%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV570+1 : TPTP v9.3.1. Released v9.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n007.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 12:59:30 PM UTC 2026
% Result : Theorem 0.41s 0.47s
% Output : Refutation 0.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 20
% Syntax : Number of formulae : 153 ( 32 unt; 11 def)
% Number of atoms : 353 ( 62 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 362 ( 162 ~; 169 |; 12 &)
% ( 16 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 15 ( 13 usr; 12 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-2 aty)
% Number of variables : 139 ( 0 sgn 137 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subq(X0,X1)
<=> ! [X2] :
( mem(X2,X0)
=> mem(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET010+0.ax',subq_def) ).
fof(f2,axiom,
! [X0,X1] :
( subq(X0,X1)
=> ( subq(X1,X0)
=> X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET010+0.ax',setext) ).
fof(f4,axiom,
! [X0] : ~ mem(X0,e),
file('/export/starexec/sandbox/benchmark/Axioms/SET010+0.ax',e_ax) ).
fof(f5,axiom,
! [X0,X1] :
( mem(X0,s(X1))
<=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SET010+0.ax',s_ax) ).
fof(f6,axiom,
! [X0,X1,X2] :
( mem(X0,u(X1,X2))
<=> ( mem(X0,X1)
| mem(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET010+0.ax',u_ax) ).
fof(f8,axiom,
! [X0,X1] : a(X0,X1) = u(X0,s(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/SET010+0.ax',a_def) ).
fof(f9,axiom,
! [X0] : n(X0) = a(X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/SET010+0.ax',n_def) ).
fof(f10,axiom,
! [X0,X1] :
( mem(X0,p(X1))
<=> subq(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET010+0.ax',p_ax) ).
fof(f26,conjecture,
~ subq(u(a(s(n(s(n(e)))),u(n(e),n(s(n(e))))),s(a(s(n(e)),n(n(e))))),a(s(u(n(e),n(s(n(e))))),a(s(n(e)),n(n(e))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nsubq_1216_1152) ).
fof(f27,negated_conjecture,
~ ~ subq(u(a(s(n(s(n(e)))),u(n(e),n(s(n(e))))),s(a(s(n(e)),n(n(e))))),a(s(u(n(e),n(s(n(e))))),a(s(n(e)),n(n(e))))),
inference(negated_conjecture,[status(cth)],[f26]) ).
fof(f28,plain,
subq(u(a(s(n(s(n(e)))),u(n(e),n(s(n(e))))),s(a(s(n(e)),n(n(e))))),a(s(u(n(e),n(s(n(e))))),a(s(n(e)),n(n(e))))),
inference(flattening,[],[f27]) ).
fof(f29,plain,
! [X0,X1] :
( subq(X0,X1)
<=> ! [X2] :
( mem(X2,X1)
| ~ mem(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f30,plain,
! [X0,X1] :
( X0 = X1
| ~ subq(X1,X0)
| ~ subq(X0,X1) ),
inference(ennf_transformation,[],[f2]) ).
fof(f31,plain,
! [X0,X1] :
( X0 = X1
| ~ subq(X1,X0)
| ~ subq(X0,X1) ),
inference(flattening,[],[f30]) ).
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(f41,plain,
! [X3,X0,X1] :
( mem(X3,X1)
| ~ mem(X3,X0)
| ~ subq(X0,X1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f42,plain,
! [X0,X1] :
( subq(X0,X1)
| mem(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f34]) ).
fof(f43,plain,
! [X0,X1] :
( subq(X0,X1)
| ~ mem(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f44,plain,
! [X0,X1] :
( X0 = X1
| ~ subq(X1,X0)
| ~ subq(X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
fof(f45,plain,
! [X0] : ~ mem(X0,e),
inference(cnf_transformation,[],[f4]) ).
