(e)),s(u(e,s(e))))) = X0
| u(u(e,s(e)),s(u(e,s(e)))) = X0
| ~ mem(X0,u(e,s(e))) ),
inference(resolution,[],[f201,f97]) ).
fof(f204,plain,
! [X0] :
( mem(X0,s(s(u(e,s(e)))))
| u(u(u(e,s(e)),s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))) = X0
| mem(X0,s(u(e,s(e))))
| s(u(u(e,s(e)),s(u(e,s(e))))) = X0
| u(u(e,s(e)),s(u(e,s(e)))) = X0
| ~ mem(X0,u(e,s(e)))
| p(s(u(e,s(e)))) = X0 ),
inference(resolution,[],[f202,f93]) ).
fof(f205,plain,
! [X0] :
( mem(X0,s(u(e,s(e))))
| u(u(u(e,s(e)),s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))) = X0
| s(u(u(e,s(e)),s(u(e,s(e))))) = X0
| u(u(e,s(e)),s(u(e,s(e)))) = X0
| ~ mem(X0,u(e,s(e)))
| p(s(u(e,s(e)))) = X0
| s(u(e,s(e))) = X0 ),
inference(resolution,[],[f204,f93]) ).
fof(f206,plain,
! [X0] :
( ~ mem(X0,u(e,s(e)))
| s(u(u(e,s(e)),s(u(e,s(e))))) = X0
| u(u(e,s(e)),s(u(e,s(e)))) = X0
| u(u(u(e,s(e)),s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))) = X0
| p(s(u(e,s(e)))) = X0
| s(u(e,s(e))) = X0
| u(e,s(e)) = X0 ),
inference(resolution,[],[f205,f93]) ).
fof(f208,plain,
! [X0] :
( ~ mem(X0,s(e))
| u(u(e,s(e)),s(u(e,s(e)))) = X0
| u(u(u(e,s(e)),s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))) = X0
| p(s(u(e,s(e)))) = X0
| s(u(e,s(e))) = X0
| u(e,s(e)) = X0
| s(u(u(e,s(e)),s(u(e,s(e))))) = X0 ),
inference(resolution,[],[f206,f96]) ).
fof(f209,plain,
( e = u(u(e,s(e)),s(u(e,s(e))))
| e = u(u(u(e,s(e)),s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))
| e = p(s(u(e,s(e))))
| e = s(u(e,s(e)))
| e = u(e,s(e))
| e = s(u(u(e,s(e)),s(u(e,s(e))))) ),
inference(resolution,[],[f208,f172]) ).
fof(f211,definition,
( spl17_3
<=> e = s(u(u(e,s(e)),s(u(e,s(e))))) ),
introduced(definition,[new_symbols(definition,[spl17_3])],[avatar_definition]) ).
fof(f212,plain,
( e = s(u(u(e,s(e)),s(u(e,s(e)))))
| ~ spl17_3 ),
inference(avatar_component_clause,[],[f211]) ).
fof(f214,definition,
( spl17_4
<=> e = u(e,s(e)) ),
introduced(definition,[new_symbols(definition,[spl17_4])],[avatar_definition]) ).
fof(f215,plain,
( e = u(e,s(e))
| ~ spl17_4 ),
inference(avatar_component_clause,[],[f214]) ).
fof(f217,definition,
( spl17_5
<=> e = s(u(e,s(e))) ),
introduced(definition,[new_symbols(definition,[spl17_5])],[avatar_definition]) ).
fof(f218,plain,
( e = s(u(e,s(e)))
| ~ spl17_5 ),
inference(avatar_component_clause,[],[f217]) ).
fof(f220,definition,
( spl17_6
<=> e = p(s(u(e,s(e)))) ),
introduced(definition,[new_symbols(definition,[spl17_6])],[avatar_definition]) ).
fof(f221,plain,
( e = p(s(u(e,s(e))))
| ~ spl17_6 ),
inference(avatar_component_clause,[],[f220]) ).
fof(f223,definition,
( spl17_7
<=> e = u(u(u(e,s(e)),s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e)))))) ),
introduced(definition,[new_symbols(definition,[spl17_7])],[avatar_definition]) ).
fof(f224,plain,
( e = u(u(u(e,s(e)),s(u(e,s(e)))),s(u(u(e,s(e)),s(u(e,s(e))))))
| ~ spl17_7 ),
inference(avatar_component_clause,[],[f223]) ).
