%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV541+1 : TPTP v9.3.1. Released v9.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 12:57:56 PM UTC 2026
% Result : Theorem 9.38s 2.17s
% Output : Refutation 9.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 45
% Syntax : Number of formulae : 310 ( 77 unt; 33 def)
% Number of atoms : 662 ( 68 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 600 ( 248 ~; 291 |; 22 &)
% ( 33 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 9 ( 1 avg)
% Number of predicates : 32 ( 30 usr; 26 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 9 con; 0-2 aty)
% Number of variables : 140 ( 0 sgn 132 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subq(X0,X1)
<=> ! [X2] :
( mem(X2,X0)
=> mem(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subq_def) ).
fof(f2,axiom,
! [X0,X1] :
( subq(X0,X1)
=> ( subq(X1,X0)
=> X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setext) ).
fof(f4,axiom,
! [X0] : ~ mem(X0,e),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_ax) ).
fof(f5,axiom,
! [X0,X1] :
( mem(X0,s(X1))
<=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s_ax) ).
fof(f6,axiom,
! [X0,X1,X2] :
( mem(X0,u(X1,X2))
<=> ( mem(X0,X1)
| mem(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_ax) ).
fof(f8,axiom,
! [X0,X1] : a(X0,X1) = u(X0,s(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_def) ).
fof(f9,axiom,
! [X0] : n(X0) = a(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',n_def) ).
fof(f10,axiom,
! [X0,X1] :
( mem(X0,p(X1))
<=> subq(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p_ax) ).
fof(f11,axiom,
! [X0] :
( atleast2p(X0)
<=> ? [X1] :
( mem(X1,X0)
& ~ subq(X0,p(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',atleast2p_def) ).
fof(f12,axiom,
! [X0] :
( atleast3p(X0)
<=> ? [X1] :
( subq(X1,X0)
& atleast2p(X1)
& ~ subq(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',atleast3p_def) ).
fof(f13,axiom,
! [X0] :
( atleast4p(X0)
<=> ? [X1] :
( subq(X1,X0)
& atleast3p(X1)
& ~ subq(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',atleast4p_def) ).
fof(f26,conjecture,
atleast4p(u(n(e),n(n(s(n(e)))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',atleast4_71) ).
fof(f27,negated_conjecture,
~ atleast4p(u(n(e),n(n(s(n(e)))))),
inference(negated_conjecture,[status(cth)],[f26]) ).
fof(f28,plain,
~ atleast4p(u(n(e),n(n(s(n(e)))))),
inference(flattening,[],[f27]) ).
fof(f29,plain,
! [X0] :
( ? [X1] :
( subq(X1,X0)
& atleast3p(X1)
& ~ subq(X0,X1) )
=> atleast4p(X0) ),
inference(unused_predicate_definition_removal,[],[f13]) ).
fof(f30,plain,
! [X0] :
( ? [X1] :
( subq(X1,X0)
& atleast2p(X1)
& ~ subq(X0,X1) )
=> atleast3p(X0) ),
inference(unused_predicate_definition_removal,[],[f12]) ).
fof(f31,plain,
! [X0] :
( ? [X1] :
( mem(X1,X0)
& ~ subq(X0,p(X1)) )
=> atleast2p(X0) ),
inference(unused_predicate_definition_removal,[],[f11]) ).
fof(f32,plain,
! [X0,X1] :
( subq(X0,X1)
<=> ! [X2] :
( mem(X2,X1)
| ~ mem(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f33,plain,
! [X0,X1] :
( X0 = X1
| ~ subq(X1,X0)
| ~ subq(X0,X1) ),
inference(ennf_transformation,[],[f2]) ).
fof(f34,plain,
! [X0,X1] :
( X0 = X1
| ~ subq(X1,X0)
| ~ subq(X0,X1) ),
inference(flattening,[],[f33]) ).
fof(f35,plain,
! [X0] :
( atleast2p(X0)
| ! [X1] :
( ~ mem(X1,X0)
| subq(X0,p(X1)) ) ),
inference(ennf_transformation,[],[f31]) ).
fof(f36,plain,
! [X0] :
( atleast3p(X0)
| ! [X1] :
( ~ subq(X1,X0)
| ~ atleast2p(X1)
| subq(X0,X1) ) ),
inference(ennf_transformation,[],[f30]) ).
fof(f37,plain,
! [X0] :
( atleast4p(X0)
| ! [X1] :
( ~ subq(X1,X0)
| ~ atleast3p(X1)
| subq(X0,X1) ) ),
inference(ennf_transformation,[],[f29]) ).
fof(f38,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,[],[f32]) ).
fof(f39,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,[],[f38]) ).
fof(f40,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))],[f39]) ).
fof(f41,plain,
! [X0,X1] :
( ( mem(X0,s(X1))
| X0 != X1 )
& ( X0 = X1
| ~ mem(X0,s(X1)) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f42,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(f43,plain,
! [X0,X1,X2] :
( ( mem(X0,u(X1,X2))
| ( ~ mem(X0,X1)
& ~ mem(X0,X2) ) )
& ( mem(X0,X1)
| mem(X0,X2)
| ~ mem(X0,u(X1,X2)) ) ),
inference(flattening,[],[f42]) ).
fof(f46,plain,
! [X0,X1] :
( ( mem(X0,p(X1))
| ~ subq(X0,X1) )
& ( subq(X0,X1)
| ~ mem(X0,p(X1)) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f47,plain,
! [X3,X0,X1] :
( ~ mem(X3,X0)
| mem(X3,X1)
| ~ subq(X0,X1) ),
inference(cnf_transformation,[],[f40]) ).
fof(f48,plain,
! [X0,X1] :
( mem(sK0(X0,X1),X0)
| subq(X0,X1) ),
inference(cnf_transformation,[],[f40]) ).
fof(f49,plain,
! [X0,X1] :
( ~ mem(sK0(X0,X1),X1)
| subq(X0,X1) ),
inference(cnf_transformation,[],[f40]) ).
fof(f50,plain,
! [X0,X1] :
( ~ subq(X1,X0)
| X0 = X1
| ~ subq(X0,X1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f51,plain,
! [X0] : ~ mem(X0,e),
inference(cnf_transformation,[],[f4]) ).
fof(f52,plain,
! [X0,X1] :
( ~ mem(X0,s(X1))
| X0 = X1 ),
inference(cnf_transformation,[],[f41]) ).
fof(f53,plain,
! [X0,X1] :
( mem(X0,s(X1))
| X0 != X1 ),
inference(cnf_transformation,[],[f41]) ).
fof(f54,plain,
! [X2,X0,X1] :
( ~ mem(X0,u(X1,X2))
| mem(X0,X2)
| mem(X0,X1) ),
inference(cnf_transformation,[],[f43]) ).
fof(f55,plain,
! [X2,X0,X1] :
( mem(X0,u(X1,X2))
| ~ mem(X0,X2) ),
inference(cnf_transformation,[],[f43]) ).
fof(f56,plain,
! [X2,X0,X1] :
( mem(X0,u(X1,X2))
| ~ mem(X0,X1) ),
inference(cnf_transformation,[],[f43]) ).
fof(f60,plain,
! [X0,X1] : a(X0,X1) = u(X0,s(X1)),
inference(cnf_transformation,[],[f8]) ).
fof(f61,plain,
! [X0] : n(X0) = a(X0,X0),
inference(cnf_transformation,[],[f9]) ).
