%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV579+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 : n010.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 12:58:23 PM UTC 2026
% Result : Theorem 1.82s 1.11s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 14
% Syntax : Number of formulae : 102 ( 36 unt; 8 def)
% Number of atoms : 207 ( 23 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 198 ( 93 ~; 81 |; 11 &)
% ( 12 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 9 ( 3 avg)
% Number of predicates : 12 ( 10 usr; 9 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-2 aty)
% Number of variables : 78 ( 0 sgn 76 !; 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(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(f26,conjecture,
subq(u(a(s(n(n(e))),p(s(n(e)))),a(n(n(s(n(e)))),n(n(n(e))))),u(u(a(s(s(n(n(e)))),n(n(n(e)))),n(a(s(s(n(e))),n(n(e))))),u(a(s(n(e)),p(s(n(e)))),a(s(n(s(n(e)))),p(n(n(e))))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subq_2158_39278) ).
fof(f27,negated_conjecture,
~ subq(u(a(s(n(n(e))),p(s(n(e)))),a(n(n(s(n(e)))),n(n(n(e))))),u(u(a(s(s(n(n(e)))),n(n(n(e)))),n(a(s(s(n(e))),n(n(e))))),u(a(s(n(e)),p(s(n(e)))),a(s(n(s(n(e)))),p(n(n(e))))))),
inference(negated_conjecture,[status(cth)],[f26]) ).
fof(f28,plain,
~ subq(u(a(s(n(n(e))),p(s(n(e)))),a(n(n(s(n(e)))),n(n(n(e))))),u(u(a(s(s(n(n(e)))),n(n(n(e)))),n(a(s(s(n(e))),n(n(e))))),u(a(s(n(e)),p(s(n(e)))),a(s(n(s(n(e)))),p(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] :
( ( 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(f33,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,[],[f32]) ).
fof(f34,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))],[f33]) ).
fof(f35,plain,
! [X0,X1] :
( ( mem(X0,s(X1))
| X0 != X1 )
& ( X0 = X1
| ~ mem(X0,s(X1)) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f36,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(f37,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,[],[f36]) ).
fof(f42,plain,
! [X0,X1] :
( subq(X0,X1)
| mem(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f34]) ).
fof(f43,plain,
! [X0,X1] :
( ~ mem(sK0(X0,X1),X1)
| subq(X0,X1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f46,plain,
! [X0,X1] :
( ~ mem(X0,s(X1))
| X0 = X1 ),
inference(cnf_transformation,[],[f35]) ).
fof(f47,plain,
! [X0,X1] :
( mem(X0,s(X1))
| X0 != X1 ),
inference(cnf_transformation,[],[f35]) ).
fof(f48,plain,
! [X2,X0,X1] :
( ~ mem(X0,u(X1,X2))
| mem(X0,X2)
| mem(X0,X1) ),
inference(cnf_transformation,[],[f37]) ).
fof(f49,plain,
! [X2,X0,X1] :
( mem(X0,u(X1,X2))
| ~ mem(X0,X2) ),
inference(cnf_transformation,[],[f37]) ).
fof(f50,plain,
! [X2,X0,X1] :
( mem(X0,u(X1,X2))
| ~ mem(X0,X1) ),
inference(cnf_transformation,[],[f37]) ).
fof(f54,plain,
! [X0,X1] : a(X0,X1) = u(X0,s(X1)),
inference(cnf_transformation,[],[f8]) ).
fof(f55,plain,
! [X0] : n(X0) = a(X0,X0),
inference(cnf_transformation,[],[f9]) ).
fof(f58,plain,
~ subq(u(a(s(n(n(e))),p(s(n(e)))),a(n(n(s(n(e)))),n(n(n(e))))),u(u(a(s(s(n(n(e)))),n(n(n(e)))),n(a(s(s(n(e))),n(n(e))))),u(a(s(n(e)),p(s(n(e)))),a(s(n(s(n(e)))),p(n(n(e))))))),
inference(cnf_transformation,[],[f28]) ).
fof(f59,plain,
! [X1] : mem(X1,s(X1)),
inference(equality_resolution,[],[f47]) ).