fof(f226,definition,
( spl17_8
<=> e = u(u(e,s(e)),s(u(e,s(e)))) ),
introduced(definition,[new_symbols(definition,[spl17_8])],[avatar_definition]) ).
fof(f227,plain,
( e = u(u(e,s(e)),s(u(e,s(e))))
| ~ spl17_8 ),
inference(avatar_component_clause,[],[f226]) ).
fof(f228,plain,
( spl17_3
| spl17_4
| spl17_5
| spl17_6
| spl17_7
| spl17_8 ),
inference(avatar_split_clause,[],[f209,f226,f223,f220,f217,f214,f211]) ).
fof(f242,plain,
( mem(u(u(e,s(e)),s(u(e,s(e)))),e)
| ~ spl17_3 ),
inference(superposition,[],[f172,f212]) ).
fof(f244,plain,
( $false
| ~ spl17_3 ),
inference(forward_subsumption_resolution,[],[f242,f91]) ).
fof(f245,plain,
~ spl17_3,
inference(avatar_contradiction_clause,[],[f244]) ).
fof(f272,plain,
( ! [X0] :
( mem(X0,e)
| ~ mem(X0,s(e)) )
| ~ spl17_4 ),
inference(superposition,[],[f96,f215]) ).
fof(f273,plain,
( ! [X0] : ~ mem(X0,s(e))
| ~ spl17_4 ),
inference(forward_subsumption_resolution,[],[f272,f91]) ).
fof(f343,plain,
( $false
| ~ spl17_4 ),
inference(unit_resulting_resolution,[],[f273,f172]) ).
fof(f346,plain,
~ spl17_4,
inference(avatar_contradiction_clause,[],[f343]) ).
fof(f366,plain,
( mem(u(e,s(e)),e)
| ~ spl17_5 ),
inference(superposition,[],[f172,f218]) ).
fof(f368,plain,
( $false
| ~ spl17_5 ),
inference(forward_subsumption_resolution,[],[f366,f91]) ).
fof(f369,plain,
~ spl17_5,
inference(avatar_contradiction_clause,[],[f368]) ).
fof(f554,plain,
( ! [X0] :
( mem(X0,e)
| ~ subq(X0,s(u(e,s(e)))) )
| ~ spl17_6 ),
inference(superposition,[],[f103,f221]) ).
fof(f555,plain,
( ! [X0] : ~ subq(X0,s(u(e,s(e))))
| ~ spl17_6 ),
inference(forward_subsumption_resolution,[],[f554,f91]) ).
fof(f557,plain,
( $false
| ~ spl17_6 ),
inference(unit_resulting_resolution,[],[f111,f91,f555]) ).
fof(f564,plain,
~ spl17_6,
inference(avatar_contradiction_clause,[],[f557]) ).
fof(f629,plain,
( ! [X0] :
( mem(X0,e)
| ~ mem(X0,u(u(e,s(e)),s(u(e,s(e))))) )
| ~ spl17_7 ),
inference(superposition,[],[f97,f224]) ).
fof(f632,plain,
( ! [X0] : ~ mem(X0,u(u(e,s(e)),s(u(e,s(e)))))
| ~ spl17_7 ),
inference(forward_subsumption_resolution,[],[f629,f91]) ).
fof(f633,plain,
( $false
| ~ spl17_7 ),
inference(unit_resulting_resolution,[],[f96,f172,f632]) ).
fof(f638,plain,
~ spl17_7,
inference(avatar_contradiction_clause,[],[f633]) ).
fof(f761,plain,
( ! [X0] :
( mem(X0,e)
| ~ mem(X0,u(e,s(e))) )
| ~ spl17_8 ),
inference(superposition,[],[f97,f227]) ).
fof(f764,plain,
( ! [X0] : ~ mem(X0,u(e,s(e)))
| ~ spl17_8 ),
inference(forward_subsumption_resolution,[],[f761,f91]) ).
fof(f772,plain,
( $false
| ~ spl17_8 ),
inference(unit_resulting_resolution,[],[f96,f172,f764]) ).
fof(f777,plain,
~ spl17_8,
inference(avatar_contradiction_clause,[],[f772]) ).
cnf(s2,plain,
( spl17_3
| spl17_4
| spl17_5
| spl17_6
| spl17_7
| spl17_8 ),
inference(sat_conversion,[],[f228]) ).