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(f56,plain,
! [X0,X1] :
( subq(X0,X1)
| ~ mem(X0,p(X1)) ),
inference(cnf_transformation,[],[f40]) ).
fof(f57,plain,
! [X0,X1] :
( mem(X0,p(X1))
| ~ subq(X0,X1) ),
inference(cnf_transformation,[],[f40]) ).
fof(f58,plain,
subq(u(a(s(n(s(n(e)))),u(n(e),n(s(n(e))))),s(a(s(n(e)),n(n(e))))),a(s(u(n(e),n(s(n(e))))),a(s(n(e)),n(n(e))))),
inference(cnf_transformation,[],[f28]) ).
fof(f59,plain,
! [X0] : n(X0) = u(X0,s(X0)),
inference(definition_unfolding,[],[f55,f54]) ).
fof(f60,plain,
subq(u(u(s(u(s(u(e,s(e))),s(s(u(e,s(e)))))),s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))))),s(u(s(u(e,s(e))),s(u(u(e,s(e)),s(u(e,s(e)))))))),u(s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))),s(u(s(u(e,s(e))),s(u(u(e,s(e)),s(u(e,s(e))))))))),
inference(definition_unfolding,[],[f58,f54,f59,f59,f59,f59,f59,f54,f59,f59,f59,f54,f59,f59,f59,f54,f59,f59,f59]) ).
fof(f61,plain,
! [X1] : mem(X1,s(X1)),
inference(equality_resolution,[],[f47]) ).
fof(f62,plain,
! [X0,X1] :
( ~ mem(sK0(X0,X1),X1)
| ~ subq(X0,X1) ),
inference(consistent_polarity_flipping,[],[f43]) ).
fof(f63,plain,
! [X0,X1] :
( mem(sK0(X0,X1),X0)
| ~ subq(X0,X1) ),
inference(consistent_polarity_flipping,[],[f42]) ).
fof(f64,plain,
! [X3,X0,X1] :
( mem(X3,X1)
| ~ mem(X3,X0)
| subq(X0,X1) ),
inference(consistent_polarity_flipping,[],[f41]) ).
fof(f65,plain,
! [X0,X1] :
( subq(X1,X0)
| X0 = X1
| subq(X0,X1) ),
inference(consistent_polarity_flipping,[],[f44]) ).
fof(f66,plain,
! [X0,X1] :
( mem(X0,p(X1))
| subq(X0,X1) ),
inference(consistent_polarity_flipping,[],[f57]) ).
fof(f67,plain,
! [X0,X1] :
( ~ mem(X0,p(X1))
| ~ subq(X0,X1) ),
inference(consistent_polarity_flipping,[],[f56]) ).
fof(f68,plain,
~ subq(u(u(s(u(s(u(e,s(e))),s(s(u(e,s(e)))))),s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))))),s(u(s(u(e,s(e))),s(u(u(e,s(e)),s(u(e,s(e)))))))),u(s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))),s(u(s(u(e,s(e))),s(u(u(e,s(e)),s(u(e,s(e))))))))),
inference(consistent_polarity_flipping,[],[f60]) ).
fof(f73,plain,
! [X2,X0,X1] :
( ~ mem(sK0(X0,u(X1,X2)),X2)
| ~ subq(X0,u(X1,X2)) ),
inference(resolution,[],[f62,f49]) ).
fof(f74,plain,
! [X0] :
( ~ subq(X0,X0)
| ~ subq(X0,X0) ),
inference(resolution,[],[f63,f62]) ).
fof(f75,plain,
! [X0] : ~ subq(e,X0),
inference(resolution,[],[f63,f45]) ).
fof(f79,plain,
! [X0,X1] :
( ~ subq(sK0(p(X0),X1),X0)
| ~ subq(p(X0),X1) ),
inference(resolution,[],[f63,f67]) ).
fof(f80,plain,
! [X0] : ~ subq(X0,X0),
inference(duplicate_literal_removal,[],[f74]) ).
fof(f81,plain,
! [X0,X1] :
( subq(X1,e)
| ~ mem(X0,X1) ),
inference(resolution,[],[f64,f45]) ).
fof(f86,plain,
! [X2,X0,X1] :
( ~ mem(sK0(X0,X1),X2)
| subq(X2,X1)
| ~ subq(X0,X1) ),
inference(resolution,[],[f64,f62]) ).
