%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ALG059+1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 : Thu Sep 24 11:47:58 AM UTC 2026
% Result : Theorem 0.85s 0.69s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 356
% Syntax : Number of formulae : 1381 ( 146 unt; 349 def)
% Number of atoms : 10740 (8351 equ)
% Maximal formula atoms : 450 ( 7 avg)
% Number of connectives : 15372 (6013 ~;3997 |;4907 &)
% ( 455 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 101 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 351 ( 349 usr; 350 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
( ( op(e4,e4) = e4
| op(e4,e4) = e3
| op(e4,e4) = e2
| op(e4,e4) = e1
| op(e4,e4) = e0 )
& ( op(e4,e3) = e4
| op(e4,e3) = e3
| op(e4,e3) = e2
| op(e4,e3) = e1
| op(e4,e3) = e0 )
& ( op(e4,e2) = e4
| op(e4,e2) = e3
| op(e4,e2) = e2
| op(e4,e2) = e1
| op(e4,e2) = e0 )
& ( op(e4,e1) = e4
| op(e4,e1) = e3
| op(e4,e1) = e2
| op(e4,e1) = e1
| op(e4,e1) = e0 )
& ( op(e4,e0) = e4
| op(e4,e0) = e3
| op(e4,e0) = e2
| op(e4,e0) = e1
| op(e4,e0) = e0 )
& ( op(e3,e4) = e4
| op(e3,e4) = e3
| op(e3,e4) = e2
| op(e3,e4) = e1
| op(e3,e4) = e0 )
& ( op(e3,e3) = e4
| op(e3,e3) = e3
| op(e3,e3) = e2
| op(e3,e3) = e1
| op(e3,e3) = e0 )
& ( op(e3,e2) = e4
| op(e3,e2) = e3
| op(e3,e2) = e2
| op(e3,e2) = e1
| op(e3,e2) = e0 )
& ( op(e3,e1) = e4
| op(e3,e1) = e3
| op(e3,e1) = e2
| op(e3,e1) = e1
| op(e3,e1) = e0 )
& ( op(e3,e0) = e4
| op(e3,e0) = e3
| op(e3,e0) = e2
| op(e3,e0) = e1
| op(e3,e0) = e0 )
& ( op(e2,e4) = e4
| op(e2,e4) = e3
| op(e2,e4) = e2
| op(e2,e4) = e1
| op(e2,e4) = e0 )
& ( op(e2,e3) = e4
| op(e2,e3) = e3
| op(e2,e3) = e2
| op(e2,e3) = e1
| op(e2,e3) = e0 )
& ( op(e2,e2) = e4
| op(e2,e2) = e3
| op(e2,e2) = e2
| op(e2,e2) = e1
| op(e2,e2) = e0 )
& ( op(e2,e1) = e4
| op(e2,e1) = e3
| op(e2,e1) = e2
| op(e2,e1) = e1
| op(e2,e1) = e0 )
& ( op(e2,e0) = e4
| op(e2,e0) = e3
| op(e2,e0) = e2
| op(e2,e0) = e1
| op(e2,e0) = e0 )
& ( op(e1,e4) = e4
| op(e1,e4) = e3
| op(e1,e4) = e2
| op(e1,e4) = e1
| op(e1,e4) = e0 )
& ( op(e1,e3) = e4
| op(e1,e3) = e3
| op(e1,e3) = e2
| op(e1,e3) = e1
| op(e1,e3) = e0 )
& ( op(e1,e2) = e4
| op(e1,e2) = e3
| op(e1,e2) = e2
| op(e1,e2) = e1
| op(e1,e2) = e0 )
& ( op(e1,e1) = e4
| op(e1,e1) = e3
| op(e1,e1) = e2
| op(e1,e1) = e1
| op(e1,e1) = e0 )
& ( op(e1,e0) = e4
| op(e1,e0) = e3
| op(e1,e0) = e2
| op(e1,e0) = e1
| op(e1,e0) = e0 )
& ( op(e0,e4) = e4
| op(e0,e4) = e3
| op(e0,e4) = e2
| op(e0,e4) = e1
| op(e0,e4) = e0 )
& ( op(e0,e3) = e4
| op(e0,e3) = e3
| op(e0,e3) = e2
| op(e0,e3) = e1
| op(e0,e3) = e0 )
& ( op(e0,e2) = e4
| op(e0,e2) = e3
| op(e0,e2) = e2
| op(e0,e2) = e1
| op(e0,e2) = e0 )
& ( op(e0,e1) = e4
| op(e0,e1) = e3
| op(e0,e1) = e2
| op(e0,e1) = e1
| op(e0,e1) = e0 )
& ( op(e0,e0) = e4
| op(e0,e0) = e3
| op(e0,e0) = e2
| op(e0,e0) = e1
| op(e0,e0) = e0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
( ( unit = e4
| unit = e3
| unit = e2
| unit = e1
| unit = e0 )
& op(e4,unit) = e4
& op(unit,e4) = e4
& op(e3,unit) = e3
& op(unit,e3) = e3
& op(e2,unit) = e2
& op(unit,e2) = e2
& op(e1,unit) = e1
& op(unit,e1) = e1
& op(e0,unit) = e0
& op(unit,e0) = e0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
( ( op(e4,e4) = e4
| op(e3,e4) = e4
| op(e2,e4) = e4
| op(e1,e4) = e4
| op(e0,e4) = e4 )
& ( op(e4,e4) = e4
| op(e4,e3) = e4
| op(e4,e2) = e4
| op(e4,e1) = e4
| op(e4,e0) = e4 )
& ( op(e4,e4) = e3
| op(e3,e4) = e3
| op(e2,e4) = e3
| op(e1,e4) = e3
| op(e0,e4) = e3 )
& ( op(e4,e4) = e3
| op(e4,e3) = e3
| op(e4,e2) = e3
| op(e4,e1) = e3
| op(e4,e0) = e3 )
& ( op(e4,e4) = e2
| op(e3,e4) = e2
| op(e2,e4) = e2
| op(e1,e4) = e2
| op(e0,e4) = e2 )
& ( op(e4,e4) = e2
| op(e4,e3) = e2
| op(e4,e2) = e2
| op(e4,e1) = e2
| op(e4,e0) = e2 )
& ( op(e4,e4) = e1
| op(e3,e4) = e1
| op(e2,e4) = e1
| op(e1,e4) = e1
| op(e0,e4) = e1 )
& ( op(e4,e4) = e1
| op(e4,e3) = e1
| op(e4,e2) = e1
| op(e4,e1) = e1
| op(e4,e0) = e1 )
& ( op(e4,e4) = e0
| op(e3,e4) = e0
| op(e2,e4) = e0
| op(e1,e4) = e0
| op(e0,e4) = e0 )
& ( op(e4,e4) = e0
| op(e4,e3) = e0
| op(e4,e2) = e0
| op(e4,e1) = e0
| op(e4,e0) = e0 )
& ( op(e4,e3) = e4
| op(e3,e3) = e4
| op(e2,e3) = e4
| op(e1,e3) = e4
| op(e0,e3) = e4 )
& ( op(e3,e4) = e4
| op(e3,e3) = e4
| op(e3,e2) = e4
| op(e3,e1) = e4
| op(e3,e0) = e4 )
& ( op(e4,e3) = e3
| op(e3,e3) = e3
| op(e2,e3) = e3
| op(e1,e3) = e3
| op(e0,e3) = e3 )
& ( op(e3,e4) = e3
| op(e3,e3) = e3
| op(e3,e2) = e3
| op(e3,e1) = e3
| op(e3,e0) = e3 )
& ( op(e4,e3) = e2
| op(e3,e3) = e2
| op(e2,e3) = e2
| op(e1,e3) = e2
| op(e0,e3) = e2 )
& ( op(e3,e4) = e2
| op(e3,e3) = e2
| op(e3,e2) = e2
| op(e3,e1) = e2
| op(e3,e0) = e2 )
& ( op(e4,e3) = e1
| op(e3,e3) = e1
| op(e2,e3) = e1
| op(e1,e3) = e1
| op(e0,e3) = e1 )
& ( op(e3,e4) = e1
| op(e3,e3) = e1
| op(e3,e2) = e1
| op(e3,e1) = e1
| op(e3,e0) = e1 )
& ( op(e4,e3) = e0
| op(e3,e3) = e0
| op(e2,e3) = e0
| op(e1,e3) = e0
| op(e0,e3) = e0 )
& ( op(e3,e4) = e0
| op(e3,e3) = e0
| op(e3,e2) = e0
| op(e3,e1) = e0
| op(e3,e0) = e0 )
& ( op(e4,e2) = e4
| op(e3,e2) = e4
| op(e2,e2) = e4
| op(e1,e2) = e4
| op(e0,e2) = e4 )
& ( op(e2,e4) = e4
| op(e2,e3) = e4
| op(e2,e2) = e4
| op(e2,e1) = e4
| op(e2,e0) = e4 )
& ( op(e4,e2) = e3
| op(e3,e2) = e3
| op(e2,e2) = e3
| op(e1,e2) = e3
| op(e0,e2) = e3 )
& ( op(e2,e4) = e3
| op(e2,e3) = e3
| op(e2,e2) = e3
| op(e2,e1) = e3
| op(e2,e0) = e3 )
& ( op(e4,e2) = e2
| op(e3,e2) = e2
| op(e2,e2) = e2
| op(e1,e2) = e2
| op(e0,e2) = e2 )
& ( op(e2,e4) = e2
| op(e2,e3) = e2
| op(e2,e2) = e2
| op(e2,e1) = e2
| op(e2,e0) = e2 )
& ( op(e4,e2) = e1
| op(e3,e2) = e1
| op(e2,e2) = e1
| op(e1,e2) = e1
| op(e0,e2) = e1 )
& ( op(e2,e4) = e1
| op(e2,e3) = e1
| op(e2,e2) = e1
| op(e2,e1) = e1
| op(e2,e0) = e1 )
& ( op(e4,e2) = e0
| op(e3,e2) = e0
| op(e2,e2) = e0
| op(e1,e2) = e0
| op(e0,e2) = e0 )
& ( op(e2,e4) = e0
| op(e2,e3) = e0
| op(e2,e2) = e0
| op(e2,e1) = e0
| op(e2,e0) = e0 )
& ( op(e4,e1) = e4
| op(e3,e1) = e4
| op(e2,e1) = e4
| op(e1,e1) = e4
| op(e0,e1) = e4 )
& ( op(e1,e4) = e4
| op(e1,e3) = e4
| op(e1,e2) = e4
| op(e1,e1) = e4
| op(e1,e0) = e4 )
& ( op(e4,e1) = e3
| op(e3,e1) = e3
| op(e2,e1) = e3
| op(e1,e1) = e3
| op(e0,e1) = e3 )
& ( op(e1,e4) = e3
| op(e1,e3) = e3
| op(e1,e2) = e3
| op(e1,e1) = e3
| op(e1,e0) = e3 )
& ( op(e4,e1) = e2
| op(e3,e1) = e2
| op(e2,e1) = e2
| op(e1,e1) = e2
| op(e0,e1) = e2 )
& ( op(e1,e4) = e2
| op(e1,e3) = e2
| op(e1,e2) = e2
| op(e1,e1) = e2
| op(e1,e0) = e2 )
& ( op(e4,e1) = e1
| op(e3,e1) = e1
| op(e2,e1) = e1
| op(e1,e1) = e1
| op(e0,e1) = e1 )
& ( op(e1,e4) = e1
| op(e1,e3) = e1
| op(e1,e2) = e1
| op(e1,e1) = e1
| op(e1,e0) = e1 )
& ( op(e4,e1) = e0
| op(e3,e1) = e0
| op(e2,e1) = e0
| op(e1,e1) = e0
| op(e0,e1) = e0 )
& ( op(e1,e4) = e0
| op(e1,e3) = e0
| op(e1,e2) = e0
| op(e1,e1) = e0
| op(e1,e0) = e0 )
& ( op(e4,e0) = e4
| op(e3,e0) = e4
| op(e2,e0) = e4
| op(e1,e0) = e4
| op(e0,e0) = e4 )
& ( op(e0,e4) = e4
| op(e0,e3) = e4
| op(e0,e2) = e4
| op(e0,e1) = e4
| op(e0,e0) = e4 )
& ( op(e4,e0) = e3
| op(e3,e0) = e3
| op(e2,e0) = e3
| op(e1,e0) = e3
| op(e0,e0) = e3 )
& ( op(e0,e4) = e3
| op(e0,e3) = e3
| op(e0,e2) = e3
| op(e0,e1) = e3
| op(e0,e0) = e3 )
& ( op(e4,e0) = e2
| op(e3,e0) = e2
| op(e2,e0) = e2
| op(e1,e0) = e2
| op(e0,e0) = e2 )
& ( op(e0,e4) = e2
| op(e0,e3) = e2
| op(e0,e2) = e2
| op(e0,e1) = e2
| op(e0,e0) = e2 )
& ( op(e4,e0) = e1
| op(e3,e0) = e1
| op(e2,e0) = e1
| op(e1,e0) = e1
| op(e0,e0) = e1 )
& ( op(e0,e4) = e1
| op(e0,e3) = e1
| op(e0,e2) = e1
| op(e0,e1) = e1
| op(e0,e0) = e1 )
& ( op(e4,e0) = e0
| op(e3,e0) = e0
| op(e2,e0) = e0
| op(e1,e0) = e0
| op(e0,e0) = e0 )
& ( op(e0,e4) = e0
| op(e0,e3) = e0
| op(e0,e2) = e0
| op(e0,e1) = e0
| op(e0,e0) = e0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
( op(e4,e3) != op(e4,e4)
& op(e4,e2) != op(e4,e4)
& op(e4,e2) != op(e4,e3)
& op(e4,e1) != op(e4,e4)
& op(e4,e1) != op(e4,e3)
& op(e4,e1) != op(e4,e2)
& op(e4,e0) != op(e4,e4)
& op(e4,e0) != op(e4,e3)
& op(e4,e0) != op(e4,e2)
& op(e4,e0) != op(e4,e1)
& op(e3,e3) != op(e3,e4)
& op(e3,e2) != op(e3,e4)
& op(e3,e2) != op(e3,e3)
& op(e3,e1) != op(e3,e4)
& op(e3,e1) != op(e3,e3)
& op(e3,e1) != op(e3,e2)
& op(e3,e0) != op(e3,e4)
& op(e3,e0) != op(e3,e3)
& op(e3,e0) != op(e3,e2)
& op(e3,e0) != op(e3,e1)
& op(e2,e3) != op(e2,e4)
& op(e2,e2) != op(e2,e4)
& op(e2,e2) != op(e2,e3)
& op(e2,e1) != op(e2,e4)
& op(e2,e1) != op(e2,e3)
& op(e2,e1) != op(e2,e2)
& op(e2,e0) != op(e2,e4)
& op(e2,e0) != op(e2,e3)
& op(e2,e0) != op(e2,e2)
& op(e2,e0) != op(e2,e1)
& op(e1,e3) != op(e1,e4)
& op(e1,e2) != op(e1,e4)
& op(e1,e2) != op(e1,e3)
& op(e1,e1) != op(e1,e4)
& op(e1,e1) != op(e1,e3)
& op(e1,e1) != op(e1,e2)
& op(e1,e0) != op(e1,e4)
& op(e1,e0) != op(e1,e3)
& op(e1,e0) != op(e1,e2)
& op(e1,e0) != op(e1,e1)
& op(e0,e3) != op(e0,e4)
& op(e0,e2) != op(e0,e4)
& op(e0,e2) != op(e0,e3)
& op(e0,e1) != op(e0,e4)
& op(e0,e1) != op(e0,e3)
& op(e0,e1) != op(e0,e2)
& op(e0,e0) != op(e0,e4)
& op(e0,e0) != op(e0,e3)
& op(e0,e0) != op(e0,e2)
& op(e0,e0) != op(e0,e1)
& op(e3,e4) != op(e4,e4)
& op(e2,e4) != op(e4,e4)
& op(e2,e4) != op(e3,e4)
& op(e1,e4) != op(e4,e4)
& op(e1,e4) != op(e3,e4)
& op(e1,e4) != op(e2,e4)
& op(e0,e4) != op(e4,e4)
& op(e0,e4) != op(e3,e4)
& op(e0,e4) != op(e2,e4)
& op(e0,e4) != op(e1,e4)
& op(e3,e3) != op(e4,e3)
& op(e2,e3) != op(e4,e3)
& op(e2,e3) != op(e3,e3)
& op(e1,e3) != op(e4,e3)
& op(e1,e3) != op(e3,e3)
& op(e1,e3) != op(e2,e3)
& op(e0,e3) != op(e4,e3)
& op(e0,e3) != op(e3,e3)
& op(e0,e3) != op(e2,e3)
& op(e0,e3) != op(e1,e3)
& op(e3,e2) != op(e4,e2)
& op(e2,e2) != op(e4,e2)
& op(e2,e2) != op(e3,e2)
& op(e1,e2) != op(e4,e2)
& op(e1,e2) != op(e3,e2)
& op(e1,e2) != op(e2,e2)
& op(e0,e2) != op(e4,e2)
& op(e0,e2) != op(e3,e2)
& op(e0,e2) != op(e2,e2)
& op(e0,e2) != op(e1,e2)
& op(e3,e1) != op(e4,e1)
& op(e2,e1) != op(e4,e1)
& op(e2,e1) != op(e3,e1)
& op(e1,e1) != op(e4,e1)
& op(e1,e1) != op(e3,e1)
& op(e1,e1) != op(e2,e1)
& op(e0,e1) != op(e4,e1)
& op(e0,e1) != op(e3,e1)
& op(e0,e1) != op(e2,e1)
& op(e0,e1) != op(e1,e1)
& op(e3,e0) != op(e4,e0)
& op(e2,e0) != op(e4,e0)
& op(e2,e0) != op(e3,e0)
& op(e1,e0) != op(e4,e0)
& op(e1,e0) != op(e3,e0)
& op(e1,e0) != op(e2,e0)
& op(e0,e0) != op(e4,e0)
& op(e0,e0) != op(e3,e0)
& op(e0,e0) != op(e2,e0)
& op(e0,e0) != op(e1,e0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
( e3 != e4
& e2 != e4
& e2 != e3
& e1 != e4
& e1 != e3
& e1 != e2
& e0 != e4
& e0 != e3
& e0 != e2
& e0 != e1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
( e4 = op(op(e2,e2),op(e2,e2))
& e3 = op(e2,e2)
& e1 = op(op(e2,e2),e2)
& e0 = op(op(op(e2,e2),e2),op(op(e2,e2),e2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,conjecture,
~ ( ( ( op(op(e4,e4),e4) != e4
& op(op(e4,e4),e4) = e4
& op(e4,e4) != op(e4,e4) )
| ( op(op(e4,e3),e4) != e3
& op(op(e4,e3),e3) = e4
& op(e3,e4) != op(e4,e3) )
| ( op(op(e4,e2),e4) != e2
& op(op(e4,e2),e2) = e4
& op(e2,e4) != op(e4,e2) )
| ( op(op(e4,e1),e4) != e1
& op(op(e4,e1),e1) = e4
& op(e1,e4) != op(e4,e1) )
| ( op(op(e4,e0),e4) != e0
& op(op(e4,e0),e0) = e4
& op(e0,e4) != op(e4,e0) )
| ( op(op(e3,e4),e3) != e4
& op(op(e3,e4),e4) = e3
& op(e4,e3) != op(e3,e4) )
| ( op(op(e3,e3),e3) != e3
& op(op(e3,e3),e3) = e3
& op(e3,e3) != op(e3,e3) )
| ( op(op(e3,e2),e3) != e2
& op(op(e3,e2),e2) = e3
& op(e2,e3) != op(e3,e2) )
| ( op(op(e3,e1),e3) != e1
& op(op(e3,e1),e1) = e3
& op(e1,e3) != op(e3,e1) )
| ( op(op(e3,e0),e3) != e0
& op(op(e3,e0),e0) = e3
& op(e0,e3) != op(e3,e0) )
| ( op(op(e2,e4),e2) != e4
& op(op(e2,e4),e4) = e2
& op(e4,e2) != op(e2,e4) )
| ( op(op(e2,e3),e2) != e3
& op(op(e2,e3),e3) = e2
& op(e3,e2) != op(e2,e3) )
| ( op(op(e2,e2),e2) != e2
& op(op(e2,e2),e2) = e2
& op(e2,e2) != op(e2,e2) )
| ( op(op(e2,e1),e2) != e1
& op(op(e2,e1),e1) = e2
& op(e1,e2) != op(e2,e1) )
| ( op(op(e2,e0),e2) != e0
& op(op(e2,e0),e0) = e2
& op(e0,e2) != op(e2,e0) )
| ( op(op(e1,e4),e1) != e4
& op(op(e1,e4),e4) = e1
& op(e4,e1) != op(e1,e4) )
| ( op(op(e1,e3),e1) != e3
& op(op(e1,e3),e3) = e1
& op(e3,e1) != op(e1,e3) )
| ( op(op(e1,e2),e1) != e2
& op(op(e1,e2),e2) = e1
& op(e2,e1) != op(e1,e2) )
| ( op(op(e1,e1),e1) != e1
& op(op(e1,e1),e1) = e1
& op(e1,e1) != op(e1,e1) )
| ( op(op(e1,e0),e1) != e0
& op(op(e1,e0),e0) = e1
& op(e0,e1) != op(e1,e0) )
| ( op(op(e0,e4),e0) != e4
& op(op(e0,e4),e4) = e0
& op(e4,e0) != op(e0,e4) )
| ( op(op(e0,e3),e0) != e3
& op(op(e0,e3),e3) = e0
& op(e3,e0) != op(e0,e3) )
| ( op(op(e0,e2),e0) != e2
& op(op(e0,e2),e2) = e0
& op(e2,e0) != op(e0,e2) )
| ( op(op(e0,e1),e0) != e1
& op(op(e0,e1),e1) = e0
& op(e1,e0) != op(e0,e1) )
| ( op(op(e0,e0),e0) != e0
& op(op(e0,e0),e0) = e0
& op(e0,e0) != op(e0,e0) ) )
& ( ( ( ( e4 != unit
& op(e4,e4) = e4 )
| op(e4,e4) != e4 )
& ( ( e4 != unit
& op(e4,e4) = e3 )
| op(e4,e3) != e4 )
& ( ( e4 != unit
& op(e4,e4) = e2 )
| op(e4,e2) != e4 )
& ( ( e4 != unit
& op(e4,e4) = e1 )
| op(e4,e1) != e4 )
& ( ( e4 != unit
& op(e4,e4) = e0 )
| op(e4,e0) != e4 )
& ( ( e4 != unit
& op(e3,e4) = e4 )
| op(e3,e4) != e4 )
& ( ( e4 != unit
& op(e3,e4) = e3 )
| op(e3,e3) != e4 )
& ( ( e4 != unit
& op(e3,e4) = e2 )
| op(e3,e2) != e4 )
& ( ( e4 != unit
& op(e3,e4) = e1 )
| op(e3,e1) != e4 )
& ( ( e4 != unit
& op(e3,e4) = e0 )
| op(e3,e0) != e4 )
& ( ( e4 != unit
& op(e2,e4) = e4 )
| op(e2,e4) != e4 )
& ( ( e4 != unit
& op(e2,e4) = e3 )
| op(e2,e3) != e4 )
& ( ( e4 != unit
& op(e2,e4) = e2 )
| op(e2,e2) != e4 )
& ( ( e4 != unit
& op(e2,e4) = e1 )
| op(e2,e1) != e4 )
& ( ( e4 != unit
& op(e2,e4) = e0 )
| op(e2,e0) != e4 )
& ( ( e4 != unit
& op(e1,e4) = e4 )
| op(e1,e4) != e4 )
& ( ( e4 != unit
& op(e1,e4) = e3 )
| op(e1,e3) != e4 )
& ( ( e4 != unit
& op(e1,e4) = e2 )
| op(e1,e2) != e4 )
& ( ( e4 != unit
& op(e1,e4) = e1 )
| op(e1,e1) != e4 )
& ( ( e4 != unit
& op(e1,e4) = e0 )
| op(e1,e0) != e4 )
& ( ( e4 != unit
& op(e0,e4) = e4 )
| op(e0,e4) != e4 )
& ( ( e4 != unit
& op(e0,e4) = e3 )
| op(e0,e3) != e4 )
& ( ( e4 != unit
& op(e0,e4) = e2 )
| op(e0,e2) != e4 )
& ( ( e4 != unit
& op(e0,e4) = e1 )
| op(e0,e1) != e4 )
& ( ( e4 != unit
& op(e0,e4) = e0 )
| op(e0,e0) != e4 ) )
| ( ( ( e3 != unit
& op(e4,e3) = e4 )
| op(e4,e4) != e3 )
& ( ( e3 != unit
& op(e4,e3) = e3 )
| op(e4,e3) != e3 )
& ( ( e3 != unit
& op(e4,e3) = e2 )
| op(e4,e2) != e3 )
& ( ( e3 != unit
& op(e4,e3) = e1 )
| op(e4,e1) != e3 )
& ( ( e3 != unit
& op(e4,e3) = e0 )
| op(e4,e0) != e3 )
& ( ( e3 != unit
& op(e3,e3) = e4 )
| op(e3,e4) != e3 )
& ( ( e3 != unit
& op(e3,e3) = e3 )
| op(e3,e3) != e3 )
& ( ( e3 != unit
& op(e3,e3) = e2 )
| op(e3,e2) != e3 )
& ( ( e3 != unit
& op(e3,e3) = e1 )
| op(e3,e1) != e3 )
& ( ( e3 != unit
& op(e3,e3) = e0 )
| op(e3,e0) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e4 )
| op(e2,e4) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e3 )
| op(e2,e3) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e2 )
| op(e2,e2) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e1 )
| op(e2,e1) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e0 )
| op(e2,e0) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e4 )
| op(e1,e4) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e3 )
| op(e1,e3) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e2 )
| op(e1,e2) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e1 )
| op(e1,e1) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e0 )
| op(e1,e0) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e4 )
| op(e0,e4) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e3 )
| op(e0,e3) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e2 )
| op(e0,e2) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e1 )
| op(e0,e1) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e0 )
| op(e0,e0) != e3 ) )
| ( ( ( e2 != unit
& op(e4,e2) = e4 )
| op(e4,e4) != e2 )
& ( ( e2 != unit
& op(e4,e2) = e3 )
| op(e4,e3) != e2 )
& ( ( e2 != unit
& op(e4,e2) = e2 )
| op(e4,e2) != e2 )
& ( ( e2 != unit
& op(e4,e2) = e1 )
| op(e4,e1) != e2 )
& ( ( e2 != unit
& op(e4,e2) = e0 )
| op(e4,e0) != e2 )
& ( ( e2 != unit
& op(e3,e2) = e4 )
| op(e3,e4) != e2 )
& ( ( e2 != unit
& op(e3,e2) = e3 )
| op(e3,e3) != e2 )
& ( ( e2 != unit
& op(e3,e2) = e2 )
| op(e3,e2) != e2 )
& ( ( e2 != unit
& op(e3,e2) = e1 )
| op(e3,e1) != e2 )
& ( ( e2 != unit
& op(e3,e2) = e0 )
| op(e3,e0) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e4 )
| op(e2,e4) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e3 )
| op(e2,e3) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e2 )
| op(e2,e2) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e1 )
| op(e2,e1) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e0 )
| op(e2,e0) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e4 )
| op(e1,e4) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e3 )
| op(e1,e3) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e2 )
| op(e1,e2) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e1 )
| op(e1,e1) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e0 )
| op(e1,e0) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e4 )
| op(e0,e4) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e3 )
| op(e0,e3) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e2 )
| op(e0,e2) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e1 )
| op(e0,e1) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e0 )
| op(e0,e0) != e2 ) )
| ( ( ( e1 != unit
& op(e4,e1) = e4 )
| op(e4,e4) != e1 )
& ( ( e1 != unit
& op(e4,e1) = e3 )
| op(e4,e3) != e1 )
& ( ( e1 != unit
& op(e4,e1) = e2 )
| op(e4,e2) != e1 )
& ( ( e1 != unit
& op(e4,e1) = e1 )
| op(e4,e1) != e1 )
& ( ( e1 != unit
& op(e4,e1) = e0 )
| op(e4,e0) != e1 )
& ( ( e1 != unit
& op(e3,e1) = e4 )
| op(e3,e4) != e1 )
& ( ( e1 != unit
& op(e3,e1) = e3 )
| op(e3,e3) != e1 )
& ( ( e1 != unit
& op(e3,e1) = e2 )
| op(e3,e2) != e1 )
& ( ( e1 != unit
& op(e3,e1) = e1 )
| op(e3,e1) != e1 )
& ( ( e1 != unit
& op(e3,e1) = e0 )
| op(e3,e0) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e4 )
| op(e2,e4) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e3 )
| op(e2,e3) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e2 )
| op(e2,e2) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e1 )
| op(e2,e1) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e0 )
| op(e2,e0) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e4 )
| op(e1,e4) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e3 )
| op(e1,e3) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e2 )
| op(e1,e2) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e1 )
| op(e1,e1) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e0 )
| op(e1,e0) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e4 )
| op(e0,e4) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e3 )
| op(e0,e3) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e2 )
| op(e0,e2) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e1 )
| op(e0,e1) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e0 )
| op(e0,e0) != e1 ) )
| ( ( ( e0 != unit
& op(e4,e0) = e4 )
| op(e4,e4) != e0 )
& ( ( e0 != unit
& op(e4,e0) = e3 )
| op(e4,e3) != e0 )
& ( ( e0 != unit
& op(e4,e0) = e2 )
| op(e4,e2) != e0 )
& ( ( e0 != unit
& op(e4,e0) = e1 )
| op(e4,e1) != e0 )
& ( ( e0 != unit
& op(e4,e0) = e0 )
| op(e4,e0) != e0 )
& ( ( e0 != unit
& op(e3,e0) = e4 )
| op(e3,e4) != e0 )
& ( ( e0 != unit
& op(e3,e0) = e3 )
| op(e3,e3) != e0 )
& ( ( e0 != unit
& op(e3,e0) = e2 )
| op(e3,e2) != e0 )
& ( ( e0 != unit
& op(e3,e0) = e1 )
| op(e3,e1) != e0 )
& ( ( e0 != unit
& op(e3,e0) = e0 )
| op(e3,e0) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e4 )
| op(e2,e4) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e3 )
| op(e2,e3) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e2 )
| op(e2,e2) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e1 )
| op(e2,e1) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e0 )
| op(e2,e0) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e4 )
| op(e1,e4) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e3 )
| op(e1,e3) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e2 )
| op(e1,e2) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e1 )
| op(e1,e1) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e0 )
| op(e1,e0) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e4 )
| op(e0,e4) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e3 )
| op(e0,e3) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e2 )
| op(e0,e2) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e1 )
| op(e0,e1) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e0 )
| op(e0,e0) != e0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
~ ~ ( ( ( op(op(e4,e4),e4) != e4
& op(op(e4,e4),e4) = e4
& op(e4,e4) != op(e4,e4) )
| ( op(op(e4,e3),e4) != e3
& op(op(e4,e3),e3) = e4
& op(e3,e4) != op(e4,e3) )
| ( op(op(e4,e2),e4) != e2
& op(op(e4,e2),e2) = e4
& op(e2,e4) != op(e4,e2) )
| ( op(op(e4,e1),e4) != e1
& op(op(e4,e1),e1) = e4
& op(e1,e4) != op(e4,e1) )
| ( op(op(e4,e0),e4) != e0
& op(op(e4,e0),e0) = e4
& op(e0,e4) != op(e4,e0) )
| ( op(op(e3,e4),e3) != e4
& op(op(e3,e4),e4) = e3
& op(e4,e3) != op(e3,e4) )
| ( op(op(e3,e3),e3) != e3
& op(op(e3,e3),e3) = e3
& op(e3,e3) != op(e3,e3) )
| ( op(op(e3,e2),e3) != e2
& op(op(e3,e2),e2) = e3
& op(e2,e3) != op(e3,e2) )
| ( op(op(e3,e1),e3) != e1
& op(op(e3,e1),e1) = e3
& op(e1,e3) != op(e3,e1) )
| ( op(op(e3,e0),e3) != e0
& op(op(e3,e0),e0) = e3
& op(e0,e3) != op(e3,e0) )
| ( op(op(e2,e4),e2) != e4
& op(op(e2,e4),e4) = e2
& op(e4,e2) != op(e2,e4) )
| ( op(op(e2,e3),e2) != e3
& op(op(e2,e3),e3) = e2
& op(e3,e2) != op(e2,e3) )
| ( op(op(e2,e2),e2) != e2
& op(op(e2,e2),e2) = e2
& op(e2,e2) != op(e2,e2) )
| ( op(op(e2,e1),e2) != e1
& op(op(e2,e1),e1) = e2
& op(e1,e2) != op(e2,e1) )
| ( op(op(e2,e0),e2) != e0
& op(op(e2,e0),e0) = e2
& op(e0,e2) != op(e2,e0) )
| ( op(op(e1,e4),e1) != e4
& op(op(e1,e4),e4) = e1
& op(e4,e1) != op(e1,e4) )
| ( op(op(e1,e3),e1) != e3
& op(op(e1,e3),e3) = e1
& op(e3,e1) != op(e1,e3) )
| ( op(op(e1,e2),e1) != e2
& op(op(e1,e2),e2) = e1
& op(e2,e1) != op(e1,e2) )
| ( op(op(e1,e1),e1) != e1
& op(op(e1,e1),e1) = e1
& op(e1,e1) != op(e1,e1) )
| ( op(op(e1,e0),e1) != e0
& op(op(e1,e0),e0) = e1
& op(e0,e1) != op(e1,e0) )
| ( op(op(e0,e4),e0) != e4
& op(op(e0,e4),e4) = e0
& op(e4,e0) != op(e0,e4) )
| ( op(op(e0,e3),e0) != e3
& op(op(e0,e3),e3) = e0
& op(e3,e0) != op(e0,e3) )
| ( op(op(e0,e2),e0) != e2
& op(op(e0,e2),e2) = e0
& op(e2,e0) != op(e0,e2) )
| ( op(op(e0,e1),e0) != e1
& op(op(e0,e1),e1) = e0
& op(e1,e0) != op(e0,e1) )
| ( op(op(e0,e0),e0) != e0
& op(op(e0,e0),e0) = e0
& op(e0,e0) != op(e0,e0) ) )
& ( ( ( ( e4 != unit
& op(e4,e4) = e4 )
| op(e4,e4) != e4 )
& ( ( e4 != unit
& op(e4,e4) = e3 )
| op(e4,e3) != e4 )
& ( ( e4 != unit
& op(e4,e4) = e2 )
| op(e4,e2) != e4 )
& ( ( e4 != unit
& op(e4,e4) = e1 )
| op(e4,e1) != e4 )
& ( ( e4 != unit
& op(e4,e4) = e0 )
| op(e4,e0) != e4 )
& ( ( e4 != unit
& op(e3,e4) = e4 )
| op(e3,e4) != e4 )
& ( ( e4 != unit
& op(e3,e4) = e3 )
| op(e3,e3) != e4 )
& ( ( e4 != unit
& op(e3,e4) = e2 )
| op(e3,e2) != e4 )
& ( ( e4 != unit
& op(e3,e4) = e1 )
| op(e3,e1) != e4 )
& ( ( e4 != unit
& op(e3,e4) = e0 )
| op(e3,e0) != e4 )
& ( ( e4 != unit
& op(e2,e4) = e4 )
| op(e2,e4) != e4 )
& ( ( e4 != unit
& op(e2,e4) = e3 )
| op(e2,e3) != e4 )
& ( ( e4 != unit
& op(e2,e4) = e2 )
| op(e2,e2) != e4 )
& ( ( e4 != unit
& op(e2,e4) = e1 )
| op(e2,e1) != e4 )
& ( ( e4 != unit
& op(e2,e4) = e0 )
| op(e2,e0) != e4 )
& ( ( e4 != unit
& op(e1,e4) = e4 )
| op(e1,e4) != e4 )
& ( ( e4 != unit
& op(e1,e4) = e3 )
| op(e1,e3) != e4 )
& ( ( e4 != unit
& op(e1,e4) = e2 )
| op(e1,e2) != e4 )
& ( ( e4 != unit
& op(e1,e4) = e1 )
| op(e1,e1) != e4 )
& ( ( e4 != unit
& op(e1,e4) = e0 )
| op(e1,e0) != e4 )
& ( ( e4 != unit
& op(e0,e4) = e4 )
| op(e0,e4) != e4 )
& ( ( e4 != unit
& op(e0,e4) = e3 )
| op(e0,e3) != e4 )
& ( ( e4 != unit
& op(e0,e4) = e2 )
| op(e0,e2) != e4 )
& ( ( e4 != unit
& op(e0,e4) = e1 )
| op(e0,e1) != e4 )
& ( ( e4 != unit
& op(e0,e4) = e0 )
| op(e0,e0) != e4 ) )
| ( ( ( e3 != unit
& op(e4,e3) = e4 )
| op(e4,e4) != e3 )
& ( ( e3 != unit
& op(e4,e3) = e3 )
| op(e4,e3) != e3 )
& ( ( e3 != unit
& op(e4,e3) = e2 )
| op(e4,e2) != e3 )
& ( ( e3 != unit
& op(e4,e3) = e1 )
| op(e4,e1) != e3 )
& ( ( e3 != unit
& op(e4,e3) = e0 )
| op(e4,e0) != e3 )
& ( ( e3 != unit
& op(e3,e3) = e4 )
| op(e3,e4) != e3 )
& ( ( e3 != unit
& op(e3,e3) = e3 )
| op(e3,e3) != e3 )
& ( ( e3 != unit
& op(e3,e3) = e2 )
| op(e3,e2) != e3 )
& ( ( e3 != unit
& op(e3,e3) = e1 )
| op(e3,e1) != e3 )
& ( ( e3 != unit
& op(e3,e3) = e0 )
| op(e3,e0) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e4 )
| op(e2,e4) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e3 )
| op(e2,e3) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e2 )
| op(e2,e2) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e1 )
| op(e2,e1) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e0 )
| op(e2,e0) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e4 )
| op(e1,e4) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e3 )
| op(e1,e3) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e2 )
| op(e1,e2) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e1 )
| op(e1,e1) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e0 )
| op(e1,e0) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e4 )
| op(e0,e4) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e3 )
| op(e0,e3) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e2 )
| op(e0,e2) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e1 )
| op(e0,e1) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e0 )
| op(e0,e0) != e3 ) )
| ( ( ( e2 != unit
& op(e4,e2) = e4 )
| op(e4,e4) != e2 )
& ( ( e2 != unit
& op(e4,e2) = e3 )
| op(e4,e3) != e2 )
& ( ( e2 != unit
& op(e4,e2) = e2 )
| op(e4,e2) != e2 )
& ( ( e2 != unit
& op(e4,e2) = e1 )
| op(e4,e1) != e2 )
& ( ( e2 != unit
& op(e4,e2) = e0 )
| op(e4,e0) != e2 )
& ( ( e2 != unit
& op(e3,e2) = e4 )
| op(e3,e4) != e2 )
& ( ( e2 != unit
& op(e3,e2) = e3 )
| op(e3,e3) != e2 )
& ( ( e2 != unit
& op(e3,e2) = e2 )
| op(e3,e2) != e2 )
& ( ( e2 != unit
& op(e3,e2) = e1 )
| op(e3,e1) != e2 )
& ( ( e2 != unit
& op(e3,e2) = e0 )
| op(e3,e0) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e4 )
| op(e2,e4) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e3 )
| op(e2,e3) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e2 )
| op(e2,e2) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e1 )
| op(e2,e1) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e0 )
| op(e2,e0) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e4 )
| op(e1,e4) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e3 )
| op(e1,e3) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e2 )
| op(e1,e2) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e1 )
| op(e1,e1) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e0 )
| op(e1,e0) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e4 )
| op(e0,e4) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e3 )
| op(e0,e3) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e2 )
| op(e0,e2) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e1 )
| op(e0,e1) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e0 )
| op(e0,e0) != e2 ) )
| ( ( ( e1 != unit
& op(e4,e1) = e4 )
| op(e4,e4) != e1 )
& ( ( e1 != unit
& op(e4,e1) = e3 )
| op(e4,e3) != e1 )
& ( ( e1 != unit
& op(e4,e1) = e2 )
| op(e4,e2) != e1 )
& ( ( e1 != unit
& op(e4,e1) = e1 )
| op(e4,e1) != e1 )
& ( ( e1 != unit
& op(e4,e1) = e0 )
| op(e4,e0) != e1 )
& ( ( e1 != unit
& op(e3,e1) = e4 )
| op(e3,e4) != e1 )
& ( ( e1 != unit
& op(e3,e1) = e3 )
| op(e3,e3) != e1 )
& ( ( e1 != unit
& op(e3,e1) = e2 )
| op(e3,e2) != e1 )
& ( ( e1 != unit
& op(e3,e1) = e1 )
| op(e3,e1) != e1 )
& ( ( e1 != unit
& op(e3,e1) = e0 )
| op(e3,e0) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e4 )
| op(e2,e4) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e3 )
| op(e2,e3) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e2 )
| op(e2,e2) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e1 )
| op(e2,e1) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e0 )
| op(e2,e0) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e4 )
| op(e1,e4) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e3 )
| op(e1,e3) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e2 )
| op(e1,e2) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e1 )
| op(e1,e1) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e0 )
| op(e1,e0) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e4 )
| op(e0,e4) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e3 )
| op(e0,e3) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e2 )
| op(e0,e2) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e1 )
| op(e0,e1) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e0 )
| op(e0,e0) != e1 ) )
| ( ( ( e0 != unit
& op(e4,e0) = e4 )
| op(e4,e4) != e0 )
& ( ( e0 != unit
& op(e4,e0) = e3 )
| op(e4,e3) != e0 )
& ( ( e0 != unit
& op(e4,e0) = e2 )
| op(e4,e2) != e0 )
& ( ( e0 != unit
& op(e4,e0) = e1 )
| op(e4,e1) != e0 )
& ( ( e0 != unit
& op(e4,e0) = e0 )
| op(e4,e0) != e0 )
& ( ( e0 != unit
& op(e3,e0) = e4 )
| op(e3,e4) != e0 )
& ( ( e0 != unit
& op(e3,e0) = e3 )
| op(e3,e3) != e0 )
& ( ( e0 != unit
& op(e3,e0) = e2 )
| op(e3,e2) != e0 )
& ( ( e0 != unit
& op(e3,e0) = e1 )
| op(e3,e1) != e0 )
& ( ( e0 != unit
& op(e3,e0) = e0 )
| op(e3,e0) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e4 )
| op(e2,e4) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e3 )
| op(e2,e3) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e2 )
| op(e2,e2) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e1 )
| op(e2,e1) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e0 )
| op(e2,e0) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e4 )
| op(e1,e4) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e3 )
| op(e1,e3) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e2 )
| op(e1,e2) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e1 )
| op(e1,e1) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e0 )
| op(e1,e0) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e4 )
| op(e0,e4) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e3 )
| op(e0,e3) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e2 )
| op(e0,e2) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e1 )
| op(e0,e1) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e0 )
| op(e0,e0) != e0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f11,plain,
( op(e0,e2) = e4
| op(e0,e2) = e3
| op(e0,e2) = e2
| op(e0,e2) = e1
| op(e0,e2) = e0 ),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f17,plain,
( op(e1,e3) = e4
| op(e1,e3) = e3
| op(e1,e3) = e2
| op(e1,e3) = e1
| op(e1,e3) = e0 ),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f22,plain,
( op(e2,e3) = e4
| op(e2,e3) = e3
| op(e2,e3) = e2
| op(e2,e3) = e1
| op(e2,e3) = e0 ),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f25,plain,
( op(e3,e1) = e4
| op(e3,e1) = e3
| op(e3,e1) = e2
| op(e3,e1) = e1
| op(e3,e1) = e0 ),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f27,plain,
( op(e3,e3) = e4
| op(e3,e3) = e3
| op(e3,e3) = e2
| op(e3,e3) = e1
| op(e3,e3) = e0 ),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f34,plain,
op(unit,e0) = e0,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f35,plain,
op(e0,unit) = e0,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f36,plain,
op(unit,e1) = e1,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f37,plain,
op(e1,unit) = e1,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f38,plain,
op(unit,e2) = e2,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f39,plain,
op(e2,unit) = e2,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f40,plain,
op(unit,e3) = e3,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f41,plain,
op(e3,unit) = e3,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f42,plain,
op(unit,e4) = e4,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f43,plain,
op(e4,unit) = e4,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f44,plain,
( unit = e4
| unit = e3
| unit = e2
| unit = e1
| unit = e0 ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f47,plain,
( op(e0,e4) = e1
| op(e0,e3) = e1
| op(e0,e2) = e1
| op(e0,e1) = e1
| op(e0,e0) = e1 ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f48,plain,
( op(e4,e0) = e1
| op(e3,e0) = e1
| op(e2,e0) = e1
| op(e1,e0) = e1
| op(e0,e0) = e1 ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f52,plain,
( op(e4,e0) = e3
| op(e3,e0) = e3
| op(e2,e0) = e3
| op(e1,e0) = e3
| op(e0,e0) = e3 ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f61,plain,
( op(e1,e4) = e3
| op(e1,e3) = e3
| op(e1,e2) = e3
| op(e1,e1) = e3
| op(e1,e0) = e3 ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f62,plain,
( op(e4,e1) = e3
| op(e3,e1) = e3
| op(e2,e1) = e3
| op(e1,e1) = e3
| op(e0,e1) = e3 ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f66,plain,
( op(e4,e2) = e0
| op(e3,e2) = e0
| op(e2,e2) = e0
| op(e1,e2) = e0
| op(e0,e2) = e0 ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f73,plain,
( op(e2,e4) = e4
| op(e2,e3) = e4
| op(e2,e2) = e4
| op(e2,e1) = e4
| op(e2,e0) = e4 ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f74,plain,
( op(e4,e2) = e4
| op(e3,e2) = e4
| op(e2,e2) = e4
| op(e1,e2) = e4
| op(e0,e2) = e4 ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f75,plain,
( op(e3,e4) = e0
| op(e3,e3) = e0
| op(e3,e2) = e0
| op(e3,e1) = e0
| op(e3,e0) = e0 ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f76,plain,
( op(e4,e3) = e0
| op(e3,e3) = e0
| op(e2,e3) = e0
| op(e1,e3) = e0
| op(e0,e3) = e0 ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f87,plain,
( op(e4,e4) = e1
| op(e4,e3) = e1
| op(e4,e2) = e1
| op(e4,e1) = e1
| op(e4,e0) = e1 ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f88,plain,
( op(e4,e4) = e1
| op(e3,e4) = e1
| op(e2,e4) = e1
| op(e1,e4) = e1
| op(e0,e4) = e1 ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f97,plain,
op(e0,e0) != op(e3,e0),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f103,plain,
op(e2,e0) != op(e4,e0),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f105,plain,
op(e0,e1) != op(e1,e1),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f108,plain,
op(e0,e1) != op(e4,e1),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f109,plain,
op(e1,e1) != op(e2,e1),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f110,plain,
op(e1,e1) != op(e3,e1),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f112,plain,
op(e2,e1) != op(e3,e1),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f114,plain,
op(e3,e1) != op(e4,e1),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f116,plain,
op(e0,e2) != op(e2,e2),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f117,plain,
op(e0,e2) != op(e3,e2),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f119,plain,
op(e1,e2) != op(e2,e2),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f121,plain,
op(e1,e2) != op(e4,e2),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f123,plain,
op(e2,e2) != op(e4,e2),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f124,plain,
op(e3,e2) != op(e4,e2),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f125,plain,
op(e0,e3) != op(e1,e3),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f127,plain,
op(e0,e3) != op(e3,e3),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f130,plain,
op(e1,e3) != op(e3,e3),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f131,plain,
op(e1,e3) != op(e4,e3),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f132,plain,
op(e2,e3) != op(e3,e3),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f136,plain,
op(e0,e4) != op(e2,e4),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f137,plain,
op(e0,e4) != op(e3,e4),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f146,plain,
op(e0,e0) != op(e0,e2),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f150,plain,
op(e0,e1) != op(e0,e3),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f153,plain,
op(e0,e2) != op(e0,e4),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f154,plain,
op(e0,e3) != op(e0,e4),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f155,plain,
op(e1,e0) != op(e1,e1),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f159,plain,
op(e1,e1) != op(e1,e2),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f160,plain,
op(e1,e1) != op(e1,e3),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f161,plain,
op(e1,e1) != op(e1,e4),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f166,plain,
op(e2,e0) != op(e2,e2),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f167,plain,
op(e2,e0) != op(e2,e3),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f169,plain,
op(e2,e1) != op(e2,e2),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f172,plain,
op(e2,e2) != op(e2,e3),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f173,plain,
op(e2,e2) != op(e2,e4),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f175,plain,
op(e3,e0) != op(e3,e1),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f177,plain,
op(e3,e0) != op(e3,e3),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f179,plain,
op(e3,e1) != op(e3,e2),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f180,plain,
op(e3,e1) != op(e3,e3),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f181,plain,
op(e3,e1) != op(e3,e4),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f184,plain,
op(e3,e3) != op(e3,e4),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f185,plain,
op(e4,e0) != op(e4,e1),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f187,plain,
op(e4,e0) != op(e4,e3),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f188,plain,
op(e4,e0) != op(e4,e4),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f191,plain,
op(e4,e1) != op(e4,e4),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f192,plain,
op(e4,e2) != op(e4,e3),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f194,plain,
op(e4,e3) != op(e4,e4),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f195,plain,
e0 != e1,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f196,plain,
