%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG067+1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 09:09:29 AM UTC 2026
% Result : Theorem 2.01s 0.73s
% Output : Refutation 2.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 95
% Syntax : Number of formulae : 430 ( 27 unt; 94 def)
% Number of atoms : 1579 ( 663 equ)
% Maximal formula atoms : 125 ( 3 avg)
% Number of connectives : 1819 ( 670 ~; 731 |; 348 &)
% ( 70 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 96 ( 94 usr; 94 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 2 ( 0 sgn 2 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,conjecture,
~ ( ( op(e0,e0) != e0
| op(e0,e0) = e0 )
& ( op(e0,e0) != e1
| op(e0,e1) = e0 )
& ( op(e0,e0) != e2
| op(e0,e2) = e0 )
& ( op(e0,e0) != e3
| op(e0,e3) = e0 )
& ( op(e0,e0) != e4
| op(e0,e4) = e0 )
& ( op(e1,e1) != e0
| op(e1,e0) = e1 )
& ( op(e1,e1) != e1
| op(e1,e1) = e1 )
& ( op(e1,e1) != e2
| op(e1,e2) = e1 )
& ( op(e1,e1) != e3
| op(e1,e3) = e1 )
& ( op(e1,e1) != e4
| op(e1,e4) = e1 )
& ( op(e2,e2) != e0
| op(e2,e0) = e2 )
& ( op(e2,e2) != e1
| op(e2,e1) = e2 )
& ( op(e2,e2) != e2
| op(e2,e2) = e2 )
& ( op(e2,e2) != e3
| op(e2,e3) = e2 )
& ( op(e2,e2) != e4
| op(e2,e4) = e2 )
& ( op(e3,e3) != e0
| op(e3,e0) = e3 )
& ( op(e3,e3) != e1
| op(e3,e1) = e3 )
& ( op(e3,e3) != e2
| op(e3,e2) = e3 )
& ( op(e3,e3) != e3
| op(e3,e3) = e3 )
& ( op(e3,e3) != e4
| op(e3,e4) = e3 )
& ( op(e4,e4) != e0
| op(e4,e0) = e4 )
& ( op(e4,e4) != e1
| op(e4,e1) = e4 )
& ( op(e4,e4) != e2
| op(e4,e2) = e4 )
& ( op(e4,e4) != e3
| op(e4,e3) = e4 )
& ( op(e4,e4) != e4
| op(e4,e4) = e4 )
& ( ( op(e0,e0) = e0
& op(e0,e0) = e0
& op(e0,e0) != e0 )
| ( op(e0,e0) = e1
& op(e1,e1) = e0
& op(e0,e1) != e0 )
| ( op(e0,e0) = e2
& op(e2,e2) = e0
& op(e0,e2) != e0 )
| ( op(e0,e0) = e3
& op(e3,e3) = e0
& op(e0,e3) != e0 )
| ( op(e0,e0) = e4
& op(e4,e4) = e0
& op(e0,e4) != e0 )
| ( op(e1,e1) = e0
& op(e0,e0) = e1
& op(e1,e0) != e1 )
| ( op(e1,e1) = e1
& op(e1,e1) = e1
& op(e1,e1) != e1 )
| ( op(e1,e1) = e2
& op(e2,e2) = e1
& op(e1,e2) != e1 )
| ( op(e1,e1) = e3
& op(e3,e3) = e1
& op(e1,e3) != e1 )
| ( op(e1,e1) = e4
& op(e4,e4) = e1
& op(e1,e4) != e1 )
| ( op(e2,e2) = e0
& op(e0,e0) = e2
& op(e2,e0) != e2 )
| ( op(e2,e2) = e1
& op(e1,e1) = e2
& op(e2,e1) != e2 )
| ( op(e2,e2) = e2
& op(e2,e2) = e2
& op(e2,e2) != e2 )
| ( op(e2,e2) = e3
& op(e3,e3) = e2
& op(e2,e3) != e2 )
| ( op(e2,e2) = e4
& op(e4,e4) = e2
& op(e2,e4) != e2 )
| ( op(e3,e3) = e0
& op(e0,e0) = e3
& op(e3,e0) != e3 )
| ( op(e3,e3) = e1
& op(e1,e1) = e3
& op(e3,e1) != e3 )
| ( op(e3,e3) = e2
& op(e2,e2) = e3
& op(e3,e2) != e3 )
| ( op(e3,e3) = e3
& op(e3,e3) = e3
& op(e3,e3) != e3 )
| ( op(e3,e3) = e4
& op(e4,e4) = e3
& op(e3,e4) != e3 )
| ( op(e4,e4) = e0
& op(e0,e0) = e4
& op(e4,e0) != e4 )
| ( op(e4,e4) = e1
& op(e1,e1) = e4
& op(e4,e1) != e4 )
| ( op(e4,e4) = e2
& op(e2,e2) = e4
& op(e4,e2) != e4 )
| ( op(e4,e4) = e3
& op(e3,e3) = e4
& op(e4,e3) != e4 )
| ( op(e4,e4) = e4
& op(e4,e4) = e4
& op(e4,e4) != e4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f8,negated_conjecture,
~ ~ ( ( op(e0,e0) != e0
| op(e0,e0) = e0 )
& ( op(e0,e0) != e1
| op(e0,e1) = e0 )
& ( op(e0,e0) != e2
| op(e0,e2) = e0 )
& ( op(e0,e0) != e3
| op(e0,e3) = e0 )
& ( op(e0,e0) != e4
| op(e0,e4) = e0 )
& ( op(e1,e1) != e0
| op(e1,e0) = e1 )
& ( op(e1,e1) != e1
| op(e1,e1) = e1 )
& ( op(e1,e1) != e2
| op(e1,e2) = e1 )
& ( op(e1,e1) != e3
| op(e1,e3) = e1 )
& ( op(e1,e1) != e4
| op(e1,e4) = e1 )
& ( op(e2,e2) != e0
| op(e2,e0) = e2 )
& ( op(e2,e2) != e1
| op(e2,e1) = e2 )
& ( op(e2,e2) != e2
| op(e2,e2) = e2 )
& ( op(e2,e2) != e3
| op(e2,e3) = e2 )
& ( op(e2,e2) != e4
| op(e2,e4) = e2 )
& ( op(e3,e3) != e0
| op(e3,e0) = e3 )
& ( op(e3,e3) != e1
| op(e3,e1) = e3 )
& ( op(e3,e3) != e2
| op(e3,e2) = e3 )
& ( op(e3,e3) != e3
| op(e3,e3) = e3 )
& ( op(e3,e3) != e4
| op(e3,e4) = e3 )
& ( op(e4,e4) != e0
| op(e4,e0) = e4 )
& ( op(e4,e4) != e1
| op(e4,e1) = e4 )
& ( op(e4,e4) != e2
| op(e4,e2) = e4 )
& ( op(e4,e4) != e3
| op(e4,e3) = e4 )
& ( op(e4,e4) != e4
| op(e4,e4) = e4 )
& ( ( op(e0,e0) = e0
& op(e0,e0) = e0
& op(e0,e0) != e0 )
| ( op(e0,e0) = e1
& op(e1,e1) = e0
& op(e0,e1) != e0 )
| ( op(e0,e0) = e2
& op(e2,e2) = e0
& op(e0,e2) != e0 )
| ( op(e0,e0) = e3
& op(e3,e3) = e0
& op(e0,e3) != e0 )
| ( op(e0,e0) = e4
& op(e4,e4) = e0
& op(e0,e4) != e0 )
| ( op(e1,e1) = e0
& op(e0,e0) = e1
& op(e1,e0) != e1 )
| ( op(e1,e1) = e1
& op(e1,e1) = e1
& op(e1,e1) != e1 )
| ( op(e1,e1) = e2
& op(e2,e2) = e1
& op(e1,e2) != e1 )
| ( op(e1,e1) = e3
& op(e3,e3) = e1
& op(e1,e3) != e1 )
| ( op(e1,e1) = e4
& op(e4,e4) = e1
& op(e1,e4) != e1 )
| ( op(e2,e2) = e0
& op(e0,e0) = e2
& op(e2,e0) != e2 )
| ( op(e2,e2) = e1
& op(e1,e1) = e2
& op(e2,e1) != e2 )
| ( op(e2,e2) = e2
& op(e2,e2) = e2
& op(e2,e2) != e2 )
| ( op(e2,e2) = e3
& op(e3,e3) = e2
& op(e2,e3) != e2 )
| ( op(e2,e2) = e4
& op(e4,e4) = e2
& op(e2,e4) != e2 )
| ( op(e3,e3) = e0
& op(e0,e0) = e3
& op(e3,e0) != e3 )
| ( op(e3,e3) = e1
& op(e1,e1) = e3
& op(e3,e1) != e3 )
| ( op(e3,e3) = e2
& op(e2,e2) = e3
& op(e3,e2) != e3 )
| ( op(e3,e3) = e3
& op(e3,e3) = e3
& op(e3,e3) != e3 )
| ( op(e3,e3) = e4
& op(e4,e4) = e3
& op(e3,e4) != e3 )
| ( op(e4,e4) = e0
& op(e0,e0) = e4
& op(e4,e0) != e4 )
| ( op(e4,e4) = e1
& op(e1,e1) = e4
& op(e4,e1) != e4 )
| ( op(e4,e4) = e2
& op(e2,e2) = e4
& op(e4,e2) != e4 )
| ( op(e4,e4) = e3
& op(e3,e3) = e4
& op(e4,e3) != e4 )
| ( op(e4,e4) = e4
& op(e4,e4) = e4
& op(e4,e4) != e4 ) ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,plain,
( ( op(e0,e0) != e0
| op(e0,e0) = e0 )
& ( op(e0,e0) != e1
| op(e0,e1) = e0 )
& ( op(e0,e0) != e2
| op(e0,e2) = e0 )
& ( op(e0,e0) != e3
| op(e0,e3) = e0 )
& ( op(e0,e0) != e4
| op(e0,e4) = e0 )
& ( op(e1,e1) != e0
| op(e1,e0) = e1 )
& ( op(e1,e1) != e1
| op(e1,e1) = e1 )
& ( op(e1,e1) != e2
| op(e1,e2) = e1 )
& ( op(e1,e1) != e3
| op(e1,e3) = e1 )
& ( op(e1,e1) != e4
| op(e1,e4) = e1 )
& ( op(e2,e2) != e0
| op(e2,e0) = e2 )
& ( op(e2,e2) != e1
| op(e2,e1) = e2 )
& ( op(e2,e2) != e2
| op(e2,e2) = e2 )
& ( op(e2,e2) != e3
| op(e2,e3) = e2 )
& ( op(e2,e2) != e4
| op(e2,e4) = e2 )
& ( op(e3,e3) != e0
| op(e3,e0) = e3 )
& ( op(e3,e3) != e1
| op(e3,e1) = e3 )
& ( op(e3,e3) != e2
| op(e3,e2) = e3 )
& ( op(e3,e3) != e3
| op(e3,e3) = e3 )
& ( op(e3,e3) != e4
| op(e3,e4) = e3 )
& ( op(e4,e4) != e0
| op(e4,e0) = e4 )
& ( op(e4,e4) != e1
| op(e4,e1) = e4 )
& ( op(e4,e4) != e2
| op(e4,e2) = e4 )
& ( op(e4,e4) != e3
| op(e4,e3) = e4 )
& ( op(e4,e4) != e4
| op(e4,e4) = e4 )
& ( ( op(e0,e0) = e0
& op(e0,e0) = e0
& op(e0,e0) != e0 )
| ( op(e0,e0) = e1
& op(e1,e1) = e0
& op(e0,e1) != e0 )
| ( op(e0,e0) = e2
& op(e2,e2) = e0
& op(e0,e2) != e0 )
| ( op(e0,e0) = e3
& op(e3,e3) = e0
& op(e0,e3) != e0 )
| ( op(e0,e0) = e4
& op(e4,e4) = e0
& op(e0,e4) != e0 )
| ( op(e1,e1) = e0
& op(e0,e0) = e1
& op(e1,e0) != e1 )
| ( op(e1,e1) = e1
& op(e1,e1) = e1
& op(e1,e1) != e1 )
| ( op(e1,e1) = e2
& op(e2,e2) = e1
& op(e1,e2) != e1 )
| ( op(e1,e1) = e3
& op(e3,e3) = e1
& op(e1,e3) != e1 )
| ( op(e1,e1) = e4
& op(e4,e4) = e1
& op(e1,e4) != e1 )
| ( op(e2,e2) = e0
& op(e0,e0) = e2
& op(e2,e0) != e2 )
| ( op(e2,e2) = e1
& op(e1,e1) = e2
& op(e2,e1) != e2 )
| ( op(e2,e2) = e2
& op(e2,e2) = e2
& op(e2,e2) != e2 )
| ( op(e2,e2) = e3
& op(e3,e3) = e2
& op(e2,e3) != e2 )
| ( op(e2,e2) = e4
& op(e4,e4) = e2
& op(e2,e4) != e2 )
| ( op(e3,e3) = e0
& op(e0,e0) = e3
& op(e3,e0) != e3 )
| ( op(e3,e3) = e1
& op(e1,e1) = e3
& op(e3,e1) != e3 )
| ( op(e3,e3) = e2
& op(e2,e2) = e3
& op(e3,e2) != e3 )
| ( op(e3,e3) = e3
& op(e3,e3) = e3
& op(e3,e3) != e3 )
| ( op(e3,e3) = e4
& op(e4,e4) = e3
& op(e3,e4) != e3 )
| ( op(e4,e4) = e0
& op(e0,e0) = e4
& op(e4,e0) != e4 )
| ( op(e4,e4) = e1
& op(e1,e1) = e4
& op(e4,e1) != e4 )
| ( op(e4,e4) = e2
& op(e2,e2) = e4
& op(e4,e2) != e4 )
| ( op(e4,e4) = e3
& op(e3,e3) = e4
& op(e4,e3) != e4 )
| ( op(e4,e4) = e4
& op(e4,e4) = e4
& op(e4,e4) != e4 ) ) ),
inference(flattening,[],[f8]) ).