fof(f61,plain,
mem(sK0(u(a(s(n(n(e))),p(s(n(e)))),a(n(n(s(n(e)))),n(n(n(e))))),u(u(a(s(s(n(n(e)))),n(n(n(e)))),n(a(s(s(n(e))),n(n(e))))),u(a(s(n(e)),p(s(n(e)))),a(s(n(s(n(e)))),p(n(n(e))))))),u(a(s(n(n(e))),p(s(n(e)))),a(n(n(s(n(e)))),n(n(n(e)))))),
inference(resolution,[],[f42,f58]) ).
fof(f63,plain,
! [X2,X0,X1] :
( subq(X0,u(X1,X2))
| ~ mem(sK0(X0,u(X1,X2)),X2) ),
inference(resolution,[],[f49,f43]) ).
fof(f64,plain,
! [X2,X0,X1] :
( subq(X0,u(X1,X2))
| ~ mem(sK0(X0,u(X1,X2)),X1) ),
inference(resolution,[],[f50,f43]) ).
fof(f65,plain,
! [X2,X0,X1] :
( mem(X2,a(X0,X1))
| ~ mem(X2,X0) ),
inference(superposition,[],[f50,f54]) ).
fof(f66,plain,
! [X2,X0,X1] :
( ~ mem(X2,s(X1))
| mem(X2,a(X0,X1)) ),
inference(superposition,[],[f49,f54]) ).
fof(f71,plain,
! [X0,X1] :
( mem(X1,n(X0))
| ~ mem(X1,X0) ),
inference(superposition,[],[f65,f55]) ).
fof(f74,plain,
! [X2,X0,X1] :
( mem(X2,s(X1))
| ~ mem(X2,a(X0,X1))
| mem(X2,X0) ),
inference(superposition,[],[f48,f54]) ).
fof(f76,plain,
( mem(sK0(u(a(s(n(n(e))),p(s(n(e)))),a(n(n(s(n(e)))),n(n(n(e))))),u(u(a(s(s(n(n(e)))),n(n(n(e)))),n(a(s(s(n(e))),n(n(e))))),u(a(s(n(e)),p(s(n(e)))),a(s(n(s(n(e)))),p(n(n(e))))))),a(n(n(s(n(e)))),n(n(n(e)))))
| mem(sK0(u(a(s(n(n(e))),p(s(n(e)))),a(n(n(s(n(e)))),n(n(n(e))))),u(u(a(s(s(n(n(e)))),n(n(n(e)))),n(a(s(s(n(e))),n(n(e))))),u(a(s(n(e)),p(s(n(e)))),a(s(n(s(n(e)))),p(n(n(e))))))),a(s(n(n(e))),p(s(n(e))))) ),
inference(resolution,[],[f61,f48]) ).
fof(f78,definition,
( spl1_1
<=> mem(sK0(u(a(s(n(n(e))),p(s(n(e)))),a(n(n(s(n(e)))),n(n(n(e))))),u(u(a(s(s(n(n(e)))),n(n(n(e)))),n(a(s(s(n(e))),n(n(e))))),u(a(s(n(e)),p(s(n(e)))),a(s(n(s(n(e)))),p(n(n(e))))))),a(s(n(n(e))),p(s(n(e))))) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
fof(f80,plain,
( mem(sK0(u(a(s(n(n(e))),p(s(n(e)))),a(n(n(s(n(e)))),n(n(n(e))))),u(u(a(s(s(n(n(e)))),n(n(n(e)))),n(a(s(s(n(e))),n(n(e))))),u(a(s(n(e)),p(s(n(e)))),a(s(n(s(n(e)))),p(n(n(e))))))),a(s(n(n(e))),p(s(n(e)))))
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f78]) ).