e0 != e2,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f197,plain,
e0 != e3,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f198,plain,
e0 != e4,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f199,plain,
e1 != e2,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f200,plain,
e1 != e3,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f201,plain,
e1 != e4,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f202,plain,
e2 != e3,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f203,plain,
e2 != e4,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f204,plain,
e3 != e4,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f205,plain,
e0 = op(op(op(e2,e2),e2),op(op(e2,e2),e2)),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f206,plain,
e1 = op(op(e2,e2),e2),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f207,plain,
e3 = op(e2,e2),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f208,plain,
e4 = op(op(e2,e2),op(e2,e2)),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f209,definition,
( sP0_prd
<=> ( ( ( ( e3 != unit
& op(e4,e3) = e4 )
| op(e4,e4) != e3 )
& ( ( e3 != unit
& op(e4,e3) = e3 )
| op(e4,e3) != e3 )
& ( ( e3 != unit
& op(e4,e3) = e2 )
| op(e4,e2) != e3 )
& ( ( e3 != unit
& op(e4,e3) = e1 )
| op(e4,e1) != e3 )
& ( ( e3 != unit
& op(e4,e3) = e0 )
| op(e4,e0) != e3 )
& ( ( e3 != unit
& op(e3,e3) = e4 )
| op(e3,e4) != e3 )
& ( ( e3 != unit
& op(e3,e3) = e3 )
| op(e3,e3) != e3 )
& ( ( e3 != unit
& op(e3,e3) = e2 )
| op(e3,e2) != e3 )
& ( ( e3 != unit
& op(e3,e3) = e1 )
| op(e3,e1) != e3 )
& ( ( e3 != unit
& op(e3,e3) = e0 )
| op(e3,e0) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e4 )
| op(e2,e4) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e3 )
| op(e2,e3) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e2 )
| op(e2,e2) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e1 )
| op(e2,e1) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e0 )
| op(e2,e0) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e4 )
| op(e1,e4) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e3 )
| op(e1,e3) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e2 )
| op(e1,e2) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e1 )
| op(e1,e1) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e0 )
| op(e1,e0) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e4 )
| op(e0,e4) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e3 )
| op(e0,e3) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e2 )
| op(e0,e2) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e1 )
| op(e0,e1) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e0 )
| op(e0,e0) != e3 ) )
| ( ( ( e2 != unit
& op(e4,e2) = e4 )
| op(e4,e4) != e2 )
& ( ( e2 != unit
& op(e4,e2) = e3 )
| op(e4,e3) != e2 )
& ( ( e2 != unit
& op(e4,e2) = e2 )
| op(e4,e2) != e2 )
& ( ( e2 != unit
& op(e4,e2) = e1 )
| op(e4,e1) != e2 )
& ( ( e2 != unit
& op(e4,e2) = e0 )
| op(e4,e0) != e2 )
& ( ( e2 != unit
& op(e3,e2) = e4 )
| op(e3,e4) != e2 )
& ( ( e2 != unit
& op(e3,e2) = e3 )
| op(e3,e3) != e2 )
& ( ( e2 != unit
& op(e3,e2) = e2 )
| op(e3,e2) != e2 )
& ( ( e2 != unit
& op(e3,e2) = e1 )
| op(e3,e1) != e2 )
& ( ( e2 != unit
& op(e3,e2) = e0 )
| op(e3,e0) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e4 )
| op(e2,e4) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e3 )
| op(e2,e3) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e2 )
| op(e2,e2) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e1 )
| op(e2,e1) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e0 )
| op(e2,e0) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e4 )
| op(e1,e4) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e3 )
| op(e1,e3) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e2 )
| op(e1,e2) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e1 )
| op(e1,e1) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e0 )
| op(e1,e0) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e4 )
| op(e0,e4) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e3 )
| op(e0,e3) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e2 )
| op(e0,e2) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e1 )
| op(e0,e1) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e0 )
| op(e0,e0) != e2 ) )
| ( ( ( e1 != unit
& op(e4,e1) = e4 )
| op(e4,e4) != e1 )
& ( ( e1 != unit
& op(e4,e1) = e3 )
| op(e4,e3) != e1 )
& ( ( e1 != unit
& op(e4,e1) = e2 )
| op(e4,e2) != e1 )
& ( ( e1 != unit
& op(e4,e1) = e1 )
| op(e4,e1) != e1 )
& ( ( e1 != unit
& op(e4,e1) = e0 )
| op(e4,e0) != e1 )
& ( ( e1 != unit
& op(e3,e1) = e4 )
| op(e3,e4) != e1 )
& ( ( e1 != unit
& op(e3,e1) = e3 )
| op(e3,e3) != e1 )
& ( ( e1 != unit
& op(e3,e1) = e2 )
| op(e3,e2) != e1 )
& ( ( e1 != unit
& op(e3,e1) = e1 )
| op(e3,e1) != e1 )
& ( ( e1 != unit
& op(e3,e1) = e0 )
| op(e3,e0) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e4 )
| op(e2,e4) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e3 )
| op(e2,e3) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e2 )
| op(e2,e2) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e1 )
| op(e2,e1) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e0 )
| op(e2,e0) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e4 )
| op(e1,e4) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e3 )
| op(e1,e3) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e2 )
| op(e1,e2) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e1 )
| op(e1,e1) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e0 )
| op(e1,e0) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e4 )
| op(e0,e4) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e3 )
| op(e0,e3) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e2 )
| op(e0,e2) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e1 )
| op(e0,e1) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e0 )
| op(e0,e0) != e1 ) )
| ( ( ( e0 != unit
& op(e4,e0) = e4 )
| op(e4,e4) != e0 )
& ( ( e0 != unit
& op(e4,e0) = e3 )
| op(e4,e3) != e0 )
& ( ( e0 != unit
& op(e4,e0) = e2 )
| op(e4,e2) != e0 )
& ( ( e0 != unit
& op(e4,e0) = e1 )
| op(e4,e1) != e0 )
& ( ( e0 != unit
& op(e4,e0) = e0 )
| op(e4,e0) != e0 )
& ( ( e0 != unit
& op(e3,e0) = e4 )
| op(e3,e4) != e0 )
& ( ( e0 != unit
& op(e3,e0) = e3 )
| op(e3,e3) != e0 )
& ( ( e0 != unit
& op(e3,e0) = e2 )
| op(e3,e2) != e0 )
& ( ( e0 != unit
& op(e3,e0) = e1 )
| op(e3,e1) != e0 )
& ( ( e0 != unit
& op(e3,e0) = e0 )
| op(e3,e0) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e4 )
| op(e2,e4) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e3 )
| op(e2,e3) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e2 )
| op(e2,e2) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e1 )
| op(e2,e1) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e0 )
| op(e2,e0) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e4 )
| op(e1,e4) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e3 )
| op(e1,e3) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e2 )
| op(e1,e2) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e1 )
| op(e1,e1) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e0 )
| op(e1,e0) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e4 )
| op(e0,e4) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e3 )
| op(e0,e3) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e2 )
| op(e0,e2) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e1 )
| op(e0,e1) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e0 )
| op(e0,e0) != e0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f210,definition,
( sP1_prd
<=> ( ( op(op(e4,e3),e4) != e3
& op(op(e4,e3),e3) = e4
& op(e3,e4) != op(e4,e3) )
| ( op(op(e4,e2),e4) != e2
& op(op(e4,e2),e2) = e4
& op(e2,e4) != op(e4,e2) )
| ( op(op(e4,e1),e4) != e1
& op(op(e4,e1),e1) = e4
& op(e1,e4) != op(e4,e1) )
| ( op(op(e4,e0),e4) != e0
& op(op(e4,e0),e0) = e4
& op(e0,e4) != op(e4,e0) )
| ( op(op(e3,e4),e3) != e4
& op(op(e3,e4),e4) = e3
& op(e4,e3) != op(e3,e4) )
| ( op(op(e3,e3),e3) != e3
& op(op(e3,e3),e3) = e3
& op(e3,e3) != op(e3,e3) )
| ( op(op(e3,e2),e3) != e2
& op(op(e3,e2),e2) = e3
& op(e2,e3) != op(e3,e2) )
| ( op(op(e3,e1),e3) != e1
& op(op(e3,e1),e1) = e3
& op(e1,e3) != op(e3,e1) )
| ( op(op(e3,e0),e3) != e0
& op(op(e3,e0),e0) = e3
& op(e0,e3) != op(e3,e0) )
| ( op(op(e2,e4),e2) != e4
& op(op(e2,e4),e4) = e2
& op(e4,e2) != op(e2,e4) )
| ( op(op(e2,e3),e2) != e3
& op(op(e2,e3),e3) = e2
& op(e3,e2) != op(e2,e3) )
| ( op(op(e2,e2),e2) != e2
& op(op(e2,e2),e2) = e2
& op(e2,e2) != op(e2,e2) )
| ( op(op(e2,e1),e2) != e1
& op(op(e2,e1),e1) = e2
& op(e1,e2) != op(e2,e1) )
| ( op(op(e2,e0),e2) != e0
& op(op(e2,e0),e0) = e2
& op(e0,e2) != op(e2,e0) )
| ( op(op(e1,e4),e1) != e4
& op(op(e1,e4),e4) = e1
& op(e4,e1) != op(e1,e4) )
| ( op(op(e1,e3),e1) != e3
& op(op(e1,e3),e3) = e1
& op(e3,e1) != op(e1,e3) )
| ( op(op(e1,e2),e1) != e2
& op(op(e1,e2),e2) = e1
& op(e2,e1) != op(e1,e2) )
| ( op(op(e1,e1),e1) != e1
& op(op(e1,e1),e1) = e1
& op(e1,e1) != op(e1,e1) )
| ( op(op(e1,e0),e1) != e0
& op(op(e1,e0),e0) = e1
& op(e0,e1) != op(e1,e0) )
| ( op(op(e0,e4),e0) != e4
& op(op(e0,e4),e4) = e0
& op(e4,e0) != op(e0,e4) )
| ( op(op(e0,e3),e0) != e3
& op(op(e0,e3),e3) = e0
& op(e3,e0) != op(e0,e3) )
| ( op(op(e0,e2),e0) != e2
& op(op(e0,e2),e2) = e0
& op(e2,e0) != op(e0,e2) )
| ( op(op(e0,e1),e0) != e1
& op(op(e0,e1),e1) = e0
& op(e1,e0) != op(e0,e1) )
| ( op(op(e0,e0),e0) != e0
& op(op(e0,e0),e0) = e0
& op(e0,e0) != op(e0,e0) ) ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f211,plain,
( ( ( op(op(e4,e4),e4) != e4
& op(op(e4,e4),e4) = e4
& op(e4,e4) != op(e4,e4) )
| sP1_prd )
& ( ( ( ( e4 != unit
& op(e4,e4) = e4 )
| op(e4,e4) != e4 )
& ( ( e4 != unit
& op(e4,e4) = e3 )
| op(e4,e3) != e4 )
& ( ( e4 != unit
& op(e4,e4) = e2 )
| op(e4,e2) != e4 )
& ( ( e4 != unit
& op(e4,e4) = e1 )
| op(e4,e1) != e4 )
& ( ( e4 != unit
& op(e4,e4) = e0 )
| op(e4,e0) != e4 )
& ( ( e4 != unit
& op(e3,e4) = e4 )
| op(e3,e4) != e4 )
& ( ( e4 != unit
& op(e3,e4) = e3 )
| op(e3,e3) != e4 )
& ( ( e4 != unit
& op(e3,e4) = e2 )
| op(e3,e2) != e4 )
& ( ( e4 != unit
& op(e3,e4) = e1 )
| op(e3,e1) != e4 )
& ( ( e4 != unit
& op(e3,e4) = e0 )
| op(e3,e0) != e4 )
& ( ( e4 != unit
& op(e2,e4) = e4 )
| op(e2,e4) != e4 )
& ( ( e4 != unit
& op(e2,e4) = e3 )
| op(e2,e3) != e4 )
& ( ( e4 != unit
& op(e2,e4) = e2 )
| op(e2,e2) != e4 )
& ( ( e4 != unit
& op(e2,e4) = e1 )
| op(e2,e1) != e4 )
& ( ( e4 != unit
& op(e2,e4) = e0 )
| op(e2,e0) != e4 )
& ( ( e4 != unit
& op(e1,e4) = e4 )
| op(e1,e4) != e4 )
& ( ( e4 != unit
& op(e1,e4) = e3 )
| op(e1,e3) != e4 )
& ( ( e4 != unit
& op(e1,e4) = e2 )
| op(e1,e2) != e4 )
& ( ( e4 != unit
& op(e1,e4) = e1 )
| op(e1,e1) != e4 )
& ( ( e4 != unit
& op(e1,e4) = e0 )
| op(e1,e0) != e4 )
& ( ( e4 != unit
& op(e0,e4) = e4 )
| op(e0,e4) != e4 )
& ( ( e4 != unit
& op(e0,e4) = e3 )
| op(e0,e3) != e4 )
& ( ( e4 != unit
& op(e0,e4) = e2 )
| op(e0,e2) != e4 )
& ( ( e4 != unit
& op(e0,e4) = e1 )
| op(e0,e1) != e4 )
& ( ( e4 != unit
& op(e0,e4) = e0 )
| op(e0,e0) != e4 ) )
| sP0_prd ) ),
inference(formula_renaming,[status(thm)],[f8,f210,f209]) ).
fof(f248,plain,
( op(e3,e4) = e3
| op(e3,e3) != e4
| sP0_prd ),
inference(cnf_transformation,[status(thm)],[f211]) ).
fof(f249,plain,
( e4 != unit
| op(e3,e3) != e4
| sP0_prd ),
inference(cnf_transformation,[status(thm)],[f211]) ).
fof(f262,plain,
( op(e4,e4) != op(e4,e4)
| sP1_prd ),
inference(cnf_transformation,[status(thm)],[f211]) ).
fof(f265,definition,
( sP2_prd
<=> ( ( ( ( e2 != unit
& op(e4,e2) = e4 )
| op(e4,e4) != e2 )
& ( ( e2 != unit
& op(e4,e2) = e3 )
| op(e4,e3) != e2 )
& ( ( e2 != unit
& op(e4,e2) = e2 )
| op(e4,e2) != e2 )
& ( ( e2 != unit
& op(e4,e2) = e1 )
| op(e4,e1) != e2 )
& ( ( e2 != unit
& op(e4,e2) = e0 )
| op(e4,e0) != e2 )
& ( ( e2 != unit
& op(e3,e2) = e4 )
| op(e3,e4) != e2 )
& ( ( e2 != unit
& op(e3,e2) = e3 )
| op(e3,e3) != e2 )
& ( ( e2 != unit
& op(e3,e2) = e2 )
| op(e3,e2) != e2 )
& ( ( e2 != unit
& op(e3,e2) = e1 )
| op(e3,e1) != e2 )
& ( ( e2 != unit
& op(e3,e2) = e0 )
| op(e3,e0) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e4 )
| op(e2,e4) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e3 )
| op(e2,e3) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e2 )
| op(e2,e2) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e1 )
| op(e2,e1) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e0 )
| op(e2,e0) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e4 )
| op(e1,e4) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e3 )
| op(e1,e3) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e2 )
| op(e1,e2) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e1 )
| op(e1,e1) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e0 )
| op(e1,e0) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e4 )
| op(e0,e4) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e3 )
| op(e0,e3) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e2 )
| op(e0,e2) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e1 )
| op(e0,e1) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e0 )
| op(e0,e0) != e2 ) )
| ( ( ( e1 != unit
& op(e4,e1) = e4 )
| op(e4,e4) != e1 )
& ( ( e1 != unit
& op(e4,e1) = e3 )
| op(e4,e3) != e1 )
& ( ( e1 != unit
& op(e4,e1) = e2 )
| op(e4,e2) != e1 )
& ( ( e1 != unit
& op(e4,e1) = e1 )
| op(e4,e1) != e1 )
& ( ( e1 != unit
& op(e4,e1) = e0 )
| op(e4,e0) != e1 )
& ( ( e1 != unit
& op(e3,e1) = e4 )
| op(e3,e4) != e1 )
& ( ( e1 != unit
& op(e3,e1) = e3 )
| op(e3,e3) != e1 )
& ( ( e1 != unit
& op(e3,e1) = e2 )
| op(e3,e2) != e1 )
& ( ( e1 != unit
& op(e3,e1) = e1 )
| op(e3,e1) != e1 )
& ( ( e1 != unit
& op(e3,e1) = e0 )
| op(e3,e0) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e4 )
| op(e2,e4) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e3 )
| op(e2,e3) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e2 )
| op(e2,e2) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e1 )
| op(e2,e1) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e0 )
| op(e2,e0) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e4 )
| op(e1,e4) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e3 )
| op(e1,e3) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e2 )
| op(e1,e2) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e1 )
| op(e1,e1) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e0 )
| op(e1,e0) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e4 )
| op(e0,e4) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e3 )
| op(e0,e3) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e2 )
| op(e0,e2) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e1 )
| op(e0,e1) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e0 )
| op(e0,e0) != e1 ) )
| ( ( ( e0 != unit
& op(e4,e0) = e4 )
| op(e4,e4) != e0 )
& ( ( e0 != unit
& op(e4,e0) = e3 )
| op(e4,e3) != e0 )
& ( ( e0 != unit
& op(e4,e0) = e2 )
| op(e4,e2) != e0 )
& ( ( e0 != unit
& op(e4,e0) = e1 )
| op(e4,e1) != e0 )
& ( ( e0 != unit
& op(e4,e0) = e0 )
| op(e4,e0) != e0 )
& ( ( e0 != unit
& op(e3,e0) = e4 )
| op(e3,e4) != e0 )
& ( ( e0 != unit
& op(e3,e0) = e3 )
| op(e3,e3) != e0 )
& ( ( e0 != unit
& op(e3,e0) = e2 )
| op(e3,e2) != e0 )
& ( ( e0 != unit
& op(e3,e0) = e1 )
| op(e3,e1) != e0 )
& ( ( e0 != unit
& op(e3,e0) = e0 )
| op(e3,e0) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e4 )
| op(e2,e4) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e3 )
| op(e2,e3) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e2 )
| op(e2,e2) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e1 )
| op(e2,e1) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e0 )
| op(e2,e0) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e4 )
| op(e1,e4) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e3 )
| op(e1,e3) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e2 )
| op(e1,e2) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e1 )
| op(e1,e1) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e0 )
| op(e1,e0) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e4 )
| op(e0,e4) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e3 )
| op(e0,e3) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e2 )
| op(e0,e2) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e1 )
| op(e0,e1) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e0 )
| op(e0,e0) != e0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2_prd])],[]) ).
fof(f266,plain,
( sP0_prd
<=> ( ( ( ( e3 != unit
& op(e4,e3) = e4 )
| op(e4,e4) != e3 )
& ( ( e3 != unit
& op(e4,e3) = e3 )
| op(e4,e3) != e3 )
& ( ( e3 != unit
& op(e4,e3) = e2 )
| op(e4,e2) != e3 )
& ( ( e3 != unit
& op(e4,e3) = e1 )
| op(e4,e1) != e3 )
& ( ( e3 != unit
& op(e4,e3) = e0 )
| op(e4,e0) != e3 )
& ( ( e3 != unit
& op(e3,e3) = e4 )
| op(e3,e4) != e3 )
& ( ( e3 != unit
& op(e3,e3) = e3 )
| op(e3,e3) != e3 )
& ( ( e3 != unit
& op(e3,e3) = e2 )
| op(e3,e2) != e3 )
& ( ( e3 != unit
& op(e3,e3) = e1 )
| op(e3,e1) != e3 )
& ( ( e3 != unit
& op(e3,e3) = e0 )
| op(e3,e0) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e4 )
| op(e2,e4) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e3 )
| op(e2,e3) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e2 )
| op(e2,e2) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e1 )
| op(e2,e1) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e0 )
| op(e2,e0) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e4 )
| op(e1,e4) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e3 )
| op(e1,e3) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e2 )
| op(e1,e2) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e1 )
| op(e1,e1) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e0 )
| op(e1,e0) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e4 )
| op(e0,e4) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e3 )
| op(e0,e3) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e2 )
| op(e0,e2) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e1 )
| op(e0,e1) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e0 )
| op(e0,e0) != e3 ) )
| sP2_prd ) ),
inference(formula_renaming,[status(thm)],[f209,f265]) ).
fof(f267,definition,
( sP3_prd
<=> ( ( ( e3 != unit
& op(e4,e3) = e3 )
| op(e4,e3) != e3 )
& ( ( e3 != unit
& op(e4,e3) = e2 )
| op(e4,e2) != e3 )
& ( ( e3 != unit
& op(e4,e3) = e1 )
| op(e4,e1) != e3 )
& ( ( e3 != unit
& op(e4,e3) = e0 )
| op(e4,e0) != e3 )
& ( ( e3 != unit
& op(e3,e3) = e4 )
| op(e3,e4) != e3 )
& ( ( e3 != unit
& op(e3,e3) = e3 )
| op(e3,e3) != e3 )
& ( ( e3 != unit
& op(e3,e3) = e2 )
| op(e3,e2) != e3 )
& ( ( e3 != unit
& op(e3,e3) = e1 )
| op(e3,e1) != e3 )
& ( ( e3 != unit
& op(e3,e3) = e0 )
| op(e3,e0) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e4 )
| op(e2,e4) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e3 )
| op(e2,e3) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e2 )
| op(e2,e2) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e1 )
| op(e2,e1) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e0 )
| op(e2,e0) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e4 )
| op(e1,e4) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e3 )
| op(e1,e3) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e2 )
| op(e1,e2) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e1 )
| op(e1,e1) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e0 )
| op(e1,e0) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e4 )
| op(e0,e4) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e3 )
| op(e0,e3) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e2 )
| op(e0,e2) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e1 )
| op(e0,e1) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e0 )
| op(e0,e0) != e3 ) ) ),
introduced(definition,[new_symbols(definition,[sP3_prd])],[]) ).
fof(f268,plain,
( sP0_prd
<=> ( ( ( ( e3 != unit
& op(e4,e3) = e4 )
| op(e4,e4) != e3 )
& sP3_prd )
| sP2_prd ) ),
inference(formula_renaming,[status(thm)],[f266,f267]) ).
fof(f269,plain,
( ( ( ( ( ( e3 = unit
| op(e4,e3) != e4 )
& op(e4,e4) = e3 )
| ~ sP3_prd )
& ~ sP2_prd )
| sP0_prd )
& ( ( ( ( e3 != unit
& op(e4,e3) = e4 )
| op(e4,e4) != e3 )
& sP3_prd )
| sP2_prd
| ~ sP0_prd ) ),
inference(NNF_transformation,[status(thm)],[f268]) ).
fof(f270,plain,
( sP3_prd
| sP2_prd
| ~ sP0_prd ),
inference(cnf_transformation,[status(thm)],[f269]) ).
fof(f276,definition,
( sP4_prd
<=> ( ( op(op(e4,e2),e4) != e2
& op(op(e4,e2),e2) = e4
& op(e2,e4) != op(e4,e2) )
| ( op(op(e4,e1),e4) != e1
& op(op(e4,e1),e1) = e4
& op(e1,e4) != op(e4,e1) )
| ( op(op(e4,e0),e4) != e0
& op(op(e4,e0),e0) = e4
& op(e0,e4) != op(e4,e0) )
| ( op(op(e3,e4),e3) != e4
& op(op(e3,e4),e4) = e3
& op(e4,e3) != op(e3,e4) )
| ( op(op(e3,e3),e3) != e3
& op(op(e3,e3),e3) = e3
& op(e3,e3) != op(e3,e3) )
| ( op(op(e3,e2),e3) != e2
& op(op(e3,e2),e2) = e3
& op(e2,e3) != op(e3,e2) )
| ( op(op(e3,e1),e3) != e1
& op(op(e3,e1),e1) = e3
& op(e1,e3) != op(e3,e1) )
| ( op(op(e3,e0),e3) != e0
& op(op(e3,e0),e0) = e3
& op(e0,e3) != op(e3,e0) )
| ( op(op(e2,e4),e2) != e4
& op(op(e2,e4),e4) = e2
& op(e4,e2) != op(e2,e4) )
| ( op(op(e2,e3),e2) != e3
& op(op(e2,e3),e3) = e2
& op(e3,e2) != op(e2,e3) )
| ( op(op(e2,e2),e2) != e2
& op(op(e2,e2),e2) = e2
& op(e2,e2) != op(e2,e2) )
| ( op(op(e2,e1),e2) != e1
& op(op(e2,e1),e1) = e2
& op(e1,e2) != op(e2,e1) )
| ( op(op(e2,e0),e2) != e0
& op(op(e2,e0),e0) = e2
& op(e0,e2) != op(e2,e0) )
| ( op(op(e1,e4),e1) != e4
& op(op(e1,e4),e4) = e1
& op(e4,e1) != op(e1,e4) )
| ( op(op(e1,e3),e1) != e3
& op(op(e1,e3),e3) = e1
& op(e3,e1) != op(e1,e3) )
| ( op(op(e1,e2),e1) != e2
& op(op(e1,e2),e2) = e1
& op(e2,e1) != op(e1,e2) )
| ( op(op(e1,e1),e1) != e1
& op(op(e1,e1),e1) = e1
& op(e1,e1) != op(e1,e1) )
| ( op(op(e1,e0),e1) != e0
& op(op(e1,e0),e0) = e1
& op(e0,e1) != op(e1,e0) )
| ( op(op(e0,e4),e0) != e4
& op(op(e0,e4),e4) = e0
& op(e4,e0) != op(e0,e4) )
| ( op(op(e0,e3),e0) != e3
& op(op(e0,e3),e3) = e0
& op(e3,e0) != op(e0,e3) )
| ( op(op(e0,e2),e0) != e2
& op(op(e0,e2),e2) = e0
& op(e2,e0) != op(e0,e2) )
| ( op(op(e0,e1),e0) != e1
& op(op(e0,e1),e1) = e0
& op(e1,e0) != op(e0,e1) )
| ( op(op(e0,e0),e0) != e0
& op(op(e0,e0),e0) = e0
& op(e0,e0) != op(e0,e0) ) ) ),
introduced(definition,[new_symbols(definition,[sP4_prd])],[]) ).
fof(f277,plain,
( sP1_prd
<=> ( ( op(op(e4,e3),e4) != e3
& op(op(e4,e3),e3) = e4
& op(e3,e4) != op(e4,e3) )
| sP4_prd ) ),
inference(formula_renaming,[status(thm)],[f210,f276]) ).
fof(f278,plain,
( ( ( ( op(op(e4,e3),e4) = e3
| op(op(e4,e3),e3) != e4
| op(e3,e4) = op(e4,e3) )
& ~ sP4_prd )
| sP1_prd )
& ( ( op(op(e4,e3),e4) != e3
& op(op(e4,e3),e3) = e4
& op(e3,e4) != op(e4,e3) )
| sP4_prd
| ~ sP1_prd ) ),
inference(NNF_transformation,[status(thm)],[f277]) ).
fof(f279,plain,
( op(e3,e4) != op(e4,e3)
| sP4_prd
| ~ sP1_prd ),
inference(cnf_transformation,[status(thm)],[f278]) ).
fof(f280,plain,
( op(op(e4,e3),e3) = e4
| sP4_prd
| ~ sP1_prd ),
inference(cnf_transformation,[status(thm)],[f278]) ).
fof(f284,definition,
( sP5_prd
<=> ( ( ( ( e1 != unit
& op(e4,e1) = e4 )
| op(e4,e4) != e1 )
& ( ( e1 != unit
& op(e4,e1) = e3 )
| op(e4,e3) != e1 )
& ( ( e1 != unit
& op(e4,e1) = e2 )
| op(e4,e2) != e1 )
& ( ( e1 != unit
& op(e4,e1) = e1 )
| op(e4,e1) != e1 )
& ( ( e1 != unit
& op(e4,e1) = e0 )
| op(e4,e0) != e1 )
& ( ( e1 != unit
& op(e3,e1) = e4 )
| op(e3,e4) != e1 )
& ( ( e1 != unit
& op(e3,e1) = e3 )
| op(e3,e3) != e1 )
& ( ( e1 != unit
& op(e3,e1) = e2 )
| op(e3,e2) != e1 )
& ( ( e1 != unit
& op(e3,e1) = e1 )
| op(e3,e1) != e1 )
& ( ( e1 != unit
& op(e3,e1) = e0 )
| op(e3,e0) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e4 )
| op(e2,e4) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e3 )
| op(e2,e3) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e2 )
| op(e2,e2) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e1 )
| op(e2,e1) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e0 )
| op(e2,e0) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e4 )
| op(e1,e4) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e3 )
| op(e1,e3) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e2 )
| op(e1,e2) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e1 )
| op(e1,e1) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e0 )
| op(e1,e0) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e4 )
| op(e0,e4) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e3 )
| op(e0,e3) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e2 )
| op(e0,e2) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e1 )
| op(e0,e1) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e0 )
| op(e0,e0) != e1 ) )
| ( ( ( e0 != unit
& op(e4,e0) = e4 )
| op(e4,e4) != e0 )
& ( ( e0 != unit
& op(e4,e0) = e3 )
| op(e4,e3) != e0 )
& ( ( e0 != unit
& op(e4,e0) = e2 )
| op(e4,e2) != e0 )
& ( ( e0 != unit
& op(e4,e0) = e1 )
| op(e4,e1) != e0 )
& ( ( e0 != unit
& op(e4,e0) = e0 )
| op(e4,e0) != e0 )
& ( ( e0 != unit
& op(e3,e0) = e4 )
| op(e3,e4) != e0 )
& ( ( e0 != unit
& op(e3,e0) = e3 )
| op(e3,e3) != e0 )
& ( ( e0 != unit
& op(e3,e0) = e2 )
| op(e3,e2) != e0 )
& ( ( e0 != unit
& op(e3,e0) = e1 )
| op(e3,e1) != e0 )
& ( ( e0 != unit
& op(e3,e0) = e0 )
| op(e3,e0) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e4 )
| op(e2,e4) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e3 )
| op(e2,e3) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e2 )
| op(e2,e2) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e1 )
| op(e2,e1) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e0 )
| op(e2,e0) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e4 )
| op(e1,e4) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e3 )
| op(e1,e3) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e2 )
| op(e1,e2) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e1 )
| op(e1,e1) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e0 )
| op(e1,e0) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e4 )
| op(e0,e4) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e3 )
| op(e0,e3) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e2 )
| op(e0,e2) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e1 )
| op(e0,e1) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e0 )
| op(e0,e0) != e0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5_prd])],[]) ).
fof(f285,plain,
( sP2_prd
<=> ( ( ( ( e2 != unit
& op(e4,e2) = e4 )
| op(e4,e4) != e2 )
& ( ( e2 != unit
& op(e4,e2) = e3 )
| op(e4,e3) != e2 )
& ( ( e2 != unit
& op(e4,e2) = e2 )
| op(e4,e2) != e2 )
& ( ( e2 != unit
& op(e4,e2) = e1 )
| op(e4,e1) != e2 )
& ( ( e2 != unit
& op(e4,e2) = e0 )
| op(e4,e0) != e2 )
& ( ( e2 != unit
& op(e3,e2) = e4 )
| op(e3,e4) != e2 )
& ( ( e2 != unit
& op(e3,e2) = e3 )
| op(e3,e3) != e2 )
& ( ( e2 != unit
& op(e3,e2) = e2 )
| op(e3,e2) != e2 )
& ( ( e2 != unit
& op(e3,e2) = e1 )
| op(e3,e1) != e2 )
& ( ( e2 != unit
& op(e3,e2) = e0 )
| op(e3,e0) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e4 )
| op(e2,e4) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e3 )
| op(e2,e3) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e2 )
| op(e2,e2) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e1 )
| op(e2,e1) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e0 )
| op(e2,e0) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e4 )
| op(e1,e4) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e3 )
| op(e1,e3) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e2 )
| op(e1,e2) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e1 )
| op(e1,e1) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e0 )
| op(e1,e0) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e4 )
| op(e0,e4) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e3 )
| op(e0,e3) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e2 )
| op(e0,e2) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e1 )
| op(e0,e1) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e0 )
| op(e0,e0) != e2 ) )
| sP5_prd ) ),
inference(formula_renaming,[status(thm)],[f265,f284]) ).
fof(f286,definition,
( sP6_prd
<=> ( ( ( e2 != unit
& op(e4,e2) = e3 )
| op(e4,e3) != e2 )
& ( ( e2 != unit
& op(e4,e2) = e2 )
| op(e4,e2) != e2 )
& ( ( e2 != unit
& op(e4,e2) = e1 )
| op(e4,e1) != e2 )
& ( ( e2 != unit
& op(e4,e2) = e0 )
| op(e4,e0) != e2 )
& ( ( e2 != unit
& op(e3,e2) = e4 )
| op(e3,e4) != e2 )
& ( ( e2 != unit
& op(e3,e2) = e3 )
| op(e3,e3) != e2 )
& ( ( e2 != unit
& op(e3,e2) = e2 )
| op(e3,e2) != e2 )
& ( ( e2 != unit
& op(e3,e2) = e1 )
| op(e3,e1) != e2 )
& ( ( e2 != unit
& op(e3,e2) = e0 )
| op(e3,e0) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e4 )
| op(e2,e4) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e3 )
| op(e2,e3) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e2 )
| op(e2,e2) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e1 )
| op(e2,e1) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e0 )
| op(e2,e0) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e4 )
| op(e1,e4) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e3 )
| op(e1,e3) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e2 )
| op(e1,e2) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e1 )
| op(e1,e1) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e0 )
| op(e1,e0) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e4 )
| op(e0,e4) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e3 )
| op(e0,e3) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e2 )
| op(e0,e2) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e1 )
| op(e0,e1) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e0 )
| op(e0,e0) != e2 ) ) ),
introduced(definition,[new_symbols(definition,[sP6_prd])],[]) ).
fof(f287,plain,
( sP2_prd
<=> ( ( ( ( e2 != unit
& op(e4,e2) = e4 )
| op(e4,e4) != e2 )
& sP6_prd )
| sP5_prd ) ),
inference(formula_renaming,[status(thm)],[f285,f286]) ).
fof(f288,plain,
( ( ( ( ( ( e2 = unit
| op(e4,e2) != e4 )
& op(e4,e4) = e2 )
| ~ sP6_prd )
& ~ sP5_prd )
| sP2_prd )
& ( ( ( ( e2 != unit
& op(e4,e2) = e4 )
| op(e4,e4) != e2 )
& sP6_prd )
| sP5_prd
| ~ sP2_prd ) ),
inference(NNF_transformation,[status(thm)],[f287]) ).
fof(f289,plain,
( sP6_prd
| sP5_prd
| ~ sP2_prd ),
inference(cnf_transformation,[status(thm)],[f288]) ).
fof(f295,definition,
( sP7_prd
<=> ( ( ( e3 != unit
& op(e4,e3) = e2 )
| op(e4,e2) != e3 )
& ( ( e3 != unit
& op(e4,e3) = e1 )
| op(e4,e1) != e3 )
& ( ( e3 != unit
& op(e4,e3) = e0 )
| op(e4,e0) != e3 )
& ( ( e3 != unit
& op(e3,e3) = e4 )
| op(e3,e4) != e3 )
& ( ( e3 != unit
& op(e3,e3) = e3 )
| op(e3,e3) != e3 )
& ( ( e3 != unit
& op(e3,e3) = e2 )
| op(e3,e2) != e3 )
& ( ( e3 != unit
& op(e3,e3) = e1 )
| op(e3,e1) != e3 )
& ( ( e3 != unit
& op(e3,e3) = e0 )
| op(e3,e0) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e4 )
| op(e2,e4) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e3 )
| op(e2,e3) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e2 )
| op(e2,e2) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e1 )
| op(e2,e1) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e0 )
| op(e2,e0) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e4 )
| op(e1,e4) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e3 )
| op(e1,e3) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e2 )
| op(e1,e2) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e1 )
| op(e1,e1) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e0 )
| op(e1,e0) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e4 )
| op(e0,e4) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e3 )
| op(e0,e3) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e2 )
| op(e0,e2) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e1 )
| op(e0,e1) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e0 )
| op(e0,e0) != e3 ) ) ),
introduced(definition,[new_symbols(definition,[sP7_prd])],[]) ).
fof(f296,plain,
( sP3_prd
<=> ( ( ( e3 != unit
& op(e4,e3) = e3 )
| op(e4,e3) != e3 )
& sP7_prd ) ),
inference(formula_renaming,[status(thm)],[f267,f295]) ).
fof(f297,plain,
( ( ( ( e3 = unit
| op(e4,e3) != e3 )
& op(e4,e3) = e3 )
| ~ sP7_prd
| sP3_prd )
& ( ( ( ( e3 != unit
& op(e4,e3) = e3 )
| op(e4,e3) != e3 )
& sP7_prd )
| ~ sP3_prd ) ),
inference(NNF_transformation,[status(thm)],[f296]) ).
fof(f298,plain,
( sP7_prd
| ~ sP3_prd ),
inference(cnf_transformation,[status(thm)],[f297]) ).
fof(f303,definition,
( sP8_prd
<=> ( ( op(op(e4,e1),e4) != e1
& op(op(e4,e1),e1) = e4
& op(e1,e4) != op(e4,e1) )
| ( op(op(e4,e0),e4) != e0
& op(op(e4,e0),e0) = e4
& op(e0,e4) != op(e4,e0) )
| ( op(op(e3,e4),e3) != e4
& op(op(e3,e4),e4) = e3
& op(e4,e3) != op(e3,e4) )
| ( op(op(e3,e3),e3) != e3
& op(op(e3,e3),e3) = e3
& op(e3,e3) != op(e3,e3) )
| ( op(op(e3,e2),e3) != e2
& op(op(e3,e2),e2) = e3
& op(e2,e3) != op(e3,e2) )
| ( op(op(e3,e1),e3) != e1
& op(op(e3,e1),e1) = e3
& op(e1,e3) != op(e3,e1) )
| ( op(op(e3,e0),e3) != e0
& op(op(e3,e0),e0) = e3
& op(e0,e3) != op(e3,e0) )
| ( op(op(e2,e4),e2) != e4
& op(op(e2,e4),e4) = e2
& op(e4,e2) != op(e2,e4) )
| ( op(op(e2,e3),e2) != e3
& op(op(e2,e3),e3) = e2
& op(e3,e2) != op(e2,e3) )
| ( op(op(e2,e2),e2) != e2
& op(op(e2,e2),e2) = e2
& op(e2,e2) != op(e2,e2) )
| ( op(op(e2,e1),e2) != e1
& op(op(e2,e1),e1) = e2
& op(e1,e2) != op(e2,e1) )
| ( op(op(e2,e0),e2) != e0
& op(op(e2,e0),e0) = e2
& op(e0,e2) != op(e2,e0) )
| ( op(op(e1,e4),e1) != e4
& op(op(e1,e4),e4) = e1
& op(e4,e1) != op(e1,e4) )
| ( op(op(e1,e3),e1) != e3
& op(op(e1,e3),e3) = e1
& op(e3,e1) != op(e1,e3) )
| ( op(op(e1,e2),e1) != e2
& op(op(e1,e2),e2) = e1
& op(e2,e1) != op(e1,e2) )
| ( op(op(e1,e1),e1) != e1
& op(op(e1,e1),e1) = e1
& op(e1,e1) != op(e1,e1) )
| ( op(op(e1,e0),e1) != e0
& op(op(e1,e0),e0) = e1
& op(e0,e1) != op(e1,e0) )
| ( op(op(e0,e4),e0) != e4
& op(op(e0,e4),e4) = e0
& op(e4,e0) != op(e0,e4) )
| ( op(op(e0,e3),e0) != e3
& op(op(e0,e3),e3) = e0
& op(e3,e0) != op(e0,e3) )
| ( op(op(e0,e2),e0) != e2
& op(op(e0,e2),e2) = e0
& op(e2,e0) != op(e0,e2) )
| ( op(op(e0,e1),e0) != e1
& op(op(e0,e1),e1) = e0
& op(e1,e0) != op(e0,e1) )
| ( op(op(e0,e0),e0) != e0
& op(op(e0,e0),e0) = e0
& op(e0,e0) != op(e0,e0) ) ) ),
introduced(definition,[new_symbols(definition,[sP8_prd])],[]) ).
fof(f304,plain,
( sP4_prd
<=> ( ( op(op(e4,e2),e4) != e2
& op(op(e4,e2),e2) = e4
& op(e2,e4) != op(e4,e2) )
| sP8_prd ) ),
inference(formula_renaming,[status(thm)],[f276,f303]) ).
fof(f305,plain,
( ( ( ( op(op(e4,e2),e4) = e2
| op(op(e4,e2),e2) != e4
| op(e2,e4) = op(e4,e2) )
& ~ sP8_prd )
| sP4_prd )
& ( ( op(op(e4,e2),e4) != e2
& op(op(e4,e2),e2) = e4
& op(e2,e4) != op(e4,e2) )
| sP8_prd
| ~ sP4_prd ) ),
inference(NNF_transformation,[status(thm)],[f304]) ).
fof(f307,plain,
( op(op(e4,e2),e2) = e4
| sP8_prd
| ~ sP4_prd ),
inference(cnf_transformation,[status(thm)],[f305]) ).
fof(f311,definition,
( sP9_prd
<=> ( ( ( e0 != unit
& op(e4,e0) = e4 )
| op(e4,e4) != e0 )
& ( ( e0 != unit
& op(e4,e0) = e3 )
| op(e4,e3) != e0 )
& ( ( e0 != unit
& op(e4,e0) = e2 )
| op(e4,e2) != e0 )
& ( ( e0 != unit
& op(e4,e0) = e1 )
| op(e4,e1) != e0 )
& ( ( e0 != unit
& op(e4,e0) = e0 )
| op(e4,e0) != e0 )
& ( ( e0 != unit
& op(e3,e0) = e4 )
| op(e3,e4) != e0 )
& ( ( e0 != unit
& op(e3,e0) = e3 )
| op(e3,e3) != e0 )
& ( ( e0 != unit
& op(e3,e0) = e2 )
| op(e3,e2) != e0 )
& ( ( e0 != unit
& op(e3,e0) = e1 )
| op(e3,e1) != e0 )
& ( ( e0 != unit
& op(e3,e0) = e0 )
| op(e3,e0) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e4 )
| op(e2,e4) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e3 )
| op(e2,e3) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e2 )
| op(e2,e2) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e1 )
| op(e2,e1) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e0 )
| op(e2,e0) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e4 )
| op(e1,e4) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e3 )
| op(e1,e3) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e2 )
| op(e1,e2) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e1 )
| op(e1,e1) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e0 )
| op(e1,e0) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e4 )
| op(e0,e4) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e3 )
| op(e0,e3) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e2 )
| op(e0,e2) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e1 )
| op(e0,e1) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e0 )
| op(e0,e0) != e0 ) ) ),
introduced(definition,[new_symbols(definition,[sP9_prd])],[]) ).
fof(f312,plain,
( sP5_prd
<=> ( ( ( ( e1 != unit
& op(e4,e1) = e4 )
| op(e4,e4) != e1 )
& ( ( e1 != unit
& op(e4,e1) = e3 )
| op(e4,e3) != e1 )
& ( ( e1 != unit
& op(e4,e1) = e2 )
| op(e4,e2) != e1 )
& ( ( e1 != unit
& op(e4,e1) = e1 )
| op(e4,e1) != e1 )
& ( ( e1 != unit
& op(e4,e1) = e0 )
| op(e4,e0) != e1 )
& ( ( e1 != unit
& op(e3,e1) = e4 )
| op(e3,e4) != e1 )
& ( ( e1 != unit
& op(e3,e1) = e3 )
| op(e3,e3) != e1 )
& ( ( e1 != unit
& op(e3,e1) = e2 )
| op(e3,e2) != e1 )
& ( ( e1 != unit
& op(e3,e1) = e1 )
| op(e3,e1) != e1 )
& ( ( e1 != unit
& op(e3,e1) = e0 )
| op(e3,e0) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e4 )
| op(e2,e4) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e3 )
| op(e2,e3) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e2 )
| op(e2,e2) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e1 )
| op(e2,e1) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e0 )
| op(e2,e0) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e4 )
| op(e1,e4) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e3 )
| op(e1,e3) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e2 )
| op(e1,e2) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e1 )
| op(e1,e1) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e0 )
| op(e1,e0) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e4 )
| op(e0,e4) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e3 )
| op(e0,e3) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e2 )
| op(e0,e2) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e1 )
| op(e0,e1) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e0 )
| op(e0,e0) != e1 ) )
| sP9_prd ) ),
inference(formula_renaming,[status(thm)],[f284,f311]) ).
