%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV581+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 : n015.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 0.83s 1.00s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 15
% Syntax : Number of formulae : 116 ( 29 unt; 8 def)
% Number of atoms : 246 ( 21 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 235 ( 105 ~; 104 |; 12 &)
% ( 13 <=>; 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 : 91 ( 0 sgn 89 !; 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(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(s(s(s(n(e)))),a(n(n(s(n(e)))),s(n(n(e))))),u(s(n(e)),a(p(n(s(n(e)))),s(n(n(e)))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subq_342_343) ).
fof(f27,negated_conjecture,
~ subq(u(s(s(s(n(e)))),a(n(n(s(n(e)))),s(n(n(e))))),u(s(n(e)),a(p(n(s(n(e)))),s(n(n(e)))))),
inference(negated_conjecture,[status(cth)],[f26]) ).
fof(f28,plain,
~ subq(u(s(s(s(n(e)))),a(n(n(s(n(e)))),s(n(n(e))))),u(s(n(e)),a(p(n(s(n(e)))),s(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(f40,plain,
! [X0,X1] :
( ( mem(X0,p(X1))
| ~ subq(X0,X1) )
& ( subq(X0,X1)
| ~ mem(X0,p(X1)) ) ),
inference(nnf_transformation,[],[f10]) ).
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(f57,plain,
! [X0,X1] :
( ~ subq(X0,X1)
| mem(X0,p(X1)) ),
inference(cnf_transformation,[],[f40]) ).
fof(f58,plain,
~ subq(u(s(s(s(n(e)))),a(n(n(s(n(e)))),s(n(n(e))))),u(s(n(e)),a(p(n(s(n(e)))),s(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(s(s(s(n(e)))),a(n(n(s(n(e)))),s(n(n(e))))),u(s(n(e)),a(p(n(s(n(e)))),s(n(n(e)))))),u(s(s(s(n(e)))),a(n(n(s(n(e)))),s(n(n(e)))))),
inference(resolution,[],[f42,f58]) ).
fof(f62,plain,
! [X0,X1] :
( mem(X0,p(X1))
| mem(sK0(X0,X1),X0) ),
inference(resolution,[],[f42,f57]) ).
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(f72,plain,
( mem(sK0(u(s(s(s(n(e)))),a(n(n(s(n(e)))),s(n(n(e))))),u(s(n(e)),a(p(n(s(n(e)))),s(n(n(e)))))),a(n(n(s(n(e)))),s(n(n(e)))))
| mem(sK0(u(s(s(s(n(e)))),a(n(n(s(n(e)))),s(n(n(e))))),u(s(n(e)),a(p(n(s(n(e)))),s(n(n(e)))))),s(s(s(n(e))))) ),
inference(resolution,[],[f48,f61]) ).
fof(f73,plain,
! [X2,X0,X1] :
( mem(X2,s(X1))
| ~ mem(X2,a(X0,X1))
| mem(X2,X0) ),
inference(superposition,[],[f48,f54]) ).
fof(f75,definition,
( spl1_1
<=> mem(sK0(u(s(s(s(n(e)))),a(n(n(s(n(e)))),s(n(n(e))))),u(s(n(e)),a(p(n(s(n(e)))),s(n(n(e)))))),s(s(s(n(e))))) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
fof(f77,plain,
( mem(sK0(u(s(s(s(n(e)))),a(n(n(s(n(e)))),s(n(n(e))))),u(s(n(e)),a(p(n(s(n(e)))),s(n(n(e)))))),s(s(s(n(e)))))
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f75]) ).
fof(f79,definition,
( spl1_2
<=> mem(sK0(u(s(s(s(n(e)))),a(n(n(s(n(e)))),s(n(n(e))))),u(s(n(e)),a(p(n(s(n(e)))),s(n(n(e)))))),a(n(n(s(n(e)))),s(n(n(e))))) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
fof(f81,plain,
( mem(sK0(u(s(s(s(n(e)))),a(n(n(s(n(e)))),s(n(n(e))))),u(s(n(e)),a(p(n(s(n(e)))),s(n(n(e)))))),a(n(n(s(n(e)))),s(n(n(e)))))
| ~ spl1_2 ),
inference(avatar_component_clause,[],[f79]) ).