fof(f82,definition,
( spl1_2
<=> mem(sK0(u(a(s(n(n(e))),p(s(n(e)))),a(n(n(s(n(e)))),n(n(n(e))))),u(u(a(s(s(n(n(e)))),n(n(n(e)))),n(a(s(s(n(e))),n(n(e))))),u(a(s(n(e)),p(s(n(e)))),a(s(n(s(n(e)))),p(n(n(e))))))),a(n(n(s(n(e)))),n(n(n(e))))) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
fof(f84,plain,
( mem(sK0(u(a(s(n(n(e))),p(s(n(e)))),a(n(n(s(n(e)))),n(n(n(e))))),u(u(a(s(s(n(n(e)))),n(n(n(e)))),n(a(s(s(n(e))),n(n(e))))),u(a(s(n(e)),p(s(n(e)))),a(s(n(s(n(e)))),p(n(n(e))))))),a(n(n(s(n(e)))),n(n(n(e)))))
| ~ spl1_2 ),
inference(avatar_component_clause,[],[f82]) ).
fof(f85,plain,
( spl1_1
| spl1_2 ),
inference(avatar_split_clause,[],[f76,f82,f78]) ).
fof(f88,plain,
! [X0,X1] : mem(X0,a(X1,X0)),
inference(resolution,[],[f66,f59]) ).
fof(f106,plain,
~ mem(sK0(u(a(s(n(n(e))),p(s(n(e)))),a(n(n(s(n(e)))),n(n(n(e))))),u(u(a(s(s(n(n(e)))),n(n(n(e)))),n(a(s(s(n(e))),n(n(e))))),u(a(s(n(e)),p(s(n(e)))),a(s(n(s(n(e)))),p(n(n(e))))))),u(a(s(n(e)),p(s(n(e)))),a(s(n(s(n(e)))),p(n(n(e)))))),
inference(resolution,[],[f63,f58]) ).
fof(f112,plain,
~ mem(sK0(u(a(s(n(n(e))),p(s(n(e)))),a(n(n(s(n(e)))),n(n(n(e))))),u(u(a(s(s(n(n(e)))),n(n(n(e)))),n(a(s(s(n(e))),n(n(e))))),u(a(s(n(e)),p(s(n(e)))),a(s(n(s(n(e)))),p(n(n(e))))))),a(s(n(e)),p(s(n(e))))),
inference(resolution,[],[f106,f50]) ).
fof(f113,plain,
~ mem(sK0(u(a(s(n(n(e))),p(s(n(e)))),a(n(n(s(n(e)))),n(n(n(e))))),u(u(a(s(s(n(n(e)))),n(n(n(e)))),n(a(s(s(n(e))),n(n(e))))),u(a(s(n(e)),p(s(n(e)))),a(s(n(s(n(e)))),p(n(n(e))))))),a(s(n(s(n(e)))),p(n(n(e))))),
inference(resolution,[],[f106,f49]) ).
fof(f114,plain,
~ mem(sK0(u(a(s(n(n(e))),p(s(n(e)))),a(n(n(s(n(e)))),n(n(n(e))))),u(u(a(s(s(n(n(e)))),n(n(n(e)))),n(a(s(s(n(e))),n(n(e))))),u(a(s(n(e)),p(s(n(e)))),a(s(n(s(n(e)))),p(n(n(e))))))),u(a(s(s(n(n(e)))),n(n(n(e)))),n(a(s(s(n(e))),n(n(e)))))),
inference(resolution,[],[f64,f58]) ).
fof(f120,plain,
~ mem(sK0(u(a(s(n(n(e))),p(s(n(e)))),a(n(n(s(n(e)))),n(n(n(e))))),u(u(a(s(s(n(n(e)))),n(n(n(e)))),n(a(s(s(n(e))),n(n(e))))),u(a(s(n(e)),p(s(n(e)))),a(s(n(s(n(e)))),p(n(n(e))))))),s(n(e))),
inference(resolution,[],[f112,f65]) ).
fof(f122,plain,
! [X2,X0,X1] :
( ~ mem(X0,a(X1,X2))
| mem(X0,X1)
| X0 = X2 ),
inference(resolution,[],[f74,f46]) ).
fof(f125,plain,
~ mem(sK0(u(a(s(n(n(e))),p(s(n(e)))),a(n(n(s(n(e)))),n(n(n(e))))),u(u(a(s(s(n(n(e)))),n(n(n(e)))),n(a(s(s(n(e))),n(n(e))))),u(a(s(n(e)),p(s(n(e)))),a(s(n(s(n(e)))),p(n(n(e))))))),a(s(s(n(n(e)))),n(n(n(e))))),
inference(resolution,[],[f114,f50]) ).