fof(f313,definition,
( sP10_prd
<=> ( ( ( e1 != unit
& op(e4,e1) = e3 )
| op(e4,e3) != e1 )
& ( ( e1 != unit
& op(e4,e1) = e2 )
| op(e4,e2) != e1 )
& ( ( e1 != unit
& op(e4,e1) = e1 )
| op(e4,e1) != e1 )
& ( ( e1 != unit
& op(e4,e1) = e0 )
| op(e4,e0) != e1 )
& ( ( e1 != unit
& op(e3,e1) = e4 )
| op(e3,e4) != e1 )
& ( ( e1 != unit
& op(e3,e1) = e3 )
| op(e3,e3) != e1 )
& ( ( e1 != unit
& op(e3,e1) = e2 )
| op(e3,e2) != e1 )
& ( ( e1 != unit
& op(e3,e1) = e1 )
| op(e3,e1) != e1 )
& ( ( e1 != unit
& op(e3,e1) = e0 )
| op(e3,e0) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e4 )
| op(e2,e4) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e3 )
| op(e2,e3) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e2 )
| op(e2,e2) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e1 )
| op(e2,e1) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e0 )
| op(e2,e0) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e4 )
| op(e1,e4) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e3 )
| op(e1,e3) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e2 )
| op(e1,e2) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e1 )
| op(e1,e1) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e0 )
| op(e1,e0) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e4 )
| op(e0,e4) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e3 )
| op(e0,e3) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e2 )
| op(e0,e2) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e1 )
| op(e0,e1) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e0 )
| op(e0,e0) != e1 ) ) ),
introduced(definition,[new_symbols(definition,[sP10_prd])],[]) ).
fof(f314,plain,
( sP5_prd
<=> ( ( ( ( e1 != unit
& op(e4,e1) = e4 )
| op(e4,e4) != e1 )
& sP10_prd )
| sP9_prd ) ),
inference(formula_renaming,[status(thm)],[f312,f313]) ).
fof(f315,plain,
( ( ( ( ( ( e1 = unit
| op(e4,e1) != e4 )
& op(e4,e4) = e1 )
| ~ sP10_prd )
& ~ sP9_prd )
| sP5_prd )
& ( ( ( ( e1 != unit
& op(e4,e1) = e4 )
| op(e4,e4) != e1 )
& sP10_prd )
| sP9_prd
| ~ sP5_prd ) ),
inference(NNF_transformation,[status(thm)],[f314]) ).
fof(f316,plain,
( sP10_prd
| sP9_prd
| ~ sP5_prd ),
inference(cnf_transformation,[status(thm)],[f315]) ).
fof(f317,plain,
( op(e4,e1) = e4
| op(e4,e4) != e1
| sP9_prd
| ~ sP5_prd ),
inference(cnf_transformation,[status(thm)],[f315]) ).
fof(f322,definition,
( sP11_prd
<=> ( ( ( e2 != unit
& op(e4,e2) = e2 )
| op(e4,e2) != e2 )
& ( ( e2 != unit
& op(e4,e2) = e1 )
| op(e4,e1) != e2 )
& ( ( e2 != unit
& op(e4,e2) = e0 )
| op(e4,e0) != e2 )
& ( ( e2 != unit
& op(e3,e2) = e4 )
| op(e3,e4) != e2 )
& ( ( e2 != unit
& op(e3,e2) = e3 )
| op(e3,e3) != e2 )
& ( ( e2 != unit
& op(e3,e2) = e2 )
| op(e3,e2) != e2 )
& ( ( e2 != unit
& op(e3,e2) = e1 )
| op(e3,e1) != e2 )
& ( ( e2 != unit
& op(e3,e2) = e0 )
| op(e3,e0) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e4 )
| op(e2,e4) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e3 )
| op(e2,e3) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e2 )
| op(e2,e2) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e1 )
| op(e2,e1) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e0 )
| op(e2,e0) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e4 )
| op(e1,e4) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e3 )
| op(e1,e3) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e2 )
| op(e1,e2) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e1 )
| op(e1,e1) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e0 )
| op(e1,e0) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e4 )
| op(e0,e4) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e3 )
| op(e0,e3) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e2 )
| op(e0,e2) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e1 )
| op(e0,e1) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e0 )
| op(e0,e0) != e2 ) ) ),
introduced(definition,[new_symbols(definition,[sP11_prd])],[]) ).
fof(f323,plain,
( sP6_prd
<=> ( ( ( e2 != unit
& op(e4,e2) = e3 )
| op(e4,e3) != e2 )
& sP11_prd ) ),
inference(formula_renaming,[status(thm)],[f286,f322]) ).
fof(f324,plain,
( ( ( ( e2 = unit
| op(e4,e2) != e3 )
& op(e4,e3) = e2 )
| ~ sP11_prd
| sP6_prd )
& ( ( ( ( e2 != unit
& op(e4,e2) = e3 )
| op(e4,e3) != e2 )
& sP11_prd )
| ~ sP6_prd ) ),
inference(NNF_transformation,[status(thm)],[f323]) ).
fof(f325,plain,
( sP11_prd
| ~ sP6_prd ),
inference(cnf_transformation,[status(thm)],[f324]) ).
fof(f330,definition,
( sP12_prd
<=> ( ( ( e3 != unit
& op(e4,e3) = e1 )
| op(e4,e1) != e3 )
& ( ( e3 != unit
& op(e4,e3) = e0 )
| op(e4,e0) != e3 )
& ( ( e3 != unit
& op(e3,e3) = e4 )
| op(e3,e4) != e3 )
& ( ( e3 != unit
& op(e3,e3) = e3 )
| op(e3,e3) != e3 )
& ( ( e3 != unit
& op(e3,e3) = e2 )
| op(e3,e2) != e3 )
& ( ( e3 != unit
& op(e3,e3) = e1 )
| op(e3,e1) != e3 )
& ( ( e3 != unit
& op(e3,e3) = e0 )
| op(e3,e0) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e4 )
| op(e2,e4) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e3 )
| op(e2,e3) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e2 )
| op(e2,e2) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e1 )
| op(e2,e1) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e0 )
| op(e2,e0) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e4 )
| op(e1,e4) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e3 )
| op(e1,e3) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e2 )
| op(e1,e2) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e1 )
| op(e1,e1) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e0 )
| op(e1,e0) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e4 )
| op(e0,e4) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e3 )
| op(e0,e3) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e2 )
| op(e0,e2) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e1 )
| op(e0,e1) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e0 )
| op(e0,e0) != e3 ) ) ),
introduced(definition,[new_symbols(definition,[sP12_prd])],[]) ).
fof(f331,plain,
( sP7_prd
<=> ( ( ( e3 != unit
& op(e4,e3) = e2 )
| op(e4,e2) != e3 )
& sP12_prd ) ),
inference(formula_renaming,[status(thm)],[f295,f330]) ).
fof(f332,plain,
( ( ( ( e3 = unit
| op(e4,e3) != e2 )
& op(e4,e2) = e3 )
| ~ sP12_prd
| sP7_prd )
& ( ( ( ( e3 != unit
& op(e4,e3) = e2 )
| op(e4,e2) != e3 )
& sP12_prd )
| ~ sP7_prd ) ),
inference(NNF_transformation,[status(thm)],[f331]) ).
fof(f333,plain,
( sP12_prd
| ~ sP7_prd ),
inference(cnf_transformation,[status(thm)],[f332]) ).
fof(f338,definition,
( sP13_prd
<=> ( ( op(op(e4,e0),e4) != e0
& op(op(e4,e0),e0) = e4
& op(e0,e4) != op(e4,e0) )
| ( op(op(e3,e4),e3) != e4
& op(op(e3,e4),e4) = e3
& op(e4,e3) != op(e3,e4) )
| ( op(op(e3,e3),e3) != e3
& op(op(e3,e3),e3) = e3
& op(e3,e3) != op(e3,e3) )
| ( op(op(e3,e2),e3) != e2
& op(op(e3,e2),e2) = e3
& op(e2,e3) != op(e3,e2) )
| ( op(op(e3,e1),e3) != e1
& op(op(e3,e1),e1) = e3
& op(e1,e3) != op(e3,e1) )
| ( op(op(e3,e0),e3) != e0
& op(op(e3,e0),e0) = e3
& op(e0,e3) != op(e3,e0) )
| ( op(op(e2,e4),e2) != e4
& op(op(e2,e4),e4) = e2
& op(e4,e2) != op(e2,e4) )
| ( op(op(e2,e3),e2) != e3
& op(op(e2,e3),e3) = e2
& op(e3,e2) != op(e2,e3) )
| ( op(op(e2,e2),e2) != e2
& op(op(e2,e2),e2) = e2
& op(e2,e2) != op(e2,e2) )
| ( op(op(e2,e1),e2) != e1
& op(op(e2,e1),e1) = e2
& op(e1,e2) != op(e2,e1) )
| ( op(op(e2,e0),e2) != e0
& op(op(e2,e0),e0) = e2
& op(e0,e2) != op(e2,e0) )
| ( op(op(e1,e4),e1) != e4
& op(op(e1,e4),e4) = e1
& op(e4,e1) != op(e1,e4) )
| ( op(op(e1,e3),e1) != e3
& op(op(e1,e3),e3) = e1
& op(e3,e1) != op(e1,e3) )
| ( op(op(e1,e2),e1) != e2
& op(op(e1,e2),e2) = e1
& op(e2,e1) != op(e1,e2) )
| ( op(op(e1,e1),e1) != e1
& op(op(e1,e1),e1) = e1
& op(e1,e1) != op(e1,e1) )
| ( op(op(e1,e0),e1) != e0
& op(op(e1,e0),e0) = e1
& op(e0,e1) != op(e1,e0) )
| ( op(op(e0,e4),e0) != e4
& op(op(e0,e4),e4) = e0
& op(e4,e0) != op(e0,e4) )
| ( op(op(e0,e3),e0) != e3
& op(op(e0,e3),e3) = e0
& op(e3,e0) != op(e0,e3) )
| ( op(op(e0,e2),e0) != e2
& op(op(e0,e2),e2) = e0
& op(e2,e0) != op(e0,e2) )
| ( op(op(e0,e1),e0) != e1
& op(op(e0,e1),e1) = e0
& op(e1,e0) != op(e0,e1) )
| ( op(op(e0,e0),e0) != e0
& op(op(e0,e0),e0) = e0
& op(e0,e0) != op(e0,e0) ) ) ),
introduced(definition,[new_symbols(definition,[sP13_prd])],[]) ).
fof(f339,plain,
( sP8_prd
<=> ( ( op(op(e4,e1),e4) != e1
& op(op(e4,e1),e1) = e4
& op(e1,e4) != op(e4,e1) )
| sP13_prd ) ),
inference(formula_renaming,[status(thm)],[f303,f338]) ).
fof(f340,plain,
( ( ( ( op(op(e4,e1),e4) = e1
| op(op(e4,e1),e1) != e4
| op(e1,e4) = op(e4,e1) )
& ~ sP13_prd )
| sP8_prd )
& ( ( op(op(e4,e1),e4) != e1
& op(op(e4,e1),e1) = e4
& op(e1,e4) != op(e4,e1) )
| sP13_prd
| ~ sP8_prd ) ),
inference(NNF_transformation,[status(thm)],[f339]) ).
fof(f341,plain,
( op(e1,e4) != op(e4,e1)
| sP13_prd
| ~ sP8_prd ),
inference(cnf_transformation,[status(thm)],[f340]) ).
fof(f346,definition,
( sP14_prd
<=> ( ( ( e0 != unit
& op(e4,e0) = e3 )
| op(e4,e3) != e0 )
& ( ( e0 != unit
& op(e4,e0) = e2 )
| op(e4,e2) != e0 )
& ( ( e0 != unit
& op(e4,e0) = e1 )
| op(e4,e1) != e0 )
& ( ( e0 != unit
& op(e4,e0) = e0 )
| op(e4,e0) != e0 )
& ( ( e0 != unit
& op(e3,e0) = e4 )
| op(e3,e4) != e0 )
& ( ( e0 != unit
& op(e3,e0) = e3 )
| op(e3,e3) != e0 )
& ( ( e0 != unit
& op(e3,e0) = e2 )
| op(e3,e2) != e0 )
& ( ( e0 != unit
& op(e3,e0) = e1 )
| op(e3,e1) != e0 )
& ( ( e0 != unit
& op(e3,e0) = e0 )
| op(e3,e0) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e4 )
| op(e2,e4) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e3 )
| op(e2,e3) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e2 )
| op(e2,e2) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e1 )
| op(e2,e1) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e0 )
| op(e2,e0) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e4 )
| op(e1,e4) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e3 )
| op(e1,e3) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e2 )
| op(e1,e2) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e1 )
| op(e1,e1) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e0 )
| op(e1,e0) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e4 )
| op(e0,e4) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e3 )
| op(e0,e3) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e2 )
| op(e0,e2) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e1 )
| op(e0,e1) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e0 )
| op(e0,e0) != e0 ) ) ),
introduced(definition,[new_symbols(definition,[sP14_prd])],[]) ).
fof(f347,plain,
( sP9_prd
<=> ( ( ( e0 != unit
& op(e4,e0) = e4 )
| op(e4,e4) != e0 )
& sP14_prd ) ),
inference(formula_renaming,[status(thm)],[f311,f346]) ).
fof(f348,plain,
( ( ( ( e0 = unit
| op(e4,e0) != e4 )
& op(e4,e4) = e0 )
| ~ sP14_prd
| sP9_prd )
& ( ( ( ( e0 != unit
& op(e4,e0) = e4 )
| op(e4,e4) != e0 )
& sP14_prd )
| ~ sP9_prd ) ),
inference(NNF_transformation,[status(thm)],[f347]) ).
fof(f349,plain,
( sP14_prd
| ~ sP9_prd ),
inference(cnf_transformation,[status(thm)],[f348]) ).
fof(f354,definition,
( sP15_prd
<=> ( ( ( e1 != unit
& op(e4,e1) = e2 )
| op(e4,e2) != e1 )
& ( ( e1 != unit
& op(e4,e1) = e1 )
| op(e4,e1) != e1 )
& ( ( e1 != unit
& op(e4,e1) = e0 )
| op(e4,e0) != e1 )
& ( ( e1 != unit
& op(e3,e1) = e4 )
| op(e3,e4) != e1 )
& ( ( e1 != unit
& op(e3,e1) = e3 )
| op(e3,e3) != e1 )
& ( ( e1 != unit
& op(e3,e1) = e2 )
| op(e3,e2) != e1 )
& ( ( e1 != unit
& op(e3,e1) = e1 )
| op(e3,e1) != e1 )
& ( ( e1 != unit
& op(e3,e1) = e0 )
| op(e3,e0) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e4 )
| op(e2,e4) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e3 )
| op(e2,e3) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e2 )
| op(e2,e2) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e1 )
| op(e2,e1) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e0 )
| op(e2,e0) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e4 )
| op(e1,e4) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e3 )
| op(e1,e3) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e2 )
| op(e1,e2) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e1 )
| op(e1,e1) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e0 )
| op(e1,e0) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e4 )
| op(e0,e4) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e3 )
| op(e0,e3) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e2 )
| op(e0,e2) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e1 )
| op(e0,e1) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e0 )
| op(e0,e0) != e1 ) ) ),
introduced(definition,[new_symbols(definition,[sP15_prd])],[]) ).
fof(f355,plain,
( sP10_prd
<=> ( ( ( e1 != unit
& op(e4,e1) = e3 )
| op(e4,e3) != e1 )
& sP15_prd ) ),
inference(formula_renaming,[status(thm)],[f313,f354]) ).
fof(f356,plain,
( ( ( ( e1 = unit
| op(e4,e1) != e3 )
& op(e4,e3) = e1 )
| ~ sP15_prd
| sP10_prd )
& ( ( ( ( e1 != unit
& op(e4,e1) = e3 )
| op(e4,e3) != e1 )
& sP15_prd )
| ~ sP10_prd ) ),
inference(NNF_transformation,[status(thm)],[f355]) ).
fof(f357,plain,
( sP15_prd
| ~ sP10_prd ),
inference(cnf_transformation,[status(thm)],[f356]) ).
fof(f358,plain,
( op(e4,e1) = e3
| op(e4,e3) != e1
| ~ sP10_prd ),
inference(cnf_transformation,[status(thm)],[f356]) ).
fof(f362,definition,
( sP16_prd
<=> ( ( ( e2 != unit
& op(e4,e2) = e1 )
| op(e4,e1) != e2 )
& ( ( e2 != unit
& op(e4,e2) = e0 )
| op(e4,e0) != e2 )
& ( ( e2 != unit
& op(e3,e2) = e4 )
| op(e3,e4) != e2 )
& ( ( e2 != unit
& op(e3,e2) = e3 )
| op(e3,e3) != e2 )
& ( ( e2 != unit
& op(e3,e2) = e2 )
| op(e3,e2) != e2 )
& ( ( e2 != unit
& op(e3,e2) = e1 )
| op(e3,e1) != e2 )
& ( ( e2 != unit
& op(e3,e2) = e0 )
| op(e3,e0) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e4 )
| op(e2,e4) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e3 )
| op(e2,e3) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e2 )
| op(e2,e2) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e1 )
| op(e2,e1) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e0 )
| op(e2,e0) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e4 )
| op(e1,e4) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e3 )
| op(e1,e3) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e2 )
| op(e1,e2) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e1 )
| op(e1,e1) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e0 )
| op(e1,e0) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e4 )
| op(e0,e4) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e3 )
| op(e0,e3) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e2 )
| op(e0,e2) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e1 )
| op(e0,e1) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e0 )
| op(e0,e0) != e2 ) ) ),
introduced(definition,[new_symbols(definition,[sP16_prd])],[]) ).
fof(f363,plain,
( sP11_prd
<=> ( ( ( e2 != unit
& op(e4,e2) = e2 )
| op(e4,e2) != e2 )
& sP16_prd ) ),
inference(formula_renaming,[status(thm)],[f322,f362]) ).
fof(f364,plain,
( ( ( ( e2 = unit
| op(e4,e2) != e2 )
& op(e4,e2) = e2 )
| ~ sP16_prd
| sP11_prd )
& ( ( ( ( e2 != unit
& op(e4,e2) = e2 )
| op(e4,e2) != e2 )
& sP16_prd )
| ~ sP11_prd ) ),
inference(NNF_transformation,[status(thm)],[f363]) ).
fof(f365,plain,
( sP16_prd
| ~ sP11_prd ),
inference(cnf_transformation,[status(thm)],[f364]) ).
fof(f370,definition,
( sP17_prd
<=> ( ( ( e3 != unit
& op(e4,e3) = e0 )
| op(e4,e0) != e3 )
& ( ( e3 != unit
& op(e3,e3) = e4 )
| op(e3,e4) != e3 )
& ( ( e3 != unit
& op(e3,e3) = e3 )
| op(e3,e3) != e3 )
& ( ( e3 != unit
& op(e3,e3) = e2 )
| op(e3,e2) != e3 )
& ( ( e3 != unit
& op(e3,e3) = e1 )
| op(e3,e1) != e3 )
& ( ( e3 != unit
& op(e3,e3) = e0 )
| op(e3,e0) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e4 )
| op(e2,e4) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e3 )
| op(e2,e3) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e2 )
| op(e2,e2) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e1 )
| op(e2,e1) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e0 )
| op(e2,e0) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e4 )
| op(e1,e4) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e3 )
| op(e1,e3) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e2 )
| op(e1,e2) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e1 )
| op(e1,e1) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e0 )
| op(e1,e0) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e4 )
| op(e0,e4) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e3 )
| op(e0,e3) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e2 )
| op(e0,e2) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e1 )
| op(e0,e1) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e0 )
| op(e0,e0) != e3 ) ) ),
introduced(definition,[new_symbols(definition,[sP17_prd])],[]) ).
fof(f371,plain,
( sP12_prd
<=> ( ( ( e3 != unit
& op(e4,e3) = e1 )
| op(e4,e1) != e3 )
& sP17_prd ) ),
inference(formula_renaming,[status(thm)],[f330,f370]) ).
fof(f372,plain,
( ( ( ( e3 = unit
| op(e4,e3) != e1 )
& op(e4,e1) = e3 )
| ~ sP17_prd
| sP12_prd )
& ( ( ( ( e3 != unit
& op(e4,e3) = e1 )
| op(e4,e1) != e3 )
& sP17_prd )
| ~ sP12_prd ) ),
inference(NNF_transformation,[status(thm)],[f371]) ).
fof(f373,plain,
( sP17_prd
| ~ sP12_prd ),
inference(cnf_transformation,[status(thm)],[f372]) ).
fof(f378,definition,
( sP18_prd
<=> ( ( op(op(e3,e4),e3) != e4
& op(op(e3,e4),e4) = e3
& op(e4,e3) != op(e3,e4) )
| ( op(op(e3,e3),e3) != e3
& op(op(e3,e3),e3) = e3
& op(e3,e3) != op(e3,e3) )
| ( op(op(e3,e2),e3) != e2
& op(op(e3,e2),e2) = e3
& op(e2,e3) != op(e3,e2) )
| ( op(op(e3,e1),e3) != e1
& op(op(e3,e1),e1) = e3
& op(e1,e3) != op(e3,e1) )
| ( op(op(e3,e0),e3) != e0
& op(op(e3,e0),e0) = e3
& op(e0,e3) != op(e3,e0) )
| ( op(op(e2,e4),e2) != e4
& op(op(e2,e4),e4) = e2
& op(e4,e2) != op(e2,e4) )
| ( op(op(e2,e3),e2) != e3
& op(op(e2,e3),e3) = e2
& op(e3,e2) != op(e2,e3) )
| ( op(op(e2,e2),e2) != e2
& op(op(e2,e2),e2) = e2
& op(e2,e2) != op(e2,e2) )
| ( op(op(e2,e1),e2) != e1
& op(op(e2,e1),e1) = e2
& op(e1,e2) != op(e2,e1) )
| ( op(op(e2,e0),e2) != e0
& op(op(e2,e0),e0) = e2
& op(e0,e2) != op(e2,e0) )
| ( op(op(e1,e4),e1) != e4
& op(op(e1,e4),e4) = e1
& op(e4,e1) != op(e1,e4) )
| ( op(op(e1,e3),e1) != e3
& op(op(e1,e3),e3) = e1
& op(e3,e1) != op(e1,e3) )
| ( op(op(e1,e2),e1) != e2
& op(op(e1,e2),e2) = e1
& op(e2,e1) != op(e1,e2) )
| ( op(op(e1,e1),e1) != e1
& op(op(e1,e1),e1) = e1
& op(e1,e1) != op(e1,e1) )
| ( op(op(e1,e0),e1) != e0
& op(op(e1,e0),e0) = e1
& op(e0,e1) != op(e1,e0) )
| ( op(op(e0,e4),e0) != e4
& op(op(e0,e4),e4) = e0
& op(e4,e0) != op(e0,e4) )
| ( op(op(e0,e3),e0) != e3
& op(op(e0,e3),e3) = e0
& op(e3,e0) != op(e0,e3) )
| ( op(op(e0,e2),e0) != e2
& op(op(e0,e2),e2) = e0
& op(e2,e0) != op(e0,e2) )
| ( op(op(e0,e1),e0) != e1
& op(op(e0,e1),e1) = e0
& op(e1,e0) != op(e0,e1) )
| ( op(op(e0,e0),e0) != e0
& op(op(e0,e0),e0) = e0
& op(e0,e0) != op(e0,e0) ) ) ),
introduced(definition,[new_symbols(definition,[sP18_prd])],[]) ).
fof(f379,plain,
( sP13_prd
<=> ( ( op(op(e4,e0),e4) != e0
& op(op(e4,e0),e0) = e4
& op(e0,e4) != op(e4,e0) )
| sP18_prd ) ),
inference(formula_renaming,[status(thm)],[f338,f378]) ).
fof(f380,plain,
( ( ( ( op(op(e4,e0),e4) = e0
| op(op(e4,e0),e0) != e4
| op(e0,e4) = op(e4,e0) )
& ~ sP18_prd )
| sP13_prd )
& ( ( op(op(e4,e0),e4) != e0
& op(op(e4,e0),e0) = e4
& op(e0,e4) != op(e4,e0) )
| sP18_prd
| ~ sP13_prd ) ),
inference(NNF_transformation,[status(thm)],[f379]) ).
fof(f381,plain,
( op(e0,e4) != op(e4,e0)
| sP18_prd
| ~ sP13_prd ),
inference(cnf_transformation,[status(thm)],[f380]) ).
fof(f386,definition,
( sP19_prd
<=> ( ( ( e0 != unit
& op(e4,e0) = e2 )
| op(e4,e2) != e0 )
& ( ( e0 != unit
& op(e4,e0) = e1 )
| op(e4,e1) != e0 )
& ( ( e0 != unit
& op(e4,e0) = e0 )
| op(e4,e0) != e0 )
& ( ( e0 != unit
& op(e3,e0) = e4 )
| op(e3,e4) != e0 )
& ( ( e0 != unit
& op(e3,e0) = e3 )
| op(e3,e3) != e0 )
& ( ( e0 != unit
& op(e3,e0) = e2 )
| op(e3,e2) != e0 )
& ( ( e0 != unit
& op(e3,e0) = e1 )
| op(e3,e1) != e0 )
& ( ( e0 != unit
& op(e3,e0) = e0 )
| op(e3,e0) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e4 )
| op(e2,e4) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e3 )
| op(e2,e3) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e2 )
| op(e2,e2) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e1 )
| op(e2,e1) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e0 )
| op(e2,e0) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e4 )
| op(e1,e4) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e3 )
| op(e1,e3) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e2 )
| op(e1,e2) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e1 )
| op(e1,e1) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e0 )
| op(e1,e0) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e4 )
| op(e0,e4) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e3 )
| op(e0,e3) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e2 )
| op(e0,e2) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e1 )
| op(e0,e1) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e0 )
| op(e0,e0) != e0 ) ) ),
introduced(definition,[new_symbols(definition,[sP19_prd])],[]) ).
fof(f387,plain,
( sP14_prd
<=> ( ( ( e0 != unit
& op(e4,e0) = e3 )
| op(e4,e3) != e0 )
& sP19_prd ) ),
inference(formula_renaming,[status(thm)],[f346,f386]) ).
fof(f388,plain,
( ( ( ( e0 = unit
| op(e4,e0) != e3 )
& op(e4,e3) = e0 )
| ~ sP19_prd
| sP14_prd )
& ( ( ( ( e0 != unit
& op(e4,e0) = e3 )
| op(e4,e3) != e0 )
& sP19_prd )
| ~ sP14_prd ) ),
inference(NNF_transformation,[status(thm)],[f387]) ).
fof(f389,plain,
( sP19_prd
| ~ sP14_prd ),
inference(cnf_transformation,[status(thm)],[f388]) ).
fof(f390,plain,
( op(e4,e0) = e3
| op(e4,e3) != e0
| ~ sP14_prd ),
inference(cnf_transformation,[status(thm)],[f388]) ).
fof(f394,definition,
( sP20_prd
<=> ( ( ( e1 != unit
& op(e4,e1) = e1 )
| op(e4,e1) != e1 )
& ( ( e1 != unit
& op(e4,e1) = e0 )
| op(e4,e0) != e1 )
& ( ( e1 != unit
& op(e3,e1) = e4 )
| op(e3,e4) != e1 )
& ( ( e1 != unit
& op(e3,e1) = e3 )
| op(e3,e3) != e1 )
& ( ( e1 != unit
& op(e3,e1) = e2 )
| op(e3,e2) != e1 )
& ( ( e1 != unit
& op(e3,e1) = e1 )
| op(e3,e1) != e1 )
& ( ( e1 != unit
& op(e3,e1) = e0 )
| op(e3,e0) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e4 )
| op(e2,e4) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e3 )
| op(e2,e3) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e2 )
| op(e2,e2) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e1 )
| op(e2,e1) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e0 )
| op(e2,e0) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e4 )
| op(e1,e4) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e3 )
| op(e1,e3) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e2 )
| op(e1,e2) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e1 )
| op(e1,e1) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e0 )
| op(e1,e0) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e4 )
| op(e0,e4) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e3 )
| op(e0,e3) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e2 )
| op(e0,e2) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e1 )
| op(e0,e1) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e0 )
| op(e0,e0) != e1 ) ) ),
introduced(definition,[new_symbols(definition,[sP20_prd])],[]) ).
fof(f395,plain,
( sP15_prd
<=> ( ( ( e1 != unit
& op(e4,e1) = e2 )
| op(e4,e2) != e1 )
& sP20_prd ) ),
inference(formula_renaming,[status(thm)],[f354,f394]) ).
fof(f396,plain,
( ( ( ( e1 = unit
| op(e4,e1) != e2 )
& op(e4,e2) = e1 )
| ~ sP20_prd
| sP15_prd )
& ( ( ( ( e1 != unit
& op(e4,e1) = e2 )
| op(e4,e2) != e1 )
& sP20_prd )
| ~ sP15_prd ) ),
inference(NNF_transformation,[status(thm)],[f395]) ).
fof(f397,plain,
( sP20_prd
| ~ sP15_prd ),
inference(cnf_transformation,[status(thm)],[f396]) ).
fof(f402,definition,
( sP21_prd
<=> ( ( ( e2 != unit
& op(e4,e2) = e0 )
| op(e4,e0) != e2 )
& ( ( e2 != unit
& op(e3,e2) = e4 )
| op(e3,e4) != e2 )
& ( ( e2 != unit
& op(e3,e2) = e3 )
| op(e3,e3) != e2 )
& ( ( e2 != unit
& op(e3,e2) = e2 )
| op(e3,e2) != e2 )
& ( ( e2 != unit
& op(e3,e2) = e1 )
| op(e3,e1) != e2 )
& ( ( e2 != unit
& op(e3,e2) = e0 )
| op(e3,e0) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e4 )
| op(e2,e4) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e3 )
| op(e2,e3) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e2 )
| op(e2,e2) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e1 )
| op(e2,e1) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e0 )
| op(e2,e0) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e4 )
| op(e1,e4) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e3 )
| op(e1,e3) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e2 )
| op(e1,e2) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e1 )
| op(e1,e1) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e0 )
| op(e1,e0) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e4 )
| op(e0,e4) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e3 )
| op(e0,e3) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e2 )
| op(e0,e2) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e1 )
| op(e0,e1) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e0 )
| op(e0,e0) != e2 ) ) ),
introduced(definition,[new_symbols(definition,[sP21_prd])],[]) ).
fof(f403,plain,
( sP16_prd
<=> ( ( ( e2 != unit
& op(e4,e2) = e1 )
| op(e4,e1) != e2 )
& sP21_prd ) ),
inference(formula_renaming,[status(thm)],[f362,f402]) ).
fof(f404,plain,
( ( ( ( e2 = unit
| op(e4,e2) != e1 )
& op(e4,e1) = e2 )
| ~ sP21_prd
| sP16_prd )
& ( ( ( ( e2 != unit
& op(e4,e2) = e1 )
| op(e4,e1) != e2 )
& sP21_prd )
| ~ sP16_prd ) ),
inference(NNF_transformation,[status(thm)],[f403]) ).
fof(f405,plain,
( sP21_prd
| ~ sP16_prd ),
inference(cnf_transformation,[status(thm)],[f404]) ).
fof(f410,definition,
( sP22_prd
<=> ( ( ( e3 != unit
& op(e3,e3) = e4 )
| op(e3,e4) != e3 )
& ( ( e3 != unit
& op(e3,e3) = e3 )
| op(e3,e3) != e3 )
& ( ( e3 != unit
& op(e3,e3) = e2 )
| op(e3,e2) != e3 )
& ( ( e3 != unit
& op(e3,e3) = e1 )
| op(e3,e1) != e3 )
& ( ( e3 != unit
& op(e3,e3) = e0 )
| op(e3,e0) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e4 )
| op(e2,e4) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e3 )
| op(e2,e3) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e2 )
| op(e2,e2) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e1 )
| op(e2,e1) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e0 )
| op(e2,e0) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e4 )
| op(e1,e4) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e3 )
| op(e1,e3) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e2 )
| op(e1,e2) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e1 )
| op(e1,e1) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e0 )
| op(e1,e0) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e4 )
| op(e0,e4) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e3 )
| op(e0,e3) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e2 )
| op(e0,e2) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e1 )
| op(e0,e1) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e0 )
| op(e0,e0) != e3 ) ) ),
introduced(definition,[new_symbols(definition,[sP22_prd])],[]) ).
fof(f411,plain,
( sP17_prd
<=> ( ( ( e3 != unit
& op(e4,e3) = e0 )
| op(e4,e0) != e3 )
& sP22_prd ) ),
inference(formula_renaming,[status(thm)],[f370,f410]) ).
fof(f412,plain,
( ( ( ( e3 = unit
| op(e4,e3) != e0 )
& op(e4,e0) = e3 )
| ~ sP22_prd
| sP17_prd )
& ( ( ( ( e3 != unit
& op(e4,e3) = e0 )
| op(e4,e0) != e3 )
& sP22_prd )
| ~ sP17_prd ) ),
inference(NNF_transformation,[status(thm)],[f411]) ).
fof(f413,plain,
( sP22_prd
| ~ sP17_prd ),
inference(cnf_transformation,[status(thm)],[f412]) ).
fof(f418,definition,
( sP23_prd
<=> ( ( op(op(e3,e3),e3) != e3
& op(op(e3,e3),e3) = e3
& op(e3,e3) != op(e3,e3) )
| ( op(op(e3,e2),e3) != e2
& op(op(e3,e2),e2) = e3
& op(e2,e3) != op(e3,e2) )
| ( op(op(e3,e1),e3) != e1
& op(op(e3,e1),e1) = e3
& op(e1,e3) != op(e3,e1) )
| ( op(op(e3,e0),e3) != e0
& op(op(e3,e0),e0) = e3
& op(e0,e3) != op(e3,e0) )
| ( op(op(e2,e4),e2) != e4
& op(op(e2,e4),e4) = e2
& op(e4,e2) != op(e2,e4) )
| ( op(op(e2,e3),e2) != e3
& op(op(e2,e3),e3) = e2
& op(e3,e2) != op(e2,e3) )
| ( op(op(e2,e2),e2) != e2
& op(op(e2,e2),e2) = e2
& op(e2,e2) != op(e2,e2) )
| ( op(op(e2,e1),e2) != e1
& op(op(e2,e1),e1) = e2
& op(e1,e2) != op(e2,e1) )
| ( op(op(e2,e0),e2) != e0
& op(op(e2,e0),e0) = e2
& op(e0,e2) != op(e2,e0) )
| ( op(op(e1,e4),e1) != e4
& op(op(e1,e4),e4) = e1
& op(e4,e1) != op(e1,e4) )
| ( op(op(e1,e3),e1) != e3
& op(op(e1,e3),e3) = e1
& op(e3,e1) != op(e1,e3) )
| ( op(op(e1,e2),e1) != e2
& op(op(e1,e2),e2) = e1
& op(e2,e1) != op(e1,e2) )
| ( op(op(e1,e1),e1) != e1
& op(op(e1,e1),e1) = e1
& op(e1,e1) != op(e1,e1) )
| ( op(op(e1,e0),e1) != e0
& op(op(e1,e0),e0) = e1
& op(e0,e1) != op(e1,e0) )
| ( op(op(e0,e4),e0) != e4
& op(op(e0,e4),e4) = e0
& op(e4,e0) != op(e0,e4) )
| ( op(op(e0,e3),e0) != e3
& op(op(e0,e3),e3) = e0
& op(e3,e0) != op(e0,e3) )
| ( op(op(e0,e2),e0) != e2
& op(op(e0,e2),e2) = e0
& op(e2,e0) != op(e0,e2) )
| ( op(op(e0,e1),e0) != e1
& op(op(e0,e1),e1) = e0
& op(e1,e0) != op(e0,e1) )
| ( op(op(e0,e0),e0) != e0
& op(op(e0,e0),e0) = e0
& op(e0,e0) != op(e0,e0) ) ) ),
introduced(definition,[new_symbols(definition,[sP23_prd])],[]) ).
fof(f419,plain,
( sP18_prd
<=> ( ( op(op(e3,e4),e3) != e4
& op(op(e3,e4),e4) = e3
& op(e4,e3) != op(e3,e4) )
| sP23_prd ) ),
inference(formula_renaming,[status(thm)],[f378,f418]) ).
fof(f420,plain,
( ( ( ( op(op(e3,e4),e3) = e4
| op(op(e3,e4),e4) != e3
| op(e4,e3) = op(e3,e4) )
& ~ sP23_prd )
| sP18_prd )
& ( ( op(op(e3,e4),e3) != e4
& op(op(e3,e4),e4) = e3
& op(e4,e3) != op(e3,e4) )
| sP23_prd
| ~ sP18_prd ) ),
inference(NNF_transformation,[status(thm)],[f419]) ).
fof(f422,plain,
( op(op(e3,e4),e4) = e3
| sP23_prd
| ~ sP18_prd ),
inference(cnf_transformation,[status(thm)],[f420]) ).
fof(f426,definition,
( sP24_prd
<=> ( ( ( e0 != unit
& op(e4,e0) = e1 )
| op(e4,e1) != e0 )
& ( ( e0 != unit
& op(e4,e0) = e0 )
| op(e4,e0) != e0 )
& ( ( e0 != unit
& op(e3,e0) = e4 )
| op(e3,e4) != e0 )
& ( ( e0 != unit
& op(e3,e0) = e3 )
| op(e3,e3) != e0 )
& ( ( e0 != unit
& op(e3,e0) = e2 )
| op(e3,e2) != e0 )
& ( ( e0 != unit
& op(e3,e0) = e1 )
| op(e3,e1) != e0 )
& ( ( e0 != unit
& op(e3,e0) = e0 )
| op(e3,e0) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e4 )
| op(e2,e4) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e3 )
| op(e2,e3) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e2 )
| op(e2,e2) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e1 )
| op(e2,e1) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e0 )
| op(e2,e0) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e4 )
| op(e1,e4) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e3 )
| op(e1,e3) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e2 )
| op(e1,e2) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e1 )
| op(e1,e1) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e0 )
| op(e1,e0) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e4 )
| op(e0,e4) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e3 )
| op(e0,e3) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e2 )
| op(e0,e2) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e1 )
| op(e0,e1) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e0 )
| op(e0,e0) != e0 ) ) ),
introduced(definition,[new_symbols(definition,[sP24_prd])],[]) ).
fof(f427,plain,
( sP19_prd
<=> ( ( ( e0 != unit
& op(e4,e0) = e2 )
| op(e4,e2) != e0 )
& sP24_prd ) ),
inference(formula_renaming,[status(thm)],[f386,f426]) ).
fof(f428,plain,
( ( ( ( e0 = unit
| op(e4,e0) != e2 )
& op(e4,e2) = e0 )
| ~ sP24_prd
| sP19_prd )
& ( ( ( ( e0 != unit
& op(e4,e0) = e2 )
| op(e4,e2) != e0 )
& sP24_prd )
| ~ sP19_prd ) ),
inference(NNF_transformation,[status(thm)],[f427]) ).
fof(f429,plain,
( sP24_prd
| ~ sP19_prd ),
inference(cnf_transformation,[status(thm)],[f428]) ).
fof(f434,definition,
( sP25_prd
<=> ( ( ( e1 != unit
& op(e4,e1) = e0 )
| op(e4,e0) != e1 )
& ( ( e1 != unit
& op(e3,e1) = e4 )
| op(e3,e4) != e1 )
& ( ( e1 != unit
& op(e3,e1) = e3 )
| op(e3,e3) != e1 )
& ( ( e1 != unit
& op(e3,e1) = e2 )
| op(e3,e2) != e1 )
& ( ( e1 != unit
& op(e3,e1) = e1 )
| op(e3,e1) != e1 )
& ( ( e1 != unit
& op(e3,e1) = e0 )
| op(e3,e0) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e4 )
| op(e2,e4) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e3 )
| op(e2,e3) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e2 )
| op(e2,e2) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e1 )
| op(e2,e1) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e0 )
| op(e2,e0) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e4 )
| op(e1,e4) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e3 )
| op(e1,e3) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e2 )
| op(e1,e2) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e1 )
| op(e1,e1) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e0 )
| op(e1,e0) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e4 )
| op(e0,e4) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e3 )
| op(e0,e3) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e2 )
| op(e0,e2) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e1 )
| op(e0,e1) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e0 )
| op(e0,e0) != e1 ) ) ),
introduced(definition,[new_symbols(definition,[sP25_prd])],[]) ).
fof(f435,plain,
( sP20_prd
<=> ( ( ( e1 != unit
& op(e4,e1) = e1 )
| op(e4,e1) != e1 )
& sP25_prd ) ),
inference(formula_renaming,[status(thm)],[f394,f434]) ).
fof(f436,plain,
( ( ( ( e1 = unit
| op(e4,e1) != e1 )
& op(e4,e1) = e1 )
| ~ sP25_prd
| sP20_prd )
& ( ( ( ( e1 != unit
& op(e4,e1) = e1 )
| op(e4,e1) != e1 )
& sP25_prd )
| ~ sP20_prd ) ),
inference(NNF_transformation,[status(thm)],[f435]) ).
fof(f437,plain,
( sP25_prd
| ~ sP20_prd ),
inference(cnf_transformation,[status(thm)],[f436]) ).
fof(f442,definition,
( sP26_prd
<=> ( ( ( e2 != unit
& op(e3,e2) = e4 )
| op(e3,e4) != e2 )
& ( ( e2 != unit
& op(e3,e2) = e3 )
| op(e3,e3) != e2 )
& ( ( e2 != unit
& op(e3,e2) = e2 )
| op(e3,e2) != e2 )
& ( ( e2 != unit
& op(e3,e2) = e1 )
| op(e3,e1) != e2 )
& ( ( e2 != unit
& op(e3,e2) = e0 )
| op(e3,e0) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e4 )
| op(e2,e4) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e3 )
| op(e2,e3) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e2 )
| op(e2,e2) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e1 )
| op(e2,e1) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e0 )
| op(e2,e0) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e4 )
| op(e1,e4) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e3 )
| op(e1,e3) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e2 )
| op(e1,e2) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e1 )
| op(e1,e1) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e0 )
| op(e1,e0) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e4 )
| op(e0,e4) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e3 )
| op(e0,e3) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e2 )
| op(e0,e2) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e1 )
| op(e0,e1) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e0 )
| op(e0,e0) != e2 ) ) ),
introduced(definition,[new_symbols(definition,[sP26_prd])],[]) ).
fof(f443,plain,
( sP21_prd
<=> ( ( ( e2 != unit
& op(e4,e2) = e0 )
| op(e4,e0) != e2 )
& sP26_prd ) ),
inference(formula_renaming,[status(thm)],[f402,f442]) ).
fof(f444,plain,
( ( ( ( e2 = unit
| op(e4,e2) != e0 )
& op(e4,e0) = e2 )
| ~ sP26_prd
| sP21_prd )
& ( ( ( ( e2 != unit
& op(e4,e2) = e0 )
| op(e4,e0) != e2 )
& sP26_prd )
| ~ sP21_prd ) ),
inference(NNF_transformation,[status(thm)],[f443]) ).
fof(f445,plain,
( sP26_prd
| ~ sP21_prd ),
inference(cnf_transformation,[status(thm)],[f444]) ).
fof(f450,definition,
( sP27_prd
<=> ( ( ( e3 != unit
& op(e3,e3) = e3 )
| op(e3,e3) != e3 )
& ( ( e3 != unit
& op(e3,e3) = e2 )
| op(e3,e2) != e3 )
& ( ( e3 != unit
& op(e3,e3) = e1 )
| op(e3,e1) != e3 )
& ( ( e3 != unit
& op(e3,e3) = e0 )
| op(e3,e0) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e4 )
| op(e2,e4) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e3 )
| op(e2,e3) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e2 )
| op(e2,e2) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e1 )
| op(e2,e1) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e0 )
| op(e2,e0) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e4 )
| op(e1,e4) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e3 )
| op(e1,e3) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e2 )
| op(e1,e2) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e1 )
| op(e1,e1) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e0 )
| op(e1,e0) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e4 )
| op(e0,e4) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e3 )
| op(e0,e3) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e2 )
| op(e0,e2) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e1 )
| op(e0,e1) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e0 )
| op(e0,e0) != e3 ) ) ),
introduced(definition,[new_symbols(definition,[sP27_prd])],[]) ).
fof(f451,plain,
( sP22_prd
<=> ( ( ( e3 != unit
& op(e3,e3) = e4 )
| op(e3,e4) != e3 )
& sP27_prd ) ),
inference(formula_renaming,[status(thm)],[f410,f450]) ).
fof(f452,plain,
( ( ( ( e3 = unit
| op(e3,e3) != e4 )
& op(e3,e4) = e3 )
| ~ sP27_prd
| sP22_prd )
& ( ( ( ( e3 != unit
& op(e3,e3) = e4 )
| op(e3,e4) != e3 )
& sP27_prd )
| ~ sP22_prd ) ),
inference(NNF_transformation,[status(thm)],[f451]) ).
fof(f453,plain,
( sP27_prd
| ~ sP22_prd ),
inference(cnf_transformation,[status(thm)],[f452]) ).
fof(f458,definition,
( sP28_prd
<=> ( ( op(op(e3,e2),e3) != e2
& op(op(e3,e2),e2) = e3
& op(e2,e3) != op(e3,e2) )
| ( op(op(e3,e1),e3) != e1
& op(op(e3,e1),e1) = e3
& op(e1,e3) != op(e3,e1) )
| ( op(op(e3,e0),e3) != e0
& op(op(e3,e0),e0) = e3
& op(e0,e3) != op(e3,e0) )
| ( op(op(e2,e4),e2) != e4
& op(op(e2,e4),e4) = e2
& op(e4,e2) != op(e2,e4) )
| ( op(op(e2,e3),e2) != e3
& op(op(e2,e3),e3) = e2
& op(e3,e2) != op(e2,e3) )
| ( op(op(e2,e2),e2) != e2
& op(op(e2,e2),e2) = e2
& op(e2,e2) != op(e2,e2) )
| ( op(op(e2,e1),e2) != e1
& op(op(e2,e1),e1) = e2
& op(e1,e2) != op(e2,e1) )
| ( op(op(e2,e0),e2) != e0
& op(op(e2,e0),e0) = e2
& op(e0,e2) != op(e2,e0) )
| ( op(op(e1,e4),e1) != e4
& op(op(e1,e4),e4) = e1
& op(e4,e1) != op(e1,e4) )
| ( op(op(e1,e3),e1) != e3
& op(op(e1,e3),e3) = e1
& op(e3,e1) != op(e1,e3) )
| ( op(op(e1,e2),e1) != e2
& op(op(e1,e2),e2) = e1
& op(e2,e1) != op(e1,e2) )
| ( op(op(e1,e1),e1) != e1
& op(op(e1,e1),e1) = e1
& op(e1,e1) != op(e1,e1) )
| ( op(op(e1,e0),e1) != e0
& op(op(e1,e0),e0) = e1
& op(e0,e1) != op(e1,e0) )
| ( op(op(e0,e4),e0) != e4
& op(op(e0,e4),e4) = e0
& op(e4,e0) != op(e0,e4) )
| ( op(op(e0,e3),e0) != e3
& op(op(e0,e3),e3) = e0
& op(e3,e0) != op(e0,e3) )
| ( op(op(e0,e2),e0) != e2
& op(op(e0,e2),e2) = e0
& op(e2,e0) != op(e0,e2) )
| ( op(op(e0,e1),e0) != e1
& op(op(e0,e1),e1) = e0
& op(e1,e0) != op(e0,e1) )
| ( op(op(e0,e0),e0) != e0
& op(op(e0,e0),e0) = e0
& op(e0,e0) != op(e0,e0) ) ) ),
introduced(definition,[new_symbols(definition,[sP28_prd])],[]) ).