fof(f82,plain,
( spl1_1
| spl1_2 ),
inference(avatar_split_clause,[],[f72,f79,f75]) ).
fof(f84,plain,
! [X0,X1] :
( mem(X1,n(X0))
| ~ mem(X1,X0) ),
inference(superposition,[],[f65,f55]) ).
fof(f88,plain,
! [X0,X1] : mem(X0,a(X1,X0)),
inference(resolution,[],[f66,f59]) ).
fof(f106,plain,
~ mem(sK0(u(s(s(s(n(e)))),a(n(n(s(n(e)))),s(n(n(e))))),u(s(n(e)),a(p(n(s(n(e)))),s(n(n(e)))))),a(p(n(s(n(e)))),s(n(n(e))))),
inference(resolution,[],[f63,f58]) ).
fof(f111,plain,
! [X2,X0,X1] :
( ~ mem(sK0(X2,a(X0,X1)),s(X1))
| subq(X2,a(X0,X1)) ),
inference(superposition,[],[f63,f54]) ).
fof(f112,plain,
~ mem(sK0(u(s(s(s(n(e)))),a(n(n(s(n(e)))),s(n(n(e))))),u(s(n(e)),a(p(n(s(n(e)))),s(n(n(e)))))),p(n(s(n(e))))),
inference(resolution,[],[f106,f65]) ).
fof(f113,plain,
~ mem(sK0(u(s(s(s(n(e)))),a(n(n(s(n(e)))),s(n(n(e))))),u(s(n(e)),a(p(n(s(n(e)))),s(n(n(e)))))),s(n(e))),
inference(resolution,[],[f64,f58]) ).
fof(f120,plain,
! [X2,X0,X1] :
( ~ mem(X0,a(X1,X2))
| mem(X0,X1)
| X0 = X2 ),
inference(resolution,[],[f73,f46]) ).
fof(f123,plain,
mem(sK0(sK0(u(s(s(s(n(e)))),a(n(n(s(n(e)))),s(n(n(e))))),u(s(n(e)),a(p(n(s(n(e)))),s(n(n(e)))))),n(s(n(e)))),sK0(u(s(s(s(n(e)))),a(n(n(s(n(e)))),s(n(n(e))))),u(s(n(e)),a(p(n(s(n(e)))),s(n(n(e))))))),
inference(resolution,[],[f112,f62]) ).
fof(f126,plain,
( mem(sK0(u(s(s(s(n(e)))),a(n(n(s(n(e)))),s(n(n(e))))),u(s(n(e)),a(p(n(s(n(e)))),s(n(n(e)))))),n(n(s(n(e)))))
| s(n(n(e))) = sK0(u(s(s(s(n(e)))),a(n(n(s(n(e)))),s(n(n(e))))),u(s(n(e)),a(p(n(s(n(e)))),s(n(n(e))))))
| ~ spl1_2 ),
inference(resolution,[],[f120,f81]) ).
fof(f128,plain,
! [X0,X1] :
( ~ mem(X1,n(X0))
| mem(X1,X0)
| X0 = X1 ),
inference(superposition,[],[f120,f55]) ).
fof(f130,definition,
( spl1_3
<=> s(n(n(e))) = sK0(u(s(s(s(n(e)))),a(n(n(s(n(e)))),s(n(n(e))))),u(s(n(e)),a(p(n(s(n(e)))),s(n(n(e)))))) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
fof(f132,plain,
( s(n(n(e))) = sK0(u(s(s(s(n(e)))),a(n(n(s(n(e)))),s(n(n(e))))),u(s(n(e)),a(p(n(s(n(e)))),s(n(n(e))))))
| ~ spl1_3 ),
inference(avatar_component_clause,[],[f130]) ).