cnf(s3,plain,
~ spl17_3,
inference(sat_conversion,[],[f245]) ).
cnf(s5,plain,
~ spl17_4,
inference(sat_conversion,[],[f346]) ).
cnf(s6,plain,
~ spl17_5,
inference(sat_conversion,[],[f369]) ).
cnf(s10,plain,
~ spl17_6,
inference(sat_conversion,[],[f564]) ).
cnf(s11,plain,
~ spl17_7,
inference(sat_conversion,[],[f638]) ).
cnf(s12,plain,
~ spl17_8,
inference(sat_conversion,[],[f777]) ).
cnf(s13,plain,
$false,
inference(rat,[],[s2,s12,s11,s10,s6,s5,s3]) ).
fof(f778,plain,
$false,
inference(avatar_sat_refutation,[],[s13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV568+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n026.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Mon Sep 28 06:41:27 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 4.31/1.55 % (3655665)Detected formulas, will run a generic FOF schedule.
% 4.31/1.55 % (3655671)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=3528940403:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.31/1.55 % (3655674)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2528572668:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.31/1.55 % (3655672)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=520609283:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.31/1.55 % (3655670)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=3152542267:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.31/1.55 % (3655673)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=487494955:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.31/1.55 % (3655673)Refutation not found, incomplete strategy
% 4.31/1.55 % (3655673)------------------------------
% 4.31/1.55 % (3655673)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.31/1.55 % (3655673)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.31/1.55 % (3655673)CaDiCaL version: 2.1.3
% 4.31/1.55 % (3655673)Termination reason: Refutation not found, incomplete strategy
% 4.31/1.55 % (3655673)Time elapsed: 0.001 s
% 4.31/1.55 % (3655673)Peak memory usage: 88 MB
% 4.31/1.55 % (3655673)Instructions burned: 1 (million)
% 4.31/1.55 % (3655676)dis-21_1_sil=8000:lcm=predicate:random_seed=1677680254: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)
% 4.31/1.55 % (3655675)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3391852109:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.31/1.55 % (3655674)Instruction limit reached!
% 4.31/1.55 % (3655674)------------------------------
% 4.31/1.55 % (3655674)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.31/1.55 % (3655674)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.31/1.55 % (3655674)CaDiCaL version: 2.1.3
% 4.31/1.55 % (3655674)Termination reason: Instruction limit
% 4.31/1.55 % (3655674)Termination phase: Saturation
% 4.31/1.55 % (3655674)Time elapsed: 0.072 s
% 4.31/1.55 % (3655674)Peak memory usage: 88 MB
% 4.31/1.55 % (3655674)Instructions burned: 120 (million)
% 4.31/1.55 % (3655676)Instruction limit reached!
% 4.31/1.55 % (3655676)------------------------------
% 4.31/1.55 % (3655676)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.31/1.55 % (3655676)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.31/1.55 % (3655676)CaDiCaL version: 2.1.3
% 4.31/1.55 % (3655676)Termination reason: Instruction limit
% 4.31/1.55 % (3655676)Termination phase: Saturation
% 4.31/1.55 % (3655676)Time elapsed: 0.070 s
% 4.31/1.55 % (3655676)Peak memory usage: 89 MB
% 4.31/1.55 % (3655676)Instructions burned: 131 (million)
% 4.31/1.55 % (3655675)Instruction limit reached!
% 4.31/1.55 % (3655675)------------------------------
% 4.31/1.55 % (3655675)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.31/1.55 % (3655675)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.31/1.55 % (3655675)CaDiCaL version: 2.1.3
% 4.31/1.55 % (3655675)Termination reason: Instruction limit
% 4.31/1.55 % (3655675)Termination phase: Saturation
% 4.31/1.55 % (3655675)Time elapsed: 0.084 s
% 4.31/1.55 % (3655675)Peak memory usage: 89 MB
% 4.31/1.55 % (3655675)Instructions burned: 139 (million)
% 4.31/1.55 % (3655684)lrs+10_1_sil=8000:sp=occurrence:random_seed=35692376:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 4.31/1.55 % (3655685)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1614455435:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.31/1.55 % (3655686)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1077438773:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.31/1.55 % (3655673)------------------------------
% 4.31/1.55 % (3655673)------------------------------
% 4.31/1.55 % (3655685)Instruction limit reached!