fof(f459,plain,
( sP23_prd
<=> ( ( op(op(e3,e3),e3) != e3
& op(op(e3,e3),e3) = e3
& op(e3,e3) != op(e3,e3) )
| sP28_prd ) ),
inference(formula_renaming,[status(thm)],[f418,f458]) ).
fof(f460,plain,
( ( ( ( op(op(e3,e3),e3) = e3
| op(op(e3,e3),e3) != e3
| op(e3,e3) = op(e3,e3) )
& ~ sP28_prd )
| sP23_prd )
& ( ( op(op(e3,e3),e3) != e3
& op(op(e3,e3),e3) = e3
& op(e3,e3) != op(e3,e3) )
| sP28_prd
| ~ sP23_prd ) ),
inference(NNF_transformation,[status(thm)],[f459]) ).
fof(f461,plain,
( op(e3,e3) != op(e3,e3)
| sP28_prd
| ~ sP23_prd ),
inference(cnf_transformation,[status(thm)],[f460]) ).
fof(f466,definition,
( sP29_prd
<=> ( ( ( e0 != unit
& op(e4,e0) = e0 )
| op(e4,e0) != e0 )
& ( ( e0 != unit
& op(e3,e0) = e4 )
| op(e3,e4) != e0 )
& ( ( e0 != unit
& op(e3,e0) = e3 )
| op(e3,e3) != e0 )
& ( ( e0 != unit
& op(e3,e0) = e2 )
| op(e3,e2) != e0 )
& ( ( e0 != unit
& op(e3,e0) = e1 )
| op(e3,e1) != e0 )
& ( ( e0 != unit
& op(e3,e0) = e0 )
| op(e3,e0) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e4 )
| op(e2,e4) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e3 )
| op(e2,e3) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e2 )
| op(e2,e2) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e1 )
| op(e2,e1) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e0 )
| op(e2,e0) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e4 )
| op(e1,e4) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e3 )
| op(e1,e3) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e2 )
| op(e1,e2) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e1 )
| op(e1,e1) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e0 )
| op(e1,e0) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e4 )
| op(e0,e4) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e3 )
| op(e0,e3) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e2 )
| op(e0,e2) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e1 )
| op(e0,e1) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e0 )
| op(e0,e0) != e0 ) ) ),
introduced(definition,[new_symbols(definition,[sP29_prd])],[]) ).
fof(f467,plain,
( sP24_prd
<=> ( ( ( e0 != unit
& op(e4,e0) = e1 )
| op(e4,e1) != e0 )
& sP29_prd ) ),
inference(formula_renaming,[status(thm)],[f426,f466]) ).
fof(f468,plain,
( ( ( ( e0 = unit
| op(e4,e0) != e1 )
& op(e4,e1) = e0 )
| ~ sP29_prd
| sP24_prd )
& ( ( ( ( e0 != unit
& op(e4,e0) = e1 )
| op(e4,e1) != e0 )
& sP29_prd )
| ~ sP24_prd ) ),
inference(NNF_transformation,[status(thm)],[f467]) ).
fof(f469,plain,
( sP29_prd
| ~ sP24_prd ),
inference(cnf_transformation,[status(thm)],[f468]) ).
fof(f474,definition,
( sP30_prd
<=> ( ( ( e1 != unit
& op(e3,e1) = e4 )
| op(e3,e4) != e1 )
& ( ( e1 != unit
& op(e3,e1) = e3 )
| op(e3,e3) != e1 )
& ( ( e1 != unit
& op(e3,e1) = e2 )
| op(e3,e2) != e1 )
& ( ( e1 != unit
& op(e3,e1) = e1 )
| op(e3,e1) != e1 )
& ( ( e1 != unit
& op(e3,e1) = e0 )
| op(e3,e0) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e4 )
| op(e2,e4) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e3 )
| op(e2,e3) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e2 )
| op(e2,e2) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e1 )
| op(e2,e1) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e0 )
| op(e2,e0) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e4 )
| op(e1,e4) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e3 )
| op(e1,e3) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e2 )
| op(e1,e2) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e1 )
| op(e1,e1) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e0 )
| op(e1,e0) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e4 )
| op(e0,e4) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e3 )
| op(e0,e3) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e2 )
| op(e0,e2) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e1 )
| op(e0,e1) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e0 )
| op(e0,e0) != e1 ) ) ),
introduced(definition,[new_symbols(definition,[sP30_prd])],[]) ).
fof(f475,plain,
( sP25_prd
<=> ( ( ( e1 != unit
& op(e4,e1) = e0 )
| op(e4,e0) != e1 )
& sP30_prd ) ),
inference(formula_renaming,[status(thm)],[f434,f474]) ).
fof(f476,plain,
( ( ( ( e1 = unit
| op(e4,e1) != e0 )
& op(e4,e0) = e1 )
| ~ sP30_prd
| sP25_prd )
& ( ( ( ( e1 != unit
& op(e4,e1) = e0 )
| op(e4,e0) != e1 )
& sP30_prd )
| ~ sP25_prd ) ),
inference(NNF_transformation,[status(thm)],[f475]) ).
fof(f477,plain,
( sP30_prd
| ~ sP25_prd ),
inference(cnf_transformation,[status(thm)],[f476]) ).
fof(f482,definition,
( sP31_prd
<=> ( ( ( e2 != unit
& op(e3,e2) = e3 )
| op(e3,e3) != e2 )
& ( ( e2 != unit
& op(e3,e2) = e2 )
| op(e3,e2) != e2 )
& ( ( e2 != unit
& op(e3,e2) = e1 )
| op(e3,e1) != e2 )
& ( ( e2 != unit
& op(e3,e2) = e0 )
| op(e3,e0) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e4 )
| op(e2,e4) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e3 )
| op(e2,e3) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e2 )
| op(e2,e2) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e1 )
| op(e2,e1) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e0 )
| op(e2,e0) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e4 )
| op(e1,e4) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e3 )
| op(e1,e3) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e2 )
| op(e1,e2) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e1 )
| op(e1,e1) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e0 )
| op(e1,e0) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e4 )
| op(e0,e4) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e3 )
| op(e0,e3) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e2 )
| op(e0,e2) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e1 )
| op(e0,e1) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e0 )
| op(e0,e0) != e2 ) ) ),
introduced(definition,[new_symbols(definition,[sP31_prd])],[]) ).
fof(f483,plain,
( sP26_prd
<=> ( ( ( e2 != unit
& op(e3,e2) = e4 )
| op(e3,e4) != e2 )
& sP31_prd ) ),
inference(formula_renaming,[status(thm)],[f442,f482]) ).
fof(f484,plain,
( ( ( ( e2 = unit
| op(e3,e2) != e4 )
& op(e3,e4) = e2 )
| ~ sP31_prd
| sP26_prd )
& ( ( ( ( e2 != unit
& op(e3,e2) = e4 )
| op(e3,e4) != e2 )
& sP31_prd )
| ~ sP26_prd ) ),
inference(NNF_transformation,[status(thm)],[f483]) ).
fof(f485,plain,
( sP31_prd
| ~ sP26_prd ),
inference(cnf_transformation,[status(thm)],[f484]) ).
fof(f490,definition,
( sP32_prd
<=> ( ( ( e3 != unit
& op(e3,e3) = e2 )
| op(e3,e2) != e3 )
& ( ( e3 != unit
& op(e3,e3) = e1 )
| op(e3,e1) != e3 )
& ( ( e3 != unit
& op(e3,e3) = e0 )
| op(e3,e0) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e4 )
| op(e2,e4) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e3 )
| op(e2,e3) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e2 )
| op(e2,e2) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e1 )
| op(e2,e1) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e0 )
| op(e2,e0) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e4 )
| op(e1,e4) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e3 )
| op(e1,e3) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e2 )
| op(e1,e2) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e1 )
| op(e1,e1) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e0 )
| op(e1,e0) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e4 )
| op(e0,e4) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e3 )
| op(e0,e3) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e2 )
| op(e0,e2) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e1 )
| op(e0,e1) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e0 )
| op(e0,e0) != e3 ) ) ),
introduced(definition,[new_symbols(definition,[sP32_prd])],[]) ).
fof(f491,plain,
( sP27_prd
<=> ( ( ( e3 != unit
& op(e3,e3) = e3 )
| op(e3,e3) != e3 )
& sP32_prd ) ),
inference(formula_renaming,[status(thm)],[f450,f490]) ).
fof(f492,plain,
( ( ( ( e3 = unit
| op(e3,e3) != e3 )
& op(e3,e3) = e3 )
| ~ sP32_prd
| sP27_prd )
& ( ( ( ( e3 != unit
& op(e3,e3) = e3 )
| op(e3,e3) != e3 )
& sP32_prd )
| ~ sP27_prd ) ),
inference(NNF_transformation,[status(thm)],[f491]) ).
fof(f493,plain,
( sP32_prd
| ~ sP27_prd ),
inference(cnf_transformation,[status(thm)],[f492]) ).
fof(f498,definition,
( sP33_prd
<=> ( ( op(op(e3,e1),e3) != e1
& op(op(e3,e1),e1) = e3
& op(e1,e3) != op(e3,e1) )
| ( op(op(e3,e0),e3) != e0
& op(op(e3,e0),e0) = e3
& op(e0,e3) != op(e3,e0) )
| ( op(op(e2,e4),e2) != e4
& op(op(e2,e4),e4) = e2
& op(e4,e2) != op(e2,e4) )
| ( op(op(e2,e3),e2) != e3
& op(op(e2,e3),e3) = e2
& op(e3,e2) != op(e2,e3) )
| ( op(op(e2,e2),e2) != e2
& op(op(e2,e2),e2) = e2
& op(e2,e2) != op(e2,e2) )
| ( op(op(e2,e1),e2) != e1
& op(op(e2,e1),e1) = e2
& op(e1,e2) != op(e2,e1) )
| ( op(op(e2,e0),e2) != e0
& op(op(e2,e0),e0) = e2
& op(e0,e2) != op(e2,e0) )
| ( op(op(e1,e4),e1) != e4
& op(op(e1,e4),e4) = e1
& op(e4,e1) != op(e1,e4) )
| ( op(op(e1,e3),e1) != e3
& op(op(e1,e3),e3) = e1
& op(e3,e1) != op(e1,e3) )
| ( op(op(e1,e2),e1) != e2
& op(op(e1,e2),e2) = e1
& op(e2,e1) != op(e1,e2) )
| ( op(op(e1,e1),e1) != e1
& op(op(e1,e1),e1) = e1
& op(e1,e1) != op(e1,e1) )
| ( op(op(e1,e0),e1) != e0
& op(op(e1,e0),e0) = e1
& op(e0,e1) != op(e1,e0) )
| ( op(op(e0,e4),e0) != e4
& op(op(e0,e4),e4) = e0
& op(e4,e0) != op(e0,e4) )
| ( op(op(e0,e3),e0) != e3
& op(op(e0,e3),e3) = e0
& op(e3,e0) != op(e0,e3) )
| ( op(op(e0,e2),e0) != e2
& op(op(e0,e2),e2) = e0
& op(e2,e0) != op(e0,e2) )
| ( op(op(e0,e1),e0) != e1
& op(op(e0,e1),e1) = e0
& op(e1,e0) != op(e0,e1) )
| ( op(op(e0,e0),e0) != e0
& op(op(e0,e0),e0) = e0
& op(e0,e0) != op(e0,e0) ) ) ),
introduced(definition,[new_symbols(definition,[sP33_prd])],[]) ).
fof(f499,plain,
( sP28_prd
<=> ( ( op(op(e3,e2),e3) != e2
& op(op(e3,e2),e2) = e3
& op(e2,e3) != op(e3,e2) )
| sP33_prd ) ),
inference(formula_renaming,[status(thm)],[f458,f498]) ).
fof(f500,plain,
( ( ( ( op(op(e3,e2),e3) = e2
| op(op(e3,e2),e2) != e3
| op(e2,e3) = op(e3,e2) )
& ~ sP33_prd )
| sP28_prd )
& ( ( op(op(e3,e2),e3) != e2
& op(op(e3,e2),e2) = e3
& op(e2,e3) != op(e3,e2) )
| sP33_prd
| ~ sP28_prd ) ),
inference(NNF_transformation,[status(thm)],[f499]) ).
fof(f502,plain,
( op(op(e3,e2),e2) = e3
| sP33_prd
| ~ sP28_prd ),
inference(cnf_transformation,[status(thm)],[f500]) ).
fof(f506,definition,
( sP34_prd
<=> ( ( ( e0 != unit
& op(e3,e0) = e4 )
| op(e3,e4) != e0 )
& ( ( e0 != unit
& op(e3,e0) = e3 )
| op(e3,e3) != e0 )
& ( ( e0 != unit
& op(e3,e0) = e2 )
| op(e3,e2) != e0 )
& ( ( e0 != unit
& op(e3,e0) = e1 )
| op(e3,e1) != e0 )
& ( ( e0 != unit
& op(e3,e0) = e0 )
| op(e3,e0) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e4 )
| op(e2,e4) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e3 )
| op(e2,e3) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e2 )
| op(e2,e2) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e1 )
| op(e2,e1) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e0 )
| op(e2,e0) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e4 )
| op(e1,e4) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e3 )
| op(e1,e3) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e2 )
| op(e1,e2) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e1 )
| op(e1,e1) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e0 )
| op(e1,e0) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e4 )
| op(e0,e4) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e3 )
| op(e0,e3) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e2 )
| op(e0,e2) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e1 )
| op(e0,e1) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e0 )
| op(e0,e0) != e0 ) ) ),
introduced(definition,[new_symbols(definition,[sP34_prd])],[]) ).
fof(f507,plain,
( sP29_prd
<=> ( ( ( e0 != unit
& op(e4,e0) = e0 )
| op(e4,e0) != e0 )
& sP34_prd ) ),
inference(formula_renaming,[status(thm)],[f466,f506]) ).
fof(f508,plain,
( ( ( ( e0 = unit
| op(e4,e0) != e0 )
& op(e4,e0) = e0 )
| ~ sP34_prd
| sP29_prd )
& ( ( ( ( e0 != unit
& op(e4,e0) = e0 )
| op(e4,e0) != e0 )
& sP34_prd )
| ~ sP29_prd ) ),
inference(NNF_transformation,[status(thm)],[f507]) ).
fof(f509,plain,
( sP34_prd
| ~ sP29_prd ),
inference(cnf_transformation,[status(thm)],[f508]) ).
fof(f514,definition,
( sP35_prd
<=> ( ( ( e1 != unit
& op(e3,e1) = e3 )
| op(e3,e3) != e1 )
& ( ( e1 != unit
& op(e3,e1) = e2 )
| op(e3,e2) != e1 )
& ( ( e1 != unit
& op(e3,e1) = e1 )
| op(e3,e1) != e1 )
& ( ( e1 != unit
& op(e3,e1) = e0 )
| op(e3,e0) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e4 )
| op(e2,e4) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e3 )
| op(e2,e3) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e2 )
| op(e2,e2) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e1 )
| op(e2,e1) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e0 )
| op(e2,e0) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e4 )
| op(e1,e4) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e3 )
| op(e1,e3) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e2 )
| op(e1,e2) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e1 )
| op(e1,e1) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e0 )
| op(e1,e0) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e4 )
| op(e0,e4) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e3 )
| op(e0,e3) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e2 )
| op(e0,e2) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e1 )
| op(e0,e1) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e0 )
| op(e0,e0) != e1 ) ) ),
introduced(definition,[new_symbols(definition,[sP35_prd])],[]) ).
fof(f515,plain,
( sP30_prd
<=> ( ( ( e1 != unit
& op(e3,e1) = e4 )
| op(e3,e4) != e1 )
& sP35_prd ) ),
inference(formula_renaming,[status(thm)],[f474,f514]) ).
fof(f516,plain,
( ( ( ( e1 = unit
| op(e3,e1) != e4 )
& op(e3,e4) = e1 )
| ~ sP35_prd
| sP30_prd )
& ( ( ( ( e1 != unit
& op(e3,e1) = e4 )
| op(e3,e4) != e1 )
& sP35_prd )
| ~ sP30_prd ) ),
inference(NNF_transformation,[status(thm)],[f515]) ).
fof(f517,plain,
( sP35_prd
| ~ sP30_prd ),
inference(cnf_transformation,[status(thm)],[f516]) ).
fof(f518,plain,
( op(e3,e1) = e4
| op(e3,e4) != e1
| ~ sP30_prd ),
inference(cnf_transformation,[status(thm)],[f516]) ).
fof(f522,definition,
( sP36_prd
<=> ( ( ( e2 != unit
& op(e3,e2) = e2 )
| op(e3,e2) != e2 )
& ( ( e2 != unit
& op(e3,e2) = e1 )
| op(e3,e1) != e2 )
& ( ( e2 != unit
& op(e3,e2) = e0 )
| op(e3,e0) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e4 )
| op(e2,e4) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e3 )
| op(e2,e3) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e2 )
| op(e2,e2) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e1 )
| op(e2,e1) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e0 )
| op(e2,e0) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e4 )
| op(e1,e4) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e3 )
| op(e1,e3) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e2 )
| op(e1,e2) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e1 )
| op(e1,e1) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e0 )
| op(e1,e0) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e4 )
| op(e0,e4) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e3 )
| op(e0,e3) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e2 )
| op(e0,e2) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e1 )
| op(e0,e1) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e0 )
| op(e0,e0) != e2 ) ) ),
introduced(definition,[new_symbols(definition,[sP36_prd])],[]) ).
fof(f523,plain,
( sP31_prd
<=> ( ( ( e2 != unit
& op(e3,e2) = e3 )
| op(e3,e3) != e2 )
& sP36_prd ) ),
inference(formula_renaming,[status(thm)],[f482,f522]) ).
fof(f524,plain,
( ( ( ( e2 = unit
| op(e3,e2) != e3 )
& op(e3,e3) = e2 )
| ~ sP36_prd
| sP31_prd )
& ( ( ( ( e2 != unit
& op(e3,e2) = e3 )
| op(e3,e3) != e2 )
& sP36_prd )
| ~ sP31_prd ) ),
inference(NNF_transformation,[status(thm)],[f523]) ).
fof(f525,plain,
( sP36_prd
| ~ sP31_prd ),
inference(cnf_transformation,[status(thm)],[f524]) ).
fof(f530,definition,
( sP37_prd
<=> ( ( ( e3 != unit
& op(e3,e3) = e1 )
| op(e3,e1) != e3 )
& ( ( e3 != unit
& op(e3,e3) = e0 )
| op(e3,e0) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e4 )
| op(e2,e4) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e3 )
| op(e2,e3) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e2 )
| op(e2,e2) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e1 )
| op(e2,e1) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e0 )
| op(e2,e0) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e4 )
| op(e1,e4) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e3 )
| op(e1,e3) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e2 )
| op(e1,e2) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e1 )
| op(e1,e1) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e0 )
| op(e1,e0) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e4 )
| op(e0,e4) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e3 )
| op(e0,e3) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e2 )
| op(e0,e2) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e1 )
| op(e0,e1) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e0 )
| op(e0,e0) != e3 ) ) ),
introduced(definition,[new_symbols(definition,[sP37_prd])],[]) ).
fof(f531,plain,
( sP32_prd
<=> ( ( ( e3 != unit
& op(e3,e3) = e2 )
| op(e3,e2) != e3 )
& sP37_prd ) ),
inference(formula_renaming,[status(thm)],[f490,f530]) ).
fof(f532,plain,
( ( ( ( e3 = unit
| op(e3,e3) != e2 )
& op(e3,e2) = e3 )
| ~ sP37_prd
| sP32_prd )
& ( ( ( ( e3 != unit
& op(e3,e3) = e2 )
| op(e3,e2) != e3 )
& sP37_prd )
| ~ sP32_prd ) ),
inference(NNF_transformation,[status(thm)],[f531]) ).
fof(f533,plain,
( sP37_prd
| ~ sP32_prd ),
inference(cnf_transformation,[status(thm)],[f532]) ).
fof(f538,definition,
( sP38_prd
<=> ( ( op(op(e3,e0),e3) != e0
& op(op(e3,e0),e0) = e3
& op(e0,e3) != op(e3,e0) )
| ( op(op(e2,e4),e2) != e4
& op(op(e2,e4),e4) = e2
& op(e4,e2) != op(e2,e4) )
| ( op(op(e2,e3),e2) != e3
& op(op(e2,e3),e3) = e2
& op(e3,e2) != op(e2,e3) )
| ( op(op(e2,e2),e2) != e2
& op(op(e2,e2),e2) = e2
& op(e2,e2) != op(e2,e2) )
| ( op(op(e2,e1),e2) != e1
& op(op(e2,e1),e1) = e2
& op(e1,e2) != op(e2,e1) )
| ( op(op(e2,e0),e2) != e0
& op(op(e2,e0),e0) = e2
& op(e0,e2) != op(e2,e0) )
| ( op(op(e1,e4),e1) != e4
& op(op(e1,e4),e4) = e1
& op(e4,e1) != op(e1,e4) )
| ( op(op(e1,e3),e1) != e3
& op(op(e1,e3),e3) = e1
& op(e3,e1) != op(e1,e3) )
| ( op(op(e1,e2),e1) != e2
& op(op(e1,e2),e2) = e1
& op(e2,e1) != op(e1,e2) )
| ( op(op(e1,e1),e1) != e1
& op(op(e1,e1),e1) = e1
& op(e1,e1) != op(e1,e1) )
| ( op(op(e1,e0),e1) != e0
& op(op(e1,e0),e0) = e1
& op(e0,e1) != op(e1,e0) )
| ( op(op(e0,e4),e0) != e4
& op(op(e0,e4),e4) = e0
& op(e4,e0) != op(e0,e4) )
| ( op(op(e0,e3),e0) != e3
& op(op(e0,e3),e3) = e0
& op(e3,e0) != op(e0,e3) )
| ( op(op(e0,e2),e0) != e2
& op(op(e0,e2),e2) = e0
& op(e2,e0) != op(e0,e2) )
| ( op(op(e0,e1),e0) != e1
& op(op(e0,e1),e1) = e0
& op(e1,e0) != op(e0,e1) )
| ( op(op(e0,e0),e0) != e0
& op(op(e0,e0),e0) = e0
& op(e0,e0) != op(e0,e0) ) ) ),
introduced(definition,[new_symbols(definition,[sP38_prd])],[]) ).
fof(f539,plain,
( sP33_prd
<=> ( ( op(op(e3,e1),e3) != e1
& op(op(e3,e1),e1) = e3
& op(e1,e3) != op(e3,e1) )
| sP38_prd ) ),
inference(formula_renaming,[status(thm)],[f498,f538]) ).
fof(f540,plain,
( ( ( ( op(op(e3,e1),e3) = e1
| op(op(e3,e1),e1) != e3
| op(e1,e3) = op(e3,e1) )
& ~ sP38_prd )
| sP33_prd )
& ( ( op(op(e3,e1),e3) != e1
& op(op(e3,e1),e1) = e3
& op(e1,e3) != op(e3,e1) )
| sP38_prd
| ~ sP33_prd ) ),
inference(NNF_transformation,[status(thm)],[f539]) ).
fof(f541,plain,
( op(e1,e3) != op(e3,e1)
| sP38_prd
| ~ sP33_prd ),
inference(cnf_transformation,[status(thm)],[f540]) ).
fof(f546,definition,
( sP39_prd
<=> ( ( ( e0 != unit
& op(e3,e0) = e3 )
| op(e3,e3) != e0 )
& ( ( e0 != unit
& op(e3,e0) = e2 )
| op(e3,e2) != e0 )
& ( ( e0 != unit
& op(e3,e0) = e1 )
| op(e3,e1) != e0 )
& ( ( e0 != unit
& op(e3,e0) = e0 )
| op(e3,e0) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e4 )
| op(e2,e4) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e3 )
| op(e2,e3) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e2 )
| op(e2,e2) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e1 )
| op(e2,e1) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e0 )
| op(e2,e0) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e4 )
| op(e1,e4) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e3 )
| op(e1,e3) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e2 )
| op(e1,e2) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e1 )
| op(e1,e1) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e0 )
| op(e1,e0) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e4 )
| op(e0,e4) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e3 )
| op(e0,e3) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e2 )
| op(e0,e2) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e1 )
| op(e0,e1) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e0 )
| op(e0,e0) != e0 ) ) ),
introduced(definition,[new_symbols(definition,[sP39_prd])],[]) ).
fof(f547,plain,
( sP34_prd
<=> ( ( ( e0 != unit
& op(e3,e0) = e4 )
| op(e3,e4) != e0 )
& sP39_prd ) ),
inference(formula_renaming,[status(thm)],[f506,f546]) ).
fof(f548,plain,
( ( ( ( e0 = unit
| op(e3,e0) != e4 )
& op(e3,e4) = e0 )
| ~ sP39_prd
| sP34_prd )
& ( ( ( ( e0 != unit
& op(e3,e0) = e4 )
| op(e3,e4) != e0 )
& sP39_prd )
| ~ sP34_prd ) ),
inference(NNF_transformation,[status(thm)],[f547]) ).
fof(f549,plain,
( sP39_prd
| ~ sP34_prd ),
inference(cnf_transformation,[status(thm)],[f548]) ).
fof(f554,definition,
( sP40_prd
<=> ( ( ( e1 != unit
& op(e3,e1) = e2 )
| op(e3,e2) != e1 )
& ( ( e1 != unit
& op(e3,e1) = e1 )
| op(e3,e1) != e1 )
& ( ( e1 != unit
& op(e3,e1) = e0 )
| op(e3,e0) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e4 )
| op(e2,e4) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e3 )
| op(e2,e3) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e2 )
| op(e2,e2) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e1 )
| op(e2,e1) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e0 )
| op(e2,e0) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e4 )
| op(e1,e4) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e3 )
| op(e1,e3) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e2 )
| op(e1,e2) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e1 )
| op(e1,e1) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e0 )
| op(e1,e0) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e4 )
| op(e0,e4) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e3 )
| op(e0,e3) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e2 )
| op(e0,e2) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e1 )
| op(e0,e1) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e0 )
| op(e0,e0) != e1 ) ) ),
introduced(definition,[new_symbols(definition,[sP40_prd])],[]) ).
fof(f555,plain,
( sP35_prd
<=> ( ( ( e1 != unit
& op(e3,e1) = e3 )
| op(e3,e3) != e1 )
& sP40_prd ) ),
inference(formula_renaming,[status(thm)],[f514,f554]) ).
fof(f556,plain,
( ( ( ( e1 = unit
| op(e3,e1) != e3 )
& op(e3,e3) = e1 )
| ~ sP40_prd
| sP35_prd )
& ( ( ( ( e1 != unit
& op(e3,e1) = e3 )
| op(e3,e3) != e1 )
& sP40_prd )
| ~ sP35_prd ) ),
inference(NNF_transformation,[status(thm)],[f555]) ).
fof(f557,plain,
( sP40_prd
| ~ sP35_prd ),
inference(cnf_transformation,[status(thm)],[f556]) ).
fof(f562,definition,
( sP41_prd
<=> ( ( ( e2 != unit
& op(e3,e2) = e1 )
| op(e3,e1) != e2 )
& ( ( e2 != unit
& op(e3,e2) = e0 )
| op(e3,e0) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e4 )
| op(e2,e4) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e3 )
| op(e2,e3) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e2 )
| op(e2,e2) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e1 )
| op(e2,e1) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e0 )
| op(e2,e0) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e4 )
| op(e1,e4) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e3 )
| op(e1,e3) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e2 )
| op(e1,e2) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e1 )
| op(e1,e1) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e0 )
| op(e1,e0) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e4 )
| op(e0,e4) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e3 )
| op(e0,e3) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e2 )
| op(e0,e2) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e1 )
| op(e0,e1) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e0 )
| op(e0,e0) != e2 ) ) ),
introduced(definition,[new_symbols(definition,[sP41_prd])],[]) ).
fof(f563,plain,
( sP36_prd
<=> ( ( ( e2 != unit
& op(e3,e2) = e2 )
| op(e3,e2) != e2 )
& sP41_prd ) ),
inference(formula_renaming,[status(thm)],[f522,f562]) ).
fof(f564,plain,
( ( ( ( e2 = unit
| op(e3,e2) != e2 )
& op(e3,e2) = e2 )
| ~ sP41_prd
| sP36_prd )
& ( ( ( ( e2 != unit
& op(e3,e2) = e2 )
| op(e3,e2) != e2 )
& sP41_prd )
| ~ sP36_prd ) ),
inference(NNF_transformation,[status(thm)],[f563]) ).
fof(f565,plain,
( sP41_prd
| ~ sP36_prd ),
inference(cnf_transformation,[status(thm)],[f564]) ).
fof(f570,definition,
( sP42_prd
<=> ( ( ( e3 != unit
& op(e3,e3) = e0 )
| op(e3,e0) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e4 )
| op(e2,e4) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e3 )
| op(e2,e3) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e2 )
| op(e2,e2) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e1 )
| op(e2,e1) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e0 )
| op(e2,e0) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e4 )
| op(e1,e4) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e3 )
| op(e1,e3) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e2 )
| op(e1,e2) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e1 )
| op(e1,e1) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e0 )
| op(e1,e0) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e4 )
| op(e0,e4) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e3 )
| op(e0,e3) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e2 )
| op(e0,e2) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e1 )
| op(e0,e1) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e0 )
| op(e0,e0) != e3 ) ) ),
introduced(definition,[new_symbols(definition,[sP42_prd])],[]) ).
fof(f571,plain,
( sP37_prd
<=> ( ( ( e3 != unit
& op(e3,e3) = e1 )
| op(e3,e1) != e3 )
& sP42_prd ) ),
inference(formula_renaming,[status(thm)],[f530,f570]) ).
fof(f572,plain,
( ( ( ( e3 = unit
| op(e3,e3) != e1 )
& op(e3,e1) = e3 )
| ~ sP42_prd
| sP37_prd )
& ( ( ( ( e3 != unit
& op(e3,e3) = e1 )
| op(e3,e1) != e3 )
& sP42_prd )
| ~ sP37_prd ) ),
inference(NNF_transformation,[status(thm)],[f571]) ).
fof(f573,plain,
( sP42_prd
| ~ sP37_prd ),
inference(cnf_transformation,[status(thm)],[f572]) ).
fof(f578,definition,
( sP43_prd
<=> ( ( op(op(e2,e4),e2) != e4
& op(op(e2,e4),e4) = e2
& op(e4,e2) != op(e2,e4) )
| ( op(op(e2,e3),e2) != e3
& op(op(e2,e3),e3) = e2
& op(e3,e2) != op(e2,e3) )
| ( op(op(e2,e2),e2) != e2
& op(op(e2,e2),e2) = e2
& op(e2,e2) != op(e2,e2) )
| ( op(op(e2,e1),e2) != e1
& op(op(e2,e1),e1) = e2
& op(e1,e2) != op(e2,e1) )
| ( op(op(e2,e0),e2) != e0
& op(op(e2,e0),e0) = e2
& op(e0,e2) != op(e2,e0) )
| ( op(op(e1,e4),e1) != e4
& op(op(e1,e4),e4) = e1
& op(e4,e1) != op(e1,e4) )
| ( op(op(e1,e3),e1) != e3
& op(op(e1,e3),e3) = e1
& op(e3,e1) != op(e1,e3) )
| ( op(op(e1,e2),e1) != e2
& op(op(e1,e2),e2) = e1
& op(e2,e1) != op(e1,e2) )
| ( op(op(e1,e1),e1) != e1
& op(op(e1,e1),e1) = e1
& op(e1,e1) != op(e1,e1) )
| ( op(op(e1,e0),e1) != e0
& op(op(e1,e0),e0) = e1
& op(e0,e1) != op(e1,e0) )
| ( op(op(e0,e4),e0) != e4
& op(op(e0,e4),e4) = e0
& op(e4,e0) != op(e0,e4) )
| ( op(op(e0,e3),e0) != e3
& op(op(e0,e3),e3) = e0
& op(e3,e0) != op(e0,e3) )
| ( op(op(e0,e2),e0) != e2
& op(op(e0,e2),e2) = e0
& op(e2,e0) != op(e0,e2) )
| ( op(op(e0,e1),e0) != e1
& op(op(e0,e1),e1) = e0
& op(e1,e0) != op(e0,e1) )
| ( op(op(e0,e0),e0) != e0
& op(op(e0,e0),e0) = e0
& op(e0,e0) != op(e0,e0) ) ) ),
introduced(definition,[new_symbols(definition,[sP43_prd])],[]) ).
fof(f579,plain,
( sP38_prd
<=> ( ( op(op(e3,e0),e3) != e0
& op(op(e3,e0),e0) = e3
& op(e0,e3) != op(e3,e0) )
| sP43_prd ) ),
inference(formula_renaming,[status(thm)],[f538,f578]) ).
fof(f580,plain,
( ( ( ( op(op(e3,e0),e3) = e0
| op(op(e3,e0),e0) != e3
| op(e0,e3) = op(e3,e0) )
& ~ sP43_prd )
| sP38_prd )
& ( ( op(op(e3,e0),e3) != e0
& op(op(e3,e0),e0) = e3
& op(e0,e3) != op(e3,e0) )
| sP43_prd
| ~ sP38_prd ) ),
inference(NNF_transformation,[status(thm)],[f579]) ).
fof(f581,plain,
( op(e0,e3) != op(e3,e0)
| sP43_prd
| ~ sP38_prd ),
inference(cnf_transformation,[status(thm)],[f580]) ).
fof(f586,definition,
( sP44_prd
<=> ( ( ( e0 != unit
& op(e3,e0) = e2 )
| op(e3,e2) != e0 )
& ( ( e0 != unit
& op(e3,e0) = e1 )
| op(e3,e1) != e0 )
& ( ( e0 != unit
& op(e3,e0) = e0 )
| op(e3,e0) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e4 )
| op(e2,e4) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e3 )
| op(e2,e3) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e2 )
| op(e2,e2) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e1 )
| op(e2,e1) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e0 )
| op(e2,e0) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e4 )
| op(e1,e4) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e3 )
| op(e1,e3) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e2 )
| op(e1,e2) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e1 )
| op(e1,e1) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e0 )
| op(e1,e0) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e4 )
| op(e0,e4) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e3 )
| op(e0,e3) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e2 )
| op(e0,e2) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e1 )
| op(e0,e1) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e0 )
| op(e0,e0) != e0 ) ) ),
introduced(definition,[new_symbols(definition,[sP44_prd])],[]) ).
fof(f587,plain,
( sP39_prd
<=> ( ( ( e0 != unit
& op(e3,e0) = e3 )
| op(e3,e3) != e0 )
& sP44_prd ) ),
inference(formula_renaming,[status(thm)],[f546,f586]) ).
fof(f588,plain,
( ( ( ( e0 = unit
| op(e3,e0) != e3 )
& op(e3,e3) = e0 )
| ~ sP44_prd
| sP39_prd )
& ( ( ( ( e0 != unit
& op(e3,e0) = e3 )
| op(e3,e3) != e0 )
& sP44_prd )
| ~ sP39_prd ) ),
inference(NNF_transformation,[status(thm)],[f587]) ).
fof(f589,plain,
( sP44_prd
| ~ sP39_prd ),
inference(cnf_transformation,[status(thm)],[f588]) ).
fof(f594,definition,
( sP45_prd
<=> ( ( ( e1 != unit
& op(e3,e1) = e1 )
| op(e3,e1) != e1 )
& ( ( e1 != unit
& op(e3,e1) = e0 )
| op(e3,e0) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e4 )
| op(e2,e4) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e3 )
| op(e2,e3) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e2 )
| op(e2,e2) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e1 )
| op(e2,e1) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e0 )
| op(e2,e0) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e4 )
| op(e1,e4) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e3 )
| op(e1,e3) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e2 )
| op(e1,e2) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e1 )
| op(e1,e1) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e0 )
| op(e1,e0) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e4 )
| op(e0,e4) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e3 )
| op(e0,e3) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e2 )
| op(e0,e2) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e1 )
| op(e0,e1) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e0 )
| op(e0,e0) != e1 ) ) ),
introduced(definition,[new_symbols(definition,[sP45_prd])],[]) ).
fof(f595,plain,
( sP40_prd
<=> ( ( ( e1 != unit
& op(e3,e1) = e2 )
| op(e3,e2) != e1 )
& sP45_prd ) ),
inference(formula_renaming,[status(thm)],[f554,f594]) ).
fof(f596,plain,
( ( ( ( e1 = unit
| op(e3,e1) != e2 )
& op(e3,e2) = e1 )
| ~ sP45_prd
| sP40_prd )
& ( ( ( ( e1 != unit
& op(e3,e1) = e2 )
| op(e3,e2) != e1 )
& sP45_prd )
| ~ sP40_prd ) ),
inference(NNF_transformation,[status(thm)],[f595]) ).
fof(f597,plain,
( sP45_prd
| ~ sP40_prd ),
inference(cnf_transformation,[status(thm)],[f596]) ).
fof(f598,plain,
( op(e3,e1) = e2
| op(e3,e2) != e1
| ~ sP40_prd ),
inference(cnf_transformation,[status(thm)],[f596]) ).
fof(f602,definition,
( sP46_prd
<=> ( ( ( e2 != unit
& op(e3,e2) = e0 )
| op(e3,e0) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e4 )
| op(e2,e4) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e3 )
| op(e2,e3) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e2 )
| op(e2,e2) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e1 )
| op(e2,e1) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e0 )
| op(e2,e0) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e4 )
| op(e1,e4) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e3 )
| op(e1,e3) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e2 )
| op(e1,e2) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e1 )
| op(e1,e1) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e0 )
| op(e1,e0) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e4 )
| op(e0,e4) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e3 )
| op(e0,e3) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e2 )
| op(e0,e2) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e1 )
| op(e0,e1) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e0 )
| op(e0,e0) != e2 ) ) ),
introduced(definition,[new_symbols(definition,[sP46_prd])],[]) ).
fof(f603,plain,
( sP41_prd
<=> ( ( ( e2 != unit
& op(e3,e2) = e1 )
| op(e3,e1) != e2 )
& sP46_prd ) ),
inference(formula_renaming,[status(thm)],[f562,f602]) ).
fof(f604,plain,
( ( ( ( e2 = unit
| op(e3,e2) != e1 )
& op(e3,e1) = e2 )
| ~ sP46_prd
| sP41_prd )
& ( ( ( ( e2 != unit
& op(e3,e2) = e1 )
| op(e3,e1) != e2 )
& sP46_prd )
| ~ sP41_prd ) ),
inference(NNF_transformation,[status(thm)],[f603]) ).
fof(f605,plain,
( sP46_prd
| ~ sP41_prd ),
inference(cnf_transformation,[status(thm)],[f604]) ).
fof(f610,definition,
( sP47_prd
<=> ( ( ( e3 != unit
& op(e2,e3) = e4 )
| op(e2,e4) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e3 )
| op(e2,e3) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e2 )
| op(e2,e2) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e1 )
| op(e2,e1) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e0 )
| op(e2,e0) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e4 )
| op(e1,e4) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e3 )
| op(e1,e3) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e2 )
| op(e1,e2) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e1 )
| op(e1,e1) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e0 )
| op(e1,e0) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e4 )
| op(e0,e4) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e3 )
| op(e0,e3) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e2 )
| op(e0,e2) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e1 )
| op(e0,e1) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e0 )
| op(e0,e0) != e3 ) ) ),
introduced(definition,[new_symbols(definition,[sP47_prd])],[]) ).
fof(f611,plain,
( sP42_prd
<=> ( ( ( e3 != unit
& op(e3,e3) = e0 )
| op(e3,e0) != e3 )
& sP47_prd ) ),
inference(formula_renaming,[status(thm)],[f570,f610]) ).
fof(f612,plain,
( ( ( ( e3 = unit
| op(e3,e3) != e0 )
& op(e3,e0) = e3 )
| ~ sP47_prd
| sP42_prd )
& ( ( ( ( e3 != unit
& op(e3,e3) = e0 )
| op(e3,e0) != e3 )
& sP47_prd )
| ~ sP42_prd ) ),
inference(NNF_transformation,[status(thm)],[f611]) ).
fof(f613,plain,
( sP47_prd
| ~ sP42_prd ),
inference(cnf_transformation,[status(thm)],[f612]) ).
fof(f618,definition,
( sP48_prd
<=> ( ( op(op(e2,e3),e2) != e3
& op(op(e2,e3),e3) = e2
& op(e3,e2) != op(e2,e3) )
| ( op(op(e2,e2),e2) != e2
& op(op(e2,e2),e2) = e2
& op(e2,e2) != op(e2,e2) )
| ( op(op(e2,e1),e2) != e1
& op(op(e2,e1),e1) = e2
& op(e1,e2) != op(e2,e1) )
| ( op(op(e2,e0),e2) != e0
& op(op(e2,e0),e0) = e2
& op(e0,e2) != op(e2,e0) )
| ( op(op(e1,e4),e1) != e4
& op(op(e1,e4),e4) = e1
& op(e4,e1) != op(e1,e4) )
| ( op(op(e1,e3),e1) != e3
& op(op(e1,e3),e3) = e1
& op(e3,e1) != op(e1,e3) )
| ( op(op(e1,e2),e1) != e2
& op(op(e1,e2),e2) = e1
& op(e2,e1) != op(e1,e2) )
| ( op(op(e1,e1),e1) != e1
& op(op(e1,e1),e1) = e1
& op(e1,e1) != op(e1,e1) )
| ( op(op(e1,e0),e1) != e0
& op(op(e1,e0),e0) = e1
& op(e0,e1) != op(e1,e0) )
| ( op(op(e0,e4),e0) != e4
& op(op(e0,e4),e4) = e0
& op(e4,e0) != op(e0,e4) )
| ( op(op(e0,e3),e0) != e3
& op(op(e0,e3),e3) = e0
& op(e3,e0) != op(e0,e3) )
| ( op(op(e0,e2),e0) != e2
& op(op(e0,e2),e2) = e0
& op(e2,e0) != op(e0,e2) )
| ( op(op(e0,e1),e0) != e1
& op(op(e0,e1),e1) = e0
& op(e1,e0) != op(e0,e1) )
| ( op(op(e0,e0),e0) != e0
& op(op(e0,e0),e0) = e0
& op(e0,e0) != op(e0,e0) ) ) ),
introduced(definition,[new_symbols(definition,[sP48_prd])],[]) ).
fof(f619,plain,
( sP43_prd
<=> ( ( op(op(e2,e4),e2) != e4
& op(op(e2,e4),e4) = e2
& op(e4,e2) != op(e2,e4) )
| sP48_prd ) ),
inference(formula_renaming,[status(thm)],[f578,f618]) ).
fof(f620,plain,
( ( ( ( op(op(e2,e4),e2) = e4
| op(op(e2,e4),e4) != e2
| op(e4,e2) = op(e2,e4) )
& ~ sP48_prd )
| sP43_prd )
& ( ( op(op(e2,e4),e2) != e4
& op(op(e2,e4),e4) = e2
& op(e4,e2) != op(e2,e4) )
| sP48_prd
| ~ sP43_prd ) ),
inference(NNF_transformation,[status(thm)],[f619]) ).
fof(f622,plain,
( op(op(e2,e4),e4) = e2
| sP48_prd
| ~ sP43_prd ),
inference(cnf_transformation,[status(thm)],[f620]) ).
fof(f626,definition,
( sP49_prd
<=> ( ( ( e0 != unit
& op(e3,e0) = e1 )
| op(e3,e1) != e0 )
& ( ( e0 != unit
& op(e3,e0) = e0 )
| op(e3,e0) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e4 )
| op(e2,e4) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e3 )
| op(e2,e3) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e2 )
| op(e2,e2) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e1 )
| op(e2,e1) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e0 )
| op(e2,e0) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e4 )
| op(e1,e4) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e3 )
| op(e1,e3) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e2 )
| op(e1,e2) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e1 )
| op(e1,e1) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e0 )
| op(e1,e0) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e4 )
| op(e0,e4) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e3 )
| op(e0,e3) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e2 )
| op(e0,e2) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e1 )
| op(e0,e1) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e0 )
| op(e0,e0) != e0 ) ) ),
introduced(definition,[new_symbols(definition,[sP49_prd])],[]) ).
fof(f627,plain,
( sP44_prd
<=> ( ( ( e0 != unit
& op(e3,e0) = e2 )
| op(e3,e2) != e0 )
& sP49_prd ) ),
inference(formula_renaming,[status(thm)],[f586,f626]) ).
fof(f628,plain,
( ( ( ( e0 = unit
| op(e3,e0) != e2 )
& op(e3,e2) = e0 )
| ~ sP49_prd
| sP44_prd )
& ( ( ( ( e0 != unit
& op(e3,e0) = e2 )
| op(e3,e2) != e0 )
& sP49_prd )
| ~ sP44_prd ) ),
inference(NNF_transformation,[status(thm)],[f627]) ).
fof(f629,plain,
( sP49_prd
| ~ sP44_prd ),
inference(cnf_transformation,[status(thm)],[f628]) ).
fof(f634,definition,
( sP50_prd
<=> ( ( ( e1 != unit
& op(e3,e1) = e0 )
| op(e3,e0) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e4 )
| op(e2,e4) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e3 )
| op(e2,e3) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e2 )
| op(e2,e2) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e1 )
| op(e2,e1) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e0 )
| op(e2,e0) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e4 )
| op(e1,e4) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e3 )
| op(e1,e3) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e2 )
| op(e1,e2) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e1 )
| op(e1,e1) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e0 )
| op(e1,e0) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e4 )
| op(e0,e4) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e3 )
| op(e0,e3) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e2 )
| op(e0,e2) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e1 )
| op(e0,e1) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e0 )
| op(e0,e0) != e1 ) ) ),
introduced(definition,[new_symbols(definition,[sP50_prd])],[]) ).