fof(f89,plain,
! [X0] :
( subq(X0,e)
| e = X0 ),
inference(resolution,[],[f65,f75]) ).
fof(f105,plain,
! [X2,X3,X0,X1] :
( subq(X3,u(X2,X1))
| mem(X0,X2)
| ~ mem(X0,X3)
| mem(X0,X1) ),
inference(resolution,[],[f48,f64]) ).
fof(f127,definition,
( spl1_3
<=> u(s(u(e,s(e))),s(s(u(e,s(e))))) = u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
fof(f129,plain,
( u(s(u(e,s(e))),s(s(u(e,s(e))))) = u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))
| ~ spl1_3 ),
inference(avatar_component_clause,[],[f127]) ).
fof(f131,definition,
( spl1_4
<=> u(s(u(e,s(e))),s(s(u(e,s(e))))) = u(s(u(e,s(e))),s(u(u(e,s(e)),s(u(e,s(e)))))) ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
fof(f133,plain,
( u(s(u(e,s(e))),s(s(u(e,s(e))))) = u(s(u(e,s(e))),s(u(u(e,s(e)),s(u(e,s(e))))))
| ~ spl1_4 ),
inference(avatar_component_clause,[],[f131]) ).
fof(f142,plain,
( ! [X0] :
( mem(X0,u(s(u(e,s(e))),s(s(u(e,s(e))))))
| ~ mem(X0,u(e,s(e))) )
| ~ spl1_3 ),
inference(superposition,[],[f50,f129]) ).
fof(f144,plain,
( ! [X0] :
( mem(X0,s(u(e,s(e))))
| mem(X0,s(s(u(e,s(e)))))
| ~ mem(X0,u(e,s(e))) )
| ~ spl1_3 ),
inference(resolution,[],[f142,f48]) ).
fof(f146,plain,
( ! [X0] :
( mem(X0,s(s(u(e,s(e)))))
| ~ mem(X0,u(e,s(e)))
| u(e,s(e)) = X0 )
| ~ spl1_3 ),
inference(resolution,[],[f144,f46]) ).
fof(f148,plain,
( ! [X0] :
( ~ mem(X0,u(e,s(e)))
| u(e,s(e)) = X0
| s(u(e,s(e))) = X0 )
| ~ spl1_3 ),
inference(resolution,[],[f146,f46]) ).
fof(f151,plain,
( ! [X0] :
( ~ mem(X0,s(e))
| s(u(e,s(e))) = X0
| u(e,s(e)) = X0 )
| ~ spl1_3 ),
inference(resolution,[],[f148,f49]) ).
fof(f154,plain,
( e = s(u(e,s(e)))
| e = u(e,s(e))
| ~ spl1_3 ),
inference(resolution,[],[f151,f61]) ).
fof(f158,definition,
( spl1_5
<=> e = u(e,s(e)) ),
introduced(definition,[new_symbols(definition,[spl1_5])],[avatar_definition]) ).
fof(f160,plain,
( e = u(e,s(e))
| ~ spl1_5 ),
inference(avatar_component_clause,[],[f158]) ).
fof(f162,definition,
( spl1_6
<=> e = s(u(e,s(e))) ),
introduced(definition,[new_symbols(definition,[spl1_6])],[avatar_definition]) ).
fof(f164,plain,
( e = s(u(e,s(e)))
| ~ spl1_6 ),
inference(avatar_component_clause,[],[f162]) ).
fof(f176,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)))))) )
| ~ spl1_4 ),
inference(superposition,[],[f49,f133]) ).
fof(f177,plain,
( ! [X0] :
( mem(X0,s(u(e,s(e))))
| mem(X0,s(s(u(e,s(e)))))
| ~ mem(X0,s(u(u(e,s(e)),s(u(e,s(e)))))) )
| ~ spl1_4 ),
inference(resolution,[],[f176,f48]) ).
fof(f179,plain,
( ! [X0] :
( mem(X0,s(s(u(e,s(e)))))
| ~ mem(X0,s(u(u(e,s(e)),s(u(e,s(e))))))
| u(e,s(e)) = X0 )
| ~ spl1_4 ),
inference(resolution,[],[f177,f46]) ).