fof(f10,definition,
( ( op(e4,e4) = e4
& op(e4,e4) = e4
& op(e4,e4) != e4 )
| ~ sP0 ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f11,definition,
( ( op(e4,e4) = e3
& op(e3,e3) = e4
& op(e4,e3) != e4 )
| ~ sP1 ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f12,definition,
( ( op(e4,e4) = e2
& op(e2,e2) = e4
& op(e4,e2) != e4 )
| ~ sP2 ),
introduced(definition,[new_symbols(definition,[sP2])],[predicate_definition_introduction]) ).
fof(f13,definition,
( ( op(e4,e4) = e1
& op(e1,e1) = e4
& op(e4,e1) != e4 )
| ~ sP3 ),
introduced(definition,[new_symbols(definition,[sP3])],[predicate_definition_introduction]) ).
fof(f14,definition,
( ( op(e4,e4) = e0
& op(e0,e0) = e4
& op(e4,e0) != e4 )
| ~ sP4 ),
introduced(definition,[new_symbols(definition,[sP4])],[predicate_definition_introduction]) ).
fof(f15,definition,
( ( op(e3,e3) = e4
& op(e4,e4) = e3
& op(e3,e4) != e3 )
| ~ sP5 ),
introduced(definition,[new_symbols(definition,[sP5])],[predicate_definition_introduction]) ).
fof(f16,definition,
( ( op(e3,e3) = e3
& op(e3,e3) = e3
& op(e3,e3) != e3 )
| ~ sP6 ),
introduced(definition,[new_symbols(definition,[sP6])],[predicate_definition_introduction]) ).
fof(f17,definition,
( ( op(e3,e3) = e2
& op(e2,e2) = e3
& op(e3,e2) != e3 )
| ~ sP7 ),
introduced(definition,[new_symbols(definition,[sP7])],[predicate_definition_introduction]) ).
fof(f18,definition,
( ( op(e3,e3) = e1
& op(e1,e1) = e3
& op(e3,e1) != e3 )
| ~ sP8 ),
introduced(definition,[new_symbols(definition,[sP8])],[predicate_definition_introduction]) ).
fof(f19,definition,
( ( op(e3,e3) = e0
& op(e0,e0) = e3
& op(e3,e0) != e3 )
| ~ sP9 ),
introduced(definition,[new_symbols(definition,[sP9])],[predicate_definition_introduction]) ).
fof(f20,definition,
( ( op(e2,e2) = e4
& op(e4,e4) = e2
& op(e2,e4) != e2 )
| ~ sP10 ),
introduced(definition,[new_symbols(definition,[sP10])],[predicate_definition_introduction]) ).
fof(f21,definition,
( ( op(e2,e2) = e3
& op(e3,e3) = e2
& op(e2,e3) != e2 )
| ~ sP11 ),
introduced(definition,[new_symbols(definition,[sP11])],[predicate_definition_introduction]) ).
fof(f22,definition,
( ( op(e2,e2) = e2
& op(e2,e2) = e2
& op(e2,e2) != e2 )
| ~ sP12 ),
introduced(definition,[new_symbols(definition,[sP12])],[predicate_definition_introduction]) ).
fof(f23,definition,
( ( op(e2,e2) = e1
& op(e1,e1) = e2
& op(e2,e1) != e2 )
| ~ sP13 ),
introduced(definition,[new_symbols(definition,[sP13])],[predicate_definition_introduction]) ).
fof(f24,definition,
( ( op(e2,e2) = e0
& op(e0,e0) = e2
& op(e2,e0) != e2 )
| ~ sP14 ),
introduced(definition,[new_symbols(definition,[sP14])],[predicate_definition_introduction]) ).
fof(f25,definition,
( ( op(e1,e1) = e4
& op(e4,e4) = e1
& op(e1,e4) != e1 )
| ~ sP15 ),
introduced(definition,[new_symbols(definition,[sP15])],[predicate_definition_introduction]) ).
fof(f26,definition,
( ( op(e1,e1) = e3
& op(e3,e3) = e1
& op(e1,e3) != e1 )
| ~ sP16 ),
introduced(definition,[new_symbols(definition,[sP16])],[predicate_definition_introduction]) ).
fof(f27,definition,
( ( op(e1,e1) = e2
& op(e2,e2) = e1
& op(e1,e2) != e1 )
| ~ sP17 ),
introduced(definition,[new_symbols(definition,[sP17])],[predicate_definition_introduction]) ).
fof(f28,definition,
( ( op(e1,e1) = e1
& op(e1,e1) = e1
& op(e1,e1) != e1 )
| ~ sP18 ),
introduced(definition,[new_symbols(definition,[sP18])],[predicate_definition_introduction]) ).
fof(f29,definition,
( ( op(e1,e1) = e0
& op(e0,e0) = e1
& op(e1,e0) != e1 )
| ~ sP19 ),
introduced(definition,[new_symbols(definition,[sP19])],[predicate_definition_introduction]) ).
fof(f30,definition,
( ( op(e0,e0) = e4
& op(e4,e4) = e0
& op(e0,e4) != e0 )
| ~ sP20 ),
introduced(definition,[new_symbols(definition,[sP20])],[predicate_definition_introduction]) ).
fof(f31,definition,
( ( op(e0,e0) = e3
& op(e3,e3) = e0
& op(e0,e3) != e0 )
| ~ sP21 ),
introduced(definition,[new_symbols(definition,[sP21])],[predicate_definition_introduction]) ).
fof(f32,definition,
( ( op(e0,e0) = e2
& op(e2,e2) = e0
& op(e0,e2) != e0 )
| ~ sP22 ),
introduced(definition,[new_symbols(definition,[sP22])],[predicate_definition_introduction]) ).
fof(f33,definition,
( ( op(e0,e0) = e1
& op(e1,e1) = e0
& op(e0,e1) != e0 )
| ~ sP23 ),
introduced(definition,[new_symbols(definition,[sP23])],[predicate_definition_introduction]) ).
fof(f34,plain,
( ( op(e0,e0) != e0
| op(e0,e0) = e0 )
& ( op(e0,e0) != e1
| op(e0,e1) = e0 )
& ( op(e0,e0) != e2
| op(e0,e2) = e0 )
& ( op(e0,e0) != e3
| op(e0,e3) = e0 )
& ( op(e0,e0) != e4
| op(e0,e4) = e0 )
& ( op(e1,e1) != e0
| op(e1,e0) = e1 )
& ( op(e1,e1) != e1
| op(e1,e1) = e1 )
& ( op(e1,e1) != e2
| op(e1,e2) = e1 )
& ( op(e1,e1) != e3
| op(e1,e3) = e1 )
& ( op(e1,e1) != e4
| op(e1,e4) = e1 )
& ( op(e2,e2) != e0
| op(e2,e0) = e2 )
& ( op(e2,e2) != e1
| op(e2,e1) = e2 )
& ( op(e2,e2) != e2
| op(e2,e2) = e2 )
& ( op(e2,e2) != e3
| op(e2,e3) = e2 )
& ( op(e2,e2) != e4
| op(e2,e4) = e2 )
& ( op(e3,e3) != e0
| op(e3,e0) = e3 )
& ( op(e3,e3) != e1
| op(e3,e1) = e3 )
& ( op(e3,e3) != e2
| op(e3,e2) = e3 )
& ( op(e3,e3) != e3
| op(e3,e3) = e3 )
& ( op(e3,e3) != e4
| op(e3,e4) = e3 )
& ( op(e4,e4) != e0
| op(e4,e0) = e4 )
& ( op(e4,e4) != e1
| op(e4,e1) = e4 )
& ( op(e4,e4) != e2
| op(e4,e2) = e4 )
& ( op(e4,e4) != e3
| op(e4,e3) = e4 )
& ( op(e4,e4) != e4
| op(e4,e4) = e4 )
& ( ( op(e0,e0) = e0
& op(e0,e0) = e0
& op(e0,e0) != e0 )
| sP23
| sP22
| sP21
| sP20
| sP19
| sP18
| sP17
| sP16
| sP15
| sP14
| sP13
| sP12
| sP11
| sP10
| sP9
| sP8
| sP7
| sP6
| sP5
| sP4
| sP3
| sP2
| sP1
| sP0 ) ),
inference(definition_folding,[],[f9,f33,f32,f31,f30,f29,f28,f27,f26,f25,f24,f23,f22,f21,f20,f19,f18,f17,f16,f15,f14,f13,f12,f11,f10]) ).
fof(f35,plain,
( ( op(e0,e0) = e1
& op(e1,e1) = e0
& op(e0,e1) != e0 )
| ~ sP23 ),
inference(nnf_transformation,[],[f33]) ).
fof(f36,plain,
( ( op(e0,e0) = e2
& op(e2,e2) = e0
& op(e0,e2) != e0 )
| ~ sP22 ),
inference(nnf_transformation,[],[f32]) ).