fof(f635,plain,
( sP45_prd
<=> ( ( ( e1 != unit
& op(e3,e1) = e1 )
| op(e3,e1) != e1 )
& sP50_prd ) ),
inference(formula_renaming,[status(thm)],[f594,f634]) ).
fof(f636,plain,
( ( ( ( e1 = unit
| op(e3,e1) != e1 )
& op(e3,e1) = e1 )
| ~ sP50_prd
| sP45_prd )
& ( ( ( ( e1 != unit
& op(e3,e1) = e1 )
| op(e3,e1) != e1 )
& sP50_prd )
| ~ sP45_prd ) ),
inference(NNF_transformation,[status(thm)],[f635]) ).
fof(f637,plain,
( sP50_prd
| ~ sP45_prd ),
inference(cnf_transformation,[status(thm)],[f636]) ).
fof(f642,definition,
( sP51_prd
<=> ( ( ( e2 != unit
& op(e2,e2) = e4 )
| op(e2,e4) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e3 )
| op(e2,e3) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e2 )
| op(e2,e2) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e1 )
| op(e2,e1) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e0 )
| op(e2,e0) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e4 )
| op(e1,e4) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e3 )
| op(e1,e3) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e2 )
| op(e1,e2) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e1 )
| op(e1,e1) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e0 )
| op(e1,e0) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e4 )
| op(e0,e4) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e3 )
| op(e0,e3) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e2 )
| op(e0,e2) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e1 )
| op(e0,e1) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e0 )
| op(e0,e0) != e2 ) ) ),
introduced(definition,[new_symbols(definition,[sP51_prd])],[]) ).
fof(f643,plain,
( sP46_prd
<=> ( ( ( e2 != unit
& op(e3,e2) = e0 )
| op(e3,e0) != e2 )
& sP51_prd ) ),
inference(formula_renaming,[status(thm)],[f602,f642]) ).
fof(f644,plain,
( ( ( ( e2 = unit
| op(e3,e2) != e0 )
& op(e3,e0) = e2 )
| ~ sP51_prd
| sP46_prd )
& ( ( ( ( e2 != unit
& op(e3,e2) = e0 )
| op(e3,e0) != e2 )
& sP51_prd )
| ~ sP46_prd ) ),
inference(NNF_transformation,[status(thm)],[f643]) ).
fof(f645,plain,
( sP51_prd
| ~ sP46_prd ),
inference(cnf_transformation,[status(thm)],[f644]) ).
fof(f650,definition,
( sP52_prd
<=> ( ( ( e3 != unit
& op(e2,e3) = e3 )
| op(e2,e3) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e2 )
| op(e2,e2) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e1 )
| op(e2,e1) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e0 )
| op(e2,e0) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e4 )
| op(e1,e4) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e3 )
| op(e1,e3) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e2 )
| op(e1,e2) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e1 )
| op(e1,e1) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e0 )
| op(e1,e0) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e4 )
| op(e0,e4) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e3 )
| op(e0,e3) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e2 )
| op(e0,e2) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e1 )
| op(e0,e1) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e0 )
| op(e0,e0) != e3 ) ) ),
introduced(definition,[new_symbols(definition,[sP52_prd])],[]) ).
fof(f651,plain,
( sP47_prd
<=> ( ( ( e3 != unit
& op(e2,e3) = e4 )
| op(e2,e4) != e3 )
& sP52_prd ) ),
inference(formula_renaming,[status(thm)],[f610,f650]) ).
fof(f652,plain,
( ( ( ( e3 = unit
| op(e2,e3) != e4 )
& op(e2,e4) = e3 )
| ~ sP52_prd
| sP47_prd )
& ( ( ( ( e3 != unit
& op(e2,e3) = e4 )
| op(e2,e4) != e3 )
& sP52_prd )
| ~ sP47_prd ) ),
inference(NNF_transformation,[status(thm)],[f651]) ).
fof(f653,plain,
( sP52_prd
| ~ sP47_prd ),
inference(cnf_transformation,[status(thm)],[f652]) ).
fof(f658,definition,
( sP53_prd
<=> ( ( op(op(e2,e2),e2) != e2
& op(op(e2,e2),e2) = e2
& op(e2,e2) != op(e2,e2) )
| ( op(op(e2,e1),e2) != e1
& op(op(e2,e1),e1) = e2
& op(e1,e2) != op(e2,e1) )
| ( op(op(e2,e0),e2) != e0
& op(op(e2,e0),e0) = e2
& op(e0,e2) != op(e2,e0) )
| ( op(op(e1,e4),e1) != e4
& op(op(e1,e4),e4) = e1
& op(e4,e1) != op(e1,e4) )
| ( op(op(e1,e3),e1) != e3
& op(op(e1,e3),e3) = e1
& op(e3,e1) != op(e1,e3) )
| ( op(op(e1,e2),e1) != e2
& op(op(e1,e2),e2) = e1
& op(e2,e1) != op(e1,e2) )
| ( op(op(e1,e1),e1) != e1
& op(op(e1,e1),e1) = e1
& op(e1,e1) != op(e1,e1) )
| ( op(op(e1,e0),e1) != e0
& op(op(e1,e0),e0) = e1
& op(e0,e1) != op(e1,e0) )
| ( op(op(e0,e4),e0) != e4
& op(op(e0,e4),e4) = e0
& op(e4,e0) != op(e0,e4) )
| ( op(op(e0,e3),e0) != e3
& op(op(e0,e3),e3) = e0
& op(e3,e0) != op(e0,e3) )
| ( op(op(e0,e2),e0) != e2
& op(op(e0,e2),e2) = e0
& op(e2,e0) != op(e0,e2) )
| ( op(op(e0,e1),e0) != e1
& op(op(e0,e1),e1) = e0
& op(e1,e0) != op(e0,e1) )
| ( op(op(e0,e0),e0) != e0
& op(op(e0,e0),e0) = e0
& op(e0,e0) != op(e0,e0) ) ) ),
introduced(definition,[new_symbols(definition,[sP53_prd])],[]) ).
fof(f659,plain,
( sP48_prd
<=> ( ( op(op(e2,e3),e2) != e3
& op(op(e2,e3),e3) = e2
& op(e3,e2) != op(e2,e3) )
| sP53_prd ) ),
inference(formula_renaming,[status(thm)],[f618,f658]) ).
fof(f660,plain,
( ( ( ( op(op(e2,e3),e2) = e3
| op(op(e2,e3),e3) != e2
| op(e3,e2) = op(e2,e3) )
& ~ sP53_prd )
| sP48_prd )
& ( ( op(op(e2,e3),e2) != e3
& op(op(e2,e3),e3) = e2
& op(e3,e2) != op(e2,e3) )
| sP53_prd
| ~ sP48_prd ) ),
inference(NNF_transformation,[status(thm)],[f659]) ).
fof(f662,plain,
( op(op(e2,e3),e3) = e2
| sP53_prd
| ~ sP48_prd ),
inference(cnf_transformation,[status(thm)],[f660]) ).
fof(f666,definition,
( sP54_prd
<=> ( ( ( e0 != unit
& op(e3,e0) = e0 )
| op(e3,e0) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e4 )
| op(e2,e4) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e3 )
| op(e2,e3) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e2 )
| op(e2,e2) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e1 )
| op(e2,e1) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e0 )
| op(e2,e0) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e4 )
| op(e1,e4) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e3 )
| op(e1,e3) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e2 )
| op(e1,e2) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e1 )
| op(e1,e1) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e0 )
| op(e1,e0) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e4 )
| op(e0,e4) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e3 )
| op(e0,e3) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e2 )
| op(e0,e2) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e1 )
| op(e0,e1) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e0 )
| op(e0,e0) != e0 ) ) ),
introduced(definition,[new_symbols(definition,[sP54_prd])],[]) ).
fof(f667,plain,
( sP49_prd
<=> ( ( ( e0 != unit
& op(e3,e0) = e1 )
| op(e3,e1) != e0 )
& sP54_prd ) ),
inference(formula_renaming,[status(thm)],[f626,f666]) ).
fof(f668,plain,
( ( ( ( e0 = unit
| op(e3,e0) != e1 )
& op(e3,e1) = e0 )
| ~ sP54_prd
| sP49_prd )
& ( ( ( ( e0 != unit
& op(e3,e0) = e1 )
| op(e3,e1) != e0 )
& sP54_prd )
| ~ sP49_prd ) ),
inference(NNF_transformation,[status(thm)],[f667]) ).
fof(f669,plain,
( sP54_prd
| ~ sP49_prd ),
inference(cnf_transformation,[status(thm)],[f668]) ).
fof(f674,definition,
( sP55_prd
<=> ( ( ( e1 != unit
& op(e2,e1) = e4 )
| op(e2,e4) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e3 )
| op(e2,e3) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e2 )
| op(e2,e2) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e1 )
| op(e2,e1) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e0 )
| op(e2,e0) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e4 )
| op(e1,e4) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e3 )
| op(e1,e3) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e2 )
| op(e1,e2) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e1 )
| op(e1,e1) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e0 )
| op(e1,e0) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e4 )
| op(e0,e4) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e3 )
| op(e0,e3) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e2 )
| op(e0,e2) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e1 )
| op(e0,e1) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e0 )
| op(e0,e0) != e1 ) ) ),
introduced(definition,[new_symbols(definition,[sP55_prd])],[]) ).
fof(f675,plain,
( sP50_prd
<=> ( ( ( e1 != unit
& op(e3,e1) = e0 )
| op(e3,e0) != e1 )
& sP55_prd ) ),
inference(formula_renaming,[status(thm)],[f634,f674]) ).
fof(f676,plain,
( ( ( ( e1 = unit
| op(e3,e1) != e0 )
& op(e3,e0) = e1 )
| ~ sP55_prd
| sP50_prd )
& ( ( ( ( e1 != unit
& op(e3,e1) = e0 )
| op(e3,e0) != e1 )
& sP55_prd )
| ~ sP50_prd ) ),
inference(NNF_transformation,[status(thm)],[f675]) ).
fof(f677,plain,
( sP55_prd
| ~ sP50_prd ),
inference(cnf_transformation,[status(thm)],[f676]) ).
fof(f678,plain,
( op(e3,e1) = e0
| op(e3,e0) != e1
| ~ sP50_prd ),
inference(cnf_transformation,[status(thm)],[f676]) ).
fof(f682,definition,
( sP56_prd
<=> ( ( ( e2 != unit
& op(e2,e2) = e3 )
| op(e2,e3) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e2 )
| op(e2,e2) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e1 )
| op(e2,e1) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e0 )
| op(e2,e0) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e4 )
| op(e1,e4) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e3 )
| op(e1,e3) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e2 )
| op(e1,e2) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e1 )
| op(e1,e1) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e0 )
| op(e1,e0) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e4 )
| op(e0,e4) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e3 )
| op(e0,e3) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e2 )
| op(e0,e2) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e1 )
| op(e0,e1) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e0 )
| op(e0,e0) != e2 ) ) ),
introduced(definition,[new_symbols(definition,[sP56_prd])],[]) ).
fof(f683,plain,
( sP51_prd
<=> ( ( ( e2 != unit
& op(e2,e2) = e4 )
| op(e2,e4) != e2 )
& sP56_prd ) ),
inference(formula_renaming,[status(thm)],[f642,f682]) ).
fof(f684,plain,
( ( ( ( e2 = unit
| op(e2,e2) != e4 )
& op(e2,e4) = e2 )
| ~ sP56_prd
| sP51_prd )
& ( ( ( ( e2 != unit
& op(e2,e2) = e4 )
| op(e2,e4) != e2 )
& sP56_prd )
| ~ sP51_prd ) ),
inference(NNF_transformation,[status(thm)],[f683]) ).
fof(f685,plain,
( sP56_prd
| ~ sP51_prd ),
inference(cnf_transformation,[status(thm)],[f684]) ).
fof(f686,plain,
( op(e2,e2) = e4
| op(e2,e4) != e2
| ~ sP51_prd ),
inference(cnf_transformation,[status(thm)],[f684]) ).
fof(f690,definition,
( sP57_prd
<=> ( ( ( e3 != unit
& op(e2,e3) = e2 )
| op(e2,e2) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e1 )
| op(e2,e1) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e0 )
| op(e2,e0) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e4 )
| op(e1,e4) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e3 )
| op(e1,e3) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e2 )
| op(e1,e2) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e1 )
| op(e1,e1) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e0 )
| op(e1,e0) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e4 )
| op(e0,e4) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e3 )
| op(e0,e3) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e2 )
| op(e0,e2) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e1 )
| op(e0,e1) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e0 )
| op(e0,e0) != e3 ) ) ),
introduced(definition,[new_symbols(definition,[sP57_prd])],[]) ).
fof(f691,plain,
( sP52_prd
<=> ( ( ( e3 != unit
& op(e2,e3) = e3 )
| op(e2,e3) != e3 )
& sP57_prd ) ),
inference(formula_renaming,[status(thm)],[f650,f690]) ).
fof(f692,plain,
( ( ( ( e3 = unit
| op(e2,e3) != e3 )
& op(e2,e3) = e3 )
| ~ sP57_prd
| sP52_prd )
& ( ( ( ( e3 != unit
& op(e2,e3) = e3 )
| op(e2,e3) != e3 )
& sP57_prd )
| ~ sP52_prd ) ),
inference(NNF_transformation,[status(thm)],[f691]) ).
fof(f693,plain,
( sP57_prd
| ~ sP52_prd ),
inference(cnf_transformation,[status(thm)],[f692]) ).
fof(f698,definition,
( sP58_prd
<=> ( ( op(op(e2,e1),e2) != e1
& op(op(e2,e1),e1) = e2
& op(e1,e2) != op(e2,e1) )
| ( op(op(e2,e0),e2) != e0
& op(op(e2,e0),e0) = e2
& op(e0,e2) != op(e2,e0) )
| ( op(op(e1,e4),e1) != e4
& op(op(e1,e4),e4) = e1
& op(e4,e1) != op(e1,e4) )
| ( op(op(e1,e3),e1) != e3
& op(op(e1,e3),e3) = e1
& op(e3,e1) != op(e1,e3) )
| ( op(op(e1,e2),e1) != e2
& op(op(e1,e2),e2) = e1
& op(e2,e1) != op(e1,e2) )
| ( op(op(e1,e1),e1) != e1
& op(op(e1,e1),e1) = e1
& op(e1,e1) != op(e1,e1) )
| ( op(op(e1,e0),e1) != e0
& op(op(e1,e0),e0) = e1
& op(e0,e1) != op(e1,e0) )
| ( op(op(e0,e4),e0) != e4
& op(op(e0,e4),e4) = e0
& op(e4,e0) != op(e0,e4) )
| ( op(op(e0,e3),e0) != e3
& op(op(e0,e3),e3) = e0
& op(e3,e0) != op(e0,e3) )
| ( op(op(e0,e2),e0) != e2
& op(op(e0,e2),e2) = e0
& op(e2,e0) != op(e0,e2) )
| ( op(op(e0,e1),e0) != e1
& op(op(e0,e1),e1) = e0
& op(e1,e0) != op(e0,e1) )
| ( op(op(e0,e0),e0) != e0
& op(op(e0,e0),e0) = e0
& op(e0,e0) != op(e0,e0) ) ) ),
introduced(definition,[new_symbols(definition,[sP58_prd])],[]) ).
fof(f699,plain,
( sP53_prd
<=> ( ( op(op(e2,e2),e2) != e2
& op(op(e2,e2),e2) = e2
& op(e2,e2) != op(e2,e2) )
| sP58_prd ) ),
inference(formula_renaming,[status(thm)],[f658,f698]) ).
fof(f700,plain,
( ( ( ( op(op(e2,e2),e2) = e2
| op(op(e2,e2),e2) != e2
| op(e2,e2) = op(e2,e2) )
& ~ sP58_prd )
| sP53_prd )
& ( ( op(op(e2,e2),e2) != e2
& op(op(e2,e2),e2) = e2
& op(e2,e2) != op(e2,e2) )
| sP58_prd
| ~ sP53_prd ) ),
inference(NNF_transformation,[status(thm)],[f699]) ).
fof(f701,plain,
( op(e2,e2) != op(e2,e2)
| sP58_prd
| ~ sP53_prd ),
inference(cnf_transformation,[status(thm)],[f700]) ).
fof(f706,definition,
( sP59_prd
<=> ( ( ( e0 != unit
& op(e2,e0) = e4 )
| op(e2,e4) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e3 )
| op(e2,e3) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e2 )
| op(e2,e2) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e1 )
| op(e2,e1) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e0 )
| op(e2,e0) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e4 )
| op(e1,e4) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e3 )
| op(e1,e3) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e2 )
| op(e1,e2) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e1 )
| op(e1,e1) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e0 )
| op(e1,e0) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e4 )
| op(e0,e4) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e3 )
| op(e0,e3) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e2 )
| op(e0,e2) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e1 )
| op(e0,e1) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e0 )
| op(e0,e0) != e0 ) ) ),
introduced(definition,[new_symbols(definition,[sP59_prd])],[]) ).
fof(f707,plain,
( sP54_prd
<=> ( ( ( e0 != unit
& op(e3,e0) = e0 )
| op(e3,e0) != e0 )
& sP59_prd ) ),
inference(formula_renaming,[status(thm)],[f666,f706]) ).
fof(f708,plain,
( ( ( ( e0 = unit
| op(e3,e0) != e0 )
& op(e3,e0) = e0 )
| ~ sP59_prd
| sP54_prd )
& ( ( ( ( e0 != unit
& op(e3,e0) = e0 )
| op(e3,e0) != e0 )
& sP59_prd )
| ~ sP54_prd ) ),
inference(NNF_transformation,[status(thm)],[f707]) ).
fof(f709,plain,
( sP59_prd
| ~ sP54_prd ),
inference(cnf_transformation,[status(thm)],[f708]) ).
fof(f714,definition,
( sP60_prd
<=> ( ( ( e1 != unit
& op(e2,e1) = e3 )
| op(e2,e3) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e2 )
| op(e2,e2) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e1 )
| op(e2,e1) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e0 )
| op(e2,e0) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e4 )
| op(e1,e4) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e3 )
| op(e1,e3) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e2 )
| op(e1,e2) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e1 )
| op(e1,e1) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e0 )
| op(e1,e0) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e4 )
| op(e0,e4) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e3 )
| op(e0,e3) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e2 )
| op(e0,e2) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e1 )
| op(e0,e1) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e0 )
| op(e0,e0) != e1 ) ) ),
introduced(definition,[new_symbols(definition,[sP60_prd])],[]) ).
fof(f715,plain,
( sP55_prd
<=> ( ( ( e1 != unit
& op(e2,e1) = e4 )
| op(e2,e4) != e1 )
& sP60_prd ) ),
inference(formula_renaming,[status(thm)],[f674,f714]) ).
fof(f716,plain,
( ( ( ( e1 = unit
| op(e2,e1) != e4 )
& op(e2,e4) = e1 )
| ~ sP60_prd
| sP55_prd )
& ( ( ( ( e1 != unit
& op(e2,e1) = e4 )
| op(e2,e4) != e1 )
& sP60_prd )
| ~ sP55_prd ) ),
inference(NNF_transformation,[status(thm)],[f715]) ).
fof(f717,plain,
( sP60_prd
| ~ sP55_prd ),
inference(cnf_transformation,[status(thm)],[f716]) ).
fof(f722,definition,
( sP61_prd
<=> ( ( ( e2 != unit
& op(e2,e2) = e2 )
| op(e2,e2) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e1 )
| op(e2,e1) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e0 )
| op(e2,e0) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e4 )
| op(e1,e4) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e3 )
| op(e1,e3) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e2 )
| op(e1,e2) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e1 )
| op(e1,e1) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e0 )
| op(e1,e0) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e4 )
| op(e0,e4) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e3 )
| op(e0,e3) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e2 )
| op(e0,e2) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e1 )
| op(e0,e1) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e0 )
| op(e0,e0) != e2 ) ) ),
introduced(definition,[new_symbols(definition,[sP61_prd])],[]) ).
fof(f723,plain,
( sP56_prd
<=> ( ( ( e2 != unit
& op(e2,e2) = e3 )
| op(e2,e3) != e2 )
& sP61_prd ) ),
inference(formula_renaming,[status(thm)],[f682,f722]) ).
fof(f724,plain,
( ( ( ( e2 = unit
| op(e2,e2) != e3 )
& op(e2,e3) = e2 )
| ~ sP61_prd
| sP56_prd )
& ( ( ( ( e2 != unit
& op(e2,e2) = e3 )
| op(e2,e3) != e2 )
& sP61_prd )
| ~ sP56_prd ) ),
inference(NNF_transformation,[status(thm)],[f723]) ).
fof(f725,plain,
( sP61_prd
| ~ sP56_prd ),
inference(cnf_transformation,[status(thm)],[f724]) ).
fof(f730,definition,
( sP62_prd
<=> ( ( ( e3 != unit
& op(e2,e3) = e1 )
| op(e2,e1) != e3 )
& ( ( e3 != unit
& op(e2,e3) = e0 )
| op(e2,e0) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e4 )
| op(e1,e4) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e3 )
| op(e1,e3) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e2 )
| op(e1,e2) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e1 )
| op(e1,e1) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e0 )
| op(e1,e0) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e4 )
| op(e0,e4) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e3 )
| op(e0,e3) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e2 )
| op(e0,e2) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e1 )
| op(e0,e1) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e0 )
| op(e0,e0) != e3 ) ) ),
introduced(definition,[new_symbols(definition,[sP62_prd])],[]) ).
fof(f731,plain,
( sP57_prd
<=> ( ( ( e3 != unit
& op(e2,e3) = e2 )
| op(e2,e2) != e3 )
& sP62_prd ) ),
inference(formula_renaming,[status(thm)],[f690,f730]) ).
fof(f732,plain,
( ( ( ( e3 = unit
| op(e2,e3) != e2 )
& op(e2,e2) = e3 )
| ~ sP62_prd
| sP57_prd )
& ( ( ( ( e3 != unit
& op(e2,e3) = e2 )
| op(e2,e2) != e3 )
& sP62_prd )
| ~ sP57_prd ) ),
inference(NNF_transformation,[status(thm)],[f731]) ).
fof(f733,plain,
( sP62_prd
| ~ sP57_prd ),
inference(cnf_transformation,[status(thm)],[f732]) ).
fof(f734,plain,
( op(e2,e3) = e2
| op(e2,e2) != e3
| ~ sP57_prd ),
inference(cnf_transformation,[status(thm)],[f732]) ).
fof(f738,definition,
( sP63_prd
<=> ( ( op(op(e2,e0),e2) != e0
& op(op(e2,e0),e0) = e2
& op(e0,e2) != op(e2,e0) )
| ( op(op(e1,e4),e1) != e4
& op(op(e1,e4),e4) = e1
& op(e4,e1) != op(e1,e4) )
| ( op(op(e1,e3),e1) != e3
& op(op(e1,e3),e3) = e1
& op(e3,e1) != op(e1,e3) )
| ( op(op(e1,e2),e1) != e2
& op(op(e1,e2),e2) = e1
& op(e2,e1) != op(e1,e2) )
| ( op(op(e1,e1),e1) != e1
& op(op(e1,e1),e1) = e1
& op(e1,e1) != op(e1,e1) )
| ( op(op(e1,e0),e1) != e0
& op(op(e1,e0),e0) = e1
& op(e0,e1) != op(e1,e0) )
| ( op(op(e0,e4),e0) != e4
& op(op(e0,e4),e4) = e0
& op(e4,e0) != op(e0,e4) )
| ( op(op(e0,e3),e0) != e3
& op(op(e0,e3),e3) = e0
& op(e3,e0) != op(e0,e3) )
| ( op(op(e0,e2),e0) != e2
& op(op(e0,e2),e2) = e0
& op(e2,e0) != op(e0,e2) )
| ( op(op(e0,e1),e0) != e1
& op(op(e0,e1),e1) = e0
& op(e1,e0) != op(e0,e1) )
| ( op(op(e0,e0),e0) != e0
& op(op(e0,e0),e0) = e0
& op(e0,e0) != op(e0,e0) ) ) ),
introduced(definition,[new_symbols(definition,[sP63_prd])],[]) ).
fof(f739,plain,
( sP58_prd
<=> ( ( op(op(e2,e1),e2) != e1
& op(op(e2,e1),e1) = e2
& op(e1,e2) != op(e2,e1) )
| sP63_prd ) ),
inference(formula_renaming,[status(thm)],[f698,f738]) ).
fof(f740,plain,
( ( ( ( op(op(e2,e1),e2) = e1
| op(op(e2,e1),e1) != e2
| op(e1,e2) = op(e2,e1) )
& ~ sP63_prd )
| sP58_prd )
& ( ( op(op(e2,e1),e2) != e1
& op(op(e2,e1),e1) = e2
& op(e1,e2) != op(e2,e1) )
| sP63_prd
| ~ sP58_prd ) ),
inference(NNF_transformation,[status(thm)],[f739]) ).
fof(f741,plain,
( op(e1,e2) != op(e2,e1)
| sP63_prd
| ~ sP58_prd ),
inference(cnf_transformation,[status(thm)],[f740]) ).
fof(f746,definition,
( sP64_prd
<=> ( ( ( e0 != unit
& op(e2,e0) = e3 )
| op(e2,e3) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e2 )
| op(e2,e2) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e1 )
| op(e2,e1) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e0 )
| op(e2,e0) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e4 )
| op(e1,e4) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e3 )
| op(e1,e3) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e2 )
| op(e1,e2) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e1 )
| op(e1,e1) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e0 )
| op(e1,e0) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e4 )
| op(e0,e4) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e3 )
| op(e0,e3) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e2 )
| op(e0,e2) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e1 )
| op(e0,e1) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e0 )
| op(e0,e0) != e0 ) ) ),
introduced(definition,[new_symbols(definition,[sP64_prd])],[]) ).
fof(f747,plain,
( sP59_prd
<=> ( ( ( e0 != unit
& op(e2,e0) = e4 )
| op(e2,e4) != e0 )
& sP64_prd ) ),
inference(formula_renaming,[status(thm)],[f706,f746]) ).
fof(f748,plain,
( ( ( ( e0 = unit
| op(e2,e0) != e4 )
& op(e2,e4) = e0 )
| ~ sP64_prd
| sP59_prd )
& ( ( ( ( e0 != unit
& op(e2,e0) = e4 )
| op(e2,e4) != e0 )
& sP64_prd )
| ~ sP59_prd ) ),
inference(NNF_transformation,[status(thm)],[f747]) ).
fof(f749,plain,
( sP64_prd
| ~ sP59_prd ),
inference(cnf_transformation,[status(thm)],[f748]) ).
fof(f754,definition,
( sP65_prd
<=> ( ( ( e1 != unit
& op(e2,e1) = e2 )
| op(e2,e2) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e1 )
| op(e2,e1) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e0 )
| op(e2,e0) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e4 )
| op(e1,e4) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e3 )
| op(e1,e3) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e2 )
| op(e1,e2) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e1 )
| op(e1,e1) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e0 )
| op(e1,e0) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e4 )
| op(e0,e4) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e3 )
| op(e0,e3) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e2 )
| op(e0,e2) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e1 )
| op(e0,e1) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e0 )
| op(e0,e0) != e1 ) ) ),
introduced(definition,[new_symbols(definition,[sP65_prd])],[]) ).
fof(f755,plain,
( sP60_prd
<=> ( ( ( e1 != unit
& op(e2,e1) = e3 )
| op(e2,e3) != e1 )
& sP65_prd ) ),
inference(formula_renaming,[status(thm)],[f714,f754]) ).
fof(f756,plain,
( ( ( ( e1 = unit
| op(e2,e1) != e3 )
& op(e2,e3) = e1 )
| ~ sP65_prd
| sP60_prd )
& ( ( ( ( e1 != unit
& op(e2,e1) = e3 )
| op(e2,e3) != e1 )
& sP65_prd )
| ~ sP60_prd ) ),
inference(NNF_transformation,[status(thm)],[f755]) ).
fof(f757,plain,
( sP65_prd
| ~ sP60_prd ),
inference(cnf_transformation,[status(thm)],[f756]) ).
fof(f758,plain,
( op(e2,e1) = e3
| op(e2,e3) != e1
| ~ sP60_prd ),
inference(cnf_transformation,[status(thm)],[f756]) ).
fof(f762,definition,
( sP66_prd
<=> ( ( ( e2 != unit
& op(e2,e2) = e1 )
| op(e2,e1) != e2 )
& ( ( e2 != unit
& op(e2,e2) = e0 )
| op(e2,e0) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e4 )
| op(e1,e4) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e3 )
| op(e1,e3) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e2 )
| op(e1,e2) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e1 )
| op(e1,e1) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e0 )
| op(e1,e0) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e4 )
| op(e0,e4) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e3 )
| op(e0,e3) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e2 )
| op(e0,e2) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e1 )
| op(e0,e1) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e0 )
| op(e0,e0) != e2 ) ) ),
introduced(definition,[new_symbols(definition,[sP66_prd])],[]) ).
fof(f763,plain,
( sP61_prd
<=> ( ( ( e2 != unit
& op(e2,e2) = e2 )
| op(e2,e2) != e2 )
& sP66_prd ) ),
inference(formula_renaming,[status(thm)],[f722,f762]) ).
fof(f764,plain,
( ( ( ( e2 = unit
| op(e2,e2) != e2 )
& op(e2,e2) = e2 )
| ~ sP66_prd
| sP61_prd )
& ( ( ( ( e2 != unit
& op(e2,e2) = e2 )
| op(e2,e2) != e2 )
& sP66_prd )
| ~ sP61_prd ) ),
inference(NNF_transformation,[status(thm)],[f763]) ).
fof(f765,plain,
( sP66_prd
| ~ sP61_prd ),
inference(cnf_transformation,[status(thm)],[f764]) ).
fof(f770,definition,
( sP67_prd
<=> ( ( ( e3 != unit
& op(e2,e3) = e0 )
| op(e2,e0) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e4 )
| op(e1,e4) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e3 )
| op(e1,e3) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e2 )
| op(e1,e2) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e1 )
| op(e1,e1) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e0 )
| op(e1,e0) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e4 )
| op(e0,e4) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e3 )
| op(e0,e3) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e2 )
| op(e0,e2) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e1 )
| op(e0,e1) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e0 )
| op(e0,e0) != e3 ) ) ),
introduced(definition,[new_symbols(definition,[sP67_prd])],[]) ).
fof(f771,plain,
( sP62_prd
<=> ( ( ( e3 != unit
& op(e2,e3) = e1 )
| op(e2,e1) != e3 )
& sP67_prd ) ),
inference(formula_renaming,[status(thm)],[f730,f770]) ).
fof(f772,plain,
( ( ( ( e3 = unit
| op(e2,e3) != e1 )
& op(e2,e1) = e3 )
| ~ sP67_prd
| sP62_prd )
& ( ( ( ( e3 != unit
& op(e2,e3) = e1 )
| op(e2,e1) != e3 )
& sP67_prd )
| ~ sP62_prd ) ),
inference(NNF_transformation,[status(thm)],[f771]) ).
fof(f773,plain,
( sP67_prd
| ~ sP62_prd ),
inference(cnf_transformation,[status(thm)],[f772]) ).
fof(f778,definition,
( sP68_prd
<=> ( ( op(op(e1,e4),e1) != e4
& op(op(e1,e4),e4) = e1
& op(e4,e1) != op(e1,e4) )
| ( op(op(e1,e3),e1) != e3
& op(op(e1,e3),e3) = e1
& op(e3,e1) != op(e1,e3) )
| ( op(op(e1,e2),e1) != e2
& op(op(e1,e2),e2) = e1
& op(e2,e1) != op(e1,e2) )
| ( op(op(e1,e1),e1) != e1
& op(op(e1,e1),e1) = e1
& op(e1,e1) != op(e1,e1) )
| ( op(op(e1,e0),e1) != e0
& op(op(e1,e0),e0) = e1
& op(e0,e1) != op(e1,e0) )
| ( op(op(e0,e4),e0) != e4
& op(op(e0,e4),e4) = e0
& op(e4,e0) != op(e0,e4) )
| ( op(op(e0,e3),e0) != e3
& op(op(e0,e3),e3) = e0
& op(e3,e0) != op(e0,e3) )
| ( op(op(e0,e2),e0) != e2
& op(op(e0,e2),e2) = e0
& op(e2,e0) != op(e0,e2) )
| ( op(op(e0,e1),e0) != e1
& op(op(e0,e1),e1) = e0
& op(e1,e0) != op(e0,e1) )
| ( op(op(e0,e0),e0) != e0
& op(op(e0,e0),e0) = e0
& op(e0,e0) != op(e0,e0) ) ) ),
introduced(definition,[new_symbols(definition,[sP68_prd])],[]) ).
fof(f779,plain,
( sP63_prd
<=> ( ( op(op(e2,e0),e2) != e0
& op(op(e2,e0),e0) = e2
& op(e0,e2) != op(e2,e0) )
| sP68_prd ) ),
inference(formula_renaming,[status(thm)],[f738,f778]) ).
fof(f780,plain,
( ( ( ( op(op(e2,e0),e2) = e0
| op(op(e2,e0),e0) != e2
| op(e0,e2) = op(e2,e0) )
& ~ sP68_prd )
| sP63_prd )
& ( ( op(op(e2,e0),e2) != e0
& op(op(e2,e0),e0) = e2
& op(e0,e2) != op(e2,e0) )
| sP68_prd
| ~ sP63_prd ) ),
inference(NNF_transformation,[status(thm)],[f779]) ).
fof(f781,plain,
( op(e0,e2) != op(e2,e0)
| sP68_prd
| ~ sP63_prd ),
inference(cnf_transformation,[status(thm)],[f780]) ).
fof(f786,definition,
( sP69_prd
<=> ( ( ( e0 != unit
& op(e2,e0) = e2 )
| op(e2,e2) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e1 )
| op(e2,e1) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e0 )
| op(e2,e0) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e4 )
| op(e1,e4) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e3 )
| op(e1,e3) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e2 )
| op(e1,e2) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e1 )
| op(e1,e1) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e0 )
| op(e1,e0) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e4 )
| op(e0,e4) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e3 )
| op(e0,e3) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e2 )
| op(e0,e2) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e1 )
| op(e0,e1) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e0 )
| op(e0,e0) != e0 ) ) ),
introduced(definition,[new_symbols(definition,[sP69_prd])],[]) ).
fof(f787,plain,
( sP64_prd
<=> ( ( ( e0 != unit
& op(e2,e0) = e3 )
| op(e2,e3) != e0 )
& sP69_prd ) ),
inference(formula_renaming,[status(thm)],[f746,f786]) ).
fof(f788,plain,
( ( ( ( e0 = unit
| op(e2,e0) != e3 )
& op(e2,e3) = e0 )
| ~ sP69_prd
| sP64_prd )
& ( ( ( ( e0 != unit
& op(e2,e0) = e3 )
| op(e2,e3) != e0 )
& sP69_prd )
| ~ sP64_prd ) ),
inference(NNF_transformation,[status(thm)],[f787]) ).
fof(f789,plain,
( sP69_prd
| ~ sP64_prd ),
inference(cnf_transformation,[status(thm)],[f788]) ).
fof(f790,plain,
( op(e2,e0) = e3
| op(e2,e3) != e0
| ~ sP64_prd ),
inference(cnf_transformation,[status(thm)],[f788]) ).
fof(f794,definition,
( sP70_prd
<=> ( ( ( e1 != unit
& op(e2,e1) = e1 )
| op(e2,e1) != e1 )
& ( ( e1 != unit
& op(e2,e1) = e0 )
| op(e2,e0) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e4 )
| op(e1,e4) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e3 )
| op(e1,e3) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e2 )
| op(e1,e2) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e1 )
| op(e1,e1) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e0 )
| op(e1,e0) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e4 )
| op(e0,e4) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e3 )
| op(e0,e3) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e2 )
| op(e0,e2) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e1 )
| op(e0,e1) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e0 )
| op(e0,e0) != e1 ) ) ),
introduced(definition,[new_symbols(definition,[sP70_prd])],[]) ).
fof(f795,plain,
( sP65_prd
<=> ( ( ( e1 != unit
& op(e2,e1) = e2 )
| op(e2,e2) != e1 )
& sP70_prd ) ),
inference(formula_renaming,[status(thm)],[f754,f794]) ).
fof(f796,plain,
( ( ( ( e1 = unit
| op(e2,e1) != e2 )
& op(e2,e2) = e1 )
| ~ sP70_prd
| sP65_prd )
& ( ( ( ( e1 != unit
& op(e2,e1) = e2 )
| op(e2,e2) != e1 )
& sP70_prd )
| ~ sP65_prd ) ),
inference(NNF_transformation,[status(thm)],[f795]) ).
fof(f797,plain,
( sP70_prd
| ~ sP65_prd ),
inference(cnf_transformation,[status(thm)],[f796]) ).
fof(f802,definition,
( sP71_prd
<=> ( ( ( e2 != unit
& op(e2,e2) = e0 )
| op(e2,e0) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e4 )
| op(e1,e4) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e3 )
| op(e1,e3) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e2 )
| op(e1,e2) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e1 )
| op(e1,e1) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e0 )
| op(e1,e0) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e4 )
| op(e0,e4) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e3 )
| op(e0,e3) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e2 )
| op(e0,e2) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e1 )
| op(e0,e1) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e0 )
| op(e0,e0) != e2 ) ) ),
introduced(definition,[new_symbols(definition,[sP71_prd])],[]) ).
fof(f803,plain,
( sP66_prd
<=> ( ( ( e2 != unit
& op(e2,e2) = e1 )
| op(e2,e1) != e2 )
& sP71_prd ) ),
inference(formula_renaming,[status(thm)],[f762,f802]) ).
fof(f804,plain,
( ( ( ( e2 = unit
| op(e2,e2) != e1 )
& op(e2,e1) = e2 )
| ~ sP71_prd
| sP66_prd )
& ( ( ( ( e2 != unit
& op(e2,e2) = e1 )
| op(e2,e1) != e2 )
& sP71_prd )
| ~ sP66_prd ) ),
inference(NNF_transformation,[status(thm)],[f803]) ).
fof(f805,plain,
( sP71_prd
| ~ sP66_prd ),
inference(cnf_transformation,[status(thm)],[f804]) ).
fof(f810,definition,
( sP72_prd
<=> ( ( ( e3 != unit
& op(e1,e3) = e4 )
| op(e1,e4) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e3 )
| op(e1,e3) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e2 )
| op(e1,e2) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e1 )
| op(e1,e1) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e0 )
| op(e1,e0) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e4 )
| op(e0,e4) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e3 )
| op(e0,e3) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e2 )
| op(e0,e2) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e1 )
| op(e0,e1) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e0 )
| op(e0,e0) != e3 ) ) ),
introduced(definition,[new_symbols(definition,[sP72_prd])],[]) ).
fof(f811,plain,
( sP67_prd
<=> ( ( ( e3 != unit
& op(e2,e3) = e0 )
| op(e2,e0) != e3 )
& sP72_prd ) ),
inference(formula_renaming,[status(thm)],[f770,f810]) ).
fof(f812,plain,
( ( ( ( e3 = unit
| op(e2,e3) != e0 )
& op(e2,e0) = e3 )
| ~ sP72_prd
| sP67_prd )
& ( ( ( ( e3 != unit
& op(e2,e3) = e0 )
| op(e2,e0) != e3 )
& sP72_prd )
| ~ sP67_prd ) ),
inference(NNF_transformation,[status(thm)],[f811]) ).
fof(f813,plain,
( sP72_prd
| ~ sP67_prd ),
inference(cnf_transformation,[status(thm)],[f812]) ).
fof(f818,definition,
( sP73_prd
<=> ( ( op(op(e1,e3),e1) != e3
& op(op(e1,e3),e3) = e1
& op(e3,e1) != op(e1,e3) )
| ( op(op(e1,e2),e1) != e2
& op(op(e1,e2),e2) = e1
& op(e2,e1) != op(e1,e2) )
| ( op(op(e1,e1),e1) != e1
& op(op(e1,e1),e1) = e1
& op(e1,e1) != op(e1,e1) )
| ( op(op(e1,e0),e1) != e0
& op(op(e1,e0),e0) = e1
& op(e0,e1) != op(e1,e0) )
| ( op(op(e0,e4),e0) != e4
& op(op(e0,e4),e4) = e0
& op(e4,e0) != op(e0,e4) )
| ( op(op(e0,e3),e0) != e3
& op(op(e0,e3),e3) = e0
& op(e3,e0) != op(e0,e3) )
| ( op(op(e0,e2),e0) != e2
& op(op(e0,e2),e2) = e0
& op(e2,e0) != op(e0,e2) )
| ( op(op(e0,e1),e0) != e1
& op(op(e0,e1),e1) = e0
& op(e1,e0) != op(e0,e1) )
| ( op(op(e0,e0),e0) != e0
& op(op(e0,e0),e0) = e0
& op(e0,e0) != op(e0,e0) ) ) ),
introduced(definition,[new_symbols(definition,[sP73_prd])],[]) ).
fof(f819,plain,
( sP68_prd
<=> ( ( op(op(e1,e4),e1) != e4
& op(op(e1,e4),e4) = e1
& op(e4,e1) != op(e1,e4) )
| sP73_prd ) ),
inference(formula_renaming,[status(thm)],[f778,f818]) ).
fof(f820,plain,
( ( ( ( op(op(e1,e4),e1) = e4
| op(op(e1,e4),e4) != e1
| op(e4,e1) = op(e1,e4) )
& ~ sP73_prd )
| sP68_prd )
& ( ( op(op(e1,e4),e1) != e4
& op(op(e1,e4),e4) = e1
& op(e4,e1) != op(e1,e4) )
| sP73_prd
| ~ sP68_prd ) ),
inference(NNF_transformation,[status(thm)],[f819]) ).
fof(f821,plain,
( op(e4,e1) != op(e1,e4)
| sP73_prd
| ~ sP68_prd ),
inference(cnf_transformation,[status(thm)],[f820]) ).
fof(f826,definition,
( sP74_prd
<=> ( ( ( e0 != unit
& op(e2,e0) = e1 )
| op(e2,e1) != e0 )
& ( ( e0 != unit
& op(e2,e0) = e0 )
| op(e2,e0) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e4 )
| op(e1,e4) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e3 )
| op(e1,e3) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e2 )
| op(e1,e2) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e1 )
| op(e1,e1) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e0 )
| op(e1,e0) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e4 )
| op(e0,e4) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e3 )
| op(e0,e3) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e2 )
| op(e0,e2) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e1 )
| op(e0,e1) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e0 )
| op(e0,e0) != e0 ) ) ),
introduced(definition,[new_symbols(definition,[sP74_prd])],[]) ).
fof(f827,plain,
( sP69_prd
<=> ( ( ( e0 != unit
& op(e2,e0) = e2 )
| op(e2,e2) != e0 )
& sP74_prd ) ),
inference(formula_renaming,[status(thm)],[f786,f826]) ).
fof(f828,plain,
( ( ( ( e0 = unit
| op(e2,e0) != e2 )
& op(e2,e2) = e0 )
| ~ sP74_prd
| sP69_prd )
& ( ( ( ( e0 != unit
& op(e2,e0) = e2 )
| op(e2,e2) != e0 )
& sP74_prd )
| ~ sP69_prd ) ),
inference(NNF_transformation,[status(thm)],[f827]) ).
fof(f829,plain,
( sP74_prd
| ~ sP69_prd ),
inference(cnf_transformation,[status(thm)],[f828]) ).
fof(f834,definition,
( sP75_prd
<=> ( ( ( e1 != unit
& op(e2,e1) = e0 )
| op(e2,e0) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e4 )
| op(e1,e4) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e3 )
| op(e1,e3) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e2 )
| op(e1,e2) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e1 )
| op(e1,e1) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e0 )
| op(e1,e0) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e4 )
| op(e0,e4) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e3 )
| op(e0,e3) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e2 )
| op(e0,e2) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e1 )
| op(e0,e1) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e0 )
| op(e0,e0) != e1 ) ) ),
introduced(definition,[new_symbols(definition,[sP75_prd])],[]) ).
fof(f835,plain,
( sP70_prd
<=> ( ( ( e1 != unit
& op(e2,e1) = e1 )
| op(e2,e1) != e1 )
& sP75_prd ) ),
inference(formula_renaming,[status(thm)],[f794,f834]) ).
fof(f836,plain,
( ( ( ( e1 = unit
| op(e2,e1) != e1 )
& op(e2,e1) = e1 )
| ~ sP75_prd
| sP70_prd )
& ( ( ( ( e1 != unit
& op(e2,e1) = e1 )
| op(e2,e1) != e1 )
& sP75_prd )
| ~ sP70_prd ) ),
inference(NNF_transformation,[status(thm)],[f835]) ).
fof(f837,plain,
( sP75_prd
| ~ sP70_prd ),
inference(cnf_transformation,[status(thm)],[f836]) ).
fof(f842,definition,
( sP76_prd
<=> ( ( ( e2 != unit
& op(e1,e2) = e4 )
| op(e1,e4) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e3 )
| op(e1,e3) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e2 )
| op(e1,e2) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e1 )
| op(e1,e1) != e2 )
& ( ( e2 != unit
& op(e1,e2) = e0 )
| op(e1,e0) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e4 )
| op(e0,e4) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e3 )
| op(e0,e3) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e2 )
| op(e0,e2) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e1 )
| op(e0,e1) != e2 )
& ( ( e2 != unit
& op(e0,e2) = e0 )
| op(e0,e0) != e2 ) ) ),
introduced(definition,[new_symbols(definition,[sP76_prd])],[]) ).
fof(f843,plain,
( sP71_prd
<=> ( ( ( e2 != unit
& op(e2,e2) = e0 )
| op(e2,e0) != e2 )
& sP76_prd ) ),
inference(formula_renaming,[status(thm)],[f802,f842]) ).
fof(f844,plain,
( ( ( ( e2 = unit
| op(e2,e2) != e0 )
& op(e2,e0) = e2 )
| ~ sP76_prd
| sP71_prd )
& ( ( ( ( e2 != unit
& op(e2,e2) = e0 )
| op(e2,e0) != e2 )
& sP76_prd )
| ~ sP71_prd ) ),
inference(NNF_transformation,[status(thm)],[f843]) ).
fof(f846,plain,
( op(e2,e2) = e0
| op(e2,e0) != e2
| ~ sP71_prd ),
inference(cnf_transformation,[status(thm)],[f844]) ).
fof(f850,definition,
( sP77_prd
<=> ( ( ( e3 != unit
& op(e1,e3) = e3 )
| op(e1,e3) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e2 )
| op(e1,e2) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e1 )
| op(e1,e1) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e0 )
| op(e1,e0) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e4 )
| op(e0,e4) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e3 )
| op(e0,e3) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e2 )
| op(e0,e2) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e1 )
| op(e0,e1) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e0 )
| op(e0,e0) != e3 ) ) ),
introduced(definition,[new_symbols(definition,[sP77_prd])],[]) ).