fof(f62,plain,
! [X0,X1] :
( ~ mem(X0,p(X1))
| subq(X0,X1) ),
inference(cnf_transformation,[],[f46]) ).
fof(f64,plain,
! [X0,X1] :
( subq(X0,p(X1))
| ~ mem(X1,X0)
| atleast2p(X0) ),
inference(cnf_transformation,[],[f35]) ).
fof(f65,plain,
! [X0,X1] :
( ~ subq(X1,X0)
| atleast3p(X0)
| ~ atleast2p(X1)
| subq(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f66,plain,
! [X0,X1] :
( ~ subq(X1,X0)
| atleast4p(X0)
| ~ atleast3p(X1)
| subq(X0,X1) ),
inference(cnf_transformation,[],[f37]) ).
fof(f67,plain,
~ atleast4p(u(n(e),n(n(s(n(e)))))),
inference(cnf_transformation,[],[f28]) ).
fof(f68,plain,
! [X0] : n(X0) = u(X0,s(X0)),
inference(definition_unfolding,[],[f61,f60]) ).
fof(f69,plain,
~ atleast4p(u(u(e,s(e)),u(u(s(u(e,s(e))),s(s(u(e,s(e))))),s(u(s(u(e,s(e))),s(s(u(e,s(e))))))))),
inference(definition_unfolding,[],[f67,f68,f68,f68,f68]) ).
fof(f70,plain,
! [X1] : mem(X1,s(X1)),
inference(equality_resolution,[],[f53]) ).
fof(f71,definition,
sF1 = s(e),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f72,plain,
s(e) = sF1,
inference(reorient_equations,[],[f71]) ).
fof(f73,definition,
sF2 = u(e,sF1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f74,plain,
u(e,sF1) = sF2,
inference(reorient_equations,[],[f73]) ).
fof(f75,definition,
sF3 = s(sF2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f76,plain,
s(sF2) = sF3,
inference(reorient_equations,[],[f75]) ).
fof(f77,definition,
sF4 = s(sF3),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f78,plain,
s(sF3) = sF4,
inference(reorient_equations,[],[f77]) ).
fof(f79,definition,
sF5 = u(sF3,sF4),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f80,plain,
u(sF3,sF4) = sF5,
inference(reorient_equations,[],[f79]) ).
fof(f81,definition,
sF6 = s(sF5),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f82,plain,
s(sF5) = sF6,
inference(reorient_equations,[],[f81]) ).
fof(f83,definition,
sF7 = u(sF5,sF6),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f84,plain,
u(sF5,sF6) = sF7,
inference(reorient_equations,[],[f83]) ).
fof(f85,definition,
sF8 = u(sF2,sF7),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f86,plain,
u(sF2,sF7) = sF8,
inference(reorient_equations,[],[f85]) ).
fof(f87,plain,
~ atleast4p(sF8),
inference(definition_folding,[],[f69,f86,f84,f82,f80,f78,f76,f74,f72,f76,f74,f72,f80,f78,f76,f74,f72,f76,f74,f72,f74,f72]) ).
fof(f88,plain,
mem(e,sF1),
inference(superposition,[],[f70,f72]) ).
fof(f89,plain,
mem(sF2,sF3),
inference(superposition,[],[f70,f76]) ).
fof(f90,plain,
mem(sF3,sF4),
inference(superposition,[],[f70,f78]) ).
fof(f91,plain,
mem(sF5,sF6),
inference(superposition,[],[f70,f82]) ).
fof(f93,plain,
! [X0] :
( ~ mem(X0,sF2)
| mem(X0,sF8) ),
inference(superposition,[],[f56,f86]) ).
fof(f94,plain,
! [X0] :
( ~ mem(X0,sF3)
| mem(X0,sF5) ),
inference(superposition,[],[f56,f80]) ).
fof(f95,plain,
! [X0] :
( ~ mem(X0,sF5)
| mem(X0,sF7) ),
inference(superposition,[],[f56,f84]) ).
fof(f96,plain,
! [X0] :
( ~ mem(X0,sF1)
| mem(X0,sF2) ),
inference(superposition,[],[f55,f74]) ).
fof(f97,plain,
! [X0] :
( ~ mem(X0,sF7)
| mem(X0,sF8) ),
inference(superposition,[],[f55,f86]) ).
fof(f98,plain,
! [X0] :
( ~ mem(X0,sF4)
| mem(X0,sF5) ),
inference(superposition,[],[f55,f80]) ).
fof(f99,plain,
! [X0] :
( ~ mem(X0,sF6)
| mem(X0,sF7) ),
inference(superposition,[],[f55,f84]) ).
fof(f105,plain,
! [X0] :
( ~ mem(X0,sF2)
| mem(X0,sF1)
| mem(X0,e) ),
inference(superposition,[],[f54,f74]) ).
fof(f106,plain,
! [X0] :
( ~ mem(X0,sF8)
| mem(X0,sF7)
| mem(X0,sF2) ),
inference(superposition,[],[f54,f86]) ).
fof(f107,plain,
! [X0] :
( ~ mem(X0,sF5)
| mem(X0,sF4)
| mem(X0,sF3) ),
inference(superposition,[],[f54,f80]) ).
fof(f108,plain,
! [X0] :
( ~ mem(X0,sF7)
| mem(X0,sF6)
| mem(X0,sF5) ),
inference(superposition,[],[f54,f84]) ).
fof(f109,plain,
! [X0] :
( ~ mem(X0,sF2)
| mem(X0,sF1) ),
inference(forward_subsumption_resolution,[],[f105,f51]) ).
fof(f112,plain,
! [X0] :
( mem(sK0(sF2,X0),sF1)
| subq(sF2,X0) ),
inference(resolution,[],[f109,f48]) ).
fof(f113,plain,
! [X0] :
( mem(sK0(sF8,X0),sF7)
| mem(sK0(sF8,X0),sF2)
| subq(sF8,X0) ),
inference(resolution,[],[f106,f48]) ).
fof(f115,plain,
! [X2,X0,X1] :
( ~ mem(sK0(X0,u(X1,X2)),X2)
| subq(X0,u(X1,X2)) ),
inference(resolution,[],[f49,f55]) ).
fof(f116,plain,
! [X2,X0,X1] :
( ~ mem(sK0(X0,u(X1,X2)),X1)
| subq(X0,u(X1,X2)) ),
inference(resolution,[],[f49,f56]) ).
fof(f119,plain,
mem(sF3,sF5),
inference(resolution,[],[f98,f90]) ).
fof(f121,plain,
mem(sF2,sF5),
inference(resolution,[],[f94,f89]) ).
fof(f124,plain,
! [X0] :
( ~ mem(X0,sF1)
| e = X0 ),
inference(superposition,[],[f52,f72]) ).
fof(f125,plain,
! [X0] :
( ~ mem(X0,sF3)
| sF2 = X0 ),
inference(superposition,[],[f52,f76]) ).
fof(f126,plain,
! [X0] :
( ~ mem(X0,sF4)
| sF3 = X0 ),
inference(superposition,[],[f52,f78]) ).
fof(f127,plain,
! [X0] :
( ~ mem(X0,sF6)
| sF5 = X0 ),
inference(superposition,[],[f52,f82]) ).
fof(f128,plain,
mem(e,sF2),
inference(resolution,[],[f96,f88]) ).