fof(f181,plain,
( ! [X0] :
( ~ mem(X0,s(u(u(e,s(e)),s(u(e,s(e))))))
| u(e,s(e)) = X0
| s(u(e,s(e))) = X0 )
| ~ spl1_4 ),
inference(resolution,[],[f179,f46]) ).
fof(f183,plain,
( u(e,s(e)) = u(u(e,s(e)),s(u(e,s(e))))
| s(u(e,s(e))) = u(u(e,s(e)),s(u(e,s(e))))
| ~ spl1_4 ),
inference(resolution,[],[f181,f61]) ).
fof(f187,definition,
( spl1_7
<=> s(u(e,s(e))) = u(u(e,s(e)),s(u(e,s(e)))) ),
introduced(definition,[new_symbols(definition,[spl1_7])],[avatar_definition]) ).
fof(f189,plain,
( s(u(e,s(e))) = u(u(e,s(e)),s(u(e,s(e))))
| ~ spl1_7 ),
inference(avatar_component_clause,[],[f187]) ).
fof(f191,definition,
( spl1_8
<=> u(e,s(e)) = u(u(e,s(e)),s(u(e,s(e)))) ),
introduced(definition,[new_symbols(definition,[spl1_8])],[avatar_definition]) ).
fof(f193,plain,
( u(e,s(e)) = u(u(e,s(e)),s(u(e,s(e))))
| ~ spl1_8 ),
inference(avatar_component_clause,[],[f191]) ).
fof(f194,plain,
( spl1_7
| spl1_8
| ~ spl1_4 ),
inference(avatar_split_clause,[],[f183,f131,f191,f187]) ).
fof(f203,plain,
( ! [X0] :
( mem(X0,s(u(e,s(e))))
| ~ mem(X0,u(e,s(e))) )
| ~ spl1_7 ),
inference(superposition,[],[f50,f189]) ).
fof(f205,plain,
( ! [X0] :
( ~ mem(X0,u(e,s(e)))
| u(e,s(e)) = X0 )
| ~ spl1_7 ),
inference(resolution,[],[f203,f46]) ).
fof(f208,plain,
( ! [X0] :
( ~ mem(X0,s(e))
| u(e,s(e)) = X0 )
| ~ spl1_7 ),
inference(resolution,[],[f205,f49]) ).
fof(f211,plain,
( e = u(e,s(e))
| ~ spl1_7 ),
inference(resolution,[],[f208,f61]) ).
fof(f214,plain,
( spl1_5
| ~ spl1_7 ),
inference(avatar_split_clause,[],[f211,f187,f158]) ).
fof(f248,plain,
( ! [X0] :
( mem(X0,u(e,s(e)))
| ~ mem(X0,s(u(e,s(e)))) )
| ~ spl1_8 ),
inference(superposition,[],[f49,f193]) ).
fof(f249,plain,
( ! [X0] :
( mem(X0,s(e))
| ~ mem(X0,s(u(e,s(e))))
| mem(X0,e) )
| ~ spl1_8 ),
inference(resolution,[],[f248,f48]) ).
fof(f251,plain,
( ! [X0] :
( mem(X0,e)
| ~ mem(X0,s(u(e,s(e))))
| e = X0 )
| ~ spl1_8 ),
inference(resolution,[],[f249,f46]) ).
fof(f253,plain,
( ! [X0] :
( ~ mem(X0,s(u(e,s(e))))
| e = X0 )
| ~ spl1_8 ),
inference(resolution,[],[f251,f45]) ).
fof(f256,plain,
( e = u(e,s(e))
| ~ spl1_8 ),
inference(resolution,[],[f253,f61]) ).
fof(f259,plain,
( spl1_5
| ~ spl1_8 ),
inference(avatar_split_clause,[],[f256,f191,f158]) ).
fof(f264,plain,
! [X0] :
( ~ subq(p(e),X0)
| e = sK0(p(e),X0) ),
inference(resolution,[],[f79,f89]) ).