fof(f851,plain,
( sP72_prd
<=> ( ( ( e3 != unit
& op(e1,e3) = e4 )
| op(e1,e4) != e3 )
& sP77_prd ) ),
inference(formula_renaming,[status(thm)],[f810,f850]) ).
fof(f852,plain,
( ( ( ( e3 = unit
| op(e1,e3) != e4 )
& op(e1,e4) = e3 )
| ~ sP77_prd
| sP72_prd )
& ( ( ( ( e3 != unit
& op(e1,e3) = e4 )
| op(e1,e4) != e3 )
& sP77_prd )
| ~ sP72_prd ) ),
inference(NNF_transformation,[status(thm)],[f851]) ).
fof(f853,plain,
( sP77_prd
| ~ sP72_prd ),
inference(cnf_transformation,[status(thm)],[f852]) ).
fof(f858,definition,
( sP78_prd
<=> ( ( op(op(e1,e2),e1) != e2
& op(op(e1,e2),e2) = e1
& op(e2,e1) != op(e1,e2) )
| ( op(op(e1,e1),e1) != e1
& op(op(e1,e1),e1) = e1
& op(e1,e1) != op(e1,e1) )
| ( op(op(e1,e0),e1) != e0
& op(op(e1,e0),e0) = e1
& op(e0,e1) != op(e1,e0) )
| ( op(op(e0,e4),e0) != e4
& op(op(e0,e4),e4) = e0
& op(e4,e0) != op(e0,e4) )
| ( op(op(e0,e3),e0) != e3
& op(op(e0,e3),e3) = e0
& op(e3,e0) != op(e0,e3) )
| ( op(op(e0,e2),e0) != e2
& op(op(e0,e2),e2) = e0
& op(e2,e0) != op(e0,e2) )
| ( op(op(e0,e1),e0) != e1
& op(op(e0,e1),e1) = e0
& op(e1,e0) != op(e0,e1) )
| ( op(op(e0,e0),e0) != e0
& op(op(e0,e0),e0) = e0
& op(e0,e0) != op(e0,e0) ) ) ),
introduced(definition,[new_symbols(definition,[sP78_prd])],[]) ).
fof(f859,plain,
( sP73_prd
<=> ( ( op(op(e1,e3),e1) != e3
& op(op(e1,e3),e3) = e1
& op(e3,e1) != op(e1,e3) )
| sP78_prd ) ),
inference(formula_renaming,[status(thm)],[f818,f858]) ).
fof(f860,plain,
( ( ( ( op(op(e1,e3),e1) = e3
| op(op(e1,e3),e3) != e1
| op(e3,e1) = op(e1,e3) )
& ~ sP78_prd )
| sP73_prd )
& ( ( op(op(e1,e3),e1) != e3
& op(op(e1,e3),e3) = e1
& op(e3,e1) != op(e1,e3) )
| sP78_prd
| ~ sP73_prd ) ),
inference(NNF_transformation,[status(thm)],[f859]) ).
fof(f861,plain,
( op(e3,e1) != op(e1,e3)
| sP78_prd
| ~ sP73_prd ),
inference(cnf_transformation,[status(thm)],[f860]) ).
fof(f866,definition,
( sP79_prd
<=> ( ( ( e0 != unit
& op(e2,e0) = e0 )
| op(e2,e0) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e4 )
| op(e1,e4) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e3 )
| op(e1,e3) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e2 )
| op(e1,e2) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e1 )
| op(e1,e1) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e0 )
| op(e1,e0) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e4 )
| op(e0,e4) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e3 )
| op(e0,e3) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e2 )
| op(e0,e2) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e1 )
| op(e0,e1) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e0 )
| op(e0,e0) != e0 ) ) ),
introduced(definition,[new_symbols(definition,[sP79_prd])],[]) ).
fof(f867,plain,
( sP74_prd
<=> ( ( ( e0 != unit
& op(e2,e0) = e1 )
| op(e2,e1) != e0 )
& sP79_prd ) ),
inference(formula_renaming,[status(thm)],[f826,f866]) ).
fof(f868,plain,
( ( ( ( e0 = unit
| op(e2,e0) != e1 )
& op(e2,e1) = e0 )
| ~ sP79_prd
| sP74_prd )
& ( ( ( ( e0 != unit
& op(e2,e0) = e1 )
| op(e2,e1) != e0 )
& sP79_prd )
| ~ sP74_prd ) ),
inference(NNF_transformation,[status(thm)],[f867]) ).
fof(f869,plain,
( sP79_prd
| ~ sP74_prd ),
inference(cnf_transformation,[status(thm)],[f868]) ).
fof(f874,definition,
( sP80_prd
<=> ( ( ( e1 != unit
& op(e1,e1) = e4 )
| op(e1,e4) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e3 )
| op(e1,e3) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e2 )
| op(e1,e2) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e1 )
| op(e1,e1) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e0 )
| op(e1,e0) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e4 )
| op(e0,e4) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e3 )
| op(e0,e3) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e2 )
| op(e0,e2) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e1 )
| op(e0,e1) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e0 )
| op(e0,e0) != e1 ) ) ),
introduced(definition,[new_symbols(definition,[sP80_prd])],[]) ).
fof(f875,plain,
( sP75_prd
<=> ( ( ( e1 != unit
& op(e2,e1) = e0 )
| op(e2,e0) != e1 )
& sP80_prd ) ),
inference(formula_renaming,[status(thm)],[f834,f874]) ).
fof(f876,plain,
( ( ( ( e1 = unit
| op(e2,e1) != e0 )
& op(e2,e0) = e1 )
| ~ sP80_prd
| sP75_prd )
& ( ( ( ( e1 != unit
& op(e2,e1) = e0 )
| op(e2,e0) != e1 )
& sP80_prd )
| ~ sP75_prd ) ),
inference(NNF_transformation,[status(thm)],[f875]) ).
fof(f877,plain,
( sP80_prd
| ~ sP75_prd ),
inference(cnf_transformation,[status(thm)],[f876]) ).
fof(f878,plain,
( op(e2,e1) = e0
| op(e2,e0) != e1
| ~ sP75_prd ),
inference(cnf_transformation,[status(thm)],[f876]) ).
fof(f890,definition,
( sP82_prd
<=> ( ( ( e3 != unit
& op(e1,e3) = e2 )
| op(e1,e2) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e1 )
| op(e1,e1) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e0 )
| op(e1,e0) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e4 )
| op(e0,e4) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e3 )
| op(e0,e3) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e2 )
| op(e0,e2) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e1 )
| op(e0,e1) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e0 )
| op(e0,e0) != e3 ) ) ),
introduced(definition,[new_symbols(definition,[sP82_prd])],[]) ).
fof(f891,plain,
( sP77_prd
<=> ( ( ( e3 != unit
& op(e1,e3) = e3 )
| op(e1,e3) != e3 )
& sP82_prd ) ),
inference(formula_renaming,[status(thm)],[f850,f890]) ).
fof(f892,plain,
( ( ( ( e3 = unit
| op(e1,e3) != e3 )
& op(e1,e3) = e3 )
| ~ sP82_prd
| sP77_prd )
& ( ( ( ( e3 != unit
& op(e1,e3) = e3 )
| op(e1,e3) != e3 )
& sP82_prd )
| ~ sP77_prd ) ),
inference(NNF_transformation,[status(thm)],[f891]) ).
fof(f893,plain,
( sP82_prd
| ~ sP77_prd ),
inference(cnf_transformation,[status(thm)],[f892]) ).
fof(f898,definition,
( sP83_prd
<=> ( ( op(op(e1,e1),e1) != e1
& op(op(e1,e1),e1) = e1
& op(e1,e1) != op(e1,e1) )
| ( op(op(e1,e0),e1) != e0
& op(op(e1,e0),e0) = e1
& op(e0,e1) != op(e1,e0) )
| ( op(op(e0,e4),e0) != e4
& op(op(e0,e4),e4) = e0
& op(e4,e0) != op(e0,e4) )
| ( op(op(e0,e3),e0) != e3
& op(op(e0,e3),e3) = e0
& op(e3,e0) != op(e0,e3) )
| ( op(op(e0,e2),e0) != e2
& op(op(e0,e2),e2) = e0
& op(e2,e0) != op(e0,e2) )
| ( op(op(e0,e1),e0) != e1
& op(op(e0,e1),e1) = e0
& op(e1,e0) != op(e0,e1) )
| ( op(op(e0,e0),e0) != e0
& op(op(e0,e0),e0) = e0
& op(e0,e0) != op(e0,e0) ) ) ),
introduced(definition,[new_symbols(definition,[sP83_prd])],[]) ).
fof(f899,plain,
( sP78_prd
<=> ( ( op(op(e1,e2),e1) != e2
& op(op(e1,e2),e2) = e1
& op(e2,e1) != op(e1,e2) )
| sP83_prd ) ),
inference(formula_renaming,[status(thm)],[f858,f898]) ).
fof(f900,plain,
( ( ( ( op(op(e1,e2),e1) = e2
| op(op(e1,e2),e2) != e1
| op(e2,e1) = op(e1,e2) )
& ~ sP83_prd )
| sP78_prd )
& ( ( op(op(e1,e2),e1) != e2
& op(op(e1,e2),e2) = e1
& op(e2,e1) != op(e1,e2) )
| sP83_prd
| ~ sP78_prd ) ),
inference(NNF_transformation,[status(thm)],[f899]) ).
fof(f901,plain,
( op(e2,e1) != op(e1,e2)
| sP83_prd
| ~ sP78_prd ),
inference(cnf_transformation,[status(thm)],[f900]) ).
fof(f906,definition,
( sP84_prd
<=> ( ( ( e0 != unit
& op(e1,e0) = e4 )
| op(e1,e4) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e3 )
| op(e1,e3) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e2 )
| op(e1,e2) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e1 )
| op(e1,e1) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e0 )
| op(e1,e0) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e4 )
| op(e0,e4) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e3 )
| op(e0,e3) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e2 )
| op(e0,e2) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e1 )
| op(e0,e1) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e0 )
| op(e0,e0) != e0 ) ) ),
introduced(definition,[new_symbols(definition,[sP84_prd])],[]) ).
fof(f907,plain,
( sP79_prd
<=> ( ( ( e0 != unit
& op(e2,e0) = e0 )
| op(e2,e0) != e0 )
& sP84_prd ) ),
inference(formula_renaming,[status(thm)],[f866,f906]) ).
fof(f908,plain,
( ( ( ( e0 = unit
| op(e2,e0) != e0 )
& op(e2,e0) = e0 )
| ~ sP84_prd
| sP79_prd )
& ( ( ( ( e0 != unit
& op(e2,e0) = e0 )
| op(e2,e0) != e0 )
& sP84_prd )
| ~ sP79_prd ) ),
inference(NNF_transformation,[status(thm)],[f907]) ).
fof(f909,plain,
( sP84_prd
| ~ sP79_prd ),
inference(cnf_transformation,[status(thm)],[f908]) ).
fof(f914,definition,
( sP85_prd
<=> ( ( ( e1 != unit
& op(e1,e1) = e3 )
| op(e1,e3) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e2 )
| op(e1,e2) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e1 )
| op(e1,e1) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e0 )
| op(e1,e0) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e4 )
| op(e0,e4) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e3 )
| op(e0,e3) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e2 )
| op(e0,e2) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e1 )
| op(e0,e1) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e0 )
| op(e0,e0) != e1 ) ) ),
introduced(definition,[new_symbols(definition,[sP85_prd])],[]) ).
fof(f915,plain,
( sP80_prd
<=> ( ( ( e1 != unit
& op(e1,e1) = e4 )
| op(e1,e4) != e1 )
& sP85_prd ) ),
inference(formula_renaming,[status(thm)],[f874,f914]) ).
fof(f916,plain,
( ( ( ( e1 = unit
| op(e1,e1) != e4 )
& op(e1,e4) = e1 )
| ~ sP85_prd
| sP80_prd )
& ( ( ( ( e1 != unit
& op(e1,e1) = e4 )
| op(e1,e4) != e1 )
& sP85_prd )
| ~ sP80_prd ) ),
inference(NNF_transformation,[status(thm)],[f915]) ).
fof(f917,plain,
( sP85_prd
| ~ sP80_prd ),
inference(cnf_transformation,[status(thm)],[f916]) ).
fof(f918,plain,
( op(e1,e1) = e4
| op(e1,e4) != e1
| ~ sP80_prd ),
inference(cnf_transformation,[status(thm)],[f916]) ).
fof(f930,definition,
( sP87_prd
<=> ( ( ( e3 != unit
& op(e1,e3) = e1 )
| op(e1,e1) != e3 )
& ( ( e3 != unit
& op(e1,e3) = e0 )
| op(e1,e0) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e4 )
| op(e0,e4) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e3 )
| op(e0,e3) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e2 )
| op(e0,e2) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e1 )
| op(e0,e1) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e0 )
| op(e0,e0) != e3 ) ) ),
introduced(definition,[new_symbols(definition,[sP87_prd])],[]) ).
fof(f931,plain,
( sP82_prd
<=> ( ( ( e3 != unit
& op(e1,e3) = e2 )
| op(e1,e2) != e3 )
& sP87_prd ) ),
inference(formula_renaming,[status(thm)],[f890,f930]) ).
fof(f932,plain,
( ( ( ( e3 = unit
| op(e1,e3) != e2 )
& op(e1,e2) = e3 )
| ~ sP87_prd
| sP82_prd )
& ( ( ( ( e3 != unit
& op(e1,e3) = e2 )
| op(e1,e2) != e3 )
& sP87_prd )
| ~ sP82_prd ) ),
inference(NNF_transformation,[status(thm)],[f931]) ).
fof(f933,plain,
( sP87_prd
| ~ sP82_prd ),
inference(cnf_transformation,[status(thm)],[f932]) ).
fof(f938,definition,
( sP88_prd
<=> ( ( op(op(e1,e0),e1) != e0
& op(op(e1,e0),e0) = e1
& op(e0,e1) != op(e1,e0) )
| ( op(op(e0,e4),e0) != e4
& op(op(e0,e4),e4) = e0
& op(e4,e0) != op(e0,e4) )
| ( op(op(e0,e3),e0) != e3
& op(op(e0,e3),e3) = e0
& op(e3,e0) != op(e0,e3) )
| ( op(op(e0,e2),e0) != e2
& op(op(e0,e2),e2) = e0
& op(e2,e0) != op(e0,e2) )
| ( op(op(e0,e1),e0) != e1
& op(op(e0,e1),e1) = e0
& op(e1,e0) != op(e0,e1) )
| ( op(op(e0,e0),e0) != e0
& op(op(e0,e0),e0) = e0
& op(e0,e0) != op(e0,e0) ) ) ),
introduced(definition,[new_symbols(definition,[sP88_prd])],[]) ).
fof(f939,plain,
( sP83_prd
<=> ( ( op(op(e1,e1),e1) != e1
& op(op(e1,e1),e1) = e1
& op(e1,e1) != op(e1,e1) )
| sP88_prd ) ),
inference(formula_renaming,[status(thm)],[f898,f938]) ).
fof(f940,plain,
( ( ( ( op(op(e1,e1),e1) = e1
| op(op(e1,e1),e1) != e1
| op(e1,e1) = op(e1,e1) )
& ~ sP88_prd )
| sP83_prd )
& ( ( op(op(e1,e1),e1) != e1
& op(op(e1,e1),e1) = e1
& op(e1,e1) != op(e1,e1) )
| sP88_prd
| ~ sP83_prd ) ),
inference(NNF_transformation,[status(thm)],[f939]) ).
fof(f941,plain,
( op(e1,e1) != op(e1,e1)
| sP88_prd
| ~ sP83_prd ),
inference(cnf_transformation,[status(thm)],[f940]) ).
fof(f946,definition,
( sP89_prd
<=> ( ( ( e0 != unit
& op(e1,e0) = e3 )
| op(e1,e3) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e2 )
| op(e1,e2) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e1 )
| op(e1,e1) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e0 )
| op(e1,e0) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e4 )
| op(e0,e4) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e3 )
| op(e0,e3) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e2 )
| op(e0,e2) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e1 )
| op(e0,e1) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e0 )
| op(e0,e0) != e0 ) ) ),
introduced(definition,[new_symbols(definition,[sP89_prd])],[]) ).
fof(f947,plain,
( sP84_prd
<=> ( ( ( e0 != unit
& op(e1,e0) = e4 )
| op(e1,e4) != e0 )
& sP89_prd ) ),
inference(formula_renaming,[status(thm)],[f906,f946]) ).
fof(f948,plain,
( ( ( ( e0 = unit
| op(e1,e0) != e4 )
& op(e1,e4) = e0 )
| ~ sP89_prd
| sP84_prd )
& ( ( ( ( e0 != unit
& op(e1,e0) = e4 )
| op(e1,e4) != e0 )
& sP89_prd )
| ~ sP84_prd ) ),
inference(NNF_transformation,[status(thm)],[f947]) ).
fof(f949,plain,
( sP89_prd
| ~ sP84_prd ),
inference(cnf_transformation,[status(thm)],[f948]) ).
fof(f954,definition,
( sP90_prd
<=> ( ( ( e1 != unit
& op(e1,e1) = e2 )
| op(e1,e2) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e1 )
| op(e1,e1) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e0 )
| op(e1,e0) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e4 )
| op(e0,e4) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e3 )
| op(e0,e3) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e2 )
| op(e0,e2) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e1 )
| op(e0,e1) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e0 )
| op(e0,e0) != e1 ) ) ),
introduced(definition,[new_symbols(definition,[sP90_prd])],[]) ).
fof(f955,plain,
( sP85_prd
<=> ( ( ( e1 != unit
& op(e1,e1) = e3 )
| op(e1,e3) != e1 )
& sP90_prd ) ),
inference(formula_renaming,[status(thm)],[f914,f954]) ).
fof(f956,plain,
( ( ( ( e1 = unit
| op(e1,e1) != e3 )
& op(e1,e3) = e1 )
| ~ sP90_prd
| sP85_prd )
& ( ( ( ( e1 != unit
& op(e1,e1) = e3 )
| op(e1,e3) != e1 )
& sP90_prd )
| ~ sP85_prd ) ),
inference(NNF_transformation,[status(thm)],[f955]) ).
fof(f957,plain,
( sP90_prd
| ~ sP85_prd ),
inference(cnf_transformation,[status(thm)],[f956]) ).
fof(f958,plain,
( op(e1,e1) = e3
| op(e1,e3) != e1
| ~ sP85_prd ),
inference(cnf_transformation,[status(thm)],[f956]) ).
fof(f970,definition,
( sP92_prd
<=> ( ( ( e3 != unit
& op(e1,e3) = e0 )
| op(e1,e0) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e4 )
| op(e0,e4) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e3 )
| op(e0,e3) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e2 )
| op(e0,e2) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e1 )
| op(e0,e1) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e0 )
| op(e0,e0) != e3 ) ) ),
introduced(definition,[new_symbols(definition,[sP92_prd])],[]) ).
fof(f971,plain,
( sP87_prd
<=> ( ( ( e3 != unit
& op(e1,e3) = e1 )
| op(e1,e1) != e3 )
& sP92_prd ) ),
inference(formula_renaming,[status(thm)],[f930,f970]) ).
fof(f972,plain,
( ( ( ( e3 = unit
| op(e1,e3) != e1 )
& op(e1,e1) = e3 )
| ~ sP92_prd
| sP87_prd )
& ( ( ( ( e3 != unit
& op(e1,e3) = e1 )
| op(e1,e1) != e3 )
& sP92_prd )
| ~ sP87_prd ) ),
inference(NNF_transformation,[status(thm)],[f971]) ).
fof(f973,plain,
( sP92_prd
| ~ sP87_prd ),
inference(cnf_transformation,[status(thm)],[f972]) ).
fof(f978,definition,
( sP93_prd
<=> ( ( op(op(e0,e4),e0) != e4
& op(op(e0,e4),e4) = e0
& op(e4,e0) != op(e0,e4) )
| ( op(op(e0,e3),e0) != e3
& op(op(e0,e3),e3) = e0
& op(e3,e0) != op(e0,e3) )
| ( op(op(e0,e2),e0) != e2
& op(op(e0,e2),e2) = e0
& op(e2,e0) != op(e0,e2) )
| ( op(op(e0,e1),e0) != e1
& op(op(e0,e1),e1) = e0
& op(e1,e0) != op(e0,e1) )
| ( op(op(e0,e0),e0) != e0
& op(op(e0,e0),e0) = e0
& op(e0,e0) != op(e0,e0) ) ) ),
introduced(definition,[new_symbols(definition,[sP93_prd])],[]) ).
fof(f979,plain,
( sP88_prd
<=> ( ( op(op(e1,e0),e1) != e0
& op(op(e1,e0),e0) = e1
& op(e0,e1) != op(e1,e0) )
| sP93_prd ) ),
inference(formula_renaming,[status(thm)],[f938,f978]) ).
fof(f980,plain,
( ( ( ( op(op(e1,e0),e1) = e0
| op(op(e1,e0),e0) != e1
| op(e0,e1) = op(e1,e0) )
& ~ sP93_prd )
| sP88_prd )
& ( ( op(op(e1,e0),e1) != e0
& op(op(e1,e0),e0) = e1
& op(e0,e1) != op(e1,e0) )
| sP93_prd
| ~ sP88_prd ) ),
inference(NNF_transformation,[status(thm)],[f979]) ).
fof(f981,plain,
( op(e0,e1) != op(e1,e0)
| sP93_prd
| ~ sP88_prd ),
inference(cnf_transformation,[status(thm)],[f980]) ).
fof(f986,definition,
( sP94_prd
<=> ( ( ( e0 != unit
& op(e1,e0) = e2 )
| op(e1,e2) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e1 )
| op(e1,e1) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e0 )
| op(e1,e0) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e4 )
| op(e0,e4) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e3 )
| op(e0,e3) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e2 )
| op(e0,e2) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e1 )
| op(e0,e1) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e0 )
| op(e0,e0) != e0 ) ) ),
introduced(definition,[new_symbols(definition,[sP94_prd])],[]) ).
fof(f987,plain,
( sP89_prd
<=> ( ( ( e0 != unit
& op(e1,e0) = e3 )
| op(e1,e3) != e0 )
& sP94_prd ) ),
inference(formula_renaming,[status(thm)],[f946,f986]) ).
fof(f988,plain,
( ( ( ( e0 = unit
| op(e1,e0) != e3 )
& op(e1,e3) = e0 )
| ~ sP94_prd
| sP89_prd )
& ( ( ( ( e0 != unit
& op(e1,e0) = e3 )
| op(e1,e3) != e0 )
& sP94_prd )
| ~ sP89_prd ) ),
inference(NNF_transformation,[status(thm)],[f987]) ).
fof(f989,plain,
( sP94_prd
| ~ sP89_prd ),
inference(cnf_transformation,[status(thm)],[f988]) ).
fof(f994,definition,
( sP95_prd
<=> ( ( ( e1 != unit
& op(e1,e1) = e1 )
| op(e1,e1) != e1 )
& ( ( e1 != unit
& op(e1,e1) = e0 )
| op(e1,e0) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e4 )
| op(e0,e4) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e3 )
| op(e0,e3) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e2 )
| op(e0,e2) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e1 )
| op(e0,e1) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e0 )
| op(e0,e0) != e1 ) ) ),
introduced(definition,[new_symbols(definition,[sP95_prd])],[]) ).
fof(f995,plain,
( sP90_prd
<=> ( ( ( e1 != unit
& op(e1,e1) = e2 )
| op(e1,e2) != e1 )
& sP95_prd ) ),
inference(formula_renaming,[status(thm)],[f954,f994]) ).
fof(f996,plain,
( ( ( ( e1 = unit
| op(e1,e1) != e2 )
& op(e1,e2) = e1 )
| ~ sP95_prd
| sP90_prd )
& ( ( ( ( e1 != unit
& op(e1,e1) = e2 )
| op(e1,e2) != e1 )
& sP95_prd )
| ~ sP90_prd ) ),
inference(NNF_transformation,[status(thm)],[f995]) ).
fof(f997,plain,
( sP95_prd
| ~ sP90_prd ),
inference(cnf_transformation,[status(thm)],[f996]) ).
fof(f1010,definition,
( sP97_prd
<=> ( ( ( e3 != unit
& op(e0,e3) = e4 )
| op(e0,e4) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e3 )
| op(e0,e3) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e2 )
| op(e0,e2) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e1 )
| op(e0,e1) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e0 )
| op(e0,e0) != e3 ) ) ),
introduced(definition,[new_symbols(definition,[sP97_prd])],[]) ).
fof(f1011,plain,
( sP92_prd
<=> ( ( ( e3 != unit
& op(e1,e3) = e0 )
| op(e1,e0) != e3 )
& sP97_prd ) ),
inference(formula_renaming,[status(thm)],[f970,f1010]) ).
fof(f1012,plain,
( ( ( ( e3 = unit
| op(e1,e3) != e0 )
& op(e1,e0) = e3 )
| ~ sP97_prd
| sP92_prd )
& ( ( ( ( e3 != unit
& op(e1,e3) = e0 )
| op(e1,e0) != e3 )
& sP97_prd )
| ~ sP92_prd ) ),
inference(NNF_transformation,[status(thm)],[f1011]) ).
fof(f1013,plain,
( sP97_prd
| ~ sP92_prd ),
inference(cnf_transformation,[status(thm)],[f1012]) ).
fof(f1014,plain,
( op(e1,e3) = e0
| op(e1,e0) != e3
| ~ sP92_prd ),
inference(cnf_transformation,[status(thm)],[f1012]) ).
fof(f1018,definition,
( sP98_prd
<=> ( ( op(op(e0,e3),e0) != e3
& op(op(e0,e3),e3) = e0
& op(e3,e0) != op(e0,e3) )
| ( op(op(e0,e2),e0) != e2
& op(op(e0,e2),e2) = e0
& op(e2,e0) != op(e0,e2) )
| ( op(op(e0,e1),e0) != e1
& op(op(e0,e1),e1) = e0
& op(e1,e0) != op(e0,e1) )
| ( op(op(e0,e0),e0) != e0
& op(op(e0,e0),e0) = e0
& op(e0,e0) != op(e0,e0) ) ) ),
introduced(definition,[new_symbols(definition,[sP98_prd])],[]) ).
fof(f1019,plain,
( sP93_prd
<=> ( ( op(op(e0,e4),e0) != e4
& op(op(e0,e4),e4) = e0
& op(e4,e0) != op(e0,e4) )
| sP98_prd ) ),
inference(formula_renaming,[status(thm)],[f978,f1018]) ).
fof(f1020,plain,
( ( ( ( op(op(e0,e4),e0) = e4
| op(op(e0,e4),e4) != e0
| op(e4,e0) = op(e0,e4) )
& ~ sP98_prd )
| sP93_prd )
& ( ( op(op(e0,e4),e0) != e4
& op(op(e0,e4),e4) = e0
& op(e4,e0) != op(e0,e4) )
| sP98_prd
| ~ sP93_prd ) ),
inference(NNF_transformation,[status(thm)],[f1019]) ).
fof(f1021,plain,
( op(e4,e0) != op(e0,e4)
| sP98_prd
| ~ sP93_prd ),
inference(cnf_transformation,[status(thm)],[f1020]) ).
fof(f1026,definition,
( sP99_prd
<=> ( ( ( e0 != unit
& op(e1,e0) = e1 )
| op(e1,e1) != e0 )
& ( ( e0 != unit
& op(e1,e0) = e0 )
| op(e1,e0) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e4 )
| op(e0,e4) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e3 )
| op(e0,e3) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e2 )
| op(e0,e2) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e1 )
| op(e0,e1) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e0 )
| op(e0,e0) != e0 ) ) ),
introduced(definition,[new_symbols(definition,[sP99_prd])],[]) ).
fof(f1027,plain,
( sP94_prd
<=> ( ( ( e0 != unit
& op(e1,e0) = e2 )
| op(e1,e2) != e0 )
& sP99_prd ) ),
inference(formula_renaming,[status(thm)],[f986,f1026]) ).
fof(f1028,plain,
( ( ( ( e0 = unit
| op(e1,e0) != e2 )
& op(e1,e2) = e0 )
| ~ sP99_prd
| sP94_prd )
& ( ( ( ( e0 != unit
& op(e1,e0) = e2 )
| op(e1,e2) != e0 )
& sP99_prd )
| ~ sP94_prd ) ),
inference(NNF_transformation,[status(thm)],[f1027]) ).
fof(f1029,plain,
( sP99_prd
| ~ sP94_prd ),
inference(cnf_transformation,[status(thm)],[f1028]) ).
fof(f1034,definition,
( sP100_prd
<=> ( ( ( e1 != unit
& op(e1,e1) = e0 )
| op(e1,e0) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e4 )
| op(e0,e4) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e3 )
| op(e0,e3) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e2 )
| op(e0,e2) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e1 )
| op(e0,e1) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e0 )
| op(e0,e0) != e1 ) ) ),
introduced(definition,[new_symbols(definition,[sP100_prd])],[]) ).
fof(f1035,plain,
( sP95_prd
<=> ( ( ( e1 != unit
& op(e1,e1) = e1 )
| op(e1,e1) != e1 )
& sP100_prd ) ),
inference(formula_renaming,[status(thm)],[f994,f1034]) ).
fof(f1036,plain,
( ( ( ( e1 = unit
| op(e1,e1) != e1 )
& op(e1,e1) = e1 )
| ~ sP100_prd
| sP95_prd )
& ( ( ( ( e1 != unit
& op(e1,e1) = e1 )
| op(e1,e1) != e1 )
& sP100_prd )
| ~ sP95_prd ) ),
inference(NNF_transformation,[status(thm)],[f1035]) ).
fof(f1037,plain,
( sP100_prd
| ~ sP95_prd ),
inference(cnf_transformation,[status(thm)],[f1036]) ).
fof(f1050,definition,
( sP102_prd
<=> ( ( ( e3 != unit
& op(e0,e3) = e3 )
| op(e0,e3) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e2 )
| op(e0,e2) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e1 )
| op(e0,e1) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e0 )
| op(e0,e0) != e3 ) ) ),
introduced(definition,[new_symbols(definition,[sP102_prd])],[]) ).
fof(f1051,plain,
( sP97_prd
<=> ( ( ( e3 != unit
& op(e0,e3) = e4 )
| op(e0,e4) != e3 )
& sP102_prd ) ),
inference(formula_renaming,[status(thm)],[f1010,f1050]) ).
fof(f1052,plain,
( ( ( ( e3 = unit
| op(e0,e3) != e4 )
& op(e0,e4) = e3 )
| ~ sP102_prd
| sP97_prd )
& ( ( ( ( e3 != unit
& op(e0,e3) = e4 )
| op(e0,e4) != e3 )
& sP102_prd )
| ~ sP97_prd ) ),
inference(NNF_transformation,[status(thm)],[f1051]) ).
fof(f1053,plain,
( sP102_prd
| ~ sP97_prd ),
inference(cnf_transformation,[status(thm)],[f1052]) ).
fof(f1058,definition,
( sP103_prd
<=> ( ( op(op(e0,e2),e0) != e2
& op(op(e0,e2),e2) = e0
& op(e2,e0) != op(e0,e2) )
| ( op(op(e0,e1),e0) != e1
& op(op(e0,e1),e1) = e0
& op(e1,e0) != op(e0,e1) )
| ( op(op(e0,e0),e0) != e0
& op(op(e0,e0),e0) = e0
& op(e0,e0) != op(e0,e0) ) ) ),
introduced(definition,[new_symbols(definition,[sP103_prd])],[]) ).
fof(f1059,plain,
( sP98_prd
<=> ( ( op(op(e0,e3),e0) != e3
& op(op(e0,e3),e3) = e0
& op(e3,e0) != op(e0,e3) )
| sP103_prd ) ),
inference(formula_renaming,[status(thm)],[f1018,f1058]) ).
fof(f1060,plain,
( ( ( ( op(op(e0,e3),e0) = e3
| op(op(e0,e3),e3) != e0
| op(e3,e0) = op(e0,e3) )
& ~ sP103_prd )
| sP98_prd )
& ( ( op(op(e0,e3),e0) != e3
& op(op(e0,e3),e3) = e0
& op(e3,e0) != op(e0,e3) )
| sP103_prd
| ~ sP98_prd ) ),
inference(NNF_transformation,[status(thm)],[f1059]) ).
fof(f1063,plain,
( op(op(e0,e3),e0) != e3
| sP103_prd
| ~ sP98_prd ),
inference(cnf_transformation,[status(thm)],[f1060]) ).
fof(f1066,definition,
( sP104_prd
<=> ( ( ( e0 != unit
& op(e1,e0) = e0 )
| op(e1,e0) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e4 )
| op(e0,e4) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e3 )
| op(e0,e3) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e2 )
| op(e0,e2) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e1 )
| op(e0,e1) != e0 )
& ( ( e0 != unit
& op(e0,e0) = e0 )
| op(e0,e0) != e0 ) ) ),
introduced(definition,[new_symbols(definition,[sP104_prd])],[]) ).
fof(f1067,plain,
( sP99_prd
<=> ( ( ( e0 != unit
& op(e1,e0) = e1 )
| op(e1,e1) != e0 )
& sP104_prd ) ),
inference(formula_renaming,[status(thm)],[f1026,f1066]) ).
fof(f1068,plain,
( ( ( ( e0 = unit
| op(e1,e0) != e1 )
& op(e1,e1) = e0 )
| ~ sP104_prd
| sP99_prd )
& ( ( ( ( e0 != unit
& op(e1,e0) = e1 )
| op(e1,e1) != e0 )
& sP104_prd )
| ~ sP99_prd ) ),
inference(NNF_transformation,[status(thm)],[f1067]) ).
fof(f1070,plain,
( op(e1,e0) = e1
| op(e1,e1) != e0
| ~ sP99_prd ),
inference(cnf_transformation,[status(thm)],[f1068]) ).
fof(f1071,plain,
( e0 != unit
| op(e1,e1) != e0
| ~ sP99_prd ),
inference(cnf_transformation,[status(thm)],[f1068]) ).
fof(f1074,definition,
( sP105_prd
<=> ( ( ( e1 != unit
& op(e0,e1) = e4 )
| op(e0,e4) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e3 )
| op(e0,e3) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e2 )
| op(e0,e2) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e1 )
| op(e0,e1) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e0 )
| op(e0,e0) != e1 ) ) ),
introduced(definition,[new_symbols(definition,[sP105_prd])],[]) ).
fof(f1075,plain,
( sP100_prd
<=> ( ( ( e1 != unit
& op(e1,e1) = e0 )
| op(e1,e0) != e1 )
& sP105_prd ) ),
inference(formula_renaming,[status(thm)],[f1034,f1074]) ).
fof(f1076,plain,
( ( ( ( e1 = unit
| op(e1,e1) != e0 )
& op(e1,e0) = e1 )
| ~ sP105_prd
| sP100_prd )
& ( ( ( ( e1 != unit
& op(e1,e1) = e0 )
| op(e1,e0) != e1 )
& sP105_prd )
| ~ sP100_prd ) ),
inference(NNF_transformation,[status(thm)],[f1075]) ).
fof(f1077,plain,
( sP105_prd
| ~ sP100_prd ),
inference(cnf_transformation,[status(thm)],[f1076]) ).
fof(f1090,definition,
( sP107_prd
<=> ( ( ( e3 != unit
& op(e0,e3) = e2 )
| op(e0,e2) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e1 )
| op(e0,e1) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e0 )
| op(e0,e0) != e3 ) ) ),
introduced(definition,[new_symbols(definition,[sP107_prd])],[]) ).
fof(f1091,plain,
( sP102_prd
<=> ( ( ( e3 != unit
& op(e0,e3) = e3 )
| op(e0,e3) != e3 )
& sP107_prd ) ),
inference(formula_renaming,[status(thm)],[f1050,f1090]) ).
fof(f1092,plain,
( ( ( ( e3 = unit
| op(e0,e3) != e3 )
& op(e0,e3) = e3 )
| ~ sP107_prd
| sP102_prd )
& ( ( ( ( e3 != unit
& op(e0,e3) = e3 )
| op(e0,e3) != e3 )
& sP107_prd )
| ~ sP102_prd ) ),
inference(NNF_transformation,[status(thm)],[f1091]) ).
fof(f1093,plain,
( sP107_prd
| ~ sP102_prd ),
inference(cnf_transformation,[status(thm)],[f1092]) ).
fof(f1098,definition,
( sP108_prd
<=> ( ( op(op(e0,e1),e0) != e1
& op(op(e0,e1),e1) = e0
& op(e1,e0) != op(e0,e1) )
| ( op(op(e0,e0),e0) != e0
& op(op(e0,e0),e0) = e0
& op(e0,e0) != op(e0,e0) ) ) ),
introduced(definition,[new_symbols(definition,[sP108_prd])],[]) ).
fof(f1099,plain,
( sP103_prd
<=> ( ( op(op(e0,e2),e0) != e2
& op(op(e0,e2),e2) = e0
& op(e2,e0) != op(e0,e2) )
| sP108_prd ) ),
inference(formula_renaming,[status(thm)],[f1058,f1098]) ).
fof(f1100,plain,
( ( ( ( op(op(e0,e2),e0) = e2
| op(op(e0,e2),e2) != e0
| op(e2,e0) = op(e0,e2) )
& ~ sP108_prd )
| sP103_prd )
& ( ( op(op(e0,e2),e0) != e2
& op(op(e0,e2),e2) = e0
& op(e2,e0) != op(e0,e2) )
| sP108_prd
| ~ sP103_prd ) ),
inference(NNF_transformation,[status(thm)],[f1099]) ).
fof(f1101,plain,
( op(e2,e0) != op(e0,e2)
| sP108_prd
| ~ sP103_prd ),
inference(cnf_transformation,[status(thm)],[f1100]) ).
fof(f1114,definition,
( sP110_prd
<=> ( ( ( e1 != unit
& op(e0,e1) = e3 )
| op(e0,e3) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e2 )
| op(e0,e2) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e1 )
| op(e0,e1) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e0 )
| op(e0,e0) != e1 ) ) ),
introduced(definition,[new_symbols(definition,[sP110_prd])],[]) ).
fof(f1115,plain,
( sP105_prd
<=> ( ( ( e1 != unit
& op(e0,e1) = e4 )
| op(e0,e4) != e1 )
& sP110_prd ) ),
inference(formula_renaming,[status(thm)],[f1074,f1114]) ).
fof(f1116,plain,
( ( ( ( e1 = unit
| op(e0,e1) != e4 )
& op(e0,e4) = e1 )
| ~ sP110_prd
| sP105_prd )
& ( ( ( ( e1 != unit
& op(e0,e1) = e4 )
| op(e0,e4) != e1 )
& sP110_prd )
| ~ sP105_prd ) ),
inference(NNF_transformation,[status(thm)],[f1115]) ).
fof(f1117,plain,
( sP110_prd
| ~ sP105_prd ),
inference(cnf_transformation,[status(thm)],[f1116]) ).
fof(f1130,definition,
( sP112_prd
<=> ( ( ( e3 != unit
& op(e0,e3) = e1 )
| op(e0,e1) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e0 )
| op(e0,e0) != e3 ) ) ),
introduced(definition,[new_symbols(definition,[sP112_prd])],[]) ).
fof(f1131,plain,
( sP107_prd
<=> ( ( ( e3 != unit
& op(e0,e3) = e2 )
| op(e0,e2) != e3 )
& sP112_prd ) ),
inference(formula_renaming,[status(thm)],[f1090,f1130]) ).
fof(f1132,plain,
( ( ( ( e3 = unit
| op(e0,e3) != e2 )
& op(e0,e2) = e3 )
| ~ sP112_prd
| sP107_prd )
& ( ( ( ( e3 != unit
& op(e0,e3) = e2 )
| op(e0,e2) != e3 )
& sP112_prd )
| ~ sP107_prd ) ),
inference(NNF_transformation,[status(thm)],[f1131]) ).
fof(f1133,plain,
( sP112_prd
| ~ sP107_prd ),
inference(cnf_transformation,[status(thm)],[f1132]) ).
fof(f1138,definition,
( sP113_prd
<=> ( op(op(e0,e0),e0) != e0
& op(op(e0,e0),e0) = e0
& op(e0,e0) != op(e0,e0) ) ),
introduced(definition,[new_symbols(definition,[sP113_prd])],[]) ).
fof(f1139,plain,
( sP108_prd
<=> ( ( op(op(e0,e1),e0) != e1
& op(op(e0,e1),e1) = e0
& op(e1,e0) != op(e0,e1) )
| sP113_prd ) ),
inference(formula_renaming,[status(thm)],[f1098,f1138]) ).
fof(f1140,plain,
( ( ( ( op(op(e0,e1),e0) = e1
| op(op(e0,e1),e1) != e0
| op(e1,e0) = op(e0,e1) )
& ~ sP113_prd )
| sP108_prd )
& ( ( op(op(e0,e1),e0) != e1
& op(op(e0,e1),e1) = e0
& op(e1,e0) != op(e0,e1) )
| sP113_prd
| ~ sP108_prd ) ),
inference(NNF_transformation,[status(thm)],[f1139]) ).
fof(f1141,plain,
( op(e1,e0) != op(e0,e1)
| sP113_prd
| ~ sP108_prd ),
inference(cnf_transformation,[status(thm)],[f1140]) ).
fof(f1154,definition,
( sP115_prd
<=> ( ( ( e1 != unit
& op(e0,e1) = e2 )
| op(e0,e2) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e1 )
| op(e0,e1) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e0 )
| op(e0,e0) != e1 ) ) ),
introduced(definition,[new_symbols(definition,[sP115_prd])],[]) ).
fof(f1155,plain,
( sP110_prd
<=> ( ( ( e1 != unit
& op(e0,e1) = e3 )
| op(e0,e3) != e1 )
& sP115_prd ) ),
inference(formula_renaming,[status(thm)],[f1114,f1154]) ).
fof(f1156,plain,
( ( ( ( e1 = unit
| op(e0,e1) != e3 )
& op(e0,e3) = e1 )
| ~ sP115_prd
| sP110_prd )
& ( ( ( ( e1 != unit
& op(e0,e1) = e3 )
| op(e0,e3) != e1 )
& sP115_prd )
| ~ sP110_prd ) ),
inference(NNF_transformation,[status(thm)],[f1155]) ).
fof(f1157,plain,
( sP115_prd
| ~ sP110_prd ),
inference(cnf_transformation,[status(thm)],[f1156]) ).
fof(f1170,plain,
( ( ( ( e3 = unit
| op(e0,e3) != e1 )
& op(e0,e1) = e3 )
| ( ( e3 = unit
| op(e0,e3) != e0 )
& op(e0,e0) = e3 )
| sP112_prd )
& ( ( ( ( e3 != unit
& op(e0,e3) = e1 )
| op(e0,e1) != e3 )
& ( ( e3 != unit
& op(e0,e3) = e0 )
| op(e0,e0) != e3 ) )
| ~ sP112_prd ) ),
inference(NNF_transformation,[status(thm)],[f1130]) ).
fof(f1171,plain,
( op(e0,e3) = e0
| op(e0,e0) != e3
| ~ sP112_prd ),
inference(cnf_transformation,[status(thm)],[f1170]) ).
fof(f1179,plain,
( ( op(op(e0,e0),e0) = e0
| op(op(e0,e0),e0) != e0
| op(e0,e0) = op(e0,e0)
| sP113_prd )
& ( ( op(op(e0,e0),e0) != e0
& op(op(e0,e0),e0) = e0
& op(e0,e0) != op(e0,e0) )
| ~ sP113_prd ) ),
inference(NNF_transformation,[status(thm)],[f1138]) ).
fof(f1180,plain,
( op(e0,e0) != op(e0,e0)
| ~ sP113_prd ),
inference(cnf_transformation,[status(thm)],[f1179]) ).
fof(f1192,definition,
( sP118_prd
<=> ( ( ( e1 != unit
& op(e0,e1) = e1 )
| op(e0,e1) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e0 )
| op(e0,e0) != e1 ) ) ),
introduced(definition,[new_symbols(definition,[sP118_prd])],[]) ).
fof(f1193,plain,
( sP115_prd
<=> ( ( ( e1 != unit
& op(e0,e1) = e2 )
| op(e0,e2) != e1 )
& sP118_prd ) ),
inference(formula_renaming,[status(thm)],[f1154,f1192]) ).
fof(f1194,plain,
( ( ( ( e1 = unit
| op(e0,e1) != e2 )
& op(e0,e2) = e1 )
| ~ sP118_prd
| sP115_prd )
& ( ( ( ( e1 != unit
& op(e0,e1) = e2 )
| op(e0,e2) != e1 )
& sP118_prd )
| ~ sP115_prd ) ),
inference(NNF_transformation,[status(thm)],[f1193]) ).
fof(f1195,plain,
( sP118_prd
| ~ sP115_prd ),
inference(cnf_transformation,[status(thm)],[f1194]) ).
fof(f1217,plain,
( ( ( ( e1 = unit
| op(e0,e1) != e1 )
& op(e0,e1) = e1 )
| ( ( e1 = unit
| op(e0,e1) != e0 )
& op(e0,e0) = e1 )
| sP118_prd )
& ( ( ( ( e1 != unit
& op(e0,e1) = e1 )
| op(e0,e1) != e1 )
& ( ( e1 != unit
& op(e0,e1) = e0 )
| op(e0,e0) != e1 ) )
| ~ sP118_prd ) ),
inference(NNF_transformation,[status(thm)],[f1192]) ).
fof(f1218,plain,
( op(e0,e1) = e0
| op(e0,e0) != e1
| ~ sP118_prd ),
inference(cnf_transformation,[status(thm)],[f1217]) ).
fof(f1238,definition,
( sQ1_spl
<=> op(e0,e0) = e1 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f1244,definition,
( sQ3_spl
<=> op(e0,e0) = e3 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f1251,definition,
( sQ5_spl
<=> op(e0,e1) = e0 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f1252,plain,
( ~ sQ5_spl
| op(e0,e1) = e0 ),
inference(component_clause,[status(thm)],[f1251]) ).
fof(f1254,definition,
( sQ6_spl
<=> op(e0,e1) = e1 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f1255,plain,
( ~ sQ6_spl
| op(e0,e1) = e1 ),
inference(component_clause,[status(thm)],[f1254]) ).
fof(f1260,definition,
( sQ8_spl
<=> op(e0,e1) = e3 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f1267,definition,
( sQ10_spl
<=> op(e0,e2) = e0 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f1270,definition,
( sQ11_spl
<=> op(e0,e2) = e1 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f1271,plain,
( ~ sQ11_spl
| op(e0,e2) = e1 ),
inference(component_clause,[status(thm)],[f1270]) ).