fof(f131,plain,
mem(e,sF8),
inference(resolution,[],[f128,f93]) ).
fof(f134,plain,
mem(sF5,sF7),
inference(resolution,[],[f99,f91]) ).
fof(f140,plain,
mem(sF3,sF7),
inference(resolution,[],[f119,f95]) ).
fof(f143,plain,
mem(sF3,sF8),
inference(resolution,[],[f140,f97]) ).
fof(f159,plain,
! [X0] :
( mem(sK0(sF8,X0),sF6)
| subq(sF8,X0)
| mem(sK0(sF8,X0),sF2)
| mem(sK0(sF8,X0),sF5) ),
inference(resolution,[],[f113,f108]) ).
fof(f163,definition,
( spl9_1
<=> subq(sF8,sF7) ),
introduced(definition,[new_symbols(definition,[spl9_1])],[avatar_definition]) ).
fof(f171,plain,
( subq(sF8,sF6)
| mem(sK0(sF8,sF6),sF2)
| mem(sK0(sF8,sF6),sF5)
| subq(sF8,sF6) ),
inference(resolution,[],[f159,f49]) ).
fof(f174,plain,
( subq(sF8,sF6)
| mem(sK0(sF8,sF6),sF2)
| mem(sK0(sF8,sF6),sF5) ),
inference(duplicate_literal_removal,[],[f171]) ).
fof(f177,definition,
( spl9_3
<=> mem(sK0(sF8,sF6),sF5) ),
introduced(definition,[new_symbols(definition,[spl9_3])],[avatar_definition]) ).
fof(f179,plain,
( mem(sK0(sF8,sF6),sF5)
| ~ spl9_3 ),
inference(avatar_component_clause,[],[f177]) ).
fof(f181,definition,
( spl9_4
<=> mem(sK0(sF8,sF6),sF2) ),
introduced(definition,[new_symbols(definition,[spl9_4])],[avatar_definition]) ).
fof(f183,plain,
( mem(sK0(sF8,sF6),sF2)
| ~ spl9_4 ),
inference(avatar_component_clause,[],[f181]) ).
fof(f185,definition,
( spl9_5
<=> subq(sF8,sF6) ),
introduced(definition,[new_symbols(definition,[spl9_5])],[avatar_definition]) ).
fof(f187,plain,
( subq(sF8,sF6)
| ~ spl9_5 ),
inference(avatar_component_clause,[],[f185]) ).
fof(f188,plain,
( spl9_3
| spl9_4
| spl9_5 ),
inference(avatar_split_clause,[],[f174,f185,f181,f177]) ).
fof(f210,plain,
! [X0] :
( ~ subq(sF2,X0)
| mem(e,X0) ),
inference(resolution,[],[f47,f128]) ).
fof(f217,plain,
! [X0] :
( ~ subq(sF5,X0)
| mem(sF2,X0) ),
inference(resolution,[],[f47,f121]) ).
fof(f223,plain,
! [X0] :
( ~ subq(sF8,X0)
| mem(sF3,X0) ),
inference(resolution,[],[f47,f143]) ).
fof(f278,definition,
( spl9_17
<=> mem(sF3,sF3) ),
introduced(definition,[new_symbols(definition,[spl9_17])],[avatar_definition]) ).
fof(f279,plain,
( mem(sF3,sF3)
| ~ spl9_17 ),
inference(avatar_component_clause,[],[f278]) ).
fof(f280,plain,
( ~ mem(sF3,sF3)
| spl9_17 ),
inference(avatar_component_clause,[],[f278]) ).
fof(f304,plain,
( subq(sF2,sF1)
| subq(sF2,sF1) ),
inference(resolution,[],[f112,f49]) ).
fof(f308,plain,
subq(sF2,sF1),
inference(duplicate_literal_removal,[],[f304]) ).
fof(f317,definition,
( spl9_22
<=> mem(sF2,sF2) ),
introduced(definition,[new_symbols(definition,[spl9_22])],[avatar_definition]) ).
fof(f318,plain,
( mem(sF2,sF2)
| ~ spl9_22 ),
inference(avatar_component_clause,[],[f317]) ).
fof(f319,plain,
( ~ mem(sF2,sF2)
| spl9_22 ),
inference(avatar_component_clause,[],[f317]) ).
fof(f328,definition,
( spl9_23
<=> mem(sF5,sF5) ),
introduced(definition,[new_symbols(definition,[spl9_23])],[avatar_definition]) ).
fof(f329,plain,
( mem(sF5,sF5)
| ~ spl9_23 ),
inference(avatar_component_clause,[],[f328]) ).
fof(f330,plain,
( ~ mem(sF5,sF5)
| spl9_23 ),
inference(avatar_component_clause,[],[f328]) ).
fof(f335,plain,
( sF1 = sF2
| ~ subq(sF1,sF2) ),
inference(resolution,[],[f50,f308]) ).
fof(f337,definition,
( spl9_24
<=> subq(sF1,sF2) ),
introduced(definition,[new_symbols(definition,[spl9_24])],[avatar_definition]) ).
fof(f339,plain,
( ~ subq(sF1,sF2)
| spl9_24 ),
inference(avatar_component_clause,[],[f337]) ).
fof(f341,definition,
( spl9_25
<=> sF1 = sF2 ),
introduced(definition,[new_symbols(definition,[spl9_25])],[avatar_definition]) ).
fof(f343,plain,
( sF1 = sF2
| ~ spl9_25 ),
inference(avatar_component_clause,[],[f341]) ).
fof(f344,plain,
( ~ spl9_24
| spl9_25 ),
inference(avatar_split_clause,[],[f335,f341,f337]) ).
fof(f456,plain,
( mem(sK0(sF8,sF6),sF1)
| ~ spl9_4 ),
inference(resolution,[],[f183,f109]) ).
fof(f462,plain,
! [X0,X1] :
( subq(X0,u(X1,X0))
| subq(X0,u(X1,X0)) ),
inference(resolution,[],[f115,f48]) ).
fof(f474,plain,
! [X0] :
( ~ mem(sK0(X0,sF8),sF7)
| subq(X0,sF8) ),
inference(superposition,[],[f115,f86]) ).
fof(f485,plain,
! [X0,X1] : subq(X0,u(X1,X0)),
inference(duplicate_literal_removal,[],[f462]) ).
fof(f487,plain,
( subq(sF7,sF8)
| subq(sF7,sF8) ),
inference(resolution,[],[f474,f48]) ).
fof(f490,plain,
subq(sF7,sF8),
inference(duplicate_literal_removal,[],[f487]) ).
fof(f617,plain,
( e = sK0(sF8,sF6)
| ~ spl9_4 ),
inference(resolution,[],[f456,f124]) ).
fof(f631,plain,
( ~ mem(e,sF6)
| subq(sF8,sF6)
| ~ spl9_4 ),
inference(superposition,[],[f49,f617]) ).
fof(f634,definition,
( spl9_49
<=> mem(e,sF6) ),
introduced(definition,[new_symbols(definition,[spl9_49])],[avatar_definition]) ).
fof(f635,plain,
( mem(e,sF6)
| ~ spl9_49 ),
inference(avatar_component_clause,[],[f634]) ).
fof(f636,plain,
( ~ mem(e,sF6)
| spl9_49 ),
inference(avatar_component_clause,[],[f634]) ).