% 4.31/1.55 % (3655685)------------------------------
% 4.31/1.55 % (3655685)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.31/1.55 % (3655685)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.31/1.55 % (3655685)CaDiCaL version: 2.1.3
% 4.31/1.55 % (3655685)Termination reason: Instruction limit
% 4.31/1.55 % (3655685)Termination phase: Saturation
% 4.31/1.55 % (3655685)Time elapsed: 0.077 s
% 4.31/1.55 % (3655685)Peak memory usage: 89 MB
% 4.31/1.55 % (3655685)Instructions burned: 157 (million)
% 4.31/1.55 % (3655684)Instruction limit reached!
% 4.31/1.55 % (3655684)------------------------------
% 4.31/1.55 % (3655684)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.31/1.55 % (3655684)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.31/1.55 % (3655684)CaDiCaL version: 2.1.3
% 4.31/1.55 % (3655684)Termination reason: Instruction limit
% 4.31/1.55 % (3655684)Termination phase: Saturation
% 4.31/1.55 % (3655684)Time elapsed: 0.168 s
% 4.31/1.55 % (3655684)Peak memory usage: 92 MB
% 4.31/1.55 % (3655684)Instructions burned: 286 (million)
% 4.31/1.55 % (3655671)First to succeed.
% 4.31/1.55 % (3655671)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3655665"
% 4.31/1.55 % (3655690)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=2233624057:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 4.31/1.55 % (3655686)Instruction limit reached!
% 4.31/1.55 % (3655686)------------------------------
% 4.31/1.55 % (3655686)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.31/1.55 % (3655686)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.31/1.55 % (3655686)CaDiCaL version: 2.1.3
% 4.31/1.55 % (3655686)Termination reason: Instruction limit
% 4.31/1.55 % (3655686)Termination phase: Saturation
% 4.31/1.55 % (3655686)Time elapsed: 0.183 s
% 4.31/1.55 % (3655686)Peak memory usage: 90 MB
% 4.31/1.55 % (3655686)Instructions burned: 325 (million)
% 4.31/1.55 % (3655691)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2268132197:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 4.31/1.55 % (3655691)Refutation not found, incomplete strategy
% 4.31/1.55 % (3655691)------------------------------
% 4.31/1.55 % (3655691)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.31/1.55 % (3655691)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.31/1.55 % (3655691)CaDiCaL version: 2.1.3
% 4.31/1.55 % (3655691)Termination reason: Refutation not found, incomplete strategy
% 4.31/1.55 % (3655691)Time elapsed: 0.002 s
% 4.31/1.55 % (3655691)Peak memory usage: 88 MB
% 4.31/1.55 % (3655691)Instructions burned: 1 (million)
% 4.31/1.55 % (3655692)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=4233934689:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 4.31/1.55 % (3655690)Instruction limit reached!
% 4.31/1.55 % (3655690)------------------------------
% 4.31/1.55 % (3655690)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.31/1.55 % (3655690)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.31/1.55 % (3655690)CaDiCaL version: 2.1.3
% 4.31/1.55 % (3655690)Termination reason: Instruction limit
% 4.31/1.55 % (3655690)Termination phase: Saturation
% 4.31/1.55 % (3655690)Time elapsed: 0.139 s
% 4.31/1.55 % (3655690)Peak memory usage: 91 MB
% 4.31/1.55 % (3655690)Instructions burned: 248 (million)
% 4.31/1.55 % (3655671)Refutation found. Thanks to Tanya!
% 4.31/1.55 % SZS status Theorem for theBenchmark
% 4.31/1.55 % SZS output start Proof for theBenchmark
% See solution above
% 5.34/1.65 % (3655671)------------------------------
% 5.34/1.65 % (3655671)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.34/1.65 % (3655671)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.34/1.65 % (3655671)CaDiCaL version: 2.1.3
% 5.34/1.65 % (3655671)Termination reason: Refutation
% 5.34/1.65 % (3655671)Time elapsed: 0.418 s
% 5.34/1.65 % (3655671)Peak memory usage: 131 MB
% 5.34/1.65 % (3655671)Instructions burned: 1075 (million)
% 5.34/1.65 % (3655671)------------------------------
% 5.34/1.65 % (3655671)------------------------------
% 5.34/1.65 % (3655665)Success in time 0.686 s
% 5.34/1.65 % Vampire exiting
%------------------------------------------------------------------------------