fof(f134,definition,
( spl1_4
<=> mem(sK0(u(s(s(s(n(e)))),a(n(n(s(n(e)))),s(n(n(e))))),u(s(n(e)),a(p(n(s(n(e)))),s(n(n(e)))))),n(n(s(n(e))))) ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
fof(f136,plain,
( mem(sK0(u(s(s(s(n(e)))),a(n(n(s(n(e)))),s(n(n(e))))),u(s(n(e)),a(p(n(s(n(e)))),s(n(n(e)))))),n(n(s(n(e)))))
| ~ spl1_4 ),
inference(avatar_component_clause,[],[f134]) ).
fof(f137,plain,
( spl1_3
| spl1_4
| ~ spl1_2 ),
inference(avatar_split_clause,[],[f126,f79,f134,f130]) ).
fof(f140,plain,
( ~ mem(s(n(n(e))),a(p(n(s(n(e)))),s(n(n(e)))))
| ~ spl1_3 ),
inference(superposition,[],[f106,f132]) ).
fof(f155,plain,
( $false
| ~ spl1_3 ),
inference(forward_subsumption_resolution,[],[f140,f88]) ).
fof(f156,plain,
~ spl1_3,
inference(avatar_contradiction_clause,[],[f155]) ).
fof(f199,plain,
! [X0,X1] :
( ~ mem(sK0(X1,n(X0)),s(X0))
| subq(X1,n(X0)) ),
inference(superposition,[],[f111,f55]) ).
fof(f221,plain,
( mem(sK0(u(s(s(s(n(e)))),a(n(n(s(n(e)))),s(n(n(e))))),u(s(n(e)),a(p(n(s(n(e)))),s(n(n(e)))))),n(s(n(e))))
| n(s(n(e))) = sK0(u(s(s(s(n(e)))),a(n(n(s(n(e)))),s(n(n(e))))),u(s(n(e)),a(p(n(s(n(e)))),s(n(n(e))))))
| ~ spl1_4 ),
inference(resolution,[],[f128,f136]) ).
fof(f226,definition,
( spl1_9
<=> n(s(n(e))) = sK0(u(s(s(s(n(e)))),a(n(n(s(n(e)))),s(n(n(e))))),u(s(n(e)),a(p(n(s(n(e)))),s(n(n(e)))))) ),
introduced(definition,[new_symbols(definition,[spl1_9])],[avatar_definition]) ).
fof(f228,plain,
( n(s(n(e))) = sK0(u(s(s(s(n(e)))),a(n(n(s(n(e)))),s(n(n(e))))),u(s(n(e)),a(p(n(s(n(e)))),s(n(n(e))))))
| ~ spl1_9 ),
inference(avatar_component_clause,[],[f226]) ).
fof(f230,definition,
( spl1_10
<=> mem(sK0(u(s(s(s(n(e)))),a(n(n(s(n(e)))),s(n(n(e))))),u(s(n(e)),a(p(n(s(n(e)))),s(n(n(e)))))),n(s(n(e)))) ),
introduced(definition,[new_symbols(definition,[spl1_10])],[avatar_definition]) ).
fof(f232,plain,
( mem(sK0(u(s(s(s(n(e)))),a(n(n(s(n(e)))),s(n(n(e))))),u(s(n(e)),a(p(n(s(n(e)))),s(n(n(e)))))),n(s(n(e))))
| ~ spl1_10 ),
inference(avatar_component_clause,[],[f230]) ).
fof(f233,plain,
( spl1_9
| spl1_10
| ~ spl1_4 ),
inference(avatar_split_clause,[],[f221,f134,f230,f226]) ).
fof(f242,plain,
( ~ mem(n(s(n(e))),p(n(s(n(e)))))
| ~ spl1_9 ),
inference(superposition,[],[f112,f228]) ).