fof(f37,plain,
( ( op(e0,e0) = e3
& op(e3,e3) = e0
& op(e0,e3) != e0 )
| ~ sP21 ),
inference(nnf_transformation,[],[f31]) ).
fof(f38,plain,
( ( op(e0,e0) = e4
& op(e4,e4) = e0
& op(e0,e4) != e0 )
| ~ sP20 ),
inference(nnf_transformation,[],[f30]) ).
fof(f39,plain,
( ( op(e1,e1) = e0
& op(e0,e0) = e1
& op(e1,e0) != e1 )
| ~ sP19 ),
inference(nnf_transformation,[],[f29]) ).
fof(f40,plain,
( ( op(e1,e1) = e1
& op(e1,e1) = e1
& op(e1,e1) != e1 )
| ~ sP18 ),
inference(nnf_transformation,[],[f28]) ).
fof(f41,plain,
( ( op(e1,e1) = e2
& op(e2,e2) = e1
& op(e1,e2) != e1 )
| ~ sP17 ),
inference(nnf_transformation,[],[f27]) ).
fof(f42,plain,
( ( op(e1,e1) = e3
& op(e3,e3) = e1
& op(e1,e3) != e1 )
| ~ sP16 ),
inference(nnf_transformation,[],[f26]) ).
fof(f43,plain,
( ( op(e1,e1) = e4
& op(e4,e4) = e1
& op(e1,e4) != e1 )
| ~ sP15 ),
inference(nnf_transformation,[],[f25]) ).
fof(f44,plain,
( ( op(e2,e2) = e0
& op(e0,e0) = e2
& op(e2,e0) != e2 )
| ~ sP14 ),
inference(nnf_transformation,[],[f24]) ).
fof(f45,plain,
( ( op(e2,e2) = e1
& op(e1,e1) = e2
& op(e2,e1) != e2 )
| ~ sP13 ),
inference(nnf_transformation,[],[f23]) ).
fof(f46,plain,
( ( op(e2,e2) = e2
& op(e2,e2) = e2
& op(e2,e2) != e2 )
| ~ sP12 ),
inference(nnf_transformation,[],[f22]) ).
fof(f47,plain,
( ( op(e2,e2) = e3
& op(e3,e3) = e2
& op(e2,e3) != e2 )
| ~ sP11 ),
inference(nnf_transformation,[],[f21]) ).
fof(f48,plain,
( ( op(e2,e2) = e4
& op(e4,e4) = e2
& op(e2,e4) != e2 )
| ~ sP10 ),
inference(nnf_transformation,[],[f20]) ).
fof(f49,plain,
( ( op(e3,e3) = e0
& op(e0,e0) = e3
& op(e3,e0) != e3 )
| ~ sP9 ),
inference(nnf_transformation,[],[f19]) ).
fof(f50,plain,
( ( op(e3,e3) = e1
& op(e1,e1) = e3
& op(e3,e1) != e3 )
| ~ sP8 ),
inference(nnf_transformation,[],[f18]) ).
fof(f51,plain,
( ( op(e3,e3) = e2
& op(e2,e2) = e3
& op(e3,e2) != e3 )
| ~ sP7 ),
inference(nnf_transformation,[],[f17]) ).
fof(f52,plain,
( ( op(e3,e3) = e3
& op(e3,e3) = e3
& op(e3,e3) != e3 )
| ~ sP6 ),
inference(nnf_transformation,[],[f16]) ).
fof(f53,plain,
( ( op(e3,e3) = e4
& op(e4,e4) = e3
& op(e3,e4) != e3 )
| ~ sP5 ),
inference(nnf_transformation,[],[f15]) ).
fof(f54,plain,
( ( op(e4,e4) = e0
& op(e0,e0) = e4
& op(e4,e0) != e4 )
| ~ sP4 ),
inference(nnf_transformation,[],[f14]) ).
fof(f55,plain,
( ( op(e4,e4) = e1
& op(e1,e1) = e4
& op(e4,e1) != e4 )
| ~ sP3 ),
inference(nnf_transformation,[],[f13]) ).
fof(f56,plain,
( ( op(e4,e4) = e2
& op(e2,e2) = e4
& op(e4,e2) != e4 )
| ~ sP2 ),
inference(nnf_transformation,[],[f12]) ).
fof(f57,plain,
( ( op(e4,e4) = e3
& op(e3,e3) = e4
& op(e4,e3) != e4 )
| ~ sP1 ),
inference(nnf_transformation,[],[f11]) ).
fof(f58,plain,
( ( op(e4,e4) = e4
& op(e4,e4) = e4
& op(e4,e4) != e4 )
| ~ sP0 ),
inference(nnf_transformation,[],[f10]) ).
fof(f258,plain,
( e0 != op(e0,e1)
| ~ sP23 ),
inference(cnf_transformation,[],[f35]) ).
fof(f260,plain,
( op(e0,e0) = e1
| ~ sP23 ),
inference(cnf_transformation,[],[f35]) ).
fof(f261,plain,
( e0 != op(e0,e2)
| ~ sP22 ),
inference(cnf_transformation,[],[f36]) ).
fof(f263,plain,
( op(e0,e0) = e2
| ~ sP22 ),
inference(cnf_transformation,[],[f36]) ).
fof(f264,plain,
( e0 != op(e0,e3)
| ~ sP21 ),
inference(cnf_transformation,[],[f37]) ).
fof(f266,plain,
( op(e0,e0) = e3
| ~ sP21 ),
inference(cnf_transformation,[],[f37]) ).
fof(f267,plain,
( e0 != op(e0,e4)
| ~ sP20 ),
inference(cnf_transformation,[],[f38]) ).
fof(f269,plain,
( op(e0,e0) = e4
| ~ sP20 ),
inference(cnf_transformation,[],[f38]) ).
fof(f270,plain,
( e1 != op(e1,e0)
| ~ sP19 ),
inference(cnf_transformation,[],[f39]) ).
fof(f272,plain,
( e0 = op(e1,e1)
| ~ sP19 ),
inference(cnf_transformation,[],[f39]) ).
fof(f273,plain,
( e1 != op(e1,e1)
| ~ sP18 ),
inference(cnf_transformation,[],[f40]) ).
fof(f275,plain,
( e1 = op(e1,e1)
| ~ sP18 ),
inference(cnf_transformation,[],[f40]) ).
fof(f276,plain,
( e1 != op(e1,e2)
| ~ sP17 ),
inference(cnf_transformation,[],[f41]) ).
fof(f278,plain,
( e2 = op(e1,e1)
| ~ sP17 ),
inference(cnf_transformation,[],[f41]) ).
fof(f279,plain,
( e1 != op(e1,e3)
| ~ sP16 ),
inference(cnf_transformation,[],[f42]) ).
fof(f281,plain,
( e3 = op(e1,e1)
| ~ sP16 ),
inference(cnf_transformation,[],[f42]) ).
fof(f282,plain,
( e1 != op(e1,e4)
| ~ sP15 ),
inference(cnf_transformation,[],[f43]) ).
fof(f284,plain,
( e4 = op(e1,e1)
| ~ sP15 ),
inference(cnf_transformation,[],[f43]) ).
fof(f285,plain,
( e2 != op(e2,e0)
| ~ sP14 ),
inference(cnf_transformation,[],[f44]) ).
fof(f287,plain,
( e0 = op(e2,e2)
| ~ sP14 ),
inference(cnf_transformation,[],[f44]) ).
fof(f288,plain,
( e2 != op(e2,e1)
| ~ sP13 ),
inference(cnf_transformation,[],[f45]) ).
fof(f290,plain,
( e1 = op(e2,e2)
| ~ sP13 ),
inference(cnf_transformation,[],[f45]) ).
fof(f291,plain,
( e2 != op(e2,e2)
| ~ sP12 ),
inference(cnf_transformation,[],[f46]) ).
fof(f293,plain,
( e2 = op(e2,e2)
| ~ sP12 ),
inference(cnf_transformation,[],[f46]) ).
fof(f294,plain,
( e2 != op(e2,e3)
| ~ sP11 ),
inference(cnf_transformation,[],[f47]) ).
fof(f296,plain,
( e3 = op(e2,e2)
| ~ sP11 ),
inference(cnf_transformation,[],[f47]) ).
fof(f297,plain,
( e2 != op(e2,e4)
| ~ sP10 ),
inference(cnf_transformation,[],[f48]) ).
fof(f299,plain,
( e4 = op(e2,e2)
| ~ sP10 ),
inference(cnf_transformation,[],[f48]) ).
fof(f300,plain,
( e3 != op(e3,e0)
| ~ sP9 ),
inference(cnf_transformation,[],[f49]) ).
fof(f302,plain,
( e0 = op(e3,e3)
| ~ sP9 ),
inference(cnf_transformation,[],[f49]) ).
fof(f303,plain,
( e3 != op(e3,e1)
| ~ sP8 ),
inference(cnf_transformation,[],[f50]) ).
fof(f305,plain,
( e1 = op(e3,e3)
| ~ sP8 ),
inference(cnf_transformation,[],[f50]) ).
fof(f306,plain,
( e3 != op(e3,e2)
| ~ sP7 ),
inference(cnf_transformation,[],[f51]) ).
fof(f308,plain,
( e2 = op(e3,e3)
| ~ sP7 ),
inference(cnf_transformation,[],[f51]) ).
fof(f309,plain,
( e3 != op(e3,e3)
| ~ sP6 ),
inference(cnf_transformation,[],[f52]) ).
fof(f311,plain,
( e3 = op(e3,e3)
| ~ sP6 ),
inference(cnf_transformation,[],[f52]) ).
fof(f312,plain,
( e3 != op(e3,e4)
| ~ sP5 ),
inference(cnf_transformation,[],[f53]) ).
fof(f314,plain,
( e4 = op(e3,e3)
| ~ sP5 ),
inference(cnf_transformation,[],[f53]) ).
fof(f315,plain,
( e4 != op(e4,e0)
| ~ sP4 ),
inference(cnf_transformation,[],[f54]) ).
fof(f317,plain,
( e0 = op(e4,e4)
| ~ sP4 ),
inference(cnf_transformation,[],[f54]) ).
fof(f318,plain,
( e4 != op(e4,e1)
| ~ sP3 ),
inference(cnf_transformation,[],[f55]) ).
fof(f320,plain,
( e1 = op(e4,e4)
| ~ sP3 ),
inference(cnf_transformation,[],[f55]) ).
fof(f321,plain,
( e4 != op(e4,e2)
| ~ sP2 ),
inference(cnf_transformation,[],[f56]) ).
fof(f323,plain,
( e2 = op(e4,e4)
| ~ sP2 ),
inference(cnf_transformation,[],[f56]) ).
fof(f324,plain,
( e4 != op(e4,e3)
| ~ sP1 ),
inference(cnf_transformation,[],[f57]) ).
fof(f326,plain,
( e3 = op(e4,e4)
| ~ sP1 ),
inference(cnf_transformation,[],[f57]) ).
fof(f327,plain,
( e4 != op(e4,e4)
| ~ sP0 ),
inference(cnf_transformation,[],[f58]) ).
fof(f329,plain,
( e4 = op(e4,e4)
| ~ sP0 ),
inference(cnf_transformation,[],[f58]) ).
fof(f330,plain,
( e0 != op(e0,e0)
| sP23
| sP22
| sP21
| sP20
| sP19
| sP18
| sP17
| sP16
| sP15
| sP14
| sP13
| sP12
| sP11
| sP10
| sP9
| sP8
| sP7
| sP6
| sP5
| sP4
| sP3
| sP2
| sP1
| sP0 ),
inference(cnf_transformation,[],[f34]) ).