fof(f637,plain,
( spl9_5
| ~ spl9_49
| ~ spl9_4 ),
inference(avatar_split_clause,[],[f631,f181,f634,f185]) ).
fof(f661,definition,
( spl9_50
<=> mem(e,sF7) ),
introduced(definition,[new_symbols(definition,[spl9_50])],[avatar_definition]) ).
fof(f662,plain,
( mem(e,sF7)
| ~ spl9_50 ),
inference(avatar_component_clause,[],[f661]) ).
fof(f663,plain,
( ~ mem(e,sF7)
| spl9_50 ),
inference(avatar_component_clause,[],[f661]) ).
fof(f666,plain,
! [X0,X1] :
( subq(X0,u(X0,X1))
| subq(X0,u(X0,X1)) ),
inference(resolution,[],[f116,f48]) ).
fof(f695,plain,
! [X0,X1] : subq(X0,u(X0,X1)),
inference(duplicate_literal_removal,[],[f666]) ).
fof(f856,plain,
subq(sF1,sF2),
inference(superposition,[],[f485,f74]) ).
fof(f860,plain,
( $false
| spl9_24 ),
inference(forward_subsumption_resolution,[],[f856,f339]) ).
fof(f861,plain,
spl9_24,
inference(avatar_contradiction_clause,[],[f860]) ).
fof(f866,plain,
( ! [X0] :
( ~ mem(X0,sF2)
| e = X0 )
| ~ spl9_25 ),
inference(superposition,[],[f124,f343]) ).
fof(f938,plain,
! [X0] :
( mem(sF2,p(X0))
| ~ mem(X0,sF5)
| atleast2p(sF5) ),
inference(resolution,[],[f217,f64]) ).
fof(f970,definition,
( spl9_66
<=> atleast2p(sF5) ),
introduced(definition,[new_symbols(definition,[spl9_66])],[avatar_definition]) ).
fof(f972,plain,
( atleast2p(sF5)
| ~ spl9_66 ),
inference(avatar_component_clause,[],[f970]) ).
fof(f974,definition,
( spl9_67
<=> ! [X0] :
( mem(sF2,p(X0))
| ~ mem(X0,sF5) ) ),
introduced(definition,[new_symbols(definition,[spl9_67])],[avatar_definition]) ).
fof(f975,plain,
( ! [X0] :
( mem(sF2,p(X0))
| ~ mem(X0,sF5) )
| ~ spl9_67 ),
inference(avatar_component_clause,[],[f974]) ).
fof(f976,plain,
( spl9_66
| spl9_67 ),
inference(avatar_split_clause,[],[f938,f974,f970]) ).
fof(f1018,plain,
( atleast4p(sF8)
| ~ atleast3p(sF7)
| subq(sF8,sF7) ),
inference(resolution,[],[f490,f66]) ).
fof(f1019,plain,
( sF7 = sF8
| ~ subq(sF8,sF7) ),
inference(resolution,[],[f490,f50]) ).
fof(f1021,definition,
( spl9_69
<=> sF7 = sF8 ),
introduced(definition,[new_symbols(definition,[spl9_69])],[avatar_definition]) ).
fof(f1023,plain,
( sF7 = sF8
| ~ spl9_69 ),
inference(avatar_component_clause,[],[f1021]) ).
fof(f1024,plain,
( ~ spl9_1
| spl9_69 ),
inference(avatar_split_clause,[],[f1019,f1021,f163]) ).
fof(f1025,plain,
( ~ atleast3p(sF7)
| subq(sF8,sF7) ),
inference(forward_subsumption_resolution,[],[f1018,f87]) ).
fof(f1027,definition,
( spl9_70
<=> atleast3p(sF7) ),
introduced(definition,[new_symbols(definition,[spl9_70])],[avatar_definition]) ).
fof(f1029,plain,
( ~ atleast3p(sF7)
| spl9_70 ),
inference(avatar_component_clause,[],[f1027]) ).
fof(f1030,plain,
( spl9_1
| ~ spl9_70 ),
inference(avatar_split_clause,[],[f1025,f1027,f163]) ).
fof(f1049,plain,
subq(sF5,sF7),
inference(superposition,[],[f695,f84]) ).
fof(f1122,definition,
( spl9_77
<=> sF3 = sF5 ),
introduced(definition,[new_symbols(definition,[spl9_77])],[avatar_definition]) ).
fof(f1123,plain,
( sF3 != sF5
| spl9_77 ),
inference(avatar_component_clause,[],[f1122]) ).
fof(f1124,plain,
( sF3 = sF5
| ~ spl9_77 ),
inference(avatar_component_clause,[],[f1122]) ).
fof(f1129,plain,
( sF5 = sF7
| ~ subq(sF7,sF5) ),
inference(resolution,[],[f1049,f50]) ).
fof(f1131,definition,
( spl9_78
<=> subq(sF7,sF5) ),
introduced(definition,[new_symbols(definition,[spl9_78])],[avatar_definition]) ).
fof(f1133,plain,
( ~ subq(sF7,sF5)
| spl9_78 ),
inference(avatar_component_clause,[],[f1131]) ).
fof(f1135,definition,
( spl9_79
<=> sF5 = sF7 ),
introduced(definition,[new_symbols(definition,[spl9_79])],[avatar_definition]) ).
fof(f1137,plain,
( sF5 = sF7
| ~ spl9_79 ),
inference(avatar_component_clause,[],[f1135]) ).
fof(f1138,plain,
( ~ spl9_78
| spl9_79 ),
inference(avatar_split_clause,[],[f1129,f1135,f1131]) ).
fof(f1204,definition,
( spl9_85
<=> mem(sF5,sF4) ),
introduced(definition,[new_symbols(definition,[spl9_85])],[avatar_definition]) ).
fof(f1205,plain,
( mem(sF5,sF4)
| ~ spl9_85 ),
inference(avatar_component_clause,[],[f1204]) ).
fof(f1206,plain,
( ~ mem(sF5,sF4)
| spl9_85 ),
inference(avatar_component_clause,[],[f1204]) ).
fof(f1231,plain,
( atleast3p(sF7)
| ~ atleast2p(sF5)
| subq(sF7,sF5) ),
inference(resolution,[],[f65,f1049]) ).
fof(f1236,plain,
( ~ atleast2p(sF5)
| subq(sF7,sF5)
| spl9_70 ),
inference(forward_subsumption_resolution,[],[f1231,f1029]) ).
fof(f1256,plain,
( subq(sF7,sF5)
| ~ spl9_66
| spl9_70 ),
inference(forward_subsumption_resolution,[],[f1236,f972]) ).
fof(f1265,plain,
( $false
| ~ spl9_66
| spl9_70
| spl9_78 ),
inference(forward_subsumption_resolution,[],[f1256,f1133]) ).
fof(f1266,plain,
( ~ spl9_66
| spl9_70
| spl9_78 ),
inference(avatar_contradiction_clause,[],[f1265]) ).
fof(f1375,definition,
( spl9_89
<=> e = sF2 ),
introduced(definition,[new_symbols(definition,[spl9_89])],[avatar_definition]) ).
fof(f1376,plain,
( e != sF2
| spl9_89 ),
inference(avatar_component_clause,[],[f1375]) ).
fof(f1377,plain,
( e = sF2
| ~ spl9_89 ),
inference(avatar_component_clause,[],[f1375]) ).
fof(f1398,definition,
( spl9_91
<=> e = sF3 ),
introduced(definition,[new_symbols(definition,[spl9_91])],[avatar_definition]) ).