fof(f245,plain,
( mem(sK0(n(s(n(e))),n(s(n(e)))),n(s(n(e))))
| ~ spl1_9 ),
inference(superposition,[],[f123,f228]) ).
fof(f276,plain,
( mem(sK0(u(s(s(s(n(e)))),a(n(n(s(n(e)))),s(n(n(e))))),u(s(n(e)),a(p(n(s(n(e)))),s(n(n(e)))))),s(n(e)))
| s(n(e)) = sK0(u(s(s(s(n(e)))),a(n(n(s(n(e)))),s(n(n(e))))),u(s(n(e)),a(p(n(s(n(e)))),s(n(n(e))))))
| ~ spl1_10 ),
inference(resolution,[],[f232,f128]) ).
fof(f277,plain,
( s(n(e)) = sK0(u(s(s(s(n(e)))),a(n(n(s(n(e)))),s(n(n(e))))),u(s(n(e)),a(p(n(s(n(e)))),s(n(n(e))))))
| ~ spl1_10 ),
inference(forward_subsumption_resolution,[],[f276,f113]) ).
fof(f285,plain,
( ~ mem(s(n(e)),p(n(s(n(e)))))
| ~ spl1_10 ),
inference(superposition,[],[f112,f277]) ).
fof(f288,plain,
( mem(sK0(s(n(e)),n(s(n(e)))),s(n(e)))
| ~ spl1_10 ),
inference(superposition,[],[f123,f277]) ).
fof(f338,plain,
( subq(n(s(n(e))),n(s(n(e))))
| ~ spl1_9 ),
inference(resolution,[],[f245,f43]) ).
fof(f408,plain,
( n(e) = sK0(s(n(e)),n(s(n(e))))
| ~ spl1_10 ),
inference(resolution,[],[f288,f46]) ).
fof(f421,plain,
( ~ mem(n(e),n(s(n(e))))
| subq(s(n(e)),n(s(n(e))))
| ~ spl1_10 ),
inference(superposition,[],[f43,f408]) ).
fof(f423,definition,
( spl1_19
<=> subq(s(n(e)),n(s(n(e)))) ),
introduced(definition,[new_symbols(definition,[spl1_19])],[avatar_definition]) ).
fof(f425,plain,
( subq(s(n(e)),n(s(n(e))))
| ~ spl1_19 ),
inference(avatar_component_clause,[],[f423]) ).
fof(f427,definition,
( spl1_20
<=> mem(n(e),n(s(n(e)))) ),
introduced(definition,[new_symbols(definition,[spl1_20])],[avatar_definition]) ).
fof(f428,plain,
( mem(n(e),n(s(n(e))))
| ~ spl1_20 ),
inference(avatar_component_clause,[],[f427]) ).
fof(f429,plain,
( ~ mem(n(e),n(s(n(e))))
| spl1_20 ),
inference(avatar_component_clause,[],[f427]) ).
fof(f441,plain,
( ~ mem(n(e),s(n(e)))
| spl1_20 ),
inference(resolution,[],[f429,f84]) ).
fof(f442,plain,
( $false
| spl1_20 ),
inference(forward_subsumption_resolution,[],[f441,f59]) ).
fof(f443,plain,
spl1_20,
inference(avatar_contradiction_clause,[],[f442]) ).
fof(f483,plain,
( mem(n(s(n(e))),p(n(s(n(e)))))
| ~ spl1_9 ),
inference(resolution,[],[f338,f57]) ).
fof(f505,plain,
( $false
| ~ spl1_9 ),
inference(forward_subsumption_resolution,[],[f483,f242]) ).
fof(f506,plain,
~ spl1_9,
inference(avatar_contradiction_clause,[],[f505]) ).
fof(f507,plain,
( subq(s(n(e)),n(s(n(e))))
| ~ spl1_10
| ~ spl1_20 ),
inference(forward_subsumption_resolution,[],[f421,f428]) ).