fof(f332,plain,
( e0 = op(e0,e0)
| sP23
| sP22
| sP21
| sP20
| sP19
| sP18
| sP17
| sP16
| sP15
| sP14
| sP13
| sP12
| sP11
| sP10
| sP9
| sP8
| sP7
| sP6
| sP5
| sP4
| sP3
| sP2
| sP1
| sP0 ),
inference(cnf_transformation,[],[f34]) ).
fof(f334,plain,
( e3 != op(e4,e4)
| e4 = op(e4,e3) ),
inference(cnf_transformation,[],[f34]) ).
fof(f335,plain,
( e2 != op(e4,e4)
| e4 = op(e4,e2) ),
inference(cnf_transformation,[],[f34]) ).
fof(f336,plain,
( e1 != op(e4,e4)
| e4 = op(e4,e1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f337,plain,
( e0 != op(e4,e4)
| e4 = op(e4,e0) ),
inference(cnf_transformation,[],[f34]) ).
fof(f338,plain,
( e4 != op(e3,e3)
| e3 = op(e3,e4) ),
inference(cnf_transformation,[],[f34]) ).
fof(f340,plain,
( e2 != op(e3,e3)
| e3 = op(e3,e2) ),
inference(cnf_transformation,[],[f34]) ).
fof(f341,plain,
( e1 != op(e3,e3)
| e3 = op(e3,e1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f342,plain,
( e0 != op(e3,e3)
| e3 = op(e3,e0) ),
inference(cnf_transformation,[],[f34]) ).
fof(f343,plain,
( e4 != op(e2,e2)
| e2 = op(e2,e4) ),
inference(cnf_transformation,[],[f34]) ).
fof(f344,plain,
( e3 != op(e2,e2)
| e2 = op(e2,e3) ),
inference(cnf_transformation,[],[f34]) ).
fof(f346,plain,
( e1 != op(e2,e2)
| e2 = op(e2,e1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f347,plain,
( e0 != op(e2,e2)
| e2 = op(e2,e0) ),
inference(cnf_transformation,[],[f34]) ).
fof(f348,plain,
( e4 != op(e1,e1)
| e1 = op(e1,e4) ),
inference(cnf_transformation,[],[f34]) ).
fof(f349,plain,
( e3 != op(e1,e1)
| e1 = op(e1,e3) ),
inference(cnf_transformation,[],[f34]) ).
fof(f350,plain,
( e2 != op(e1,e1)
| e1 = op(e1,e2) ),
inference(cnf_transformation,[],[f34]) ).
fof(f352,plain,
( e0 != op(e1,e1)
| e1 = op(e1,e0) ),
inference(cnf_transformation,[],[f34]) ).
fof(f353,plain,
( op(e0,e0) != e4
| e0 = op(e0,e4) ),
inference(cnf_transformation,[],[f34]) ).
fof(f354,plain,
( op(e0,e0) != e3
| e0 = op(e0,e3) ),
inference(cnf_transformation,[],[f34]) ).
fof(f355,plain,
( op(e0,e0) != e2
| e0 = op(e0,e2) ),
inference(cnf_transformation,[],[f34]) ).
fof(f356,plain,
( op(e0,e0) != e1
| e0 = op(e0,e1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f358,definition,
! [X0,X1] :
( sQ24_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ24_eqProxy])],[equality_proxy_definition]) ).
fof(f558,plain,
( sQ24_eqProxy(op(e0,e0),e1)
| ~ sP23 ),
inference(equality_proxy_replacement,[],[f260,f358]) ).
fof(f560,plain,
( ~ sQ24_eqProxy(e0,op(e0,e1))
| ~ sP23 ),
inference(equality_proxy_replacement,[],[f258,f358]) ).
fof(f561,plain,
( sQ24_eqProxy(op(e0,e0),e2)
| ~ sP22 ),
inference(equality_proxy_replacement,[],[f263,f358]) ).
fof(f563,plain,
( ~ sQ24_eqProxy(e0,op(e0,e2))
| ~ sP22 ),
inference(equality_proxy_replacement,[],[f261,f358]) ).
fof(f564,plain,
( sQ24_eqProxy(op(e0,e0),e3)
| ~ sP21 ),
inference(equality_proxy_replacement,[],[f266,f358]) ).
fof(f566,plain,
( ~ sQ24_eqProxy(e0,op(e0,e3))
| ~ sP21 ),
inference(equality_proxy_replacement,[],[f264,f358]) ).
fof(f567,plain,
( sQ24_eqProxy(op(e0,e0),e4)
| ~ sP20 ),
inference(equality_proxy_replacement,[],[f269,f358]) ).
fof(f569,plain,
( ~ sQ24_eqProxy(e0,op(e0,e4))
| ~ sP20 ),
inference(equality_proxy_replacement,[],[f267,f358]) ).
fof(f570,plain,
( sQ24_eqProxy(e0,op(e1,e1))
| ~ sP19 ),
inference(equality_proxy_replacement,[],[f272,f358]) ).
fof(f572,plain,
( ~ sQ24_eqProxy(e1,op(e1,e0))
| ~ sP19 ),
inference(equality_proxy_replacement,[],[f270,f358]) ).
fof(f573,plain,
( sQ24_eqProxy(e1,op(e1,e1))
| ~ sP18 ),
inference(equality_proxy_replacement,[],[f275,f358]) ).
fof(f575,plain,
( ~ sQ24_eqProxy(e1,op(e1,e1))
| ~ sP18 ),
inference(equality_proxy_replacement,[],[f273,f358]) ).
fof(f576,plain,
( sQ24_eqProxy(e2,op(e1,e1))
| ~ sP17 ),
inference(equality_proxy_replacement,[],[f278,f358]) ).
fof(f578,plain,
( ~ sQ24_eqProxy(e1,op(e1,e2))
| ~ sP17 ),
inference(equality_proxy_replacement,[],[f276,f358]) ).
fof(f579,plain,
( sQ24_eqProxy(e3,op(e1,e1))
| ~ sP16 ),
inference(equality_proxy_replacement,[],[f281,f358]) ).
fof(f581,plain,
( ~ sQ24_eqProxy(e1,op(e1,e3))
| ~ sP16 ),
inference(equality_proxy_replacement,[],[f279,f358]) ).
fof(f582,plain,
( sQ24_eqProxy(e4,op(e1,e1))
| ~ sP15 ),
inference(equality_proxy_replacement,[],[f284,f358]) ).
fof(f584,plain,
( ~ sQ24_eqProxy(e1,op(e1,e4))
| ~ sP15 ),
inference(equality_proxy_replacement,[],[f282,f358]) ).
fof(f585,plain,
( sQ24_eqProxy(e0,op(e2,e2))
| ~ sP14 ),
inference(equality_proxy_replacement,[],[f287,f358]) ).
fof(f587,plain,
( ~ sQ24_eqProxy(e2,op(e2,e0))
| ~ sP14 ),
inference(equality_proxy_replacement,[],[f285,f358]) ).
fof(f588,plain,
( sQ24_eqProxy(e1,op(e2,e2))
| ~ sP13 ),
inference(equality_proxy_replacement,[],[f290,f358]) ).
fof(f590,plain,
( ~ sQ24_eqProxy(e2,op(e2,e1))
| ~ sP13 ),
inference(equality_proxy_replacement,[],[f288,f358]) ).
fof(f591,plain,
( sQ24_eqProxy(e2,op(e2,e2))
| ~ sP12 ),
inference(equality_proxy_replacement,[],[f293,f358]) ).
fof(f593,plain,
( ~ sQ24_eqProxy(e2,op(e2,e2))
| ~ sP12 ),
inference(equality_proxy_replacement,[],[f291,f358]) ).
fof(f594,plain,
( sQ24_eqProxy(e3,op(e2,e2))
| ~ sP11 ),
inference(equality_proxy_replacement,[],[f296,f358]) ).
fof(f596,plain,
( ~ sQ24_eqProxy(e2,op(e2,e3))
| ~ sP11 ),
inference(equality_proxy_replacement,[],[f294,f358]) ).
fof(f597,plain,
( sQ24_eqProxy(e4,op(e2,e2))
| ~ sP10 ),
inference(equality_proxy_replacement,[],[f299,f358]) ).
fof(f599,plain,
( ~ sQ24_eqProxy(e2,op(e2,e4))
| ~ sP10 ),
inference(equality_proxy_replacement,[],[f297,f358]) ).
fof(f600,plain,
( sQ24_eqProxy(e0,op(e3,e3))
| ~ sP9 ),
inference(equality_proxy_replacement,[],[f302,f358]) ).
fof(f602,plain,
( ~ sQ24_eqProxy(e3,op(e3,e0))
| ~ sP9 ),
inference(equality_proxy_replacement,[],[f300,f358]) ).
fof(f603,plain,
( sQ24_eqProxy(e1,op(e3,e3))
| ~ sP8 ),
inference(equality_proxy_replacement,[],[f305,f358]) ).
fof(f605,plain,
( ~ sQ24_eqProxy(e3,op(e3,e1))
| ~ sP8 ),
inference(equality_proxy_replacement,[],[f303,f358]) ).
fof(f606,plain,
( sQ24_eqProxy(e2,op(e3,e3))
| ~ sP7 ),
inference(equality_proxy_replacement,[],[f308,f358]) ).
fof(f608,plain,
( ~ sQ24_eqProxy(e3,op(e3,e2))
| ~ sP7 ),
inference(equality_proxy_replacement,[],[f306,f358]) ).
fof(f609,plain,
( sQ24_eqProxy(e3,op(e3,e3))
| ~ sP6 ),
inference(equality_proxy_replacement,[],[f311,f358]) ).
fof(f611,plain,
( ~ sQ24_eqProxy(e3,op(e3,e3))
| ~ sP6 ),
inference(equality_proxy_replacement,[],[f309,f358]) ).
fof(f612,plain,
( sQ24_eqProxy(e4,op(e3,e3))
| ~ sP5 ),
inference(equality_proxy_replacement,[],[f314,f358]) ).
fof(f614,plain,
( ~ sQ24_eqProxy(e3,op(e3,e4))
| ~ sP5 ),
inference(equality_proxy_replacement,[],[f312,f358]) ).
fof(f615,plain,
( sQ24_eqProxy(e0,op(e4,e4))
| ~ sP4 ),
inference(equality_proxy_replacement,[],[f317,f358]) ).
fof(f617,plain,
( ~ sQ24_eqProxy(e4,op(e4,e0))
| ~ sP4 ),
inference(equality_proxy_replacement,[],[f315,f358]) ).
fof(f618,plain,
( sQ24_eqProxy(e1,op(e4,e4))
| ~ sP3 ),
inference(equality_proxy_replacement,[],[f320,f358]) ).
fof(f620,plain,
( ~ sQ24_eqProxy(e4,op(e4,e1))
| ~ sP3 ),
inference(equality_proxy_replacement,[],[f318,f358]) ).
fof(f621,plain,
( sQ24_eqProxy(e2,op(e4,e4))
| ~ sP2 ),
inference(equality_proxy_replacement,[],[f323,f358]) ).
fof(f623,plain,
( ~ sQ24_eqProxy(e4,op(e4,e2))
| ~ sP2 ),
inference(equality_proxy_replacement,[],[f321,f358]) ).
fof(f624,plain,
( sQ24_eqProxy(e3,op(e4,e4))
| ~ sP1 ),
inference(equality_proxy_replacement,[],[f326,f358]) ).