fof(f126,plain,
~ mem(sK0(u(a(s(n(n(e))),p(s(n(e)))),a(n(n(s(n(e)))),n(n(n(e))))),u(u(a(s(s(n(n(e)))),n(n(n(e)))),n(a(s(s(n(e))),n(n(e))))),u(a(s(n(e)),p(s(n(e)))),a(s(n(s(n(e)))),p(n(n(e))))))),n(a(s(s(n(e))),n(n(e))))),
inference(resolution,[],[f114,f49]) ).
fof(f127,plain,
~ mem(sK0(u(a(s(n(n(e))),p(s(n(e)))),a(n(n(s(n(e)))),n(n(n(e))))),u(u(a(s(s(n(n(e)))),n(n(n(e)))),n(a(s(s(n(e))),n(n(e))))),u(a(s(n(e)),p(s(n(e)))),a(s(n(s(n(e)))),p(n(n(e))))))),a(s(s(n(e))),n(n(e)))),
inference(resolution,[],[f126,f71]) ).
fof(f132,plain,
! [X0,X1] :
( ~ mem(X1,n(X0))
| mem(X1,X0)
| X0 = X1 ),
inference(superposition,[],[f122,f55]) ).
fof(f134,definition,
( spl1_3
<=> n(n(n(e))) = sK0(u(a(s(n(n(e))),p(s(n(e)))),a(n(n(s(n(e)))),n(n(n(e))))),u(u(a(s(s(n(n(e)))),n(n(n(e)))),n(a(s(s(n(e))),n(n(e))))),u(a(s(n(e)),p(s(n(e)))),a(s(n(s(n(e)))),p(n(n(e))))))) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
fof(f136,plain,
( n(n(n(e))) = sK0(u(a(s(n(n(e))),p(s(n(e)))),a(n(n(s(n(e)))),n(n(n(e))))),u(u(a(s(s(n(n(e)))),n(n(n(e)))),n(a(s(s(n(e))),n(n(e))))),u(a(s(n(e)),p(s(n(e)))),a(s(n(s(n(e)))),p(n(n(e)))))))
| ~ spl1_3 ),
inference(avatar_component_clause,[],[f134]) ).
fof(f138,definition,
( spl1_4
<=> mem(sK0(u(a(s(n(n(e))),p(s(n(e)))),a(n(n(s(n(e)))),n(n(n(e))))),u(u(a(s(s(n(n(e)))),n(n(n(e)))),n(a(s(s(n(e))),n(n(e))))),u(a(s(n(e)),p(s(n(e)))),a(s(n(s(n(e)))),p(n(n(e))))))),n(n(s(n(e))))) ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
fof(f140,plain,
( mem(sK0(u(a(s(n(n(e))),p(s(n(e)))),a(n(n(s(n(e)))),n(n(n(e))))),u(u(a(s(s(n(n(e)))),n(n(n(e)))),n(a(s(s(n(e))),n(n(e))))),u(a(s(n(e)),p(s(n(e)))),a(s(n(s(n(e)))),p(n(n(e))))))),n(n(s(n(e)))))
| ~ spl1_4 ),
inference(avatar_component_clause,[],[f138]) ).
fof(f169,plain,
~ mem(sK0(u(a(s(n(n(e))),p(s(n(e)))),a(n(n(s(n(e)))),n(n(n(e))))),u(u(a(s(s(n(n(e)))),n(n(n(e)))),n(a(s(s(n(e))),n(n(e))))),u(a(s(n(e)),p(s(n(e)))),a(s(n(s(n(e)))),p(n(n(e))))))),s(s(n(e)))),
inference(resolution,[],[f127,f65]) ).
fof(f184,plain,
~ mem(sK0(u(a(s(n(n(e))),p(s(n(e)))),a(n(n(s(n(e)))),n(n(n(e))))),u(u(a(s(s(n(n(e)))),n(n(n(e)))),n(a(s(s(n(e))),n(n(e))))),u(a(s(n(e)),p(s(n(e)))),a(s(n(s(n(e)))),p(n(n(e))))))),s(n(s(n(e))))),
inference(resolution,[],[f113,f65]) ).