fof(f1399,plain,
( e != sF3
| spl9_91 ),
inference(avatar_component_clause,[],[f1398]) ).
fof(f1400,plain,
( e = sF3
| ~ spl9_91 ),
inference(avatar_component_clause,[],[f1398]) ).
fof(f1411,definition,
( spl9_92
<=> sF2 = sF3 ),
introduced(definition,[new_symbols(definition,[spl9_92])],[avatar_definition]) ).
fof(f1412,plain,
( sF2 != sF3
| spl9_92 ),
inference(avatar_component_clause,[],[f1411]) ).
fof(f1413,plain,
( sF2 = sF3
| ~ spl9_92 ),
inference(avatar_component_clause,[],[f1411]) ).
fof(f1437,definition,
( spl9_94
<=> e = sF5 ),
introduced(definition,[new_symbols(definition,[spl9_94])],[avatar_definition]) ).
fof(f1439,plain,
( e = sF5
| ~ spl9_94 ),
inference(avatar_component_clause,[],[f1437]) ).
fof(f1612,plain,
( e = sF2
| ~ spl9_22
| ~ spl9_25 ),
inference(resolution,[],[f318,f866]) ).
fof(f1617,plain,
( spl9_89
| ~ spl9_22
| ~ spl9_25 ),
inference(avatar_split_clause,[],[f1612,f341,f317,f1375]) ).
fof(f1625,plain,
( mem(sF2,e)
| ~ spl9_91 ),
inference(superposition,[],[f89,f1400]) ).
fof(f1652,plain,
( $false
| ~ spl9_91 ),
inference(forward_subsumption_resolution,[],[f1625,f51]) ).
fof(f1653,plain,
~ spl9_91,
inference(avatar_contradiction_clause,[],[f1652]) ).
fof(f1696,plain,
( mem(sF3,sF6)
| ~ spl9_5 ),
inference(resolution,[],[f187,f223]) ).
fof(f1709,plain,
( e = sF5
| ~ spl9_49 ),
inference(resolution,[],[f635,f127]) ).
fof(f1732,plain,
( mem(sF2,sF2)
| ~ spl9_92 ),
inference(superposition,[],[f89,f1413]) ).
fof(f1752,plain,
( $false
| spl9_22
| ~ spl9_92 ),
inference(forward_subsumption_resolution,[],[f1732,f319]) ).
fof(f1753,plain,
( spl9_22
| ~ spl9_92 ),
inference(avatar_contradiction_clause,[],[f1752]) ).
fof(f1822,plain,
( mem(sF3,sF3)
| ~ spl9_77 ),
inference(superposition,[],[f119,f1124]) ).
fof(f1845,plain,
( $false
| spl9_17
| ~ spl9_77 ),
inference(forward_subsumption_resolution,[],[f1822,f280]) ).
fof(f1846,plain,
( spl9_17
| ~ spl9_77 ),
inference(avatar_contradiction_clause,[],[f1845]) ).
fof(f1958,plain,
( sF2 = sF3
| ~ spl9_17 ),
inference(resolution,[],[f279,f125]) ).
fof(f1961,plain,
( $false
| ~ spl9_17
| spl9_92 ),
inference(forward_subsumption_resolution,[],[f1958,f1412]) ).
fof(f1962,plain,
( ~ spl9_17
| spl9_92 ),
inference(avatar_contradiction_clause,[],[f1961]) ).
fof(f1979,definition,
( spl9_104
<=> mem(sF3,sF6) ),
introduced(definition,[new_symbols(definition,[spl9_104])],[avatar_definition]) ).
fof(f1980,plain,
( ~ mem(sF3,sF6)
| spl9_104 ),
inference(avatar_component_clause,[],[f1979]) ).
fof(f1981,plain,
( mem(sF3,sF6)
| ~ spl9_104 ),
inference(avatar_component_clause,[],[f1979]) ).
fof(f2001,plain,
( mem(sF5,sF4)
| mem(sF5,sF3)
| ~ spl9_23 ),
inference(resolution,[],[f329,f107]) ).
fof(f2008,plain,
( mem(e,sF7)
| ~ spl9_69 ),
inference(superposition,[],[f131,f1023]) ).
fof(f2177,plain,
( mem(sF5,sF5)
| ~ spl9_79 ),
inference(superposition,[],[f134,f1137]) ).
fof(f2198,plain,
( sF3 = sF5
| ~ spl9_85 ),
inference(resolution,[],[f1205,f126]) ).
fof(f2201,plain,
( $false
| spl9_77
| ~ spl9_85 ),
inference(forward_subsumption_resolution,[],[f2198,f1123]) ).
fof(f2202,plain,
( spl9_77
| ~ spl9_85 ),
inference(avatar_contradiction_clause,[],[f2201]) ).
fof(f2203,plain,
( mem(sF5,sF3)
| ~ spl9_23
| spl9_85 ),
inference(forward_subsumption_resolution,[],[f2001,f1206]) ).
fof(f2227,plain,
( sF2 = sF5
| ~ spl9_23
| spl9_85 ),
inference(resolution,[],[f2203,f125]) ).
fof(f2236,plain,
( mem(sF2,sF2)
| ~ spl9_23
| spl9_85 ),
inference(superposition,[],[f121,f2227]) ).
fof(f2252,plain,
( $false
| spl9_22
| ~ spl9_23
| spl9_85 ),
inference(forward_subsumption_resolution,[],[f2236,f319]) ).
fof(f2253,plain,
( spl9_22
| ~ spl9_23
| spl9_85 ),
inference(avatar_contradiction_clause,[],[f2252]) ).
fof(f2264,plain,
( $false
| spl9_23
| ~ spl9_79 ),
inference(forward_subsumption_resolution,[],[f2177,f330]) ).
fof(f2265,plain,
( spl9_23
| ~ spl9_79 ),
inference(avatar_contradiction_clause,[],[f2264]) ).
fof(f2351,definition,
( spl9_118
<=> mem(e,sF4) ),
introduced(definition,[new_symbols(definition,[spl9_118])],[avatar_definition]) ).
fof(f2352,plain,
( ~ mem(e,sF4)
| spl9_118 ),
inference(avatar_component_clause,[],[f2351]) ).
fof(f2353,plain,
( mem(e,sF4)
| ~ spl9_118 ),
inference(avatar_component_clause,[],[f2351]) ).
fof(f2430,plain,
( sF3 = sF5
| ~ spl9_104 ),
inference(resolution,[],[f1981,f127]) ).
fof(f2433,plain,
( $false
| spl9_77
| ~ spl9_104 ),
inference(forward_subsumption_resolution,[],[f2430,f1123]) ).
fof(f2434,plain,
( spl9_77
| ~ spl9_104 ),
inference(avatar_contradiction_clause,[],[f2433]) ).
fof(f2633,plain,
( ! [X0] :
( ~ mem(X0,sF5)
| subq(sF2,X0) )
| ~ spl9_67 ),
inference(resolution,[],[f975,f62]) ).
fof(f2643,plain,
( subq(sF2,sF3)
| ~ spl9_67 ),
inference(resolution,[],[f2633,f119]) ).
fof(f2644,plain,
( mem(e,sF3)
| ~ spl9_67 ),
inference(resolution,[],[f2643,f210]) ).