fof(f626,plain,
( ~ sQ24_eqProxy(e4,op(e4,e3))
| ~ sP1 ),
inference(equality_proxy_replacement,[],[f324,f358]) ).
fof(f627,plain,
( sQ24_eqProxy(e4,op(e4,e4))
| ~ sP0 ),
inference(equality_proxy_replacement,[],[f329,f358]) ).
fof(f629,plain,
( ~ sQ24_eqProxy(e4,op(e4,e4))
| ~ sP0 ),
inference(equality_proxy_replacement,[],[f327,f358]) ).
fof(f631,plain,
( ~ sQ24_eqProxy(op(e0,e0),e1)
| sQ24_eqProxy(e0,op(e0,e1)) ),
inference(equality_proxy_replacement,[],[f356,f358,f358]) ).
fof(f632,plain,
( ~ sQ24_eqProxy(op(e0,e0),e2)
| sQ24_eqProxy(e0,op(e0,e2)) ),
inference(equality_proxy_replacement,[],[f355,f358,f358]) ).
fof(f633,plain,
( ~ sQ24_eqProxy(op(e0,e0),e3)
| sQ24_eqProxy(e0,op(e0,e3)) ),
inference(equality_proxy_replacement,[],[f354,f358,f358]) ).
fof(f634,plain,
( ~ sQ24_eqProxy(op(e0,e0),e4)
| sQ24_eqProxy(e0,op(e0,e4)) ),
inference(equality_proxy_replacement,[],[f353,f358,f358]) ).
fof(f635,plain,
( ~ sQ24_eqProxy(e0,op(e1,e1))
| sQ24_eqProxy(e1,op(e1,e0)) ),
inference(equality_proxy_replacement,[],[f352,f358,f358]) ).
fof(f637,plain,
( ~ sQ24_eqProxy(e2,op(e1,e1))
| sQ24_eqProxy(e1,op(e1,e2)) ),
inference(equality_proxy_replacement,[],[f350,f358,f358]) ).
fof(f638,plain,
( ~ sQ24_eqProxy(e3,op(e1,e1))
| sQ24_eqProxy(e1,op(e1,e3)) ),
inference(equality_proxy_replacement,[],[f349,f358,f358]) ).
fof(f639,plain,
( ~ sQ24_eqProxy(e4,op(e1,e1))
| sQ24_eqProxy(e1,op(e1,e4)) ),
inference(equality_proxy_replacement,[],[f348,f358,f358]) ).
fof(f640,plain,
( ~ sQ24_eqProxy(e0,op(e2,e2))
| sQ24_eqProxy(e2,op(e2,e0)) ),
inference(equality_proxy_replacement,[],[f347,f358,f358]) ).
fof(f641,plain,
( ~ sQ24_eqProxy(e1,op(e2,e2))
| sQ24_eqProxy(e2,op(e2,e1)) ),
inference(equality_proxy_replacement,[],[f346,f358,f358]) ).
fof(f643,plain,
( ~ sQ24_eqProxy(e3,op(e2,e2))
| sQ24_eqProxy(e2,op(e2,e3)) ),
inference(equality_proxy_replacement,[],[f344,f358,f358]) ).
fof(f644,plain,
( ~ sQ24_eqProxy(e4,op(e2,e2))
| sQ24_eqProxy(e2,op(e2,e4)) ),
inference(equality_proxy_replacement,[],[f343,f358,f358]) ).
fof(f645,plain,
( ~ sQ24_eqProxy(e0,op(e3,e3))
| sQ24_eqProxy(e3,op(e3,e0)) ),
inference(equality_proxy_replacement,[],[f342,f358,f358]) ).
fof(f646,plain,
( ~ sQ24_eqProxy(e1,op(e3,e3))
| sQ24_eqProxy(e3,op(e3,e1)) ),
inference(equality_proxy_replacement,[],[f341,f358,f358]) ).
fof(f647,plain,
( ~ sQ24_eqProxy(e2,op(e3,e3))
| sQ24_eqProxy(e3,op(e3,e2)) ),
inference(equality_proxy_replacement,[],[f340,f358,f358]) ).
fof(f649,plain,
( ~ sQ24_eqProxy(e4,op(e3,e3))
| sQ24_eqProxy(e3,op(e3,e4)) ),
inference(equality_proxy_replacement,[],[f338,f358,f358]) ).
fof(f650,plain,
( ~ sQ24_eqProxy(e0,op(e4,e4))
| sQ24_eqProxy(e4,op(e4,e0)) ),
inference(equality_proxy_replacement,[],[f337,f358,f358]) ).
fof(f651,plain,
( ~ sQ24_eqProxy(e1,op(e4,e4))
| sQ24_eqProxy(e4,op(e4,e1)) ),
inference(equality_proxy_replacement,[],[f336,f358,f358]) ).
fof(f652,plain,
( ~ sQ24_eqProxy(e2,op(e4,e4))
| sQ24_eqProxy(e4,op(e4,e2)) ),
inference(equality_proxy_replacement,[],[f335,f358,f358]) ).
fof(f653,plain,
( ~ sQ24_eqProxy(e3,op(e4,e4))
| sQ24_eqProxy(e4,op(e4,e3)) ),
inference(equality_proxy_replacement,[],[f334,f358,f358]) ).
fof(f655,plain,
( sQ24_eqProxy(e0,op(e0,e0))
| sP23
| sP22
| sP21
| sP20
| sP19
| sP18
| sP17
| sP16
| sP15
| sP14
| sP13
| sP12
| sP11
| sP10
| sP9
| sP8
| sP7
| sP6
| sP5
| sP4
| sP3
| sP2
| sP1
| sP0 ),
inference(equality_proxy_replacement,[],[f332,f358]) ).
fof(f657,plain,
( ~ sQ24_eqProxy(e0,op(e0,e0))
| sP23
| sP22
| sP21
| sP20
| sP19
| sP18
| sP17
| sP16
| sP15
| sP14
| sP13
| sP12
| sP11
| sP10
| sP9
| sP8
| sP7
| sP6
| sP5
| sP4
| sP3
| sP2
| sP1
| sP0 ),
inference(equality_proxy_replacement,[],[f330,f358]) ).
fof(f661,definition,
( spl25_1
<=> sP0 ),
introduced(definition,[new_symbols(definition,[spl25_1])],[avatar_definition]) ).
fof(f664,definition,
( spl25_2
<=> sP1 ),
introduced(definition,[new_symbols(definition,[spl25_2])],[avatar_definition]) ).
fof(f667,definition,
( spl25_3
<=> sP2 ),
introduced(definition,[new_symbols(definition,[spl25_3])],[avatar_definition]) ).
fof(f670,definition,
( spl25_4
<=> sP3 ),
introduced(definition,[new_symbols(definition,[spl25_4])],[avatar_definition]) ).
fof(f673,definition,
( spl25_5
<=> sP4 ),
introduced(definition,[new_symbols(definition,[spl25_5])],[avatar_definition]) ).
fof(f676,definition,
( spl25_6
<=> sP5 ),
introduced(definition,[new_symbols(definition,[spl25_6])],[avatar_definition]) ).
fof(f679,definition,
( spl25_7
<=> sP6 ),
introduced(definition,[new_symbols(definition,[spl25_7])],[avatar_definition]) ).
fof(f682,definition,
( spl25_8
<=> sP7 ),
introduced(definition,[new_symbols(definition,[spl25_8])],[avatar_definition]) ).
fof(f685,definition,
( spl25_9
<=> sP8 ),
introduced(definition,[new_symbols(definition,[spl25_9])],[avatar_definition]) ).
fof(f688,definition,
( spl25_10
<=> sP9 ),
introduced(definition,[new_symbols(definition,[spl25_10])],[avatar_definition]) ).
fof(f691,definition,
( spl25_11
<=> sP10 ),
introduced(definition,[new_symbols(definition,[spl25_11])],[avatar_definition]) ).
fof(f694,definition,
( spl25_12
<=> sP11 ),
introduced(definition,[new_symbols(definition,[spl25_12])],[avatar_definition]) ).
fof(f697,definition,
( spl25_13
<=> sP12 ),
introduced(definition,[new_symbols(definition,[spl25_13])],[avatar_definition]) ).
fof(f700,definition,
( spl25_14
<=> sP13 ),
introduced(definition,[new_symbols(definition,[spl25_14])],[avatar_definition]) ).
fof(f703,definition,
( spl25_15
<=> sP14 ),
introduced(definition,[new_symbols(definition,[spl25_15])],[avatar_definition]) ).
fof(f706,definition,
( spl25_16
<=> sP15 ),
introduced(definition,[new_symbols(definition,[spl25_16])],[avatar_definition]) ).
fof(f709,definition,
( spl25_17
<=> sP16 ),
introduced(definition,[new_symbols(definition,[spl25_17])],[avatar_definition]) ).
fof(f712,definition,
( spl25_18
<=> sP17 ),
introduced(definition,[new_symbols(definition,[spl25_18])],[avatar_definition]) ).
fof(f715,definition,
( spl25_19
<=> sP18 ),
introduced(definition,[new_symbols(definition,[spl25_19])],[avatar_definition]) ).
fof(f718,definition,
( spl25_20
<=> sP19 ),
introduced(definition,[new_symbols(definition,[spl25_20])],[avatar_definition]) ).
fof(f721,definition,
( spl25_21
<=> sP20 ),
introduced(definition,[new_symbols(definition,[spl25_21])],[avatar_definition]) ).
fof(f724,definition,
( spl25_22
<=> sP21 ),
introduced(definition,[new_symbols(definition,[spl25_22])],[avatar_definition]) ).
fof(f727,definition,
( spl25_23
<=> sP22 ),
introduced(definition,[new_symbols(definition,[spl25_23])],[avatar_definition]) ).
fof(f730,definition,
( spl25_24
<=> sP23 ),
introduced(definition,[new_symbols(definition,[spl25_24])],[avatar_definition]) ).
fof(f733,definition,
( spl25_25
<=> sQ24_eqProxy(e0,op(e0,e0)) ),
introduced(definition,[new_symbols(definition,[spl25_25])],[avatar_definition]) ).
fof(f735,plain,
( spl25_1
| spl25_2
| spl25_3
| spl25_4
| spl25_5
| spl25_6
| spl25_7
| spl25_8
| spl25_9
| spl25_10
| spl25_11
| spl25_12
| spl25_13
| spl25_14
| spl25_15
| spl25_16
| spl25_17
| spl25_18
| spl25_19
| spl25_20
| spl25_21
| spl25_22
| spl25_23
| spl25_24
| ~ spl25_25 ),
inference(avatar_split_clause,[],[f657,f733,f730,f727,f724,f721,f718,f715,f712,f709,f706,f703,f700,f697,f694,f691,f688,f685,f682,f679,f676,f673,f670,f667,f664,f661]) ).
fof(f738,plain,
( spl25_1
| spl25_2
| spl25_3
| spl25_4
| spl25_5
| spl25_6
| spl25_7
| spl25_8
| spl25_9
| spl25_10
| spl25_11
| spl25_12
| spl25_13
| spl25_14
| spl25_15
| spl25_16
| spl25_17
| spl25_18
| spl25_19
| spl25_20
| spl25_21
| spl25_22
| spl25_23
| spl25_24
| spl25_25 ),
inference(avatar_split_clause,[],[f655,f733,f730,f727,f724,f721,f718,f715,f712,f709,f706,f703,f700,f697,f694,f691,f688,f685,f682,f679,f676,f673,f670,f667,f664,f661]) ).