fof(f508,plain,
( spl1_19
| ~ spl1_10
| ~ spl1_20 ),
inference(avatar_split_clause,[],[f507,f427,f230,f423]) ).
fof(f632,plain,
( mem(s(n(e)),p(n(s(n(e)))))
| ~ spl1_19 ),
inference(resolution,[],[f425,f57]) ).
fof(f665,plain,
( $false
| ~ spl1_10
| ~ spl1_19 ),
inference(forward_subsumption_resolution,[],[f632,f285]) ).
fof(f666,plain,
( ~ spl1_10
| ~ spl1_19 ),
inference(avatar_contradiction_clause,[],[f665]) ).
fof(f698,plain,
( s(s(n(e))) = sK0(u(s(s(s(n(e)))),a(n(n(s(n(e)))),s(n(n(e))))),u(s(n(e)),a(p(n(s(n(e)))),s(n(n(e))))))
| ~ spl1_1 ),
inference(resolution,[],[f77,f46]) ).
fof(f979,plain,
( ~ mem(s(s(n(e))),p(n(s(n(e)))))
| ~ spl1_1 ),
inference(superposition,[],[f112,f698]) ).
fof(f982,plain,
( mem(sK0(s(s(n(e))),n(s(n(e)))),s(s(n(e))))
| ~ spl1_1 ),
inference(superposition,[],[f123,f698]) ).
fof(f2074,plain,
( subq(s(s(n(e))),n(s(n(e))))
| ~ spl1_1 ),
inference(resolution,[],[f982,f199]) ).
fof(f2094,plain,
( mem(s(s(n(e))),p(n(s(n(e)))))
| ~ spl1_1 ),
inference(resolution,[],[f2074,f57]) ).
fof(f2095,plain,
( $false
| ~ spl1_1 ),
inference(forward_subsumption_resolution,[],[f2094,f979]) ).
fof(f2096,plain,
~ spl1_1,
inference(avatar_contradiction_clause,[],[f2095]) ).
cnf(s1,plain,
( spl1_1
| spl1_2 ),
inference(sat_conversion,[],[f82]) ).
cnf(s2,plain,
( ~ spl1_2
| spl1_3
| spl1_4 ),
inference(sat_conversion,[],[f137]) ).
cnf(s5,plain,
~ spl1_3,
inference(sat_conversion,[],[f156]) ).
cnf(s8,plain,
( ~ spl1_4
| spl1_9
| spl1_10 ),
inference(sat_conversion,[],[f233]) ).
cnf(s21,plain,
spl1_20,
inference(sat_conversion,[],[f443]) ).
cnf(s24,plain,
~ spl1_9,
inference(sat_conversion,[],[f506]) ).
cnf(s26,plain,
( ~ spl1_10
| spl1_19
| ~ spl1_20 ),
inference(sat_conversion,[],[f508]) ).
cnf(s27,plain,
( ~ spl1_10
| ~ spl1_19 ),
inference(sat_conversion,[],[f666]) ).
cnf(s76,plain,
~ spl1_1,
inference(sat_conversion,[],[f2096]) ).
cnf(s89,plain,
( ~ spl1_4
| spl1_10 ),
inference(rat,[],[s8,s24]) ).
cnf(s90,plain,
( ~ spl1_2
| spl1_4 ),
inference(rat,[],[s2,s5]) ).
cnf(s91,plain,
spl1_2,
inference(rat,[],[s1,s76]) ).
cnf(s92,plain,
spl1_4,
inference(rat,[],[s90,s91]) ).
cnf(s93,plain,
spl1_10,
inference(rat,[],[s89,s92]) ).
cnf(s94,plain,
~ spl1_19,
inference(rat,[],[s27,s93]) ).
cnf(s95,plain,
$false,
inference(rat,[],[s26,s21,s94,s93]) ).