fof(f2699,plain,
( mem(e,sF6)
| mem(e,sF5)
| ~ spl9_50 ),
inference(resolution,[],[f662,f108]) ).
fof(f2702,plain,
( mem(e,sF5)
| spl9_49
| ~ spl9_50 ),
inference(forward_subsumption_resolution,[],[f2699,f636]) ).
fof(f2762,plain,
( mem(e,e)
| ~ spl9_89 ),
inference(superposition,[],[f128,f1377]) ).
fof(f2792,plain,
( $false
| ~ spl9_89 ),
inference(forward_subsumption_resolution,[],[f2762,f51]) ).
fof(f2793,plain,
~ spl9_89,
inference(avatar_contradiction_clause,[],[f2792]) ).
fof(f2804,plain,
( $false
| ~ spl9_5
| spl9_104 ),
inference(forward_subsumption_resolution,[],[f1696,f1980]) ).
fof(f2805,plain,
( ~ spl9_5
| spl9_104 ),
inference(avatar_contradiction_clause,[],[f2804]) ).
fof(f2809,plain,
( spl9_94
| ~ spl9_49 ),
inference(avatar_split_clause,[],[f1709,f634,f1437]) ).
fof(f2829,plain,
( mem(sK0(sF8,sF6),e)
| ~ spl9_3
| ~ spl9_94 ),
inference(forward_demodulation,[],[f179,f1439]) ).
fof(f2839,plain,
( $false
| ~ spl9_3
| ~ spl9_94 ),
inference(forward_subsumption_resolution,[],[f2829,f51]) ).
fof(f2840,plain,
( ~ spl9_3
| ~ spl9_94 ),
inference(avatar_contradiction_clause,[],[f2839]) ).
fof(f2850,plain,
( mem(e,sF4)
| mem(e,sF3)
| spl9_49
| ~ spl9_50 ),
inference(resolution,[],[f2702,f107]) ).
fof(f2852,plain,
( mem(e,sF3)
| spl9_49
| ~ spl9_50
| spl9_118 ),
inference(forward_subsumption_resolution,[],[f2850,f2352]) ).
fof(f2867,plain,
( e = sF2
| spl9_49
| ~ spl9_50
| spl9_118 ),
inference(resolution,[],[f2852,f125]) ).
fof(f2870,plain,
( $false
| spl9_49
| ~ spl9_50
| spl9_89
| spl9_118 ),
inference(forward_subsumption_resolution,[],[f2867,f1376]) ).
fof(f2871,plain,
( spl9_49
| ~ spl9_50
| spl9_89
| spl9_118 ),
inference(avatar_contradiction_clause,[],[f2870]) ).
fof(f2873,plain,
( e = sF3
| ~ spl9_118 ),
inference(resolution,[],[f2353,f126]) ).
fof(f2876,plain,
( $false
| spl9_91
| ~ spl9_118 ),
inference(forward_subsumption_resolution,[],[f2873,f1399]) ).
fof(f2877,plain,
( spl9_91
| ~ spl9_118 ),
inference(avatar_contradiction_clause,[],[f2876]) ).
fof(f2878,plain,
( $false
| spl9_50
| ~ spl9_69 ),
inference(forward_subsumption_resolution,[],[f2008,f663]) ).
fof(f2879,plain,
( spl9_50
| ~ spl9_69 ),
inference(avatar_contradiction_clause,[],[f2878]) ).
fof(f2908,plain,
( e = sF2
| ~ spl9_67 ),
inference(resolution,[],[f2644,f125]) ).
fof(f2911,plain,
( $false
| ~ spl9_67
| spl9_89 ),
inference(forward_subsumption_resolution,[],[f2908,f1376]) ).
fof(f2912,plain,
( ~ spl9_67
| spl9_89 ),
inference(avatar_contradiction_clause,[],[f2911]) ).
cnf(s2,plain,
( spl9_3
| spl9_4
| spl9_5 ),
inference(sat_conversion,[],[f188]) ).
cnf(s10,plain,
( ~ spl9_24
| spl9_25 ),
inference(sat_conversion,[],[f344]) ).
cnf(s23,plain,
( ~ spl9_4
| spl9_5
| ~ spl9_49 ),
inference(sat_conversion,[],[f637]) ).
cnf(s30,plain,
spl9_24,
inference(sat_conversion,[],[f861]) ).
cnf(s37,plain,
( spl9_66
| spl9_67 ),
inference(sat_conversion,[],[f976]) ).
cnf(s41,plain,
( ~ spl9_1
| spl9_69 ),
inference(sat_conversion,[],[f1024]) ).
cnf(s42,plain,
( spl9_1
| ~ spl9_70 ),
inference(sat_conversion,[],[f1030]) ).
cnf(s51,plain,
( ~ spl9_78
| spl9_79 ),
inference(sat_conversion,[],[f1138]) ).
cnf(s59,plain,
( ~ spl9_66
| spl9_70
| spl9_78 ),
inference(sat_conversion,[],[f1266]) ).
cnf(s119,plain,
( ~ spl9_22
| ~ spl9_25
| spl9_89 ),
inference(sat_conversion,[],[f1617]) ).
cnf(s125,plain,
~ spl9_91,
inference(sat_conversion,[],[f1653]) ).
cnf(s135,plain,
( spl9_22
| ~ spl9_92 ),
inference(sat_conversion,[],[f1753]) ).
cnf(s141,plain,
( spl9_17
| ~ spl9_77 ),
inference(sat_conversion,[],[f1846]) ).
cnf(s152,plain,
( ~ spl9_17
| spl9_92 ),
inference(sat_conversion,[],[f1962]) ).
cnf(s172,plain,
( spl9_77
| ~ spl9_85 ),
inference(sat_conversion,[],[f2202]) ).
cnf(s178,plain,
( spl9_22
| ~ spl9_23
| spl9_85 ),
inference(sat_conversion,[],[f2253]) ).
cnf(s181,plain,
( spl9_23
| ~ spl9_79 ),
inference(sat_conversion,[],[f2265]) ).
cnf(s198,plain,
( spl9_77
| ~ spl9_104 ),
inference(sat_conversion,[],[f2434]) ).
cnf(s226,plain,
~ spl9_89,
inference(sat_conversion,[],[f2793]) ).
cnf(s228,plain,
( ~ spl9_5
| spl9_104 ),
inference(sat_conversion,[],[f2805]) ).
cnf(s230,plain,
( ~ spl9_49
| spl9_94 ),
inference(sat_conversion,[],[f2809]) ).
cnf(s236,plain,
( ~ spl9_3
| ~ spl9_94 ),
inference(sat_conversion,[],[f2840]) ).
cnf(s242,plain,
( spl9_49
| ~ spl9_50
| spl9_89
| spl9_118 ),
inference(sat_conversion,[],[f2871]) ).
cnf(s243,plain,
( spl9_91
| ~ spl9_118 ),
inference(sat_conversion,[],[f2877]) ).
cnf(s244,plain,
( spl9_50
| ~ spl9_69 ),
inference(sat_conversion,[],[f2879]) ).
cnf(s246,plain,
( ~ spl9_67
| spl9_89 ),
inference(sat_conversion,[],[f2912]) ).
cnf(s247,plain,
~ spl9_67,
inference(rat,[],[s246,s226]) ).
cnf(s251,plain,
~ spl9_118,
inference(rat,[],[s243,s125]) ).
cnf(s252,plain,
( ~ spl9_22
| ~ spl9_25 ),
inference(rat,[],[s119,s226]) ).