fof(f740,definition,
( spl25_26
<=> sQ24_eqProxy(e4,op(e4,e3)) ),
introduced(definition,[new_symbols(definition,[spl25_26])],[avatar_definition]) ).
fof(f743,definition,
( spl25_27
<=> sQ24_eqProxy(e3,op(e4,e4)) ),
introduced(definition,[new_symbols(definition,[spl25_27])],[avatar_definition]) ).
fof(f745,plain,
( spl25_26
| ~ spl25_27 ),
inference(avatar_split_clause,[],[f653,f743,f740]) ).
fof(f747,definition,
( spl25_28
<=> sQ24_eqProxy(e4,op(e4,e2)) ),
introduced(definition,[new_symbols(definition,[spl25_28])],[avatar_definition]) ).
fof(f750,definition,
( spl25_29
<=> sQ24_eqProxy(e2,op(e4,e4)) ),
introduced(definition,[new_symbols(definition,[spl25_29])],[avatar_definition]) ).
fof(f752,plain,
( spl25_28
| ~ spl25_29 ),
inference(avatar_split_clause,[],[f652,f750,f747]) ).
fof(f754,definition,
( spl25_30
<=> sQ24_eqProxy(e4,op(e4,e1)) ),
introduced(definition,[new_symbols(definition,[spl25_30])],[avatar_definition]) ).
fof(f757,definition,
( spl25_31
<=> sQ24_eqProxy(e1,op(e4,e4)) ),
introduced(definition,[new_symbols(definition,[spl25_31])],[avatar_definition]) ).
fof(f759,plain,
( spl25_30
| ~ spl25_31 ),
inference(avatar_split_clause,[],[f651,f757,f754]) ).
fof(f761,definition,
( spl25_32
<=> sQ24_eqProxy(e4,op(e4,e0)) ),
introduced(definition,[new_symbols(definition,[spl25_32])],[avatar_definition]) ).
fof(f764,definition,
( spl25_33
<=> sQ24_eqProxy(e0,op(e4,e4)) ),
introduced(definition,[new_symbols(definition,[spl25_33])],[avatar_definition]) ).
fof(f766,plain,
( spl25_32
| ~ spl25_33 ),
inference(avatar_split_clause,[],[f650,f764,f761]) ).
fof(f768,definition,
( spl25_34
<=> sQ24_eqProxy(e3,op(e3,e4)) ),
introduced(definition,[new_symbols(definition,[spl25_34])],[avatar_definition]) ).
fof(f771,definition,
( spl25_35
<=> sQ24_eqProxy(e4,op(e3,e3)) ),
introduced(definition,[new_symbols(definition,[spl25_35])],[avatar_definition]) ).
fof(f773,plain,
( spl25_34
| ~ spl25_35 ),
inference(avatar_split_clause,[],[f649,f771,f768]) ).
fof(f775,definition,
( spl25_36
<=> sQ24_eqProxy(e3,op(e3,e2)) ),
introduced(definition,[new_symbols(definition,[spl25_36])],[avatar_definition]) ).
fof(f778,definition,
( spl25_37
<=> sQ24_eqProxy(e2,op(e3,e3)) ),
introduced(definition,[new_symbols(definition,[spl25_37])],[avatar_definition]) ).
fof(f780,plain,
( spl25_36
| ~ spl25_37 ),
inference(avatar_split_clause,[],[f647,f778,f775]) ).
fof(f782,definition,
( spl25_38
<=> sQ24_eqProxy(e3,op(e3,e1)) ),
introduced(definition,[new_symbols(definition,[spl25_38])],[avatar_definition]) ).
fof(f785,definition,
( spl25_39
<=> sQ24_eqProxy(e1,op(e3,e3)) ),
introduced(definition,[new_symbols(definition,[spl25_39])],[avatar_definition]) ).
fof(f787,plain,
( spl25_38
| ~ spl25_39 ),
inference(avatar_split_clause,[],[f646,f785,f782]) ).
fof(f789,definition,
( spl25_40
<=> sQ24_eqProxy(e3,op(e3,e0)) ),
introduced(definition,[new_symbols(definition,[spl25_40])],[avatar_definition]) ).
fof(f792,definition,
( spl25_41
<=> sQ24_eqProxy(e0,op(e3,e3)) ),
introduced(definition,[new_symbols(definition,[spl25_41])],[avatar_definition]) ).
fof(f794,plain,
( spl25_40
| ~ spl25_41 ),
inference(avatar_split_clause,[],[f645,f792,f789]) ).
fof(f796,definition,
( spl25_42
<=> sQ24_eqProxy(e2,op(e2,e4)) ),
introduced(definition,[new_symbols(definition,[spl25_42])],[avatar_definition]) ).
fof(f799,definition,
( spl25_43
<=> sQ24_eqProxy(e4,op(e2,e2)) ),
introduced(definition,[new_symbols(definition,[spl25_43])],[avatar_definition]) ).
fof(f801,plain,
( spl25_42
| ~ spl25_43 ),
inference(avatar_split_clause,[],[f644,f799,f796]) ).
fof(f803,definition,
( spl25_44
<=> sQ24_eqProxy(e2,op(e2,e3)) ),
introduced(definition,[new_symbols(definition,[spl25_44])],[avatar_definition]) ).
fof(f806,definition,
( spl25_45
<=> sQ24_eqProxy(e3,op(e2,e2)) ),
introduced(definition,[new_symbols(definition,[spl25_45])],[avatar_definition]) ).
fof(f808,plain,
( spl25_44
| ~ spl25_45 ),
inference(avatar_split_clause,[],[f643,f806,f803]) ).
fof(f810,definition,
( spl25_46
<=> sQ24_eqProxy(e2,op(e2,e1)) ),
introduced(definition,[new_symbols(definition,[spl25_46])],[avatar_definition]) ).
fof(f813,definition,
( spl25_47
<=> sQ24_eqProxy(e1,op(e2,e2)) ),
introduced(definition,[new_symbols(definition,[spl25_47])],[avatar_definition]) ).
fof(f815,plain,
( spl25_46
| ~ spl25_47 ),
inference(avatar_split_clause,[],[f641,f813,f810]) ).
fof(f817,definition,
( spl25_48
<=> sQ24_eqProxy(e2,op(e2,e0)) ),
introduced(definition,[new_symbols(definition,[spl25_48])],[avatar_definition]) ).
fof(f820,definition,
( spl25_49
<=> sQ24_eqProxy(e0,op(e2,e2)) ),
introduced(definition,[new_symbols(definition,[spl25_49])],[avatar_definition]) ).
fof(f822,plain,
( spl25_48
| ~ spl25_49 ),
inference(avatar_split_clause,[],[f640,f820,f817]) ).
fof(f824,definition,
( spl25_50
<=> sQ24_eqProxy(e1,op(e1,e4)) ),
introduced(definition,[new_symbols(definition,[spl25_50])],[avatar_definition]) ).
fof(f827,definition,
( spl25_51
<=> sQ24_eqProxy(e4,op(e1,e1)) ),
introduced(definition,[new_symbols(definition,[spl25_51])],[avatar_definition]) ).
fof(f829,plain,
( spl25_50
| ~ spl25_51 ),
inference(avatar_split_clause,[],[f639,f827,f824]) ).
fof(f831,definition,
( spl25_52
<=> sQ24_eqProxy(e1,op(e1,e3)) ),
introduced(definition,[new_symbols(definition,[spl25_52])],[avatar_definition]) ).
fof(f834,definition,
( spl25_53
<=> sQ24_eqProxy(e3,op(e1,e1)) ),
introduced(definition,[new_symbols(definition,[spl25_53])],[avatar_definition]) ).
fof(f836,plain,
( spl25_52
| ~ spl25_53 ),
inference(avatar_split_clause,[],[f638,f834,f831]) ).
fof(f838,definition,
( spl25_54
<=> sQ24_eqProxy(e1,op(e1,e2)) ),
introduced(definition,[new_symbols(definition,[spl25_54])],[avatar_definition]) ).
fof(f841,definition,
( spl25_55
<=> sQ24_eqProxy(e2,op(e1,e1)) ),
introduced(definition,[new_symbols(definition,[spl25_55])],[avatar_definition]) ).
fof(f843,plain,
( spl25_54
| ~ spl25_55 ),
inference(avatar_split_clause,[],[f637,f841,f838]) ).
fof(f845,definition,
( spl25_56
<=> sQ24_eqProxy(e1,op(e1,e0)) ),
introduced(definition,[new_symbols(definition,[spl25_56])],[avatar_definition]) ).
fof(f848,definition,
( spl25_57
<=> sQ24_eqProxy(e0,op(e1,e1)) ),
introduced(definition,[new_symbols(definition,[spl25_57])],[avatar_definition]) ).
fof(f850,plain,
( spl25_56
| ~ spl25_57 ),
inference(avatar_split_clause,[],[f635,f848,f845]) ).
fof(f852,definition,
( spl25_58
<=> sQ24_eqProxy(e0,op(e0,e4)) ),
introduced(definition,[new_symbols(definition,[spl25_58])],[avatar_definition]) ).
fof(f855,definition,
( spl25_59
<=> sQ24_eqProxy(op(e0,e0),e4) ),
introduced(definition,[new_symbols(definition,[spl25_59])],[avatar_definition]) ).
fof(f857,plain,
( spl25_58
| ~ spl25_59 ),
inference(avatar_split_clause,[],[f634,f855,f852]) ).
fof(f859,definition,
( spl25_60
<=> sQ24_eqProxy(e0,op(e0,e3)) ),
introduced(definition,[new_symbols(definition,[spl25_60])],[avatar_definition]) ).
fof(f862,definition,
( spl25_61
<=> sQ24_eqProxy(op(e0,e0),e3) ),
introduced(definition,[new_symbols(definition,[spl25_61])],[avatar_definition]) ).
fof(f864,plain,
( spl25_60
| ~ spl25_61 ),
inference(avatar_split_clause,[],[f633,f862,f859]) ).
fof(f866,definition,
( spl25_62
<=> sQ24_eqProxy(e0,op(e0,e2)) ),
introduced(definition,[new_symbols(definition,[spl25_62])],[avatar_definition]) ).
fof(f869,definition,
( spl25_63
<=> sQ24_eqProxy(op(e0,e0),e2) ),
introduced(definition,[new_symbols(definition,[spl25_63])],[avatar_definition]) ).
fof(f871,plain,
( spl25_62
| ~ spl25_63 ),
inference(avatar_split_clause,[],[f632,f869,f866]) ).
fof(f873,definition,
( spl25_64
<=> sQ24_eqProxy(e0,op(e0,e1)) ),
introduced(definition,[new_symbols(definition,[spl25_64])],[avatar_definition]) ).
fof(f876,definition,
( spl25_65
<=> sQ24_eqProxy(op(e0,e0),e1) ),
introduced(definition,[new_symbols(definition,[spl25_65])],[avatar_definition]) ).
fof(f878,plain,
( spl25_64
| ~ spl25_65 ),
inference(avatar_split_clause,[],[f631,f876,f873]) ).
fof(f881,definition,
( spl25_66
<=> sQ24_eqProxy(e4,op(e4,e4)) ),
introduced(definition,[new_symbols(definition,[spl25_66])],[avatar_definition]) ).
fof(f883,plain,
( ~ spl25_1
| ~ spl25_66 ),
inference(avatar_split_clause,[],[f629,f881,f661]) ).
fof(f886,plain,
( ~ spl25_1
| spl25_66 ),
inference(avatar_split_clause,[],[f627,f881,f661]) ).