fof(f2115,plain,
$false,
inference(avatar_sat_refutation,[],[s95]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV581+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 % Computer : n015.cluster.edu
% 0.11/0.40 % Model : x86_64 x86_64
% 0.11/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.40 % Memory : 8046.5625MB
% 0.11/0.40 % OS : Linux 6.8.0-71-generic
% 0.11/0.40 % CPULimit : 300
% 0.11/0.40 % WCLimit : 300
% 0.11/0.40 % DateTime : Mon Sep 28 06:42:17 UTC 2026
% 0.11/0.40 % CPUTime :
% 0.11/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 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
% 0.83/1.00 % (2428633)Detected formulas, will run a generic FOF schedule.
% 0.83/1.00 % (2428639)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=2027135933:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.83/1.00 % (2428642)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2224919455:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.83/1.00 % (2428638)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=3971878463:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.83/1.00 % (2428640)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=3031533923:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.83/1.00 % (2428643)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=385746370:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.83/1.00 % (2428644)dis-21_1_sil=8000:lcm=predicate:random_seed=2088858694: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)
% 0.83/1.00 % (2428641)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1833507890:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.83/1.00 % (2428641)Refutation not found, incomplete strategy
% 0.83/1.00 % (2428641)------------------------------
% 0.83/1.00 % (2428641)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.83/1.00 % (2428641)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/1.00 % (2428641)CaDiCaL version: 2.1.3
% 0.83/1.00 % (2428641)Termination reason: Refutation not found, incomplete strategy
% 0.83/1.00 % (2428641)Time elapsed: 0.001 s
% 0.83/1.00 % (2428641)Peak memory usage: 88 MB
% 0.83/1.00 % (2428643)First to succeed.
% 0.83/1.00 % (2428643)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2428633"
% 0.83/1.00 % (2428642)Instruction limit reached!
% 0.83/1.00 % (2428642)------------------------------
% 0.83/1.00 % (2428642)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.83/1.00 % (2428642)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/1.00 % (2428642)CaDiCaL version: 2.1.3
% 0.83/1.00 % (2428642)Termination reason: Instruction limit
% 0.83/1.00 % (2428642)Termination phase: Saturation
% 0.83/1.00 % (2428642)Time elapsed: 0.071 s
% 0.83/1.00 % (2428642)Peak memory usage: 88 MB
% 0.83/1.00 % (2428642)Instructions burned: 119 (million)
% 0.83/1.00 % (2428644)Instruction limit reached!
% 0.83/1.00 % (2428644)------------------------------
% 0.83/1.00 % (2428644)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.83/1.00 % (2428644)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/1.00 % (2428644)CaDiCaL version: 2.1.3
% 0.83/1.00 % (2428644)Termination reason: Instruction limit
% 0.83/1.00 % (2428644)Termination phase: Saturation
% 0.83/1.00 % (2428644)Time elapsed: 0.072 s
% 0.83/1.00 % (2428644)Peak memory usage: 89 MB
% 0.83/1.00 % (2428644)Instructions burned: 130 (million)
% 0.83/1.00 % (2428643)Refutation found. Thanks to Tanya!
% 0.83/1.00 % SZS status Theorem for theBenchmark
% 0.83/1.00 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/1.20 % (2428643)------------------------------
% 0.18/1.20 % (2428643)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/1.20 % (2428643)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/1.20 % (2428643)CaDiCaL version: 2.1.3
% 0.18/1.20 % (2428643)Termination reason: Refutation
% 0.18/1.20 % (2428643)Time elapsed: 0.046 s
% 0.18/1.20 % (2428643)Peak memory usage: 90 MB
% 0.18/1.20 % (2428643)Instructions burned: 125 (million)
% 0.18/1.20 % (2428643)------------------------------
% 0.18/1.20 % (2428643)------------------------------
% 0.18/1.20 % (2428633)Success in time 0.37 s
% 0.18/1.20 % Vampire exiting
%------------------------------------------------------------------------------