fof(f231,definition,
( spl1_7
<=> n(s(n(e))) = sK0(u(a(s(n(n(e))),p(s(n(e)))),a(n(n(s(n(e)))),n(n(n(e))))),u(u(a(s(s(n(n(e)))),n(n(n(e)))),n(a(s(s(n(e))),n(n(e))))),u(a(s(n(e)),p(s(n(e)))),a(s(n(s(n(e)))),p(n(n(e))))))) ),
introduced(definition,[new_symbols(definition,[spl1_7])],[avatar_definition]) ).
fof(f233,plain,
( n(s(n(e))) = sK0(u(a(s(n(n(e))),p(s(n(e)))),a(n(n(s(n(e)))),n(n(n(e))))),u(u(a(s(s(n(n(e)))),n(n(n(e)))),n(a(s(s(n(e))),n(n(e))))),u(a(s(n(e)),p(s(n(e)))),a(s(n(s(n(e)))),p(n(n(e)))))))
| ~ spl1_7 ),
inference(avatar_component_clause,[],[f231]) ).
fof(f235,definition,
( spl1_8
<=> mem(sK0(u(a(s(n(n(e))),p(s(n(e)))),a(n(n(s(n(e)))),n(n(n(e))))),u(u(a(s(s(n(n(e)))),n(n(n(e)))),n(a(s(s(n(e))),n(n(e))))),u(a(s(n(e)),p(s(n(e)))),a(s(n(s(n(e)))),p(n(n(e))))))),n(s(n(e)))) ),
introduced(definition,[new_symbols(definition,[spl1_8])],[avatar_definition]) ).
fof(f237,plain,
( mem(sK0(u(a(s(n(n(e))),p(s(n(e)))),a(n(n(s(n(e)))),n(n(n(e))))),u(u(a(s(s(n(n(e)))),n(n(n(e)))),n(a(s(s(n(e))),n(n(e))))),u(a(s(n(e)),p(s(n(e)))),a(s(n(s(n(e)))),p(n(n(e))))))),n(s(n(e))))
| ~ spl1_8 ),
inference(avatar_component_clause,[],[f235]) ).
fof(f246,definition,
( spl1_10
<=> p(s(n(e))) = sK0(u(a(s(n(n(e))),p(s(n(e)))),a(n(n(s(n(e)))),n(n(n(e))))),u(u(a(s(s(n(n(e)))),n(n(n(e)))),n(a(s(s(n(e))),n(n(e))))),u(a(s(n(e)),p(s(n(e)))),a(s(n(s(n(e)))),p(n(n(e))))))) ),
introduced(definition,[new_symbols(definition,[spl1_10])],[avatar_definition]) ).
fof(f248,plain,
( p(s(n(e))) = sK0(u(a(s(n(n(e))),p(s(n(e)))),a(n(n(s(n(e)))),n(n(n(e))))),u(u(a(s(s(n(n(e)))),n(n(n(e)))),n(a(s(s(n(e))),n(n(e))))),u(a(s(n(e)),p(s(n(e)))),a(s(n(s(n(e)))),p(n(n(e)))))))
| ~ spl1_10 ),
inference(avatar_component_clause,[],[f246]) ).
fof(f250,definition,
( spl1_11
<=> mem(sK0(u(a(s(n(n(e))),p(s(n(e)))),a(n(n(s(n(e)))),n(n(n(e))))),u(u(a(s(s(n(n(e)))),n(n(n(e)))),n(a(s(s(n(e))),n(n(e))))),u(a(s(n(e)),p(s(n(e)))),a(s(n(s(n(e)))),p(n(n(e))))))),s(n(n(e)))) ),
introduced(definition,[new_symbols(definition,[spl1_11])],[avatar_definition]) ).
fof(f252,plain,
( mem(sK0(u(a(s(n(n(e))),p(s(n(e)))),a(n(n(s(n(e)))),n(n(n(e))))),u(u(a(s(s(n(n(e)))),n(n(n(e)))),n(a(s(s(n(e))),n(n(e))))),u(a(s(n(e)),p(s(n(e)))),a(s(n(s(n(e)))),p(n(n(e))))))),s(n(n(e))))
| ~ spl1_11 ),
inference(avatar_component_clause,[],[f250]) ).