fof(f889,plain,
( ~ spl25_2
| ~ spl25_26 ),
inference(avatar_split_clause,[],[f626,f740,f664]) ).
fof(f893,plain,
( ~ spl25_2
| spl25_27 ),
inference(avatar_split_clause,[],[f624,f743,f664]) ).
fof(f896,plain,
( ~ spl25_3
| ~ spl25_28 ),
inference(avatar_split_clause,[],[f623,f747,f667]) ).
fof(f900,plain,
( ~ spl25_3
| spl25_29 ),
inference(avatar_split_clause,[],[f621,f750,f667]) ).
fof(f903,plain,
( ~ spl25_4
| ~ spl25_30 ),
inference(avatar_split_clause,[],[f620,f754,f670]) ).
fof(f907,plain,
( ~ spl25_4
| spl25_31 ),
inference(avatar_split_clause,[],[f618,f757,f670]) ).
fof(f910,plain,
( ~ spl25_5
| ~ spl25_32 ),
inference(avatar_split_clause,[],[f617,f761,f673]) ).
fof(f914,plain,
( ~ spl25_5
| spl25_33 ),
inference(avatar_split_clause,[],[f615,f764,f673]) ).
fof(f917,plain,
( ~ spl25_6
| ~ spl25_34 ),
inference(avatar_split_clause,[],[f614,f768,f676]) ).
fof(f919,plain,
( ~ spl25_6
| spl25_35 ),
inference(avatar_split_clause,[],[f612,f771,f676]) ).
fof(f922,definition,
( spl25_67
<=> sQ24_eqProxy(e3,op(e3,e3)) ),
introduced(definition,[new_symbols(definition,[spl25_67])],[avatar_definition]) ).
fof(f924,plain,
( ~ spl25_7
| ~ spl25_67 ),
inference(avatar_split_clause,[],[f611,f922,f679]) ).
fof(f927,plain,
( ~ spl25_7
| spl25_67 ),
inference(avatar_split_clause,[],[f609,f922,f679]) ).
fof(f930,plain,
( ~ spl25_8
| ~ spl25_36 ),
inference(avatar_split_clause,[],[f608,f775,f682]) ).
fof(f934,plain,
( ~ spl25_8
| spl25_37 ),
inference(avatar_split_clause,[],[f606,f778,f682]) ).
fof(f937,plain,
( ~ spl25_9
| ~ spl25_38 ),
inference(avatar_split_clause,[],[f605,f782,f685]) ).
fof(f941,plain,
( ~ spl25_9
| spl25_39 ),
inference(avatar_split_clause,[],[f603,f785,f685]) ).
fof(f944,plain,
( ~ spl25_10
| ~ spl25_40 ),
inference(avatar_split_clause,[],[f602,f789,f688]) ).
fof(f948,plain,
( ~ spl25_10
| spl25_41 ),
inference(avatar_split_clause,[],[f600,f792,f688]) ).
fof(f951,plain,
( ~ spl25_11
| ~ spl25_42 ),
inference(avatar_split_clause,[],[f599,f796,f691]) ).
fof(f953,plain,
( ~ spl25_11
| spl25_43 ),
inference(avatar_split_clause,[],[f597,f799,f691]) ).
fof(f956,plain,
( ~ spl25_12
| ~ spl25_44 ),
inference(avatar_split_clause,[],[f596,f803,f694]) ).
fof(f958,plain,
( ~ spl25_12
| spl25_45 ),
inference(avatar_split_clause,[],[f594,f806,f694]) ).
fof(f961,definition,
( spl25_68
<=> sQ24_eqProxy(e2,op(e2,e2)) ),
introduced(definition,[new_symbols(definition,[spl25_68])],[avatar_definition]) ).
fof(f963,plain,
( ~ spl25_13
| ~ spl25_68 ),
inference(avatar_split_clause,[],[f593,f961,f697]) ).
fof(f966,plain,
( ~ spl25_13
| spl25_68 ),
inference(avatar_split_clause,[],[f591,f961,f697]) ).
fof(f969,plain,
( ~ spl25_14
| ~ spl25_46 ),
inference(avatar_split_clause,[],[f590,f810,f700]) ).
fof(f973,plain,
( ~ spl25_14
| spl25_47 ),
inference(avatar_split_clause,[],[f588,f813,f700]) ).
fof(f976,plain,
( ~ spl25_15
| ~ spl25_48 ),
inference(avatar_split_clause,[],[f587,f817,f703]) ).
fof(f980,plain,
( ~ spl25_15
| spl25_49 ),
inference(avatar_split_clause,[],[f585,f820,f703]) ).
fof(f983,plain,
( ~ spl25_16
| ~ spl25_50 ),
inference(avatar_split_clause,[],[f584,f824,f706]) ).
fof(f985,plain,
( ~ spl25_16
| spl25_51 ),
inference(avatar_split_clause,[],[f582,f827,f706]) ).
fof(f988,plain,
( ~ spl25_17
| ~ spl25_52 ),
inference(avatar_split_clause,[],[f581,f831,f709]) ).
fof(f990,plain,
( ~ spl25_17
| spl25_53 ),
inference(avatar_split_clause,[],[f579,f834,f709]) ).
fof(f993,plain,
( ~ spl25_18
| ~ spl25_54 ),
inference(avatar_split_clause,[],[f578,f838,f712]) ).
fof(f995,plain,
( ~ spl25_18
| spl25_55 ),
inference(avatar_split_clause,[],[f576,f841,f712]) ).
fof(f998,definition,
( spl25_69
<=> sQ24_eqProxy(e1,op(e1,e1)) ),
introduced(definition,[new_symbols(definition,[spl25_69])],[avatar_definition]) ).
fof(f1000,plain,
( ~ spl25_19
| ~ spl25_69 ),
inference(avatar_split_clause,[],[f575,f998,f715]) ).
fof(f1003,plain,
( ~ spl25_19
| spl25_69 ),
inference(avatar_split_clause,[],[f573,f998,f715]) ).
fof(f1006,plain,
( ~ spl25_20
| ~ spl25_56 ),
inference(avatar_split_clause,[],[f572,f845,f718]) ).
fof(f1010,plain,
( ~ spl25_20
| spl25_57 ),
inference(avatar_split_clause,[],[f570,f848,f718]) ).
fof(f1013,plain,
( ~ spl25_21
| ~ spl25_58 ),
inference(avatar_split_clause,[],[f569,f852,f721]) ).
fof(f1015,plain,
( ~ spl25_21
| spl25_59 ),
inference(avatar_split_clause,[],[f567,f855,f721]) ).
fof(f1018,plain,
( ~ spl25_22
| ~ spl25_60 ),
inference(avatar_split_clause,[],[f566,f859,f724]) ).
fof(f1020,plain,
( ~ spl25_22
| spl25_61 ),
inference(avatar_split_clause,[],[f564,f862,f724]) ).
fof(f1023,plain,
( ~ spl25_23
| ~ spl25_62 ),
inference(avatar_split_clause,[],[f563,f866,f727]) ).
fof(f1025,plain,
( ~ spl25_23
| spl25_63 ),
inference(avatar_split_clause,[],[f561,f869,f727]) ).
fof(f1028,plain,
( ~ spl25_24
| ~ spl25_64 ),
inference(avatar_split_clause,[],[f560,f873,f730]) ).
fof(f1030,plain,
( ~ spl25_24
| spl25_65 ),
inference(avatar_split_clause,[],[f558,f876,f730]) ).
cnf(s1,plain,
( spl25_1
| spl25_2
| spl25_3
| spl25_4
| spl25_5
| spl25_6
| spl25_7
| spl25_8
| spl25_9
| spl25_10
| spl25_11
| spl25_12
| spl25_13
| spl25_14
| spl25_15
| spl25_16
| spl25_17
| spl25_18
| spl25_19
| spl25_20
| spl25_21
| spl25_22
| spl25_23
| spl25_24
| ~ spl25_25 ),
inference(sat_conversion,[],[f735]) ).
cnf(s3,plain,
( spl25_1
| spl25_2
| spl25_3
| spl25_4
| spl25_5
| spl25_6
| spl25_7
| spl25_8
| spl25_9
| spl25_10
| spl25_11
| spl25_12
| spl25_13
| spl25_14
| spl25_15
| spl25_16
| spl25_17
| spl25_18
| spl25_19
| spl25_20
| spl25_21
| spl25_22
| spl25_23
| spl25_24
| spl25_25 ),
inference(sat_conversion,[],[f738]) ).
cnf(s4,plain,
( spl25_26
| ~ spl25_27 ),
inference(sat_conversion,[],[f745]) ).
cnf(s5,plain,
( spl25_28
| ~ spl25_29 ),
inference(sat_conversion,[],[f752]) ).
cnf(s6,plain,
( spl25_30
| ~ spl25_31 ),
inference(sat_conversion,[],[f759]) ).
cnf(s7,plain,
( spl25_32
| ~ spl25_33 ),
inference(sat_conversion,[],[f766]) ).
cnf(s8,plain,
( spl25_34
| ~ spl25_35 ),
inference(sat_conversion,[],[f773]) ).
cnf(s9,plain,
( spl25_36
| ~ spl25_37 ),
inference(sat_conversion,[],[f780]) ).
cnf(s10,plain,
( spl25_38
| ~ spl25_39 ),
inference(sat_conversion,[],[f787]) ).
cnf(s11,plain,
( spl25_40
| ~ spl25_41 ),
inference(sat_conversion,[],[f794]) ).
cnf(s12,plain,
( spl25_42
| ~ spl25_43 ),
inference(sat_conversion,[],[f801]) ).
cnf(s13,plain,
( spl25_44
| ~ spl25_45 ),
inference(sat_conversion,[],[f808]) ).
cnf(s14,plain,
( spl25_46
| ~ spl25_47 ),
inference(sat_conversion,[],[f815]) ).
cnf(s15,plain,
( spl25_48
| ~ spl25_49 ),
inference(sat_conversion,[],[f822]) ).
cnf(s16,plain,
( spl25_50
| ~ spl25_51 ),
inference(sat_conversion,[],[f829]) ).
cnf(s17,plain,
( spl25_52
| ~ spl25_53 ),
inference(sat_conversion,[],[f836]) ).
cnf(s18,plain,
( spl25_54
| ~ spl25_55 ),
inference(sat_conversion,[],[f843]) ).
cnf(s19,plain,
( spl25_56
| ~ spl25_57 ),
inference(sat_conversion,[],[f850]) ).
cnf(s20,plain,
( spl25_58
| ~ spl25_59 ),
inference(sat_conversion,[],[f857]) ).
cnf(s21,plain,
( spl25_60
| ~ spl25_61 ),
inference(sat_conversion,[],[f864]) ).
cnf(s22,plain,
( spl25_62
| ~ spl25_63 ),
inference(sat_conversion,[],[f871]) ).
cnf(s23,plain,
( spl25_64
| ~ spl25_65 ),
inference(sat_conversion,[],[f878]) ).
cnf(s24,plain,
( ~ spl25_1
| ~ spl25_66 ),
inference(sat_conversion,[],[f883]) ).
cnf(s26,plain,
( ~ spl25_1
| spl25_66 ),
inference(sat_conversion,[],[f886]) ).
cnf(s27,plain,
( ~ spl25_2
| ~ spl25_26 ),
inference(sat_conversion,[],[f889]) ).
cnf(s29,plain,
( ~ spl25_2
| spl25_27 ),
inference(sat_conversion,[],[f893]) ).