cnf(s263,plain,
spl9_66,
inference(rat,[],[s37,s247]) ).
cnf(s264,plain,
spl9_25,
inference(rat,[],[s10,s30]) ).
cnf(s265,plain,
~ spl9_22,
inference(rat,[],[s252,s264]) ).
cnf(s269,plain,
~ spl9_92,
inference(rat,[],[s135,s265]) ).
cnf(s271,plain,
~ spl9_17,
inference(rat,[],[s152,s269]) ).
cnf(s275,plain,
~ spl9_77,
inference(rat,[],[s141,s271]) ).
cnf(s277,plain,
~ spl9_104,
inference(rat,[],[s198,s275]) ).
cnf(s278,plain,
~ spl9_85,
inference(rat,[],[s172,s275]) ).
cnf(s282,plain,
~ spl9_5,
inference(rat,[],[s228,s277]) ).
cnf(s285,plain,
~ spl9_23,
inference(rat,[],[s178,s265,s278]) ).
cnf(s288,plain,
~ spl9_79,
inference(rat,[],[s181,s285]) ).
cnf(s289,plain,
~ spl9_78,
inference(rat,[],[s51,s288]) ).
cnf(s290,plain,
spl9_70,
inference(rat,[],[s59,s263,s289]) ).
cnf(s291,plain,
spl9_1,
inference(rat,[],[s42,s290]) ).
cnf(s292,plain,
spl9_69,
inference(rat,[],[s41,s291]) ).
cnf(s293,plain,
spl9_50,
inference(rat,[],[s244,s292]) ).
cnf(s296,plain,
spl9_49,
inference(rat,[],[s242,s251,s226,s293]) ).
cnf(s299,plain,
spl9_94,
inference(rat,[],[s230,s296]) ).
cnf(s300,plain,
~ spl9_4,
inference(rat,[],[s23,s282,s296]) ).
cnf(s303,plain,
~ spl9_3,
inference(rat,[],[s236,s299]) ).
cnf(s311,plain,
$false,
inference(rat,[],[s2,s282,s300,s303]) ).
fof(f2913,plain,
$false,
inference(avatar_sat_refutation,[],[s311]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV541+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n008.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 06:32:24 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.38/2.17 % (2046025)Detected formulas, will run a generic FOF schedule.
% 9.38/2.17 % (2046033)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1116910353:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 9.38/2.17 % (2046033)Refutation not found, incomplete strategy
% 9.38/2.17 % (2046033)------------------------------
% 9.38/2.17 % (2046033)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.38/2.17 % (2046033)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.38/2.17 % (2046033)CaDiCaL version: 2.1.3
% 9.38/2.17 % (2046033)Termination reason: Refutation not found, incomplete strategy
% 9.38/2.17 % (2046033)Time elapsed: 0.001 s
% 9.38/2.17 % (2046033)Peak memory usage: 88 MB
% 9.38/2.17 % (2046030)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=1309679009:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 9.38/2.17 % (2046032)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=3513021009:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 9.38/2.17 % (2046031)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=1390446983:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 9.38/2.17 % (2046034)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1862582997:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 9.38/2.17 % (2046035)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2815225008:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 9.38/2.17 % (2046036)dis-21_1_sil=8000:lcm=predicate:random_seed=894244440: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)
% 9.38/2.17 % (2046034)Instruction limit reached!
% 9.38/2.17 % (2046034)------------------------------
% 9.38/2.17 % (2046034)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.38/2.17 % (2046034)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.38/2.17 % (2046034)CaDiCaL version: 2.1.3
% 9.38/2.17 % (2046034)Termination reason: Instruction limit
% 9.38/2.17 % (2046034)Termination phase: Saturation
% 9.38/2.17 % (2046034)Time elapsed: 0.074 s
% 9.38/2.17 % (2046034)Peak memory usage: 89 MB
% 9.38/2.17 % (2046034)Instructions burned: 120 (million)
% 9.38/2.17 % (2046036)Instruction limit reached!
% 9.38/2.17 % (2046036)------------------------------
% 9.38/2.17 % (2046036)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.38/2.17 % (2046036)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.38/2.17 % (2046036)CaDiCaL version: 2.1.3
% 9.38/2.17 % (2046036)Termination reason: Instruction limit
% 9.38/2.17 % (2046036)Termination phase: Saturation
% 9.38/2.17 % (2046036)Time elapsed: 0.075 s
% 9.38/2.17 % (2046036)Peak memory usage: 89 MB
% 9.38/2.17 % (2046036)Instructions burned: 129 (million)
% 9.38/2.17 % (2046035)Instruction limit reached!
% 9.38/2.17 % (2046035)------------------------------
% 9.38/2.17 % (2046035)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.38/2.17 % (2046035)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.38/2.17 % (2046035)CaDiCaL version: 2.1.3
% 9.38/2.17 % (2046035)Termination reason: Instruction limit
% 9.38/2.17 % (2046035)Termination phase: Saturation
% 9.38/2.17 % (2046035)Time elapsed: 0.086 s
% 9.38/2.17 % (2046035)Peak memory usage: 88 MB
% 9.38/2.17 % (2046035)Instructions burned: 140 (million)
% 9.38/2.17 % (2046033)------------------------------
% 9.38/2.17 % (2046033)------------------------------
% 9.38/2.17 % (2046044)lrs+10_1_sil=8000:sp=occurrence:random_seed=1952668699:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 9.38/2.17 % (2046045)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1794290555:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 9.38/2.17 % (2046046)lrs+1011_1_sil=32000:sp=occurrence:random_seed=14281785:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 9.38/2.17 % (2046046)Refutation not found, incomplete strategy
% 9.38/2.17 % (2046046)------------------------------
% 9.38/2.17 % (2046046)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.38/2.17 % (2046046)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.38/2.17 % (2046046)CaDiCaL version: 2.1.3
% 9.38/2.17 % (2046046)Termination reason: Refutation not found, incomplete strategy
% 9.38/2.17 % (2046046)Time elapsed: 0.001 s
% 9.38/2.17 % (2046046)Peak memory usage: 88 MB
% 9.38/2.17 % (2046047)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=1588269503:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 9.38/2.17 % (2046045)Instruction limit reached!
% 9.38/2.17 % (2046045)------------------------------
% 9.38/2.17 % (2046045)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.38/2.17 % (2046045)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.38/2.17 % (2046045)CaDiCaL version: 2.1.3
% 9.38/2.17 % (2046045)Termination reason: Instruction limit
% 9.38/2.17 % (2046045)Termination phase: Saturation
% 9.38/2.17 % (2046045)Time elapsed: 0.076 s
% 9.38/2.17 % (2046045)Peak memory usage: 89 MB
% 9.38/2.17 % (2046045)Instructions burned: 158 (million)
% 9.38/2.17 % (2046047)Instruction limit reached!
% 9.38/2.17 % (2046047)------------------------------
% 9.38/2.17 % (2046047)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.38/2.17 % (2046047)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.38/2.17 % (2046047)CaDiCaL version: 2.1.3
% 9.38/2.17 % (2046047)Termination reason: Instruction limit
% 9.38/2.17 % (2046047)Termination phase: Saturation
% 9.38/2.17 % (2046047)Time elapsed: 0.074 s
% 9.38/2.17 % (2046047)Peak memory usage: 91 MB
% 9.38/2.17 % (2046047)Instructions burned: 248 (million)
% 9.38/2.17 % (2046044)Instruction limit reached!