fof(f1273,definition,
( sQ12_spl
<=> op(e0,e2) = e2 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f1276,definition,
( sQ13_spl
<=> op(e0,e2) = e3 ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f1277,plain,
( ~ sQ13_spl
| op(e0,e2) = e3 ),
inference(component_clause,[status(thm)],[f1276]) ).
fof(f1279,definition,
( sQ14_spl
<=> op(e0,e2) = e4 ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f1280,plain,
( ~ sQ14_spl
| op(e0,e2) = e4 ),
inference(component_clause,[status(thm)],[f1279]) ).
fof(f1282,plain,
( sQ14_spl
| sQ13_spl
| sQ12_spl
| sQ11_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f11,f1267,f1270,f1273,f1276,f1279]) ).
fof(f1283,definition,
( sQ15_spl
<=> op(e0,e3) = e0 ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f1284,plain,
( ~ sQ15_spl
| op(e0,e3) = e0 ),
inference(component_clause,[status(thm)],[f1283]) ).
fof(f1286,definition,
( sQ16_spl
<=> op(e0,e3) = e1 ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f1287,plain,
( ~ sQ16_spl
| op(e0,e3) = e1 ),
inference(component_clause,[status(thm)],[f1286]) ).
fof(f1292,definition,
( sQ18_spl
<=> op(e0,e3) = e3 ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f1293,plain,
( ~ sQ18_spl
| op(e0,e3) = e3 ),
inference(component_clause,[status(thm)],[f1292]) ).
fof(f1294,plain,
( sQ18_spl
| op(e0,e3) != e3 ),
inference(component_clause,[status(thm)],[f1292]) ).
fof(f1295,definition,
( sQ19_spl
<=> op(e0,e3) = e4 ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f1296,plain,
( ~ sQ19_spl
| op(e0,e3) = e4 ),
inference(component_clause,[status(thm)],[f1295]) ).
fof(f1299,definition,
( sQ20_spl
<=> op(e0,e4) = e0 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f1300,plain,
( ~ sQ20_spl
| op(e0,e4) = e0 ),
inference(component_clause,[status(thm)],[f1299]) ).
fof(f1302,definition,
( sQ21_spl
<=> op(e0,e4) = e1 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f1303,plain,
( ~ sQ21_spl
| op(e0,e4) = e1 ),
inference(component_clause,[status(thm)],[f1302]) ).
fof(f1308,definition,
( sQ23_spl
<=> op(e0,e4) = e3 ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f1311,definition,
( sQ24_spl
<=> op(e0,e4) = e4 ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f1313,plain,
( sQ24_spl
| op(e0,e4) != e4 ),
inference(component_clause,[status(thm)],[f1311]) ).
fof(f1315,definition,
( sQ25_spl
<=> op(e1,e0) = e0 ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f1316,plain,
( ~ sQ25_spl
| op(e1,e0) = e0 ),
inference(component_clause,[status(thm)],[f1315]) ).
fof(f1318,definition,
( sQ26_spl
<=> op(e1,e0) = e1 ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f1319,plain,
( ~ sQ26_spl
| op(e1,e0) = e1 ),
inference(component_clause,[status(thm)],[f1318]) ).
fof(f1324,definition,
( sQ28_spl
<=> op(e1,e0) = e3 ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f1325,plain,
( ~ sQ28_spl
| op(e1,e0) = e3 ),
inference(component_clause,[status(thm)],[f1324]) ).
fof(f1331,definition,
( sQ30_spl
<=> op(e1,e1) = e0 ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f1333,plain,
( sQ30_spl
| op(e1,e1) != e0 ),
inference(component_clause,[status(thm)],[f1331]) ).
fof(f1337,definition,
( sQ32_spl
<=> op(e1,e1) = e2 ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f1338,plain,
( ~ sQ32_spl
| op(e1,e1) = e2 ),
inference(component_clause,[status(thm)],[f1337]) ).
fof(f1340,definition,
( sQ33_spl
<=> op(e1,e1) = e3 ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f1341,plain,
( ~ sQ33_spl
| op(e1,e1) = e3 ),
inference(component_clause,[status(thm)],[f1340]) ).
fof(f1343,definition,
( sQ34_spl
<=> op(e1,e1) = e4 ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f1344,plain,
( ~ sQ34_spl
| op(e1,e1) = e4 ),
inference(component_clause,[status(thm)],[f1343]) ).
fof(f1347,definition,
( sQ35_spl
<=> op(e1,e2) = e0 ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f1348,plain,
( ~ sQ35_spl
| op(e1,e2) = e0 ),
inference(component_clause,[status(thm)],[f1347]) ).
fof(f1353,definition,
( sQ37_spl
<=> op(e1,e2) = e2 ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f1354,plain,
( ~ sQ37_spl
| op(e1,e2) = e2 ),
inference(component_clause,[status(thm)],[f1353]) ).
fof(f1356,definition,
( sQ38_spl
<=> op(e1,e2) = e3 ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f1357,plain,
( ~ sQ38_spl
| op(e1,e2) = e3 ),
inference(component_clause,[status(thm)],[f1356]) ).
fof(f1359,definition,
( sQ39_spl
<=> op(e1,e2) = e4 ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f1360,plain,
( ~ sQ39_spl
| op(e1,e2) = e4 ),
inference(component_clause,[status(thm)],[f1359]) ).
fof(f1363,definition,
( sQ40_spl
<=> op(e1,e3) = e0 ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f1364,plain,
( ~ sQ40_spl
| op(e1,e3) = e0 ),
inference(component_clause,[status(thm)],[f1363]) ).
fof(f1366,definition,
( sQ41_spl
<=> op(e1,e3) = e1 ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f1369,definition,
( sQ42_spl
<=> op(e1,e3) = e2 ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f1372,definition,
( sQ43_spl
<=> op(e1,e3) = e3 ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f1373,plain,
( ~ sQ43_spl
| op(e1,e3) = e3 ),
inference(component_clause,[status(thm)],[f1372]) ).
fof(f1375,definition,
( sQ44_spl
<=> op(e1,e3) = e4 ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f1376,plain,
( ~ sQ44_spl
| op(e1,e3) = e4 ),
inference(component_clause,[status(thm)],[f1375]) ).
fof(f1378,plain,
( sQ44_spl
| sQ43_spl
| sQ42_spl
| sQ41_spl
| sQ40_spl ),
inference(split_clause,[status(thm)],[f17,f1363,f1366,f1369,f1372,f1375]) ).
fof(f1379,definition,
( sQ45_spl
<=> op(e1,e4) = e0 ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f1380,plain,
( ~ sQ45_spl
| op(e1,e4) = e0 ),
inference(component_clause,[status(thm)],[f1379]) ).
fof(f1382,definition,
( sQ46_spl
<=> op(e1,e4) = e1 ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f1383,plain,
( ~ sQ46_spl
| op(e1,e4) = e1 ),
inference(component_clause,[status(thm)],[f1382]) ).
fof(f1388,definition,
( sQ48_spl
<=> op(e1,e4) = e3 ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f1391,definition,
( sQ49_spl
<=> op(e1,e4) = e4 ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f1392,plain,
( ~ sQ49_spl
| op(e1,e4) = e4 ),
inference(component_clause,[status(thm)],[f1391]) ).
fof(f1398,definition,
( sQ51_spl
<=> op(e2,e0) = e1 ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f1401,definition,
( sQ52_spl
<=> op(e2,e0) = e2 ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f1403,plain,
( sQ52_spl
| op(e2,e0) != e2 ),
inference(component_clause,[status(thm)],[f1401]) ).
fof(f1404,definition,
( sQ53_spl
<=> op(e2,e0) = e3 ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f1405,plain,
( ~ sQ53_spl
| op(e2,e0) = e3 ),
inference(component_clause,[status(thm)],[f1404]) ).
fof(f1407,definition,
( sQ54_spl
<=> op(e2,e0) = e4 ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f1408,plain,
( ~ sQ54_spl
| op(e2,e0) = e4 ),
inference(component_clause,[status(thm)],[f1407]) ).
fof(f1411,definition,
( sQ55_spl
<=> op(e2,e1) = e0 ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f1412,plain,
( ~ sQ55_spl
| op(e2,e1) = e0 ),
inference(component_clause,[status(thm)],[f1411]) ).
fof(f1417,definition,
( sQ57_spl
<=> op(e2,e1) = e2 ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f1420,definition,
( sQ58_spl
<=> op(e2,e1) = e3 ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f1421,plain,
( ~ sQ58_spl
| op(e2,e1) = e3 ),
inference(component_clause,[status(thm)],[f1420]) ).
fof(f1423,definition,
( sQ59_spl
<=> op(e2,e1) = e4 ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f1427,definition,
( sQ60_spl
<=> op(e2,e2) = e0 ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f1428,plain,
( ~ sQ60_spl
| op(e2,e2) = e0 ),
inference(component_clause,[status(thm)],[f1427]) ).
fof(f1430,definition,
( sQ61_spl
<=> op(e2,e2) = e1 ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f1431,plain,
( ~ sQ61_spl
| op(e2,e2) = e1 ),
inference(component_clause,[status(thm)],[f1430]) ).
fof(f1433,definition,
( sQ62_spl
<=> op(e2,e2) = e2 ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f1434,plain,
( ~ sQ62_spl
| op(e2,e2) = e2 ),
inference(component_clause,[status(thm)],[f1433]) ).
fof(f1436,definition,
( sQ63_spl
<=> op(e2,e2) = e3 ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f1438,plain,
( sQ63_spl
| op(e2,e2) != e3 ),
inference(component_clause,[status(thm)],[f1436]) ).
fof(f1439,definition,
( sQ64_spl
<=> op(e2,e2) = e4 ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f1440,plain,
( ~ sQ64_spl
| op(e2,e2) = e4 ),
inference(component_clause,[status(thm)],[f1439]) ).
fof(f1443,definition,
( sQ65_spl
<=> op(e2,e3) = e0 ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f1444,plain,
( ~ sQ65_spl
| op(e2,e3) = e0 ),
inference(component_clause,[status(thm)],[f1443]) ).
fof(f1446,definition,
( sQ66_spl
<=> op(e2,e3) = e1 ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f1449,definition,
( sQ67_spl
<=> op(e2,e3) = e2 ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f1450,plain,
( ~ sQ67_spl
| op(e2,e3) = e2 ),
inference(component_clause,[status(thm)],[f1449]) ).
fof(f1452,definition,
( sQ68_spl
<=> op(e2,e3) = e3 ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f1453,plain,
( ~ sQ68_spl
| op(e2,e3) = e3 ),
inference(component_clause,[status(thm)],[f1452]) ).
fof(f1455,definition,
( sQ69_spl
<=> op(e2,e3) = e4 ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f1456,plain,
( ~ sQ69_spl
| op(e2,e3) = e4 ),
inference(component_clause,[status(thm)],[f1455]) ).
fof(f1458,plain,
( sQ69_spl
| sQ68_spl
| sQ67_spl
| sQ66_spl
| sQ65_spl ),
inference(split_clause,[status(thm)],[f22,f1443,f1446,f1449,f1452,f1455]) ).
fof(f1459,definition,
( sQ70_spl
<=> op(e2,e4) = e0 ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f1462,definition,
( sQ71_spl
<=> op(e2,e4) = e1 ),
introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition]) ).
fof(f1463,plain,
( ~ sQ71_spl
| op(e2,e4) = e1 ),
inference(component_clause,[status(thm)],[f1462]) ).
fof(f1465,definition,
( sQ72_spl
<=> op(e2,e4) = e2 ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f1466,plain,
( ~ sQ72_spl
| op(e2,e4) = e2 ),
inference(component_clause,[status(thm)],[f1465]) ).
fof(f1468,definition,
( sQ73_spl
<=> op(e2,e4) = e3 ),
introduced(definition,[new_symbols(definition,[sQ73_spl])],[split_symbol_definition]) ).
fof(f1469,plain,
( ~ sQ73_spl
| op(e2,e4) = e3 ),
inference(component_clause,[status(thm)],[f1468]) ).
fof(f1471,definition,
( sQ74_spl
<=> op(e2,e4) = e4 ),
introduced(definition,[new_symbols(definition,[sQ74_spl])],[split_symbol_definition]) ).
fof(f1472,plain,
( ~ sQ74_spl
| op(e2,e4) = e4 ),
inference(component_clause,[status(thm)],[f1471]) ).
fof(f1475,definition,
( sQ75_spl
<=> op(e3,e0) = e0 ),
introduced(definition,[new_symbols(definition,[sQ75_spl])],[split_symbol_definition]) ).
fof(f1476,plain,
( ~ sQ75_spl
| op(e3,e0) = e0 ),
inference(component_clause,[status(thm)],[f1475]) ).
fof(f1478,definition,
( sQ76_spl
<=> op(e3,e0) = e1 ),
introduced(definition,[new_symbols(definition,[sQ76_spl])],[split_symbol_definition]) ).
fof(f1481,definition,
( sQ77_spl
<=> op(e3,e0) = e2 ),
introduced(definition,[new_symbols(definition,[sQ77_spl])],[split_symbol_definition]) ).
fof(f1482,plain,
( ~ sQ77_spl
| op(e3,e0) = e2 ),
inference(component_clause,[status(thm)],[f1481]) ).
fof(f1484,definition,
( sQ78_spl
<=> op(e3,e0) = e3 ),
introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition]) ).
fof(f1485,plain,
( ~ sQ78_spl
| op(e3,e0) = e3 ),
inference(component_clause,[status(thm)],[f1484]) ).
fof(f1487,definition,
( sQ79_spl
<=> op(e3,e0) = e4 ),
introduced(definition,[new_symbols(definition,[sQ79_spl])],[split_symbol_definition]) ).
fof(f1488,plain,
( ~ sQ79_spl
| op(e3,e0) = e4 ),
inference(component_clause,[status(thm)],[f1487]) ).
fof(f1491,definition,
( sQ80_spl
<=> op(e3,e1) = e0 ),
introduced(definition,[new_symbols(definition,[sQ80_spl])],[split_symbol_definition]) ).
fof(f1492,plain,
( ~ sQ80_spl
| op(e3,e1) = e0 ),
inference(component_clause,[status(thm)],[f1491]) ).
fof(f1494,definition,
( sQ81_spl
<=> op(e3,e1) = e1 ),
introduced(definition,[new_symbols(definition,[sQ81_spl])],[split_symbol_definition]) ).
fof(f1495,plain,
( ~ sQ81_spl
| op(e3,e1) = e1 ),
inference(component_clause,[status(thm)],[f1494]) ).
fof(f1497,definition,
( sQ82_spl
<=> op(e3,e1) = e2 ),
introduced(definition,[new_symbols(definition,[sQ82_spl])],[split_symbol_definition]) ).
fof(f1498,plain,
( ~ sQ82_spl
| op(e3,e1) = e2 ),
inference(component_clause,[status(thm)],[f1497]) ).
fof(f1500,definition,
( sQ83_spl
<=> op(e3,e1) = e3 ),
introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition]) ).
fof(f1503,definition,
( sQ84_spl
<=> op(e3,e1) = e4 ),
introduced(definition,[new_symbols(definition,[sQ84_spl])],[split_symbol_definition]) ).
fof(f1504,plain,
( ~ sQ84_spl
| op(e3,e1) = e4 ),
inference(component_clause,[status(thm)],[f1503]) ).
fof(f1506,plain,
( sQ84_spl
| sQ83_spl
| sQ82_spl
| sQ81_spl
| sQ80_spl ),
inference(split_clause,[status(thm)],[f25,f1491,f1494,f1497,f1500,f1503]) ).
fof(f1507,definition,
( sQ85_spl
<=> op(e3,e2) = e0 ),
introduced(definition,[new_symbols(definition,[sQ85_spl])],[split_symbol_definition]) ).
fof(f1508,plain,
( ~ sQ85_spl
| op(e3,e2) = e0 ),
inference(component_clause,[status(thm)],[f1507]) ).
fof(f1510,definition,
( sQ86_spl
<=> op(e3,e2) = e1 ),
introduced(definition,[new_symbols(definition,[sQ86_spl])],[split_symbol_definition]) ).
fof(f1512,plain,
( sQ86_spl
| op(e3,e2) != e1 ),
inference(component_clause,[status(thm)],[f1510]) ).
fof(f1513,definition,
( sQ87_spl
<=> op(e3,e2) = e2 ),
introduced(definition,[new_symbols(definition,[sQ87_spl])],[split_symbol_definition]) ).
fof(f1514,plain,
( ~ sQ87_spl
| op(e3,e2) = e2 ),
inference(component_clause,[status(thm)],[f1513]) ).
fof(f1516,definition,
( sQ88_spl
<=> op(e3,e2) = e3 ),
introduced(definition,[new_symbols(definition,[sQ88_spl])],[split_symbol_definition]) ).
fof(f1517,plain,
( ~ sQ88_spl
| op(e3,e2) = e3 ),
inference(component_clause,[status(thm)],[f1516]) ).
fof(f1519,definition,
( sQ89_spl
<=> op(e3,e2) = e4 ),
introduced(definition,[new_symbols(definition,[sQ89_spl])],[split_symbol_definition]) ).
fof(f1520,plain,
( ~ sQ89_spl
| op(e3,e2) = e4 ),
inference(component_clause,[status(thm)],[f1519]) ).
fof(f1523,definition,
( sQ90_spl
<=> op(e3,e3) = e0 ),
introduced(definition,[new_symbols(definition,[sQ90_spl])],[split_symbol_definition]) ).
fof(f1524,plain,
( ~ sQ90_spl
| op(e3,e3) = e0 ),
inference(component_clause,[status(thm)],[f1523]) ).
fof(f1526,definition,
( sQ91_spl
<=> op(e3,e3) = e1 ),
introduced(definition,[new_symbols(definition,[sQ91_spl])],[split_symbol_definition]) ).
fof(f1527,plain,
( ~ sQ91_spl
| op(e3,e3) = e1 ),
inference(component_clause,[status(thm)],[f1526]) ).
fof(f1529,definition,
( sQ92_spl
<=> op(e3,e3) = e2 ),
introduced(definition,[new_symbols(definition,[sQ92_spl])],[split_symbol_definition]) ).
fof(f1530,plain,
( ~ sQ92_spl
| op(e3,e3) = e2 ),
inference(component_clause,[status(thm)],[f1529]) ).
fof(f1532,definition,
( sQ93_spl
<=> op(e3,e3) = e3 ),
introduced(definition,[new_symbols(definition,[sQ93_spl])],[split_symbol_definition]) ).
fof(f1533,plain,
( ~ sQ93_spl
| op(e3,e3) = e3 ),
inference(component_clause,[status(thm)],[f1532]) ).
fof(f1535,definition,
( sQ94_spl
<=> op(e3,e3) = e4 ),
introduced(definition,[new_symbols(definition,[sQ94_spl])],[split_symbol_definition]) ).
fof(f1538,plain,
( sQ94_spl
| sQ93_spl
| sQ92_spl
| sQ91_spl
| sQ90_spl ),
inference(split_clause,[status(thm)],[f27,f1523,f1526,f1529,f1532,f1535]) ).
fof(f1539,definition,
( sQ95_spl
<=> op(e3,e4) = e0 ),
introduced(definition,[new_symbols(definition,[sQ95_spl])],[split_symbol_definition]) ).
fof(f1540,plain,
( ~ sQ95_spl
| op(e3,e4) = e0 ),
inference(component_clause,[status(thm)],[f1539]) ).
fof(f1542,definition,
( sQ96_spl
<=> op(e3,e4) = e1 ),
introduced(definition,[new_symbols(definition,[sQ96_spl])],[split_symbol_definition]) ).
fof(f1543,plain,
( ~ sQ96_spl
| op(e3,e4) = e1 ),
inference(component_clause,[status(thm)],[f1542]) ).
fof(f1545,definition,
( sQ97_spl
<=> op(e3,e4) = e2 ),
introduced(definition,[new_symbols(definition,[sQ97_spl])],[split_symbol_definition]) ).
fof(f1548,definition,
( sQ98_spl
<=> op(e3,e4) = e3 ),
introduced(definition,[new_symbols(definition,[sQ98_spl])],[split_symbol_definition]) ).
fof(f1549,plain,
( ~ sQ98_spl
| op(e3,e4) = e3 ),
inference(component_clause,[status(thm)],[f1548]) ).
fof(f1551,definition,
( sQ99_spl
<=> op(e3,e4) = e4 ),
introduced(definition,[new_symbols(definition,[sQ99_spl])],[split_symbol_definition]) ).
fof(f1552,plain,
( ~ sQ99_spl
| op(e3,e4) = e4 ),
inference(component_clause,[status(thm)],[f1551]) ).
fof(f1555,definition,
( sQ100_spl
<=> op(e4,e0) = e0 ),
introduced(definition,[new_symbols(definition,[sQ100_spl])],[split_symbol_definition]) ).
fof(f1556,plain,
( ~ sQ100_spl
| op(e4,e0) = e0 ),
inference(component_clause,[status(thm)],[f1555]) ).
fof(f1558,definition,
( sQ101_spl
<=> op(e4,e0) = e1 ),
introduced(definition,[new_symbols(definition,[sQ101_spl])],[split_symbol_definition]) ).
fof(f1559,plain,
( ~ sQ101_spl
| op(e4,e0) = e1 ),
inference(component_clause,[status(thm)],[f1558]) ).
fof(f1561,definition,
( sQ102_spl
<=> op(e4,e0) = e2 ),
introduced(definition,[new_symbols(definition,[sQ102_spl])],[split_symbol_definition]) ).
fof(f1562,plain,
( ~ sQ102_spl
| op(e4,e0) = e2 ),
inference(component_clause,[status(thm)],[f1561]) ).
fof(f1564,definition,
( sQ103_spl
<=> op(e4,e0) = e3 ),
introduced(definition,[new_symbols(definition,[sQ103_spl])],[split_symbol_definition]) ).
fof(f1565,plain,
( ~ sQ103_spl
| op(e4,e0) = e3 ),
inference(component_clause,[status(thm)],[f1564]) ).
fof(f1567,definition,
( sQ104_spl
<=> op(e4,e0) = e4 ),
introduced(definition,[new_symbols(definition,[sQ104_spl])],[split_symbol_definition]) ).
fof(f1569,plain,
( sQ104_spl
| op(e4,e0) != e4 ),
inference(component_clause,[status(thm)],[f1567]) ).
fof(f1574,definition,
( sQ106_spl
<=> op(e4,e1) = e1 ),
introduced(definition,[new_symbols(definition,[sQ106_spl])],[split_symbol_definition]) ).
fof(f1575,plain,
( ~ sQ106_spl
| op(e4,e1) = e1 ),
inference(component_clause,[status(thm)],[f1574]) ).
fof(f1577,definition,
( sQ107_spl
<=> op(e4,e1) = e2 ),
introduced(definition,[new_symbols(definition,[sQ107_spl])],[split_symbol_definition]) ).
fof(f1578,plain,
( ~ sQ107_spl
| op(e4,e1) = e2 ),
inference(component_clause,[status(thm)],[f1577]) ).
fof(f1580,definition,
( sQ108_spl
<=> op(e4,e1) = e3 ),
introduced(definition,[new_symbols(definition,[sQ108_spl])],[split_symbol_definition]) ).
fof(f1581,plain,
( ~ sQ108_spl
| op(e4,e1) = e3 ),
inference(component_clause,[status(thm)],[f1580]) ).
fof(f1583,definition,
( sQ109_spl
<=> op(e4,e1) = e4 ),
introduced(definition,[new_symbols(definition,[sQ109_spl])],[split_symbol_definition]) ).
fof(f1584,plain,
( ~ sQ109_spl
| op(e4,e1) = e4 ),
inference(component_clause,[status(thm)],[f1583]) ).
fof(f1587,definition,
( sQ110_spl
<=> op(e4,e2) = e0 ),
introduced(definition,[new_symbols(definition,[sQ110_spl])],[split_symbol_definition]) ).
fof(f1588,plain,
( ~ sQ110_spl
| op(e4,e2) = e0 ),
inference(component_clause,[status(thm)],[f1587]) ).
fof(f1590,definition,
( sQ111_spl
<=> op(e4,e2) = e1 ),
introduced(definition,[new_symbols(definition,[sQ111_spl])],[split_symbol_definition]) ).
fof(f1591,plain,
( ~ sQ111_spl
| op(e4,e2) = e1 ),
inference(component_clause,[status(thm)],[f1590]) ).
fof(f1593,definition,
( sQ112_spl
<=> op(e4,e2) = e2 ),
introduced(definition,[new_symbols(definition,[sQ112_spl])],[split_symbol_definition]) ).
fof(f1596,definition,
( sQ113_spl
<=> op(e4,e2) = e3 ),
introduced(definition,[new_symbols(definition,[sQ113_spl])],[split_symbol_definition]) ).
fof(f1597,plain,
( ~ sQ113_spl
| op(e4,e2) = e3 ),
inference(component_clause,[status(thm)],[f1596]) ).
fof(f1599,definition,
( sQ114_spl
<=> op(e4,e2) = e4 ),
introduced(definition,[new_symbols(definition,[sQ114_spl])],[split_symbol_definition]) ).
fof(f1600,plain,
( ~ sQ114_spl
| op(e4,e2) = e4 ),
inference(component_clause,[status(thm)],[f1599]) ).
fof(f1603,definition,
( sQ115_spl
<=> op(e4,e3) = e0 ),
introduced(definition,[new_symbols(definition,[sQ115_spl])],[split_symbol_definition]) ).
fof(f1606,definition,
( sQ116_spl
<=> op(e4,e3) = e1 ),
introduced(definition,[new_symbols(definition,[sQ116_spl])],[split_symbol_definition]) ).
fof(f1607,plain,
( ~ sQ116_spl
| op(e4,e3) = e1 ),
inference(component_clause,[status(thm)],[f1606]) ).
fof(f1609,definition,
( sQ117_spl
<=> op(e4,e3) = e2 ),
introduced(definition,[new_symbols(definition,[sQ117_spl])],[split_symbol_definition]) ).
fof(f1610,plain,
( ~ sQ117_spl
| op(e4,e3) = e2 ),
inference(component_clause,[status(thm)],[f1609]) ).
fof(f1612,definition,
( sQ118_spl
<=> op(e4,e3) = e3 ),
introduced(definition,[new_symbols(definition,[sQ118_spl])],[split_symbol_definition]) ).
fof(f1613,plain,
( ~ sQ118_spl
| op(e4,e3) = e3 ),
inference(component_clause,[status(thm)],[f1612]) ).
fof(f1619,definition,
( sQ120_spl
<=> op(e4,e4) = e0 ),
introduced(definition,[new_symbols(definition,[sQ120_spl])],[split_symbol_definition]) ).
fof(f1620,plain,
( ~ sQ120_spl
| op(e4,e4) = e0 ),
inference(component_clause,[status(thm)],[f1619]) ).
fof(f1622,definition,
( sQ121_spl
<=> op(e4,e4) = e1 ),
introduced(definition,[new_symbols(definition,[sQ121_spl])],[split_symbol_definition]) ).
fof(f1628,definition,
( sQ123_spl
<=> op(e4,e4) = e3 ),
introduced(definition,[new_symbols(definition,[sQ123_spl])],[split_symbol_definition]) ).
fof(f1631,definition,
( sQ124_spl
<=> op(e4,e4) = e4 ),
introduced(definition,[new_symbols(definition,[sQ124_spl])],[split_symbol_definition]) ).
fof(f1632,plain,
( ~ sQ124_spl
| op(e4,e4) = e4 ),
inference(component_clause,[status(thm)],[f1631]) ).
fof(f1635,definition,
( sQ125_spl
<=> unit = e0 ),
introduced(definition,[new_symbols(definition,[sQ125_spl])],[split_symbol_definition]) ).
fof(f1636,plain,
( ~ sQ125_spl
| unit = e0 ),
inference(component_clause,[status(thm)],[f1635]) ).
fof(f1638,definition,
( sQ126_spl
<=> unit = e1 ),
introduced(definition,[new_symbols(definition,[sQ126_spl])],[split_symbol_definition]) ).
fof(f1639,plain,
( ~ sQ126_spl
| unit = e1 ),
inference(component_clause,[status(thm)],[f1638]) ).
fof(f1641,definition,
( sQ127_spl
<=> unit = e2 ),
introduced(definition,[new_symbols(definition,[sQ127_spl])],[split_symbol_definition]) ).
fof(f1642,plain,
( ~ sQ127_spl
| unit = e2 ),
inference(component_clause,[status(thm)],[f1641]) ).
fof(f1644,definition,
( sQ128_spl
<=> unit = e3 ),
introduced(definition,[new_symbols(definition,[sQ128_spl])],[split_symbol_definition]) ).
fof(f1645,plain,
( ~ sQ128_spl
| unit = e3 ),
inference(component_clause,[status(thm)],[f1644]) ).
fof(f1647,definition,
( sQ129_spl
<=> unit = e4 ),
introduced(definition,[new_symbols(definition,[sQ129_spl])],[split_symbol_definition]) ).
fof(f1648,plain,
( ~ sQ129_spl
| unit = e4 ),
inference(component_clause,[status(thm)],[f1647]) ).
fof(f1650,plain,
( sQ129_spl
| sQ128_spl
| sQ127_spl
| sQ126_spl
| sQ125_spl ),
inference(split_clause,[status(thm)],[f44,f1635,f1638,f1641,f1644,f1647]) ).
fof(f1653,plain,
( sQ21_spl
| sQ16_spl
| sQ11_spl
| sQ6_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f47,f1238,f1254,f1270,f1286,f1302]) ).
fof(f1654,plain,
( sQ101_spl
| sQ76_spl
| sQ51_spl
| sQ26_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f48,f1238,f1318,f1398,f1478,f1558]) ).
fof(f1658,plain,
( sQ103_spl
| sQ78_spl
| sQ53_spl
| sQ28_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f52,f1244,f1324,f1404,f1484,f1564]) ).
fof(f1667,plain,
( sQ48_spl
| sQ43_spl
| sQ38_spl
| sQ33_spl
| sQ28_spl ),
inference(split_clause,[status(thm)],[f61,f1324,f1340,f1356,f1372,f1388]) ).
fof(f1668,plain,
( sQ108_spl
| sQ83_spl
| sQ58_spl
| sQ33_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f62,f1260,f1340,f1420,f1500,f1580]) ).
fof(f1672,plain,
( sQ110_spl
| sQ85_spl
| sQ60_spl
| sQ35_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f66,f1267,f1347,f1427,f1507,f1587]) ).
fof(f1679,plain,
( sQ74_spl
| sQ69_spl
| sQ64_spl
| sQ59_spl
| sQ54_spl ),
inference(split_clause,[status(thm)],[f73,f1407,f1423,f1439,f1455,f1471]) ).
fof(f1680,plain,
( sQ114_spl
| sQ89_spl
| sQ64_spl
| sQ39_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f74,f1279,f1359,f1439,f1519,f1599]) ).
fof(f1681,plain,
( sQ95_spl
| sQ90_spl
| sQ85_spl
| sQ80_spl
| sQ75_spl ),
inference(split_clause,[status(thm)],[f75,f1475,f1491,f1507,f1523,f1539]) ).
fof(f1682,plain,
( sQ115_spl
| sQ90_spl
| sQ65_spl
| sQ40_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f76,f1283,f1363,f1443,f1523,f1603]) ).
fof(f1693,plain,
( sQ121_spl
| sQ116_spl
| sQ111_spl
| sQ106_spl
| sQ101_spl ),
inference(split_clause,[status(thm)],[f87,f1558,f1574,f1590,f1606,f1622]) ).
fof(f1694,plain,
( sQ121_spl
| sQ96_spl
| sQ71_spl
| sQ46_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f88,f1302,f1382,f1462,f1542,f1622]) ).
fof(f1701,definition,
( sQ130_spl
<=> sP0_prd ),
introduced(definition,[new_symbols(definition,[sQ130_spl])],[split_symbol_definition]) ).
fof(f1740,plain,
( sQ98_spl
| ~ sQ94_spl
| sQ130_spl ),
inference(split_clause,[status(thm)],[f248,f1701,f1535,f1548]) ).
fof(f1741,plain,
( ~ sQ129_spl
| ~ sQ94_spl
| sQ130_spl ),
inference(split_clause,[status(thm)],[f249,f1701,f1535,f1647]) ).
fof(f1754,definition,
( sQ131_spl
<=> sP1_prd ),
introduced(definition,[new_symbols(definition,[sQ131_spl])],[split_symbol_definition]) ).
fof(f1757,definition,
( sQ132_spl
<=> op(e4,e4) = op(e4,e4) ),
introduced(definition,[new_symbols(definition,[sQ132_spl])],[split_symbol_definition]) ).
fof(f1759,plain,
( sQ132_spl
| op(e4,e4) != op(e4,e4) ),
inference(component_clause,[status(thm)],[f1757]) ).
fof(f1760,plain,
( ~ sQ132_spl
| sQ131_spl ),
inference(split_clause,[status(thm)],[f262,f1754,f1757]) ).
fof(f1766,definition,
( sQ134_spl
<=> sP2_prd ),
introduced(definition,[new_symbols(definition,[sQ134_spl])],[split_symbol_definition]) ).
fof(f1769,definition,
( sQ135_spl
<=> sP3_prd ),
introduced(definition,[new_symbols(definition,[sQ135_spl])],[split_symbol_definition]) ).
fof(f1772,plain,
( sQ135_spl
| sQ134_spl
| ~ sQ130_spl ),
inference(split_clause,[status(thm)],[f270,f1701,f1766,f1769]) ).
fof(f1778,definition,
( sQ136_spl
<=> sP4_prd ),
introduced(definition,[new_symbols(definition,[sQ136_spl])],[split_symbol_definition]) ).
fof(f1781,definition,
( sQ137_spl
<=> op(e3,e4) = op(e4,e3) ),
introduced(definition,[new_symbols(definition,[sQ137_spl])],[split_symbol_definition]) ).
fof(f1783,plain,
( sQ137_spl
| op(e3,e4) != op(e4,e3) ),
inference(component_clause,[status(thm)],[f1781]) ).
fof(f1784,plain,
( ~ sQ137_spl
| sQ136_spl
| ~ sQ131_spl ),
inference(split_clause,[status(thm)],[f279,f1754,f1778,f1781]) ).
fof(f1785,definition,
( sQ138_spl
<=> op(op(e4,e3),e3) = e4 ),
introduced(definition,[new_symbols(definition,[sQ138_spl])],[split_symbol_definition]) ).
fof(f1786,plain,
( ~ sQ138_spl
| op(op(e4,e3),e3) = e4 ),
inference(component_clause,[status(thm)],[f1785]) ).
fof(f1788,plain,
( sQ138_spl
| sQ136_spl
| ~ sQ131_spl ),
inference(split_clause,[status(thm)],[f280,f1754,f1778,f1785]) ).
fof(f1795,definition,
( sQ140_spl
<=> sP5_prd ),
introduced(definition,[new_symbols(definition,[sQ140_spl])],[split_symbol_definition]) ).
fof(f1798,definition,
( sQ141_spl
<=> sP6_prd ),
introduced(definition,[new_symbols(definition,[sQ141_spl])],[split_symbol_definition]) ).
fof(f1801,plain,
( sQ141_spl
| sQ140_spl
| ~ sQ134_spl ),
inference(split_clause,[status(thm)],[f289,f1766,f1795,f1798]) ).
fof(f1807,definition,
( sQ142_spl
<=> sP7_prd ),
introduced(definition,[new_symbols(definition,[sQ142_spl])],[split_symbol_definition]) ).
fof(f1810,plain,
( sQ142_spl
| ~ sQ135_spl ),
inference(split_clause,[status(thm)],[f298,f1769,f1807]) ).
fof(f1815,definition,
( sQ143_spl
<=> sP8_prd ),
introduced(definition,[new_symbols(definition,[sQ143_spl])],[split_symbol_definition]) ).
fof(f1822,definition,
( sQ145_spl
<=> op(op(e4,e2),e2) = e4 ),
introduced(definition,[new_symbols(definition,[sQ145_spl])],[split_symbol_definition]) ).
fof(f1823,plain,
( ~ sQ145_spl
| op(op(e4,e2),e2) = e4 ),
inference(component_clause,[status(thm)],[f1822]) ).
fof(f1825,plain,
( sQ145_spl
| sQ143_spl
| ~ sQ136_spl ),
inference(split_clause,[status(thm)],[f307,f1778,f1815,f1822]) ).
fof(f1832,definition,
( sQ147_spl
<=> sP9_prd ),
introduced(definition,[new_symbols(definition,[sQ147_spl])],[split_symbol_definition]) ).
fof(f1835,definition,
( sQ148_spl
<=> sP10_prd ),
introduced(definition,[new_symbols(definition,[sQ148_spl])],[split_symbol_definition]) ).
fof(f1838,plain,
( sQ148_spl
| sQ147_spl
| ~ sQ140_spl ),
inference(split_clause,[status(thm)],[f316,f1795,f1832,f1835]) ).
fof(f1839,plain,
( sQ109_spl
| ~ sQ121_spl
| sQ147_spl
| ~ sQ140_spl ),
inference(split_clause,[status(thm)],[f317,f1795,f1832,f1622,f1583]) ).
fof(f1844,definition,
( sQ149_spl
<=> sP11_prd ),
introduced(definition,[new_symbols(definition,[sQ149_spl])],[split_symbol_definition]) ).
fof(f1847,plain,
( sQ149_spl
| ~ sQ141_spl ),
inference(split_clause,[status(thm)],[f325,f1798,f1844]) ).
fof(f1852,definition,
( sQ150_spl
<=> sP12_prd ),
introduced(definition,[new_symbols(definition,[sQ150_spl])],[split_symbol_definition]) ).
fof(f1855,plain,
( sQ150_spl
| ~ sQ142_spl ),
inference(split_clause,[status(thm)],[f333,f1807,f1852]) ).
fof(f1860,definition,
( sQ151_spl
<=> sP13_prd ),
introduced(definition,[new_symbols(definition,[sQ151_spl])],[split_symbol_definition]) ).
fof(f1863,definition,
( sQ152_spl
<=> op(e1,e4) = op(e4,e1) ),
introduced(definition,[new_symbols(definition,[sQ152_spl])],[split_symbol_definition]) ).
fof(f1864,plain,
( ~ sQ152_spl
| op(e1,e4) = op(e4,e1) ),
inference(component_clause,[status(thm)],[f1863]) ).
fof(f1865,plain,
( sQ152_spl
| op(e1,e4) != op(e4,e1) ),
inference(component_clause,[status(thm)],[f1863]) ).
fof(f1866,plain,
( ~ sQ152_spl
| sQ151_spl
| ~ sQ143_spl ),
inference(split_clause,[status(thm)],[f341,f1815,f1860,f1863]) ).
fof(f1877,definition,
( sQ155_spl
<=> sP14_prd ),
introduced(definition,[new_symbols(definition,[sQ155_spl])],[split_symbol_definition]) ).
fof(f1880,plain,
( sQ155_spl
| ~ sQ147_spl ),
inference(split_clause,[status(thm)],[f349,f1832,f1877]) ).
fof(f1885,definition,
( sQ156_spl
<=> sP15_prd ),
introduced(definition,[new_symbols(definition,[sQ156_spl])],[split_symbol_definition]) ).
fof(f1888,plain,
( sQ156_spl
| ~ sQ148_spl ),
inference(split_clause,[status(thm)],[f357,f1835,f1885]) ).
fof(f1889,plain,
( sQ108_spl
| ~ sQ116_spl
| ~ sQ148_spl ),
inference(split_clause,[status(thm)],[f358,f1835,f1606,f1580]) ).
fof(f1893,definition,
( sQ157_spl
<=> sP16_prd ),
introduced(definition,[new_symbols(definition,[sQ157_spl])],[split_symbol_definition]) ).
fof(f1896,plain,
( sQ157_spl
| ~ sQ149_spl ),
inference(split_clause,[status(thm)],[f365,f1844,f1893]) ).
fof(f1901,definition,
( sQ158_spl
<=> sP17_prd ),
introduced(definition,[new_symbols(definition,[sQ158_spl])],[split_symbol_definition]) ).
fof(f1904,plain,
( sQ158_spl
| ~ sQ150_spl ),
inference(split_clause,[status(thm)],[f373,f1852,f1901]) ).
fof(f1909,definition,
( sQ159_spl
<=> sP18_prd ),
introduced(definition,[new_symbols(definition,[sQ159_spl])],[split_symbol_definition]) ).
fof(f1912,definition,
( sQ160_spl
<=> op(e0,e4) = op(e4,e0) ),
introduced(definition,[new_symbols(definition,[sQ160_spl])],[split_symbol_definition]) ).
fof(f1914,plain,
( sQ160_spl
| op(e0,e4) != op(e4,e0) ),
inference(component_clause,[status(thm)],[f1912]) ).
fof(f1915,plain,
( ~ sQ160_spl
| sQ159_spl
| ~ sQ151_spl ),
inference(split_clause,[status(thm)],[f381,f1860,f1909,f1912]) ).
fof(f1926,definition,
( sQ163_spl
<=> sP19_prd ),
introduced(definition,[new_symbols(definition,[sQ163_spl])],[split_symbol_definition]) ).
fof(f1929,plain,
( sQ163_spl
| ~ sQ155_spl ),
inference(split_clause,[status(thm)],[f389,f1877,f1926]) ).
fof(f1930,plain,
( sQ103_spl
| ~ sQ115_spl
| ~ sQ155_spl ),
inference(split_clause,[status(thm)],[f390,f1877,f1603,f1564]) ).
fof(f1934,definition,
( sQ164_spl
<=> sP20_prd ),
introduced(definition,[new_symbols(definition,[sQ164_spl])],[split_symbol_definition]) ).
fof(f1937,plain,
( sQ164_spl
| ~ sQ156_spl ),
inference(split_clause,[status(thm)],[f397,f1885,f1934]) ).
fof(f1942,definition,
( sQ165_spl
<=> sP21_prd ),
introduced(definition,[new_symbols(definition,[sQ165_spl])],[split_symbol_definition]) ).
fof(f1945,plain,
( sQ165_spl
| ~ sQ157_spl ),
inference(split_clause,[status(thm)],[f405,f1893,f1942]) ).
fof(f1950,definition,
( sQ166_spl
<=> sP22_prd ),
introduced(definition,[new_symbols(definition,[sQ166_spl])],[split_symbol_definition]) ).
fof(f1953,plain,
( sQ166_spl
| ~ sQ158_spl ),
inference(split_clause,[status(thm)],[f413,f1901,f1950]) ).
fof(f1958,definition,
( sQ167_spl
<=> sP23_prd ),
introduced(definition,[new_symbols(definition,[sQ167_spl])],[split_symbol_definition]) ).
fof(f1962,definition,
( sQ168_spl
<=> op(op(e3,e4),e4) = e3 ),
introduced(definition,[new_symbols(definition,[sQ168_spl])],[split_symbol_definition]) ).
fof(f1963,plain,
( ~ sQ168_spl
| op(op(e3,e4),e4) = e3 ),
inference(component_clause,[status(thm)],[f1962]) ).
fof(f1964,plain,
( sQ168_spl
| op(op(e3,e4),e4) != e3 ),
inference(component_clause,[status(thm)],[f1962]) ).
fof(f1965,plain,
( sQ168_spl
| sQ167_spl
| ~ sQ159_spl ),
inference(split_clause,[status(thm)],[f422,f1909,f1958,f1962]) ).
fof(f1972,definition,
( sQ170_spl
<=> sP24_prd ),
introduced(definition,[new_symbols(definition,[sQ170_spl])],[split_symbol_definition]) ).
fof(f1975,plain,
( sQ170_spl
| ~ sQ163_spl ),
inference(split_clause,[status(thm)],[f429,f1926,f1972]) ).
fof(f1980,definition,
( sQ171_spl
<=> sP25_prd ),
introduced(definition,[new_symbols(definition,[sQ171_spl])],[split_symbol_definition]) ).
fof(f1983,plain,
( sQ171_spl
| ~ sQ164_spl ),
inference(split_clause,[status(thm)],[f437,f1934,f1980]) ).
fof(f1988,definition,
( sQ172_spl
<=> sP26_prd ),
introduced(definition,[new_symbols(definition,[sQ172_spl])],[split_symbol_definition]) ).
fof(f1991,plain,
( sQ172_spl
| ~ sQ165_spl ),
inference(split_clause,[status(thm)],[f445,f1942,f1988]) ).
fof(f1996,definition,
( sQ173_spl
<=> sP27_prd ),
introduced(definition,[new_symbols(definition,[sQ173_spl])],[split_symbol_definition]) ).
fof(f1999,plain,
( sQ173_spl
| ~ sQ166_spl ),
inference(split_clause,[status(thm)],[f453,f1950,f1996]) ).
fof(f2004,definition,
( sQ174_spl
<=> sP28_prd ),
introduced(definition,[new_symbols(definition,[sQ174_spl])],[split_symbol_definition]) ).
fof(f2007,definition,
( sQ175_spl
<=> op(e3,e3) = op(e3,e3) ),
introduced(definition,[new_symbols(definition,[sQ175_spl])],[split_symbol_definition]) ).
fof(f2009,plain,
( sQ175_spl
| op(e3,e3) != op(e3,e3) ),
inference(component_clause,[status(thm)],[f2007]) ).
fof(f2010,plain,
( ~ sQ175_spl
| sQ174_spl
| ~ sQ167_spl ),
inference(split_clause,[status(thm)],[f461,f1958,f2004,f2007]) ).
fof(f2018,definition,
( sQ177_spl
<=> sP29_prd ),
introduced(definition,[new_symbols(definition,[sQ177_spl])],[split_symbol_definition]) ).
fof(f2021,plain,
( sQ177_spl
| ~ sQ170_spl ),
inference(split_clause,[status(thm)],[f469,f1972,f2018]) ).
fof(f2026,definition,
( sQ178_spl
<=> sP30_prd ),
introduced(definition,[new_symbols(definition,[sQ178_spl])],[split_symbol_definition]) ).
fof(f2029,plain,
( sQ178_spl
| ~ sQ171_spl ),
inference(split_clause,[status(thm)],[f477,f1980,f2026]) ).
fof(f2034,definition,
( sQ179_spl
<=> sP31_prd ),
introduced(definition,[new_symbols(definition,[sQ179_spl])],[split_symbol_definition]) ).
fof(f2037,plain,
( sQ179_spl
| ~ sQ172_spl ),
inference(split_clause,[status(thm)],[f485,f1988,f2034]) ).
fof(f2042,definition,
( sQ180_spl
<=> sP32_prd ),
introduced(definition,[new_symbols(definition,[sQ180_spl])],[split_symbol_definition]) ).
fof(f2045,plain,
( sQ180_spl
| ~ sQ173_spl ),
inference(split_clause,[status(thm)],[f493,f1996,f2042]) ).
fof(f2050,definition,
( sQ181_spl
<=> sP33_prd ),
introduced(definition,[new_symbols(definition,[sQ181_spl])],[split_symbol_definition]) ).
fof(f2057,definition,
( sQ183_spl
<=> op(op(e3,e2),e2) = e3 ),
introduced(definition,[new_symbols(definition,[sQ183_spl])],[split_symbol_definition]) ).