fof(f284,plain,
( e = sK0(p(e),e)
| e = p(e) ),
inference(resolution,[],[f264,f89]) ).
fof(f289,definition,
( spl1_9
<=> ! [X0] : ~ mem(X0,p(e)) ),
introduced(definition,[new_symbols(definition,[spl1_9])],[avatar_definition]) ).
fof(f290,plain,
( ! [X0] : ~ mem(X0,p(e))
| ~ spl1_9 ),
inference(avatar_component_clause,[],[f289]) ).
fof(f292,definition,
( spl1_10
<=> e = sK0(p(e),e) ),
introduced(definition,[new_symbols(definition,[spl1_10])],[avatar_definition]) ).
fof(f294,plain,
( e = sK0(p(e),e)
| ~ spl1_10 ),
inference(avatar_component_clause,[],[f292]) ).
fof(f297,definition,
( spl1_11
<=> e = p(e) ),
introduced(definition,[new_symbols(definition,[spl1_11])],[avatar_definition]) ).
fof(f299,plain,
( e = p(e)
| ~ spl1_11 ),
inference(avatar_component_clause,[],[f297]) ).
fof(f300,plain,
( spl1_11
| spl1_10 ),
inference(avatar_split_clause,[],[f284,f292,f297]) ).
fof(f301,plain,
( ! [X0] : subq(X0,e)
| ~ spl1_9 ),
inference(resolution,[],[f290,f66]) ).
fof(f308,plain,
( $false
| ~ spl1_9 ),
inference(resolution,[],[f301,f80]) ).
fof(f313,plain,
~ spl1_9,
inference(avatar_contradiction_clause,[],[f308]) ).
fof(f332,definition,
( spl1_12
<=> subq(p(e),e) ),
introduced(definition,[new_symbols(definition,[spl1_12])],[avatar_definition]) ).
fof(f333,plain,
( subq(p(e),e)
| ~ spl1_12 ),
inference(avatar_component_clause,[],[f332]) ).
fof(f334,plain,
( ~ subq(p(e),e)
| spl1_12 ),
inference(avatar_component_clause,[],[f332]) ).
fof(f341,plain,
( ! [X0] : ~ mem(X0,p(e))
| spl1_12 ),
inference(resolution,[],[f334,f81]) ).
fof(f344,plain,
( spl1_9
| spl1_12 ),
inference(avatar_split_clause,[],[f341,f332,f289]) ).
fof(f345,plain,
( subq(e,e)
| ~ spl1_11
| ~ spl1_12 ),
inference(superposition,[],[f333,f299]) ).
fof(f348,plain,
( $false
| ~ spl1_11
| ~ spl1_12 ),
inference(resolution,[],[f345,f75]) ).
fof(f351,plain,
( ~ spl1_11
| ~ spl1_12 ),
inference(avatar_contradiction_clause,[],[f348]) ).
fof(f401,plain,
! [X0,X1] :
( subq(s(sK0(X0,X1)),X1)
| ~ subq(X0,X1) ),
inference(resolution,[],[f86,f61]) ).
fof(f411,plain,
( subq(s(e),e)
| ~ subq(p(e),e)
| ~ spl1_10 ),
inference(superposition,[],[f401,f294]) ).
fof(f413,definition,
( spl1_14
<=> subq(s(e),e) ),
introduced(definition,[new_symbols(definition,[spl1_14])],[avatar_definition]) ).
fof(f416,plain,
( ~ spl1_12
| spl1_14
| ~ spl1_10 ),
inference(avatar_split_clause,[],[f411,f292,f413,f332]) ).
fof(f426,plain,
! [X0,X1] :
( ~ subq(X0,u(X1,X0))
| ~ subq(X0,u(X1,X0)) ),
inference(resolution,[],[f73,f63]) ).
fof(f432,plain,
! [X0,X1] : ~ subq(X0,u(X1,X0)),
inference(duplicate_literal_removal,[],[f426]) ).