fof(f263,plain,
( mem(sK0(u(a(s(n(n(e))),p(s(n(e)))),a(n(n(s(n(e)))),n(n(n(e))))),u(u(a(s(s(n(n(e)))),n(n(n(e)))),n(a(s(s(n(e))),n(n(e))))),u(a(s(n(e)),p(s(n(e)))),a(s(n(s(n(e)))),p(n(n(e))))))),n(n(s(n(e)))))
| n(n(n(e))) = sK0(u(a(s(n(n(e))),p(s(n(e)))),a(n(n(s(n(e)))),n(n(n(e))))),u(u(a(s(s(n(n(e)))),n(n(n(e)))),n(a(s(s(n(e))),n(n(e))))),u(a(s(n(e)),p(s(n(e)))),a(s(n(s(n(e)))),p(n(n(e)))))))
| ~ spl1_2 ),
inference(resolution,[],[f84,f122]) ).
fof(f264,plain,
( spl1_3
| spl1_4
| ~ spl1_2 ),
inference(avatar_split_clause,[],[f263,f82,f138,f134]) ).
fof(f373,plain,
( ~ mem(n(n(n(e))),a(s(s(n(n(e)))),n(n(n(e)))))
| ~ spl1_3 ),
inference(superposition,[],[f125,f136]) ).
fof(f405,plain,
( $false
| ~ spl1_3 ),
inference(forward_subsumption_resolution,[],[f373,f88]) ).
fof(f406,plain,
~ spl1_3,
inference(avatar_contradiction_clause,[],[f405]) ).
fof(f410,plain,
( mem(sK0(u(a(s(n(n(e))),p(s(n(e)))),a(n(n(s(n(e)))),n(n(n(e))))),u(u(a(s(s(n(n(e)))),n(n(n(e)))),n(a(s(s(n(e))),n(n(e))))),u(a(s(n(e)),p(s(n(e)))),a(s(n(s(n(e)))),p(n(n(e))))))),n(s(n(e))))
| n(s(n(e))) = sK0(u(a(s(n(n(e))),p(s(n(e)))),a(n(n(s(n(e)))),n(n(n(e))))),u(u(a(s(s(n(n(e)))),n(n(n(e)))),n(a(s(s(n(e))),n(n(e))))),u(a(s(n(e)),p(s(n(e)))),a(s(n(s(n(e)))),p(n(n(e)))))))
| ~ spl1_4 ),
inference(resolution,[],[f140,f132]) ).
fof(f411,plain,
( spl1_7
| spl1_8
| ~ spl1_4 ),
inference(avatar_split_clause,[],[f410,f138,f235,f231]) ).
fof(f426,plain,
( ~ mem(n(s(n(e))),s(n(s(n(e)))))
| ~ spl1_7 ),
inference(superposition,[],[f184,f233]) ).
fof(f443,plain,
( $false
| ~ spl1_7 ),
inference(forward_subsumption_resolution,[],[f426,f59]) ).
fof(f444,plain,
~ spl1_7,
inference(avatar_contradiction_clause,[],[f443]) ).
fof(f472,plain,
( mem(sK0(u(a(s(n(n(e))),p(s(n(e)))),a(n(n(s(n(e)))),n(n(n(e))))),u(u(a(s(s(n(n(e)))),n(n(n(e)))),n(a(s(s(n(e))),n(n(e))))),u(a(s(n(e)),p(s(n(e)))),a(s(n(s(n(e)))),p(n(n(e))))))),s(n(e)))
| s(n(e)) = sK0(u(a(s(n(n(e))),p(s(n(e)))),a(n(n(s(n(e)))),n(n(n(e))))),u(u(a(s(s(n(n(e)))),n(n(n(e)))),n(a(s(s(n(e))),n(n(e))))),u(a(s(n(e)),p(s(n(e)))),a(s(n(s(n(e)))),p(n(n(e)))))))
| ~ spl1_8 ),
inference(resolution,[],[f237,f132]) ).