cnf(s30,plain,
( ~ spl25_3
| ~ spl25_28 ),
inference(sat_conversion,[],[f896]) ).
cnf(s32,plain,
( ~ spl25_3
| spl25_29 ),
inference(sat_conversion,[],[f900]) ).
cnf(s33,plain,
( ~ spl25_4
| ~ spl25_30 ),
inference(sat_conversion,[],[f903]) ).
cnf(s35,plain,
( ~ spl25_4
| spl25_31 ),
inference(sat_conversion,[],[f907]) ).
cnf(s36,plain,
( ~ spl25_5
| ~ spl25_32 ),
inference(sat_conversion,[],[f910]) ).
cnf(s38,plain,
( ~ spl25_5
| spl25_33 ),
inference(sat_conversion,[],[f914]) ).
cnf(s39,plain,
( ~ spl25_6
| ~ spl25_34 ),
inference(sat_conversion,[],[f917]) ).
cnf(s41,plain,
( ~ spl25_6
| spl25_35 ),
inference(sat_conversion,[],[f919]) ).
cnf(s42,plain,
( ~ spl25_7
| ~ spl25_67 ),
inference(sat_conversion,[],[f924]) ).
cnf(s44,plain,
( ~ spl25_7
| spl25_67 ),
inference(sat_conversion,[],[f927]) ).
cnf(s45,plain,
( ~ spl25_8
| ~ spl25_36 ),
inference(sat_conversion,[],[f930]) ).
cnf(s47,plain,
( ~ spl25_8
| spl25_37 ),
inference(sat_conversion,[],[f934]) ).
cnf(s48,plain,
( ~ spl25_9
| ~ spl25_38 ),
inference(sat_conversion,[],[f937]) ).
cnf(s50,plain,
( ~ spl25_9
| spl25_39 ),
inference(sat_conversion,[],[f941]) ).
cnf(s51,plain,
( ~ spl25_10
| ~ spl25_40 ),
inference(sat_conversion,[],[f944]) ).
cnf(s53,plain,
( ~ spl25_10
| spl25_41 ),
inference(sat_conversion,[],[f948]) ).
cnf(s54,plain,
( ~ spl25_11
| ~ spl25_42 ),
inference(sat_conversion,[],[f951]) ).
cnf(s56,plain,
( ~ spl25_11
| spl25_43 ),
inference(sat_conversion,[],[f953]) ).
cnf(s57,plain,
( ~ spl25_12
| ~ spl25_44 ),
inference(sat_conversion,[],[f956]) ).
cnf(s59,plain,
( ~ spl25_12
| spl25_45 ),
inference(sat_conversion,[],[f958]) ).
cnf(s60,plain,
( ~ spl25_13
| ~ spl25_68 ),
inference(sat_conversion,[],[f963]) ).
cnf(s62,plain,
( ~ spl25_13
| spl25_68 ),
inference(sat_conversion,[],[f966]) ).
cnf(s63,plain,
( ~ spl25_14
| ~ spl25_46 ),
inference(sat_conversion,[],[f969]) ).
cnf(s65,plain,
( ~ spl25_14
| spl25_47 ),
inference(sat_conversion,[],[f973]) ).
cnf(s66,plain,
( ~ spl25_15
| ~ spl25_48 ),
inference(sat_conversion,[],[f976]) ).
cnf(s68,plain,
( ~ spl25_15
| spl25_49 ),
inference(sat_conversion,[],[f980]) ).
cnf(s69,plain,
( ~ spl25_16
| ~ spl25_50 ),
inference(sat_conversion,[],[f983]) ).
cnf(s71,plain,
( ~ spl25_16
| spl25_51 ),
inference(sat_conversion,[],[f985]) ).
cnf(s72,plain,
( ~ spl25_17
| ~ spl25_52 ),
inference(sat_conversion,[],[f988]) ).
cnf(s74,plain,
( ~ spl25_17
| spl25_53 ),
inference(sat_conversion,[],[f990]) ).
cnf(s75,plain,
( ~ spl25_18
| ~ spl25_54 ),
inference(sat_conversion,[],[f993]) ).
cnf(s77,plain,
( ~ spl25_18
| spl25_55 ),
inference(sat_conversion,[],[f995]) ).
cnf(s78,plain,
( ~ spl25_19
| ~ spl25_69 ),
inference(sat_conversion,[],[f1000]) ).
cnf(s80,plain,
( ~ spl25_19
| spl25_69 ),
inference(sat_conversion,[],[f1003]) ).
cnf(s81,plain,
( ~ spl25_20
| ~ spl25_56 ),
inference(sat_conversion,[],[f1006]) ).
cnf(s83,plain,
( ~ spl25_20
| spl25_57 ),
inference(sat_conversion,[],[f1010]) ).
cnf(s84,plain,
( ~ spl25_21
| ~ spl25_58 ),
inference(sat_conversion,[],[f1013]) ).
cnf(s86,plain,
( ~ spl25_21
| spl25_59 ),
inference(sat_conversion,[],[f1015]) ).
cnf(s87,plain,
( ~ spl25_22
| ~ spl25_60 ),
inference(sat_conversion,[],[f1018]) ).
cnf(s89,plain,
( ~ spl25_22
| spl25_61 ),
inference(sat_conversion,[],[f1020]) ).
cnf(s90,plain,
( ~ spl25_23
| ~ spl25_62 ),
inference(sat_conversion,[],[f1023]) ).
cnf(s92,plain,
( ~ spl25_23
| spl25_63 ),
inference(sat_conversion,[],[f1025]) ).
cnf(s93,plain,
( ~ spl25_24
| ~ spl25_64 ),
inference(sat_conversion,[],[f1028]) ).
cnf(s95,plain,
( ~ spl25_24
| spl25_65 ),
inference(sat_conversion,[],[f1030]) ).
cnf(s172,plain,
( spl25_24
| spl25_23
| spl25_22
| spl25_21
| spl25_6
| spl25_4
| spl25_5
| spl25_3
| spl25_1
| spl25_2
| spl25_7
| spl25_8
| spl25_9
| spl25_10
| spl25_11
| spl25_12
| spl25_13
| spl25_14
| spl25_15
| spl25_16
| spl25_17
| spl25_18
| spl25_19
| spl25_20 ),
inference(rat,[],[s3,s1]) ).
cnf(s173,plain,
~ spl25_24,
inference(rat,[],[s23,s93,s95]) ).
cnf(s174,plain,
~ spl25_23,
inference(rat,[],[s22,s90,s92]) ).
cnf(s175,plain,
~ spl25_22,
inference(rat,[],[s21,s87,s89]) ).
cnf(s176,plain,
~ spl25_21,
inference(rat,[],[s20,s84,s86]) ).
cnf(s177,plain,
~ spl25_20,
inference(rat,[],[s19,s81,s83]) ).
cnf(s178,plain,
~ spl25_19,
inference(rat,[],[s78,s80]) ).
cnf(s179,plain,
~ spl25_18,
inference(rat,[],[s18,s75,s77]) ).
cnf(s180,plain,
~ spl25_17,
inference(rat,[],[s17,s72,s74]) ).
cnf(s181,plain,
~ spl25_16,
inference(rat,[],[s16,s69,s71]) ).
cnf(s182,plain,
~ spl25_15,
inference(rat,[],[s15,s66,s68]) ).
cnf(s183,plain,
~ spl25_14,
inference(rat,[],[s14,s63,s65]) ).
cnf(s184,plain,
~ spl25_13,
inference(rat,[],[s60,s62]) ).
cnf(s185,plain,
~ spl25_12,
inference(rat,[],[s13,s57,s59]) ).
cnf(s186,plain,
~ spl25_11,
inference(rat,[],[s12,s54,s56]) ).
cnf(s187,plain,
~ spl25_10,
inference(rat,[],[s11,s51,s53]) ).
cnf(s188,plain,
~ spl25_9,
inference(rat,[],[s10,s48,s50]) ).
cnf(s189,plain,
~ spl25_8,
inference(rat,[],[s9,s45,s47]) ).
cnf(s190,plain,
~ spl25_7,
inference(rat,[],[s42,s44]) ).
cnf(s191,plain,
~ spl25_6,
inference(rat,[],[s8,s39,s41]) ).
cnf(s192,plain,
~ spl25_5,
inference(rat,[],[s7,s36,s38]) ).
cnf(s193,plain,
~ spl25_4,
inference(rat,[],[s6,s33,s35]) ).
cnf(s194,plain,
~ spl25_3,
inference(rat,[],[s5,s30,s32]) ).
cnf(s195,plain,
~ spl25_2,
inference(rat,[],[s4,s27,s29]) ).
cnf(s196,plain,
spl25_1,
inference(rat,[],[s172,s176,s178,s180,s182,s184,s186,s188,s190,s192,s193,s191,s189,s187,s185,s183,s194,s181,s179,s177,s175,s173,s174,s195]) ).
cnf(s197,plain,
spl25_66,
inference(rat,[],[s26,s196]) ).
cnf(s198,plain,
$false,
inference(rat,[],[s24,s197,s196]) ).
fof(f1362,plain,
$false,
inference(avatar_sat_refutation,[],[s198]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG067+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n004.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Mon Sep 28 19:24:37 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running first-order theorem proving
% 0.07/0.22 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
% 2.01/0.72 % (671395)Detected formulas, will run a generic FOF schedule.
% 2.01/0.72 % (671473)dis-21_1_sil=8000:lcm=predicate:random_seed=3629515226: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)
% 2.01/0.72 % (671473)First to succeed.
% 2.01/0.72 % (671473)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-671395"
% 2.01/0.72 % (671468)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=120630801:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.01/0.72 % (671467)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=4058646218:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.01/0.72 % (671471)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1159369563:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.01/0.72 % (671470)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3060347063:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.01/0.73 % (671472)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2906556812:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.01/0.73 % (671469)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=1472945085:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.01/0.73 % (671472)Also succeeded, but the first one will report.
% 2.01/0.73 % (671471)Also succeeded, but the first one will report.
% 2.01/0.73 % (671470)Instruction limit reached!
% 2.01/0.73 % (671470)------------------------------
% 2.01/0.73 % (671470)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.01/0.73 % (671470)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.01/0.73 % (671470)CaDiCaL version: 2.1.3
% 2.01/0.73 % (671470)Termination reason: Instruction limit
% 2.01/0.73 % (671470)Termination phase: Saturation
% 2.01/0.73 % (671470)Time elapsed: 0.053 s
% 2.01/0.73 % (671470)Peak memory usage: 89 MB
% 2.01/0.73 % (671470)Instructions burned: 109 (million)
% 2.01/0.73 % (671473)Refutation found. Thanks to Tanya!
% 2.01/0.73 % SZS status Theorem for theBenchmark
% 2.01/0.73 % SZS output start Proof for theBenchmark
% See solution above
% 2.33/0.82 % (671473)------------------------------
% 2.33/0.82 % (671473)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.33/0.82 % (671473)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.33/0.82 % (671473)CaDiCaL version: 2.1.3
% 2.33/0.82 % (671473)Termination reason: Refutation
% 2.33/0.82 % (671473)Time elapsed: 0.009 s
% 2.33/0.82 % (671473)Peak memory usage: 90 MB
% 2.33/0.82 % (671473)Instructions burned: 27 (million)
% 2.33/0.82 % (671473)------------------------------
% 2.33/0.82 % (671473)------------------------------
% 2.33/0.82 % (671395)Success in time 0.292 s
% 2.33/0.82 % Vampire exiting
%------------------------------------------------------------------------------