fof(f677,plain,
! [X0] :
( mem(X0,s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))))
| ~ mem(X0,u(u(s(u(s(u(e,s(e))),s(s(u(e,s(e)))))),s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))))),s(u(s(u(e,s(e))),s(u(u(e,s(e)),s(u(e,s(e)))))))))
| mem(X0,s(u(s(u(e,s(e))),s(u(u(e,s(e)),s(u(e,s(e)))))))) ),
inference(resolution,[],[f105,f68]) ).
fof(f883,plain,
! [X0] :
( mem(X0,s(u(s(u(e,s(e))),s(u(u(e,s(e)),s(u(e,s(e))))))))
| ~ mem(X0,u(u(s(u(s(u(e,s(e))),s(s(u(e,s(e)))))),s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))))),s(u(s(u(e,s(e))),s(u(u(e,s(e)),s(u(e,s(e)))))))))
| u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))) = X0 ),
inference(resolution,[],[f677,f46]) ).
fof(f889,plain,
! [X0] :
( ~ mem(X0,u(u(s(u(s(u(e,s(e))),s(s(u(e,s(e)))))),s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))))),s(u(s(u(e,s(e))),s(u(u(e,s(e)),s(u(e,s(e)))))))))
| u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))) = X0
| u(s(u(e,s(e))),s(u(u(e,s(e)),s(u(e,s(e)))))) = X0 ),
inference(resolution,[],[f883,f46]) ).
fof(f895,plain,
! [X0] :
( ~ mem(X0,u(s(u(s(u(e,s(e))),s(s(u(e,s(e)))))),s(u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))))))
| u(s(u(e,s(e))),s(u(u(e,s(e)),s(u(e,s(e)))))) = X0
| u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))) = X0 ),
inference(resolution,[],[f889,f50]) ).
fof(f900,plain,
! [X0] :
( ~ mem(X0,s(u(s(u(e,s(e))),s(s(u(e,s(e)))))))
| u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e)))))) = X0
| u(s(u(e,s(e))),s(u(u(e,s(e)),s(u(e,s(e)))))) = X0 ),
inference(resolution,[],[f895,f50]) ).
fof(f932,plain,
( u(s(u(e,s(e))),s(s(u(e,s(e))))) = u(u(e,s(e)),u(s(u(e,s(e))),s(s(u(e,s(e))))))
| u(s(u(e,s(e))),s(s(u(e,s(e))))) = u(s(u(e,s(e))),s(u(u(e,s(e)),s(u(e,s(e)))))) ),
inference(resolution,[],[f900,f61]) ).
fof(f937,plain,
( spl1_4
| spl1_3 ),
inference(avatar_split_clause,[],[f932,f127,f131]) ).
fof(f938,plain,
( spl1_5
| spl1_6
| ~ spl1_3 ),
inference(avatar_split_clause,[],[f154,f127,f162,f158]) ).
fof(f955,plain,
( mem(u(e,s(e)),e)
| ~ spl1_6 ),
inference(superposition,[],[f61,f164]) ).
fof(f956,plain,
( $false
| ~ spl1_6 ),
inference(resolution,[],[f955,f45]) ).
fof(f957,plain,
~ spl1_6,
inference(avatar_contradiction_clause,[],[f956]) ).
fof(f976,plain,
( ~ subq(s(e),e)
| ~ spl1_5 ),
inference(superposition,[],[f432,f160]) ).
fof(f989,plain,
( ~ spl1_14
| ~ spl1_5 ),
inference(avatar_split_clause,[],[f976,f158,f413]) ).
cnf(s4,plain,
( ~ spl1_4
| spl1_7
| spl1_8 ),
inference(sat_conversion,[],[f194]) ).
cnf(s5,plain,
( spl1_5
| ~ spl1_7 ),
inference(sat_conversion,[],[f214]) ).
cnf(s8,plain,
( spl1_5
| ~ spl1_8 ),
inference(sat_conversion,[],[f259]) ).
cnf(s10,plain,
( spl1_10
| spl1_11 ),
inference(sat_conversion,[],[f300]) ).
cnf(s12,plain,
~ spl1_9,
inference(sat_conversion,[],[f313]) ).