fof(f473,plain,
( s(n(e)) = sK0(u(a(s(n(n(e))),p(s(n(e)))),a(n(n(s(n(e)))),n(n(n(e))))),u(u(a(s(s(n(n(e)))),n(n(n(e)))),n(a(s(s(n(e))),n(n(e))))),u(a(s(n(e)),p(s(n(e)))),a(s(n(s(n(e)))),p(n(n(e)))))))
| ~ spl1_8 ),
inference(forward_subsumption_resolution,[],[f472,f120]) ).
fof(f491,plain,
( ~ mem(s(n(e)),s(s(n(e))))
| ~ spl1_8 ),
inference(superposition,[],[f169,f473]) ).
fof(f511,plain,
( $false
| ~ spl1_8 ),
inference(forward_subsumption_resolution,[],[f491,f59]) ).
fof(f512,plain,
~ spl1_8,
inference(avatar_contradiction_clause,[],[f511]) ).
fof(f515,plain,
( mem(sK0(u(a(s(n(n(e))),p(s(n(e)))),a(n(n(s(n(e)))),n(n(n(e))))),u(u(a(s(s(n(n(e)))),n(n(n(e)))),n(a(s(s(n(e))),n(n(e))))),u(a(s(n(e)),p(s(n(e)))),a(s(n(s(n(e)))),p(n(n(e))))))),s(n(n(e))))
| p(s(n(e))) = sK0(u(a(s(n(n(e))),p(s(n(e)))),a(n(n(s(n(e)))),n(n(n(e))))),u(u(a(s(s(n(n(e)))),n(n(n(e)))),n(a(s(s(n(e))),n(n(e))))),u(a(s(n(e)),p(s(n(e)))),a(s(n(s(n(e)))),p(n(n(e)))))))
| ~ spl1_1 ),
inference(resolution,[],[f80,f122]) ).
fof(f516,plain,
( spl1_10
| spl1_11
| ~ spl1_1 ),
inference(avatar_split_clause,[],[f515,f78,f250,f246]) ).
fof(f519,plain,
( n(n(e)) = sK0(u(a(s(n(n(e))),p(s(n(e)))),a(n(n(s(n(e)))),n(n(n(e))))),u(u(a(s(s(n(n(e)))),n(n(n(e)))),n(a(s(s(n(e))),n(n(e))))),u(a(s(n(e)),p(s(n(e)))),a(s(n(s(n(e)))),p(n(n(e)))))))
| ~ spl1_11 ),
inference(resolution,[],[f252,f46]) ).
fof(f532,plain,
( ~ mem(n(n(e)),a(s(s(n(e))),n(n(e))))
| ~ spl1_11 ),
inference(superposition,[],[f127,f519]) ).
fof(f553,plain,
( $false
| ~ spl1_11 ),
inference(forward_subsumption_resolution,[],[f532,f88]) ).
fof(f554,plain,
~ spl1_11,
inference(avatar_contradiction_clause,[],[f553]) ).
fof(f560,plain,
( ~ mem(p(s(n(e))),a(s(n(e)),p(s(n(e)))))
| ~ spl1_10 ),
inference(superposition,[],[f112,f248]) ).
fof(f586,plain,
( $false
| ~ spl1_10 ),
inference(forward_subsumption_resolution,[],[f560,f88]) ).
fof(f587,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f586]) ).
cnf(s1,plain,
( spl1_1
| spl1_2 ),
inference(sat_conversion,[],[f85]) ).
cnf(s11,plain,
( ~ spl1_2
| spl1_3
| spl1_4 ),
inference(sat_conversion,[],[f264]) ).
cnf(s19,plain,
~ spl1_3,
inference(sat_conversion,[],[f406]) ).
cnf(s21,plain,
( ~ spl1_4
| spl1_7
| spl1_8 ),
inference(sat_conversion,[],[f411]) ).
cnf(s26,plain,
~ spl1_7,
inference(sat_conversion,[],[f444]) ).
cnf(s34,plain,
~ spl1_8,
inference(sat_conversion,[],[f512]) ).
cnf(s36,plain,
( ~ spl1_1
| spl1_10
| spl1_11 ),
inference(sat_conversion,[],[f516]) ).
cnf(s43,plain,
~ spl1_11,
inference(sat_conversion,[],[f554]) ).