% 9.38/2.17 % (2046044)------------------------------
% 9.38/2.17 % (2046044)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.38/2.17 % (2046044)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.38/2.17 % (2046044)CaDiCaL version: 2.1.3
% 9.38/2.17 % (2046044)Termination reason: Instruction limit
% 9.38/2.17 % (2046044)Termination phase: Saturation
% 9.38/2.17 % (2046044)Time elapsed: 0.184 s
% 9.38/2.17 % (2046044)Peak memory usage: 91 MB
% 9.38/2.17 % (2046044)Instructions burned: 285 (million)
% 9.38/2.17 % (2046052)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=444581314:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 9.38/2.17 % (2046052)Refutation not found, incomplete strategy
% 9.38/2.17 % (2046052)------------------------------
% 9.38/2.17 % (2046052)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.38/2.17 % (2046052)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.38/2.17 % (2046052)CaDiCaL version: 2.1.3
% 9.38/2.17 % (2046052)Termination reason: Refutation not found, incomplete strategy
% 9.38/2.17 % (2046052)Time elapsed: 0.002 s
% 9.38/2.17 % (2046052)Peak memory usage: 88 MB
% 9.38/2.17 % (2046052)Instructions burned: 1 (million)
% 9.38/2.17 % (2046053)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2050644974:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 9.38/2.17 % (2046046)------------------------------
% 9.38/2.17 % (2046046)------------------------------
% 9.38/2.17 % (2046032)Refutation not found, incomplete strategy
% 9.38/2.17 % (2046032)------------------------------
% 9.38/2.17 % (2046032)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.38/2.17 % (2046032)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.38/2.17 % (2046032)CaDiCaL version: 2.1.3
% 9.38/2.17 % (2046032)Termination reason: Refutation not found, incomplete strategy
% 9.38/2.17 % (2046032)Time elapsed: 0.556 s
% 9.38/2.17 % (2046032)Peak memory usage: 125 MB
% 9.38/2.17 % (2046032)Instructions burned: 828 (million)
% 9.38/2.17 % (2046054)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1884003431:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 9.38/2.17 % (2046054)Instruction limit reached!
% 9.38/2.17 % (2046054)------------------------------
% 9.38/2.17 % (2046054)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.38/2.17 % (2046054)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.38/2.17 % (2046054)CaDiCaL version: 2.1.3
% 9.38/2.17 % (2046054)Termination reason: Instruction limit
% 9.38/2.17 % (2046054)Termination phase: Saturation
% 9.38/2.17 % (2046054)Time elapsed: 0.070 s
% 9.38/2.17 % (2046054)Peak memory usage: 89 MB
% 9.38/2.17 % (2046054)Instructions burned: 113 (million)
% 9.38/2.17 % (2046057)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3223526919:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 9.38/2.17 % (2046052)------------------------------
% 9.38/2.17 % (2046052)------------------------------
% 9.38/2.17 % (2046057)Instruction limit reached!
% 9.38/2.17 % (2046057)------------------------------
% 9.38/2.17 % (2046057)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.38/2.17 % (2046057)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.38/2.17 % (2046057)CaDiCaL version: 2.1.3
% 9.38/2.17 % (2046057)Termination reason: Instruction limit
% 9.38/2.17 % (2046057)Termination phase: Saturation
% 9.38/2.17 % (2046057)Time elapsed: 0.062 s
% 9.38/2.17 % (2046057)Peak memory usage: 88 MB
% 9.38/2.17 % (2046057)Instructions burned: 127 (million)
% 9.38/2.17 % (2046059)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=1047102414:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2991 on theBenchmark for (2991ds/114Mi)
% 9.38/2.17 % (2046032)------------------------------
% 9.38/2.17 % (2046032)------------------------------
% 9.38/2.17 % (2046061)lrs+10_1_sil=8000:sp=occurrence:random_seed=524740317:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 9.38/2.17 % (2046059)Instruction limit reached!
% 9.38/2.17 % (2046059)------------------------------
% 9.38/2.17 % (2046059)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.38/2.17 % (2046059)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.38/2.17 % (2046059)CaDiCaL version: 2.1.3
% 9.38/2.17 % (2046059)Termination reason: Instruction limit
% 9.38/2.17 % (2046059)Termination phase: Saturation
% 9.38/2.17 % (2046059)Time elapsed: 0.058 s
% 9.38/2.17 % (2046059)Peak memory usage: 88 MB
% 9.38/2.17 % (2046059)Instructions burned: 114 (million)
% 9.38/2.17 % (2046062)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=844615060:i=437:sd=1:aac=none:ss=included_2990 on theBenchmark for (2990ds/437Mi)
% 9.38/2.17 % (2046062)Refutation not found, incomplete strategy
% 9.38/2.17 % (2046062)------------------------------
% 9.38/2.17 % (2046062)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.38/2.17 % (2046062)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.38/2.17 % (2046062)CaDiCaL version: 2.1.3
% 9.38/2.17 % (2046062)Termination reason: Refutation not found, incomplete strategy
% 9.38/2.17 % (2046062)Time elapsed: 0.001 s
% 9.38/2.17 % (2046062)Peak memory usage: 88 MB
% 9.38/2.17 % (2046053)First to succeed.
% 9.38/2.17 % (2046064)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=486463953:i=5202:ss=axioms:sgt=16_2990 on theBenchmark for (2990ds/5202Mi)
% 9.38/2.17 % (2046053)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2046025"
% 9.38/2.17 % (2046066)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=2466927155:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2989 on theBenchmark for (2989ds/134Mi)
% 9.38/2.17 % (2046066)Instruction limit reached!
% 9.38/2.17 % (2046066)------------------------------
% 9.38/2.17 % (2046066)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.38/2.17 % (2046066)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.38/2.17 % (2046066)CaDiCaL version: 2.1.3
% 9.38/2.17 % (2046066)Termination reason: Instruction limit
% 9.38/2.17 % (2046066)Termination phase: Saturation
% 9.38/2.17 % (2046066)Time elapsed: 0.066 s
% 9.38/2.17 % (2046066)Peak memory usage: 89 MB
% 9.38/2.17 % (2046066)Instructions burned: 134 (million)
% 9.38/2.17 % (2046062)------------------------------
% 9.38/2.17 % (2046062)------------------------------
% 9.38/2.17 % (2046053)Refutation found. Thanks to Tanya!
% 9.38/2.17 % SZS status Theorem for theBenchmark
% 9.38/2.17 % SZS output start Proof for theBenchmark
% See solution above
% 9.84/2.38 % (2046053)------------------------------
% 9.84/2.38 % (2046053)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.84/2.38 % (2046053)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.84/2.38 % (2046053)CaDiCaL version: 2.1.3
% 9.84/2.38 % (2046053)Termination reason: Refutation
% 9.84/2.38 % (2046053)Time elapsed: 0.505 s
% 9.84/2.38 % (2046053)Peak memory usage: 132 MB
% 9.84/2.38 % (2046053)Instructions burned: 1218 (million)
% 9.84/2.38 % (2046053)------------------------------
% 9.84/2.38 % (2046053)------------------------------
% 9.84/2.38 % (2046025)Success in time 1.31 s
% 9.84/2.38 % Vampire exiting
%------------------------------------------------------------------------------