cnf(s14,plain,
( spl1_9
| spl1_12 ),
inference(sat_conversion,[],[f344]) ).
cnf(s16,plain,
( ~ spl1_11
| ~ spl1_12 ),
inference(sat_conversion,[],[f351]) ).
cnf(s17,plain,
( ~ spl1_10
| ~ spl1_12
| spl1_14 ),
inference(sat_conversion,[],[f416]) ).
cnf(s20,plain,
( spl1_3
| spl1_4 ),
inference(sat_conversion,[],[f937]) ).
cnf(s21,plain,
( ~ spl1_3
| spl1_5
| spl1_6 ),
inference(sat_conversion,[],[f938]) ).
cnf(s22,plain,
~ spl1_6,
inference(sat_conversion,[],[f957]) ).
cnf(s24,plain,
( ~ spl1_5
| ~ spl1_14 ),
inference(sat_conversion,[],[f989]) ).
cnf(s25,plain,
( ~ spl1_3
| spl1_5 ),
inference(rat,[],[s21,s22]) ).
cnf(s28,plain,
spl1_12,
inference(rat,[],[s14,s12]) ).
cnf(s29,plain,
~ spl1_11,
inference(rat,[],[s16,s28]) ).
cnf(s30,plain,
spl1_10,
inference(rat,[],[s10,s29]) ).
cnf(s31,plain,
spl1_14,
inference(rat,[],[s17,s28,s30]) ).
cnf(s33,plain,
~ spl1_5,
inference(rat,[],[s24,s31]) ).
cnf(s34,plain,
~ spl1_3,
inference(rat,[],[s25,s33]) ).
cnf(s35,plain,
spl1_4,
inference(rat,[],[s20,s34]) ).
cnf(s36,plain,
~ spl1_8,
inference(rat,[],[s8,s33]) ).
cnf(s37,plain,
~ spl1_7,
inference(rat,[],[s5,s33]) ).
cnf(s38,plain,
$false,
inference(rat,[],[s4,s36,s37,s35]) ).
fof(f990,plain,
$false,
inference(avatar_sat_refutation,[],[s38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV570+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.35 % Computer : n007.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 28 06:36:29 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.38 Running first-order model finding
% 0.13/0.38 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.41/0.47 % (2187556)Will run a generic schedule for satisfiability detection.
% 0.41/0.47 % (2187562)% WARNING: option uhcvi not known.
% 0.41/0.47 % (2187562)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1789013539:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.41/0.47 % (2187563)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3184097566:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.41/0.47 % (2187561)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2229843064_2999 on theBenchmark for (2999ds/0Mi)
% 0.41/0.47 % (2187566)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1998077015:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.41/0.47 % (2187564)dis+10_1_sil=32000:sp=arity:random_seed=3425952719:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.41/0.47 % (2187565)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2274714238:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.41/0.47 % (2187567)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3629232542:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.41/0.47 % TRYING [1]
% 0.41/0.47 % TRYING [2]
% 0.41/0.47 % TRYING [3]
% 0.41/0.47 % TRYING [4]
% 0.41/0.47 % TRYING [5]
% 0.41/0.47 % TRYING [6]
% 0.41/0.47 % TRYING [7]
% 0.41/0.47 % (2187567) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2187556-2187567"...
% 0.41/0.47 % (2187567)...printing done.
% 0.41/0.47 % (2187567)Refutation found. Thanks to Tanya!
% 0.41/0.47 % SZS status Theorem for theBenchmark
% 0.41/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.41/0.47 % (2187567)------------------------------
% 0.41/0.47 % (2187567)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.41/0.47 % (2187567)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.41/0.47 % (2187567)CaDiCaL version: 2.1.3
% 0.41/0.47 % (2187567)Termination reason: Refutation
% 0.41/0.47 % (2187567)Time elapsed: 0.030 s
% 0.41/0.47 % (2187567)Peak memory usage: 13 MB
% 0.41/0.47 % (2187567)Instructions burned: 42 (million)
% 0.41/0.47 % (2187556)Success in time 0.078 s
% 0.41/0.47 % Vampire exiting
%------------------------------------------------------------------------------