cnf(s49,plain,
~ spl1_10,
inference(sat_conversion,[],[f587]) ).
cnf(s52,plain,
~ spl1_1,
inference(rat,[],[s36,s43,s49]) ).
cnf(s53,plain,
~ spl1_4,
inference(rat,[],[s21,s34,s26]) ).
cnf(s55,plain,
~ spl1_2,
inference(rat,[],[s11,s53,s19]) ).
cnf(s56,plain,
$false,
inference(rat,[],[s1,s55,s52]) ).
fof(f589,plain,
$false,
inference(avatar_sat_refutation,[],[s56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV579+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.35 % Computer : n010.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 28 06:39:32 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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
% 1.82/1.11 % (1722405)Detected formulas, will run a generic FOF schedule.
% 1.82/1.11 % (1722415)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3848270461:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 1.82/1.11 % (1722415)First to succeed.
% 1.82/1.11 % (1722415)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1722405"
% 1.82/1.11 % (1722414)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1507710708:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 1.82/1.11 % (1722413)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2560327077:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 1.82/1.11 % (1722410)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=619392181:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 1.82/1.11 % (1722411)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=3806135661:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 1.82/1.11 % (1722412)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=2242772051:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 1.82/1.11 % (1722413)Refutation not found, incomplete strategy
% 1.82/1.11 % (1722413)------------------------------
% 1.82/1.11 % (1722413)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.82/1.11 % (1722413)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.82/1.11 % (1722413)CaDiCaL version: 2.1.3
% 1.82/1.11 % (1722413)Termination reason: Refutation not found, incomplete strategy
% 1.82/1.11 % (1722413)Time elapsed: 0.001 s
% 1.82/1.11 % (1722413)Peak memory usage: 88 MB
% 1.82/1.11 % (1722413)Instructions burned: 1 (million)
% 1.82/1.11 % (1722416)dis-21_1_sil=8000:lcm=predicate:random_seed=1060146082: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)
% 1.82/1.11 % (1722414)Instruction limit reached!
% 1.82/1.11 % (1722414)------------------------------
% 1.82/1.11 % (1722414)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.82/1.11 % (1722414)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.82/1.11 % (1722414)CaDiCaL version: 2.1.3
% 1.82/1.11 % (1722414)Termination reason: Instruction limit
% 1.82/1.11 % (1722414)Termination phase: Saturation
% 1.82/1.11 % (1722414)Time elapsed: 0.074 s
% 1.82/1.11 % (1722414)Peak memory usage: 88 MB
% 1.82/1.11 % (1722414)Instructions burned: 119 (million)
% 1.82/1.11 % (1722416)Instruction limit reached!
% 1.82/1.11 % (1722416)------------------------------
% 1.82/1.11 % (1722416)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.82/1.11 % (1722416)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.82/1.11 % (1722416)CaDiCaL version: 2.1.3
% 1.82/1.11 % (1722416)Termination reason: Instruction limit
% 1.82/1.11 % (1722416)Termination phase: Saturation
% 1.82/1.11 % (1722416)Time elapsed: 0.064 s
% 1.82/1.11 % (1722416)Peak memory usage: 89 MB
% 1.82/1.11 % (1722416)Instructions burned: 130 (million)
% 1.82/1.11 % (1722415)Refutation found. Thanks to Tanya!
% 1.82/1.11 % SZS status Theorem for theBenchmark
% 1.82/1.11 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/1.30 % (1722415)------------------------------
% 0.15/1.30 % (1722415)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.15/1.30 % (1722415)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/1.30 % (1722415)CaDiCaL version: 2.1.3
% 0.15/1.30 % (1722415)Termination reason: Refutation
% 0.15/1.30 % (1722415)Time elapsed: 0.017 s
% 0.15/1.30 % (1722415)Peak memory usage: 90 MB
% 0.15/1.30 % (1722415)Instructions burned: 48 (million)
% 0.15/1.30 % (1722415)------------------------------
% 0.15/1.30 % (1722415)------------------------------
% 0.15/1.30 % (1722405)Success in time 0.282 s
% 0.15/1.30 % Vampire exiting
%------------------------------------------------------------------------------