fof(f2058,plain,
( ~ sQ183_spl
| op(op(e3,e2),e2) = e3 ),
inference(component_clause,[status(thm)],[f2057]) ).
fof(f2060,plain,
( sQ183_spl
| sQ181_spl
| ~ sQ174_spl ),
inference(split_clause,[status(thm)],[f502,f2004,f2050,f2057]) ).
fof(f2067,definition,
( sQ185_spl
<=> sP34_prd ),
introduced(definition,[new_symbols(definition,[sQ185_spl])],[split_symbol_definition]) ).
fof(f2070,plain,
( sQ185_spl
| ~ sQ177_spl ),
inference(split_clause,[status(thm)],[f509,f2018,f2067]) ).
fof(f2075,definition,
( sQ186_spl
<=> sP35_prd ),
introduced(definition,[new_symbols(definition,[sQ186_spl])],[split_symbol_definition]) ).
fof(f2078,plain,
( sQ186_spl
| ~ sQ178_spl ),
inference(split_clause,[status(thm)],[f517,f2026,f2075]) ).
fof(f2079,plain,
( sQ84_spl
| ~ sQ96_spl
| ~ sQ178_spl ),
inference(split_clause,[status(thm)],[f518,f2026,f1542,f1503]) ).
fof(f2083,definition,
( sQ187_spl
<=> sP36_prd ),
introduced(definition,[new_symbols(definition,[sQ187_spl])],[split_symbol_definition]) ).
fof(f2086,plain,
( sQ187_spl
| ~ sQ179_spl ),
inference(split_clause,[status(thm)],[f525,f2034,f2083]) ).
fof(f2091,definition,
( sQ188_spl
<=> sP37_prd ),
introduced(definition,[new_symbols(definition,[sQ188_spl])],[split_symbol_definition]) ).
fof(f2094,plain,
( sQ188_spl
| ~ sQ180_spl ),
inference(split_clause,[status(thm)],[f533,f2042,f2091]) ).
fof(f2099,definition,
( sQ189_spl
<=> sP38_prd ),
introduced(definition,[new_symbols(definition,[sQ189_spl])],[split_symbol_definition]) ).
fof(f2102,definition,
( sQ190_spl
<=> op(e1,e3) = op(e3,e1) ),
introduced(definition,[new_symbols(definition,[sQ190_spl])],[split_symbol_definition]) ).
fof(f2104,plain,
( sQ190_spl
| op(e1,e3) != op(e3,e1) ),
inference(component_clause,[status(thm)],[f2102]) ).
fof(f2105,plain,
( ~ sQ190_spl
| sQ189_spl
| ~ sQ181_spl ),
inference(split_clause,[status(thm)],[f541,f2050,f2099,f2102]) ).
fof(f2116,definition,
( sQ193_spl
<=> sP39_prd ),
introduced(definition,[new_symbols(definition,[sQ193_spl])],[split_symbol_definition]) ).
fof(f2119,plain,
( sQ193_spl
| ~ sQ185_spl ),
inference(split_clause,[status(thm)],[f549,f2067,f2116]) ).
fof(f2124,definition,
( sQ194_spl
<=> sP40_prd ),
introduced(definition,[new_symbols(definition,[sQ194_spl])],[split_symbol_definition]) ).
fof(f2127,plain,
( sQ194_spl
| ~ sQ186_spl ),
inference(split_clause,[status(thm)],[f557,f2075,f2124]) ).
fof(f2132,definition,
( sQ195_spl
<=> sP41_prd ),
introduced(definition,[new_symbols(definition,[sQ195_spl])],[split_symbol_definition]) ).
fof(f2135,plain,
( sQ195_spl
| ~ sQ187_spl ),
inference(split_clause,[status(thm)],[f565,f2083,f2132]) ).
fof(f2140,definition,
( sQ196_spl
<=> sP42_prd ),
introduced(definition,[new_symbols(definition,[sQ196_spl])],[split_symbol_definition]) ).
fof(f2143,plain,
( sQ196_spl
| ~ sQ188_spl ),
inference(split_clause,[status(thm)],[f573,f2091,f2140]) ).
fof(f2148,definition,
( sQ197_spl
<=> sP43_prd ),
introduced(definition,[new_symbols(definition,[sQ197_spl])],[split_symbol_definition]) ).
fof(f2151,definition,
( sQ198_spl
<=> op(e0,e3) = op(e3,e0) ),
introduced(definition,[new_symbols(definition,[sQ198_spl])],[split_symbol_definition]) ).
fof(f2153,plain,
( sQ198_spl
| op(e0,e3) != op(e3,e0) ),
inference(component_clause,[status(thm)],[f2151]) ).
fof(f2154,plain,
( ~ sQ198_spl
| sQ197_spl
| ~ sQ189_spl ),
inference(split_clause,[status(thm)],[f581,f2099,f2148,f2151]) ).
fof(f2165,definition,
( sQ201_spl
<=> sP44_prd ),
introduced(definition,[new_symbols(definition,[sQ201_spl])],[split_symbol_definition]) ).
fof(f2168,plain,
( sQ201_spl
| ~ sQ193_spl ),
inference(split_clause,[status(thm)],[f589,f2116,f2165]) ).
fof(f2173,definition,
( sQ202_spl
<=> sP45_prd ),
introduced(definition,[new_symbols(definition,[sQ202_spl])],[split_symbol_definition]) ).
fof(f2176,plain,
( sQ202_spl
| ~ sQ194_spl ),
inference(split_clause,[status(thm)],[f597,f2124,f2173]) ).
fof(f2177,plain,
( sQ82_spl
| ~ sQ86_spl
| ~ sQ194_spl ),
inference(split_clause,[status(thm)],[f598,f2124,f1510,f1497]) ).
fof(f2181,definition,
( sQ203_spl
<=> sP46_prd ),
introduced(definition,[new_symbols(definition,[sQ203_spl])],[split_symbol_definition]) ).
fof(f2184,plain,
( sQ203_spl
| ~ sQ195_spl ),
inference(split_clause,[status(thm)],[f605,f2132,f2181]) ).
fof(f2189,definition,
( sQ204_spl
<=> sP47_prd ),
introduced(definition,[new_symbols(definition,[sQ204_spl])],[split_symbol_definition]) ).
fof(f2192,plain,
( sQ204_spl
| ~ sQ196_spl ),
inference(split_clause,[status(thm)],[f613,f2140,f2189]) ).
fof(f2197,definition,
( sQ205_spl
<=> sP48_prd ),
introduced(definition,[new_symbols(definition,[sQ205_spl])],[split_symbol_definition]) ).
fof(f2201,definition,
( sQ206_spl
<=> op(op(e2,e4),e4) = e2 ),
introduced(definition,[new_symbols(definition,[sQ206_spl])],[split_symbol_definition]) ).
fof(f2202,plain,
( ~ sQ206_spl
| op(op(e2,e4),e4) = e2 ),
inference(component_clause,[status(thm)],[f2201]) ).
fof(f2204,plain,
( sQ206_spl
| sQ205_spl
| ~ sQ197_spl ),
inference(split_clause,[status(thm)],[f622,f2148,f2197,f2201]) ).
fof(f2211,definition,
( sQ208_spl
<=> sP49_prd ),
introduced(definition,[new_symbols(definition,[sQ208_spl])],[split_symbol_definition]) ).
fof(f2214,plain,
( sQ208_spl
| ~ sQ201_spl ),
inference(split_clause,[status(thm)],[f629,f2165,f2211]) ).
fof(f2219,definition,
( sQ209_spl
<=> sP50_prd ),
introduced(definition,[new_symbols(definition,[sQ209_spl])],[split_symbol_definition]) ).
fof(f2222,plain,
( sQ209_spl
| ~ sQ202_spl ),
inference(split_clause,[status(thm)],[f637,f2173,f2219]) ).
fof(f2227,definition,
( sQ210_spl
<=> sP51_prd ),
introduced(definition,[new_symbols(definition,[sQ210_spl])],[split_symbol_definition]) ).
fof(f2230,plain,
( sQ210_spl
| ~ sQ203_spl ),
inference(split_clause,[status(thm)],[f645,f2181,f2227]) ).
fof(f2235,definition,
( sQ211_spl
<=> sP52_prd ),
introduced(definition,[new_symbols(definition,[sQ211_spl])],[split_symbol_definition]) ).
fof(f2238,plain,
( sQ211_spl
| ~ sQ204_spl ),
inference(split_clause,[status(thm)],[f653,f2189,f2235]) ).
fof(f2243,definition,
( sQ212_spl
<=> sP53_prd ),
introduced(definition,[new_symbols(definition,[sQ212_spl])],[split_symbol_definition]) ).
fof(f2247,definition,
( sQ213_spl
<=> op(op(e2,e3),e3) = e2 ),
introduced(definition,[new_symbols(definition,[sQ213_spl])],[split_symbol_definition]) ).
fof(f2248,plain,
( ~ sQ213_spl
| op(op(e2,e3),e3) = e2 ),
inference(component_clause,[status(thm)],[f2247]) ).
fof(f2250,plain,
( sQ213_spl
| sQ212_spl
| ~ sQ205_spl ),
inference(split_clause,[status(thm)],[f662,f2197,f2243,f2247]) ).
fof(f2257,definition,
( sQ215_spl
<=> sP54_prd ),
introduced(definition,[new_symbols(definition,[sQ215_spl])],[split_symbol_definition]) ).
fof(f2260,plain,
( sQ215_spl
| ~ sQ208_spl ),
inference(split_clause,[status(thm)],[f669,f2211,f2257]) ).
fof(f2265,definition,
( sQ216_spl
<=> sP55_prd ),
introduced(definition,[new_symbols(definition,[sQ216_spl])],[split_symbol_definition]) ).
fof(f2268,plain,
( sQ216_spl
| ~ sQ209_spl ),
inference(split_clause,[status(thm)],[f677,f2219,f2265]) ).
fof(f2269,plain,
( sQ80_spl
| ~ sQ76_spl
| ~ sQ209_spl ),
inference(split_clause,[status(thm)],[f678,f2219,f1478,f1491]) ).
fof(f2273,definition,
( sQ217_spl
<=> sP56_prd ),
introduced(definition,[new_symbols(definition,[sQ217_spl])],[split_symbol_definition]) ).
fof(f2276,plain,
( sQ217_spl
| ~ sQ210_spl ),
inference(split_clause,[status(thm)],[f685,f2227,f2273]) ).
fof(f2277,plain,
( sQ64_spl
| ~ sQ72_spl
| ~ sQ210_spl ),
inference(split_clause,[status(thm)],[f686,f2227,f1465,f1439]) ).
fof(f2281,definition,
( sQ218_spl
<=> sP57_prd ),
introduced(definition,[new_symbols(definition,[sQ218_spl])],[split_symbol_definition]) ).
fof(f2284,plain,
( sQ218_spl
| ~ sQ211_spl ),
inference(split_clause,[status(thm)],[f693,f2235,f2281]) ).
fof(f2289,definition,
( sQ219_spl
<=> sP58_prd ),
introduced(definition,[new_symbols(definition,[sQ219_spl])],[split_symbol_definition]) ).
fof(f2292,definition,
( sQ220_spl
<=> op(e2,e2) = op(e2,e2) ),
introduced(definition,[new_symbols(definition,[sQ220_spl])],[split_symbol_definition]) ).
fof(f2294,plain,
( sQ220_spl
| op(e2,e2) != op(e2,e2) ),
inference(component_clause,[status(thm)],[f2292]) ).
fof(f2295,plain,
( ~ sQ220_spl
| sQ219_spl
| ~ sQ212_spl ),
inference(split_clause,[status(thm)],[f701,f2243,f2289,f2292]) ).
fof(f2296,definition,
( sQ221_spl
<=> op(op(e2,e2),e2) = e2 ),
introduced(definition,[new_symbols(definition,[sQ221_spl])],[split_symbol_definition]) ).
fof(f2297,plain,
( ~ sQ221_spl
| op(op(e2,e2),e2) = e2 ),
inference(component_clause,[status(thm)],[f2296]) ).
fof(f2303,definition,
( sQ222_spl
<=> sP59_prd ),
introduced(definition,[new_symbols(definition,[sQ222_spl])],[split_symbol_definition]) ).
fof(f2306,plain,
( sQ222_spl
| ~ sQ215_spl ),
inference(split_clause,[status(thm)],[f709,f2257,f2303]) ).
fof(f2311,definition,
( sQ223_spl
<=> sP60_prd ),
introduced(definition,[new_symbols(definition,[sQ223_spl])],[split_symbol_definition]) ).
fof(f2314,plain,
( sQ223_spl
| ~ sQ216_spl ),
inference(split_clause,[status(thm)],[f717,f2265,f2311]) ).
fof(f2319,definition,
( sQ224_spl
<=> sP61_prd ),
introduced(definition,[new_symbols(definition,[sQ224_spl])],[split_symbol_definition]) ).
fof(f2322,plain,
( sQ224_spl
| ~ sQ217_spl ),
inference(split_clause,[status(thm)],[f725,f2273,f2319]) ).
fof(f2327,definition,
( sQ225_spl
<=> sP62_prd ),
introduced(definition,[new_symbols(definition,[sQ225_spl])],[split_symbol_definition]) ).
fof(f2330,plain,
( sQ225_spl
| ~ sQ218_spl ),
inference(split_clause,[status(thm)],[f733,f2281,f2327]) ).
fof(f2331,plain,
( sQ67_spl
| ~ sQ63_spl
| ~ sQ218_spl ),
inference(split_clause,[status(thm)],[f734,f2281,f1436,f1449]) ).
fof(f2335,definition,
( sQ226_spl
<=> sP63_prd ),
introduced(definition,[new_symbols(definition,[sQ226_spl])],[split_symbol_definition]) ).
fof(f2338,definition,
( sQ227_spl
<=> op(e1,e2) = op(e2,e1) ),
introduced(definition,[new_symbols(definition,[sQ227_spl])],[split_symbol_definition]) ).
fof(f2340,plain,
( sQ227_spl
| op(e1,e2) != op(e2,e1) ),
inference(component_clause,[status(thm)],[f2338]) ).
fof(f2341,plain,
( ~ sQ227_spl
| sQ226_spl
| ~ sQ219_spl ),
inference(split_clause,[status(thm)],[f741,f2289,f2335,f2338]) ).
fof(f2352,definition,
( sQ230_spl
<=> sP64_prd ),
introduced(definition,[new_symbols(definition,[sQ230_spl])],[split_symbol_definition]) ).
fof(f2355,plain,
( sQ230_spl
| ~ sQ222_spl ),
inference(split_clause,[status(thm)],[f749,f2303,f2352]) ).
fof(f2360,definition,
( sQ231_spl
<=> sP65_prd ),
introduced(definition,[new_symbols(definition,[sQ231_spl])],[split_symbol_definition]) ).
fof(f2363,plain,
( sQ231_spl
| ~ sQ223_spl ),
inference(split_clause,[status(thm)],[f757,f2311,f2360]) ).
fof(f2364,plain,
( sQ58_spl
| ~ sQ66_spl
| ~ sQ223_spl ),
inference(split_clause,[status(thm)],[f758,f2311,f1446,f1420]) ).
fof(f2368,definition,
( sQ232_spl
<=> sP66_prd ),
introduced(definition,[new_symbols(definition,[sQ232_spl])],[split_symbol_definition]) ).
fof(f2371,plain,
( sQ232_spl
| ~ sQ224_spl ),
inference(split_clause,[status(thm)],[f765,f2319,f2368]) ).
fof(f2376,definition,
( sQ233_spl
<=> sP67_prd ),
introduced(definition,[new_symbols(definition,[sQ233_spl])],[split_symbol_definition]) ).
fof(f2379,plain,
( sQ233_spl
| ~ sQ225_spl ),
inference(split_clause,[status(thm)],[f773,f2327,f2376]) ).
fof(f2384,definition,
( sQ234_spl
<=> sP68_prd ),
introduced(definition,[new_symbols(definition,[sQ234_spl])],[split_symbol_definition]) ).
fof(f2387,definition,
( sQ235_spl
<=> op(e0,e2) = op(e2,e0) ),
introduced(definition,[new_symbols(definition,[sQ235_spl])],[split_symbol_definition]) ).
fof(f2388,plain,
( ~ sQ235_spl
| op(e0,e2) = op(e2,e0) ),
inference(component_clause,[status(thm)],[f2387]) ).
fof(f2389,plain,
( sQ235_spl
| op(e0,e2) != op(e2,e0) ),
inference(component_clause,[status(thm)],[f2387]) ).
fof(f2390,plain,
( ~ sQ235_spl
| sQ234_spl
| ~ sQ226_spl ),
inference(split_clause,[status(thm)],[f781,f2335,f2384,f2387]) ).
fof(f2401,definition,
( sQ238_spl
<=> sP69_prd ),
introduced(definition,[new_symbols(definition,[sQ238_spl])],[split_symbol_definition]) ).
fof(f2404,plain,
( sQ238_spl
| ~ sQ230_spl ),
inference(split_clause,[status(thm)],[f789,f2352,f2401]) ).
fof(f2405,plain,
( sQ53_spl
| ~ sQ65_spl
| ~ sQ230_spl ),
inference(split_clause,[status(thm)],[f790,f2352,f1443,f1404]) ).
fof(f2409,definition,
( sQ239_spl
<=> sP70_prd ),
introduced(definition,[new_symbols(definition,[sQ239_spl])],[split_symbol_definition]) ).
fof(f2412,plain,
( sQ239_spl
| ~ sQ231_spl ),
inference(split_clause,[status(thm)],[f797,f2360,f2409]) ).
fof(f2417,definition,
( sQ240_spl
<=> sP71_prd ),
introduced(definition,[new_symbols(definition,[sQ240_spl])],[split_symbol_definition]) ).
fof(f2420,plain,
( sQ240_spl
| ~ sQ232_spl ),
inference(split_clause,[status(thm)],[f805,f2368,f2417]) ).
fof(f2425,definition,
( sQ241_spl
<=> sP72_prd ),
introduced(definition,[new_symbols(definition,[sQ241_spl])],[split_symbol_definition]) ).
fof(f2428,plain,
( sQ241_spl
| ~ sQ233_spl ),
inference(split_clause,[status(thm)],[f813,f2376,f2425]) ).
fof(f2433,definition,
( sQ242_spl
<=> sP73_prd ),
introduced(definition,[new_symbols(definition,[sQ242_spl])],[split_symbol_definition]) ).
fof(f2436,plain,
( ~ sQ152_spl
| sQ242_spl
| ~ sQ234_spl ),
inference(split_clause,[status(thm)],[f821,f2384,f2433,f1863]) ).
fof(f2447,definition,
( sQ245_spl
<=> sP74_prd ),
introduced(definition,[new_symbols(definition,[sQ245_spl])],[split_symbol_definition]) ).
fof(f2450,plain,
( sQ245_spl
| ~ sQ238_spl ),
inference(split_clause,[status(thm)],[f829,f2401,f2447]) ).
fof(f2455,definition,
( sQ246_spl
<=> sP75_prd ),
introduced(definition,[new_symbols(definition,[sQ246_spl])],[split_symbol_definition]) ).
fof(f2458,plain,
( sQ246_spl
| ~ sQ239_spl ),
inference(split_clause,[status(thm)],[f837,f2409,f2455]) ).
fof(f2467,plain,
( sQ60_spl
| ~ sQ52_spl
| ~ sQ240_spl ),
inference(split_clause,[status(thm)],[f846,f2417,f1401,f1427]) ).
fof(f2471,definition,
( sQ248_spl
<=> sP77_prd ),
introduced(definition,[new_symbols(definition,[sQ248_spl])],[split_symbol_definition]) ).
fof(f2474,plain,
( sQ248_spl
| ~ sQ241_spl ),
inference(split_clause,[status(thm)],[f853,f2425,f2471]) ).
fof(f2479,definition,
( sQ249_spl
<=> sP78_prd ),
introduced(definition,[new_symbols(definition,[sQ249_spl])],[split_symbol_definition]) ).
fof(f2482,plain,
( ~ sQ190_spl
| sQ249_spl
| ~ sQ242_spl ),
inference(split_clause,[status(thm)],[f861,f2433,f2479,f2102]) ).
fof(f2493,definition,
( sQ252_spl
<=> sP79_prd ),
introduced(definition,[new_symbols(definition,[sQ252_spl])],[split_symbol_definition]) ).
fof(f2496,plain,
( sQ252_spl
| ~ sQ245_spl ),
inference(split_clause,[status(thm)],[f869,f2447,f2493]) ).
fof(f2501,definition,
( sQ253_spl
<=> sP80_prd ),
introduced(definition,[new_symbols(definition,[sQ253_spl])],[split_symbol_definition]) ).
fof(f2504,plain,
( sQ253_spl
| ~ sQ246_spl ),
inference(split_clause,[status(thm)],[f877,f2455,f2501]) ).
fof(f2505,plain,
( sQ55_spl
| ~ sQ51_spl
| ~ sQ246_spl ),
inference(split_clause,[status(thm)],[f878,f2455,f1398,f1411]) ).
fof(f2517,definition,
( sQ255_spl
<=> sP82_prd ),
introduced(definition,[new_symbols(definition,[sQ255_spl])],[split_symbol_definition]) ).
fof(f2520,plain,
( sQ255_spl
| ~ sQ248_spl ),
inference(split_clause,[status(thm)],[f893,f2471,f2517]) ).
fof(f2525,definition,
( sQ256_spl
<=> sP83_prd ),
introduced(definition,[new_symbols(definition,[sQ256_spl])],[split_symbol_definition]) ).
fof(f2528,plain,
( ~ sQ227_spl
| sQ256_spl
| ~ sQ249_spl ),
inference(split_clause,[status(thm)],[f901,f2479,f2525,f2338]) ).
fof(f2539,definition,
( sQ259_spl
<=> sP84_prd ),
introduced(definition,[new_symbols(definition,[sQ259_spl])],[split_symbol_definition]) ).
fof(f2542,plain,
( sQ259_spl
| ~ sQ252_spl ),
inference(split_clause,[status(thm)],[f909,f2493,f2539]) ).
fof(f2547,definition,
( sQ260_spl
<=> sP85_prd ),
introduced(definition,[new_symbols(definition,[sQ260_spl])],[split_symbol_definition]) ).
fof(f2550,plain,
( sQ260_spl
| ~ sQ253_spl ),
inference(split_clause,[status(thm)],[f917,f2501,f2547]) ).
fof(f2551,plain,
( sQ34_spl
| ~ sQ46_spl
| ~ sQ253_spl ),
inference(split_clause,[status(thm)],[f918,f2501,f1382,f1343]) ).
fof(f2563,definition,
( sQ262_spl
<=> sP87_prd ),
introduced(definition,[new_symbols(definition,[sQ262_spl])],[split_symbol_definition]) ).
fof(f2566,plain,
( sQ262_spl
| ~ sQ255_spl ),
inference(split_clause,[status(thm)],[f933,f2517,f2563]) ).
fof(f2571,definition,
( sQ263_spl
<=> sP88_prd ),
introduced(definition,[new_symbols(definition,[sQ263_spl])],[split_symbol_definition]) ).
fof(f2574,definition,
( sQ264_spl
<=> op(e1,e1) = op(e1,e1) ),
introduced(definition,[new_symbols(definition,[sQ264_spl])],[split_symbol_definition]) ).
fof(f2576,plain,
( sQ264_spl
| op(e1,e1) != op(e1,e1) ),
inference(component_clause,[status(thm)],[f2574]) ).
fof(f2577,plain,
( ~ sQ264_spl
| sQ263_spl
| ~ sQ256_spl ),
inference(split_clause,[status(thm)],[f941,f2525,f2571,f2574]) ).
fof(f2585,definition,
( sQ266_spl
<=> sP89_prd ),
introduced(definition,[new_symbols(definition,[sQ266_spl])],[split_symbol_definition]) ).
fof(f2588,plain,
( sQ266_spl
| ~ sQ259_spl ),
inference(split_clause,[status(thm)],[f949,f2539,f2585]) ).
fof(f2593,definition,
( sQ267_spl
<=> sP90_prd ),
introduced(definition,[new_symbols(definition,[sQ267_spl])],[split_symbol_definition]) ).
fof(f2596,plain,
( sQ267_spl
| ~ sQ260_spl ),
inference(split_clause,[status(thm)],[f957,f2547,f2593]) ).
fof(f2597,plain,
( sQ33_spl
| ~ sQ41_spl
| ~ sQ260_spl ),
inference(split_clause,[status(thm)],[f958,f2547,f1366,f1340]) ).
fof(f2609,definition,
( sQ269_spl
<=> sP92_prd ),
introduced(definition,[new_symbols(definition,[sQ269_spl])],[split_symbol_definition]) ).
fof(f2612,plain,
( sQ269_spl
| ~ sQ262_spl ),
inference(split_clause,[status(thm)],[f973,f2563,f2609]) ).
fof(f2617,definition,
( sQ270_spl
<=> sP93_prd ),
introduced(definition,[new_symbols(definition,[sQ270_spl])],[split_symbol_definition]) ).
fof(f2620,definition,
( sQ271_spl
<=> op(e0,e1) = op(e1,e0) ),
introduced(definition,[new_symbols(definition,[sQ271_spl])],[split_symbol_definition]) ).
fof(f2622,plain,
( sQ271_spl
| op(e0,e1) != op(e1,e0) ),
inference(component_clause,[status(thm)],[f2620]) ).
fof(f2623,plain,
( ~ sQ271_spl
| sQ270_spl
| ~ sQ263_spl ),
inference(split_clause,[status(thm)],[f981,f2571,f2617,f2620]) ).
fof(f2628,definition,
( sQ273_spl
<=> op(op(e1,e0),e1) = e0 ),
introduced(definition,[new_symbols(definition,[sQ273_spl])],[split_symbol_definition]) ).
fof(f2629,plain,
( ~ sQ273_spl
| op(op(e1,e0),e1) = e0 ),
inference(component_clause,[status(thm)],[f2628]) ).
fof(f2630,plain,
( sQ273_spl
| op(op(e1,e0),e1) != e0 ),
inference(component_clause,[status(thm)],[f2628]) ).
fof(f2634,definition,
( sQ274_spl
<=> sP94_prd ),
introduced(definition,[new_symbols(definition,[sQ274_spl])],[split_symbol_definition]) ).
fof(f2637,plain,
( sQ274_spl
| ~ sQ266_spl ),
inference(split_clause,[status(thm)],[f989,f2585,f2634]) ).
fof(f2642,definition,
( sQ275_spl
<=> sP95_prd ),
introduced(definition,[new_symbols(definition,[sQ275_spl])],[split_symbol_definition]) ).
fof(f2645,plain,
( sQ275_spl
| ~ sQ267_spl ),
inference(split_clause,[status(thm)],[f997,f2593,f2642]) ).
fof(f2658,definition,
( sQ277_spl
<=> sP97_prd ),
introduced(definition,[new_symbols(definition,[sQ277_spl])],[split_symbol_definition]) ).
fof(f2661,plain,
( sQ277_spl
| ~ sQ269_spl ),
inference(split_clause,[status(thm)],[f1013,f2609,f2658]) ).
fof(f2662,plain,
( sQ40_spl
| ~ sQ28_spl
| ~ sQ269_spl ),
inference(split_clause,[status(thm)],[f1014,f2609,f1324,f1363]) ).
fof(f2666,definition,
( sQ278_spl
<=> sP98_prd ),
introduced(definition,[new_symbols(definition,[sQ278_spl])],[split_symbol_definition]) ).
fof(f2669,plain,
( ~ sQ160_spl
| sQ278_spl
| ~ sQ270_spl ),
inference(split_clause,[status(thm)],[f1021,f2617,f2666,f1912]) ).
fof(f2680,definition,
( sQ281_spl
<=> sP99_prd ),
introduced(definition,[new_symbols(definition,[sQ281_spl])],[split_symbol_definition]) ).
fof(f2683,plain,
( sQ281_spl
| ~ sQ274_spl ),
inference(split_clause,[status(thm)],[f1029,f2634,f2680]) ).
fof(f2688,definition,
( sQ282_spl
<=> sP100_prd ),
introduced(definition,[new_symbols(definition,[sQ282_spl])],[split_symbol_definition]) ).
fof(f2691,plain,
( sQ282_spl
| ~ sQ275_spl ),
inference(split_clause,[status(thm)],[f1037,f2642,f2688]) ).
fof(f2704,definition,
( sQ284_spl
<=> sP102_prd ),
introduced(definition,[new_symbols(definition,[sQ284_spl])],[split_symbol_definition]) ).
fof(f2707,plain,
( sQ284_spl
| ~ sQ277_spl ),
inference(split_clause,[status(thm)],[f1053,f2658,f2704]) ).
fof(f2712,definition,
( sQ285_spl
<=> sP103_prd ),
introduced(definition,[new_symbols(definition,[sQ285_spl])],[split_symbol_definition]) ).
fof(f2720,definition,
( sQ287_spl
<=> op(op(e0,e3),e0) = e3 ),
introduced(definition,[new_symbols(definition,[sQ287_spl])],[split_symbol_definition]) ).
fof(f2721,plain,
( ~ sQ287_spl
| op(op(e0,e3),e0) = e3 ),
inference(component_clause,[status(thm)],[f2720]) ).
fof(f2722,plain,
( sQ287_spl
| op(op(e0,e3),e0) != e3 ),
inference(component_clause,[status(thm)],[f2720]) ).
fof(f2723,plain,
( ~ sQ287_spl
| sQ285_spl
| ~ sQ278_spl ),
inference(split_clause,[status(thm)],[f1063,f2666,f2712,f2720]) ).
fof(f2730,plain,
( sQ26_spl
| ~ sQ30_spl
| ~ sQ281_spl ),
inference(split_clause,[status(thm)],[f1070,f2680,f1331,f1318]) ).
fof(f2731,plain,
( ~ sQ125_spl
| ~ sQ30_spl
| ~ sQ281_spl ),
inference(split_clause,[status(thm)],[f1071,f2680,f1331,f1635]) ).
fof(f2734,definition,
( sQ289_spl
<=> sP105_prd ),
introduced(definition,[new_symbols(definition,[sQ289_spl])],[split_symbol_definition]) ).
fof(f2737,plain,
( sQ289_spl
| ~ sQ282_spl ),
inference(split_clause,[status(thm)],[f1077,f2688,f2734]) ).
fof(f2750,definition,
( sQ291_spl
<=> sP107_prd ),
introduced(definition,[new_symbols(definition,[sQ291_spl])],[split_symbol_definition]) ).
fof(f2753,plain,
( sQ291_spl
| ~ sQ284_spl ),
inference(split_clause,[status(thm)],[f1093,f2704,f2750]) ).
fof(f2758,definition,
( sQ292_spl
<=> sP108_prd ),
introduced(definition,[new_symbols(definition,[sQ292_spl])],[split_symbol_definition]) ).
fof(f2761,plain,
( ~ sQ235_spl
| sQ292_spl
| ~ sQ285_spl ),
inference(split_clause,[status(thm)],[f1101,f2712,f2758,f2387]) ).
fof(f2780,definition,
( sQ296_spl
<=> sP110_prd ),
introduced(definition,[new_symbols(definition,[sQ296_spl])],[split_symbol_definition]) ).
fof(f2783,plain,
( sQ296_spl
| ~ sQ289_spl ),
inference(split_clause,[status(thm)],[f1117,f2734,f2780]) ).
fof(f2796,definition,
( sQ298_spl
<=> sP112_prd ),
introduced(definition,[new_symbols(definition,[sQ298_spl])],[split_symbol_definition]) ).
fof(f2799,plain,
( sQ298_spl
| ~ sQ291_spl ),
inference(split_clause,[status(thm)],[f1133,f2750,f2796]) ).
fof(f2804,definition,
( sQ299_spl
<=> sP113_prd ),
introduced(definition,[new_symbols(definition,[sQ299_spl])],[split_symbol_definition]) ).
fof(f2807,plain,
( ~ sQ271_spl
| sQ299_spl
| ~ sQ292_spl ),
inference(split_clause,[status(thm)],[f1141,f2758,f2804,f2620]) ).
fof(f2826,definition,
( sQ303_spl
<=> sP115_prd ),
introduced(definition,[new_symbols(definition,[sQ303_spl])],[split_symbol_definition]) ).
fof(f2829,plain,
( sQ303_spl
| ~ sQ296_spl ),
inference(split_clause,[status(thm)],[f1157,f2780,f2826]) ).
fof(f2842,plain,
( sQ15_spl
| ~ sQ3_spl
| ~ sQ298_spl ),
inference(split_clause,[status(thm)],[f1171,f2796,f1244,f1283]) ).
fof(f2850,definition,
( sQ305_spl
<=> op(e0,e0) = op(e0,e0) ),
introduced(definition,[new_symbols(definition,[sQ305_spl])],[split_symbol_definition]) ).
fof(f2852,plain,
( sQ305_spl
| op(e0,e0) != op(e0,e0) ),
inference(component_clause,[status(thm)],[f2850]) ).
fof(f2853,plain,
( ~ sQ305_spl
| ~ sQ299_spl ),
inference(split_clause,[status(thm)],[f1180,f2804,f2850]) ).
fof(f2868,definition,
( sQ308_spl
<=> sP118_prd ),
introduced(definition,[new_symbols(definition,[sQ308_spl])],[split_symbol_definition]) ).
fof(f2871,plain,
( sQ308_spl
| ~ sQ303_spl ),
inference(split_clause,[status(thm)],[f1195,f2826,f2868]) ).
fof(f2892,plain,
( sQ5_spl
| ~ sQ1_spl
| ~ sQ308_spl ),
inference(split_clause,[status(thm)],[f1218,f2868,f1238,f1251]) ).
fof(f2908,plain,
( sQ264_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f2576]) ).
fof(f2909,plain,
sQ264_spl,
inference(contradiction_clause,[status(thm)],[f2908]) ).
fof(f2910,plain,
( sQ220_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f2294]) ).
fof(f2911,plain,
sQ220_spl,
inference(contradiction_clause,[status(thm)],[f2910]) ).
fof(f2912,plain,
( sQ175_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f2009]) ).
fof(f2913,plain,
sQ175_spl,
inference(contradiction_clause,[status(thm)],[f2912]) ).
fof(f2914,plain,
( sQ132_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1759]) ).
fof(f2915,plain,
sQ132_spl,
inference(contradiction_clause,[status(thm)],[f2914]) ).
fof(f2916,plain,
( sQ305_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f2852]) ).
fof(f2917,plain,
sQ305_spl,
inference(contradiction_clause,[status(thm)],[f2916]) ).
fof(f2923,plain,
( ~ sQ127_spl
| op(e2,e2) = e2 ),
inference(backward_demodulation,[status(thm)],[f1642,f39]) ).
fof(f2929,plain,
( ~ sQ127_spl
| sQ62_spl ),
inference(split_clause,[status(thm)],[f2923,f1433,f1641]) ).
fof(f2946,plain,
e3 != op(e4,e2),
inference(backward_demodulation,[status(thm)],[f207,f123]) ).
fof(f2948,plain,
op(e1,e2) != e3,
inference(backward_demodulation,[status(thm)],[f207,f119]) ).
fof(f2949,plain,
op(e0,e2) != e3,
inference(backward_demodulation,[status(thm)],[f207,f116]) ).
fof(f2951,plain,
( ~ sQ20_spl
| e0 != op(e3,e4) ),
inference(backward_demodulation,[status(thm)],[f1300,f137]) ).
fof(f2952,plain,
( ~ sQ20_spl
| e0 != op(e2,e4) ),
inference(backward_demodulation,[status(thm)],[f1300,f136]) ).
fof(f2954,plain,
( ~ sQ21_spl
| ~ sQ20_spl
| e0 = e1 ),
inference(forward_demodulation,[status(thm)],[f1300,f1303]) ).
fof(f2955,plain,
( ~ sQ21_spl
| ~ sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2954,f195]) ).
fof(f2956,plain,
( ~ sQ21_spl
| ~ sQ20_spl ),
inference(contradiction_clause,[status(thm)],[f2955]) ).
fof(f2962,plain,
( ~ sQ61_spl
| e3 = e1 ),
inference(forward_demodulation,[status(thm)],[f207,f1431]) ).
fof(f2963,plain,
( ~ sQ61_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2962,f200]) ).
fof(f2964,plain,
~ sQ61_spl,
inference(contradiction_clause,[status(thm)],[f2963]) ).
fof(f2995,plain,
( ~ sQ45_spl
| op(e1,e1) != e0 ),
inference(backward_demodulation,[status(thm)],[f1380,f161]) ).
fof(f3000,plain,
( ~ sQ45_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f2995,f1331,f1379]) ).
fof(f3006,plain,
op(e2,e1) != e3,
inference(forward_demodulation,[status(thm)],[f207,f169]) ).
fof(f3016,plain,
e3 != op(e2,e3),
inference(forward_demodulation,[status(thm)],[f207,f172]) ).
fof(f3017,plain,
e3 != op(e2,e4),
inference(forward_demodulation,[status(thm)],[f207,f173]) ).
fof(f3024,plain,
( sQ52_spl
| ~ sQ235_spl
| op(e0,e2) != e2 ),
inference(forward_demodulation,[status(thm)],[f2388,f1403]) ).
fof(f3046,plain,
( sQ63_spl
| e3 != e3 ),
inference(forward_demodulation,[status(thm)],[f207,f1438]) ).
fof(f3047,plain,
( sQ63_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f3046]) ).
fof(f3048,plain,
sQ63_spl,
inference(contradiction_clause,[status(thm)],[f3047]) ).
fof(f3050,plain,
( ~ sQ64_spl
| e3 = e4 ),
inference(forward_demodulation,[status(thm)],[f207,f1440]) ).
fof(f3051,plain,
( ~ sQ64_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3050,f204]) ).
fof(f3052,plain,
~ sQ64_spl,
inference(contradiction_clause,[status(thm)],[f3051]) ).
fof(f3053,plain,
( sQ52_spl
| ~ sQ235_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f3024,f1273,f2387,f1401]) ).
fof(f3054,plain,
op(e2,e0) != e3,
inference(forward_demodulation,[status(thm)],[f207,f166]) ).
fof(f3063,plain,
( ~ sQ60_spl
| e3 = e0 ),
inference(forward_demodulation,[status(thm)],[f207,f1428]) ).
fof(f3064,plain,
( ~ sQ60_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3063,f197]) ).
fof(f3065,plain,
~ sQ60_spl,
inference(contradiction_clause,[status(thm)],[f3064]) ).
fof(f3073,plain,
e0 = op(op(e3,e2),op(op(e2,e2),e2)),
inference(forward_demodulation,[status(thm)],[f207,f205]) ).
fof(f3074,plain,
e0 = op(op(e3,e2),op(e3,e2)),
inference(forward_demodulation,[status(thm)],[f207,f3073]) ).
fof(f3075,plain,
e0 = op(op(e3,e2),e1),
inference(backward_demodulation,[status(thm)],[f3081,f3074]) ).
fof(f3077,plain,
op(e3,e1) != e1,
inference(backward_demodulation,[status(thm)],[f3081,f179]) ).
fof(f3078,plain,
e1 != op(e4,e2),
inference(backward_demodulation,[status(thm)],[f3081,f124]) ).
fof(f3080,plain,
op(e0,e2) != e1,
inference(backward_demodulation,[status(thm)],[f3081,f117]) ).
fof(f3081,plain,
e1 = op(e3,e2),
inference(forward_demodulation,[status(thm)],[f207,f206]) ).
fof(f3082,plain,
e0 = op(e1,e1),
inference(forward_demodulation,[status(thm)],[f3081,f3075]) ).
fof(f3092,plain,
e4 = op(e3,op(e2,e2)),
inference(forward_demodulation,[status(thm)],[f207,f208]) ).
fof(f3093,plain,
op(e3,e1) != e4,
inference(backward_demodulation,[status(thm)],[f3098,f180]) ).
fof(f3095,plain,
op(e2,e3) != e4,
inference(backward_demodulation,[status(thm)],[f3098,f132]) ).
fof(f3096,plain,
op(e1,e3) != e4,
inference(backward_demodulation,[status(thm)],[f3098,f130]) ).
fof(f3097,plain,
op(e0,e3) != e4,
inference(backward_demodulation,[status(thm)],[f3098,f127]) ).
fof(f3098,plain,
e4 = op(e3,e3),
inference(forward_demodulation,[status(thm)],[f207,f3092]) ).
fof(f3102,plain,
( ~ sQ96_spl
| ~ sQ98_spl
| e3 = e1 ),
inference(forward_demodulation,[status(thm)],[f1549,f1543]) ).
fof(f3103,plain,
( ~ sQ96_spl
| ~ sQ98_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3102,f200]) ).
fof(f3104,plain,
( ~ sQ96_spl
| ~ sQ98_spl ),
inference(contradiction_clause,[status(thm)],[f3103]) ).
fof(f3119,plain,
( ~ sQ91_spl
| e4 = e1 ),
inference(forward_demodulation,[status(thm)],[f3098,f1527]) ).
fof(f3120,plain,
( ~ sQ91_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3119,f201]) ).
fof(f3121,plain,
~ sQ91_spl,
inference(contradiction_clause,[status(thm)],[f3120]) ).
fof(f3122,plain,
( ~ sQ85_spl
| e1 = e0 ),
inference(forward_demodulation,[status(thm)],[f3081,f1508]) ).
fof(f3123,plain,
( ~ sQ85_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3122,f195]) ).
fof(f3124,plain,
~ sQ85_spl,
inference(contradiction_clause,[status(thm)],[f3123]) ).
fof(f3125,plain,
( ~ sQ88_spl
| e1 = e3 ),
inference(forward_demodulation,[status(thm)],[f3081,f1517]) ).
fof(f3126,plain,
( ~ sQ88_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3125,f200]) ).
fof(f3127,plain,
~ sQ88_spl,
inference(contradiction_clause,[status(thm)],[f3126]) ).
fof(f3136,plain,
( ~ sQ287_spl
| ~ sQ18_spl
| op(e3,e0) = e3 ),
inference(backward_demodulation,[status(thm)],[f1293,f2721]) ).
fof(f3137,plain,
( ~ sQ18_spl
| op(e0,e1) != e3 ),
inference(backward_demodulation,[status(thm)],[f1293,f150]) ).
fof(f3141,plain,
( ~ sQ18_spl
| e3 != op(e1,e3) ),
inference(backward_demodulation,[status(thm)],[f1293,f125]) ).
fof(f3152,plain,
( ~ sQ273_spl
| ~ sQ28_spl
| op(e3,e1) = e0 ),
inference(backward_demodulation,[status(thm)],[f1325,f2629]) ).
fof(f3159,plain,
( ~ sQ37_spl
| e2 != op(e4,e2) ),
inference(backward_demodulation,[status(thm)],[f1354,f121]) ).
fof(f3163,plain,
( ~ sQ37_spl
| ~ sQ112_spl ),
inference(split_clause,[status(thm)],[f3159,f1593,f1353]) ).
fof(f3164,plain,
( ~ sQ16_spl
| ~ sQ18_spl
| e3 = e1 ),
inference(forward_demodulation,[status(thm)],[f1293,f1287]) ).
fof(f3165,plain,
( ~ sQ16_spl
| ~ sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3164,f200]) ).
fof(f3166,plain,
( ~ sQ16_spl
| ~ sQ18_spl ),
inference(contradiction_clause,[status(thm)],[f3165]) ).
fof(f3168,plain,
( ~ sQ43_spl
| e3 != op(e4,e3) ),
inference(backward_demodulation,[status(thm)],[f1373,f131]) ).
fof(f3188,plain,
( ~ sQ68_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1453,f3016]) ).
fof(f3189,plain,
~ sQ68_spl,
inference(contradiction_clause,[status(thm)],[f3188]) ).
fof(f3196,plain,
( ~ sQ78_spl
| ~ sQ75_spl
| e0 = e3 ),
inference(forward_demodulation,[status(thm)],[f1476,f1485]) ).
fof(f3197,plain,
( ~ sQ78_spl
| ~ sQ75_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3196,f197]) ).
fof(f3198,plain,
( ~ sQ78_spl
| ~ sQ75_spl ),
inference(contradiction_clause,[status(thm)],[f3197]) ).
fof(f3203,plain,
( ~ sQ93_spl
| e4 = e3 ),
inference(forward_demodulation,[status(thm)],[f3098,f1533]) ).
fof(f3204,plain,
( ~ sQ93_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3203,f204]) ).
fof(f3205,plain,
~ sQ93_spl,
inference(contradiction_clause,[status(thm)],[f3204]) ).
fof(f3207,plain,
( ~ sQ102_spl
| ~ sQ100_spl
| e0 = e2 ),
inference(forward_demodulation,[status(thm)],[f1556,f1562]) ).
fof(f3208,plain,
( ~ sQ102_spl
| ~ sQ100_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3207,f196]) ).
fof(f3209,plain,
( ~ sQ102_spl
| ~ sQ100_spl ),
inference(contradiction_clause,[status(thm)],[f3208]) ).
fof(f3212,plain,
( ~ sQ106_spl
| op(e0,e1) != e1 ),
inference(backward_demodulation,[status(thm)],[f1575,f108]) ).
fof(f3213,plain,
( ~ sQ106_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f3212,f1254,f1574]) ).
fof(f3214,plain,
( ~ sQ108_spl
| ~ sQ106_spl
| e1 = e3 ),
inference(forward_demodulation,[status(thm)],[f1575,f1581]) ).
fof(f3215,plain,
( ~ sQ108_spl
| ~ sQ106_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3214,f200]) ).
fof(f3216,plain,
( ~ sQ108_spl
| ~ sQ106_spl ),
inference(contradiction_clause,[status(thm)],[f3215]) ).
fof(f3218,plain,
( ~ sQ117_spl
| op(e4,e2) != e2 ),
inference(backward_demodulation,[status(thm)],[f1610,f192]) ).
fof(f3222,plain,
( ~ sQ117_spl
| ~ sQ112_spl ),
inference(split_clause,[status(thm)],[f3218,f1593,f1609]) ).
fof(f3240,plain,
( ~ sQ273_spl
| ~ sQ28_spl
| sQ80_spl ),
inference(split_clause,[status(thm)],[f3152,f1491,f1324,f2628]) ).
fof(f3246,plain,
( ~ sQ124_spl
| op(e4,e0) != e4 ),
inference(forward_demodulation,[status(thm)],[f1632,f188]) ).
fof(f3248,plain,
( ~ sQ90_spl
| e4 = e0 ),
inference(forward_demodulation,[status(thm)],[f3098,f1524]) ).
fof(f3249,plain,
( ~ sQ90_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3248,f198]) ).
fof(f3250,plain,
~ sQ90_spl,
inference(contradiction_clause,[status(thm)],[f3249]) ).
fof(f3257,plain,
( ~ sQ62_spl
| e3 = e2 ),
inference(forward_demodulation,[status(thm)],[f207,f1434]) ).
fof(f3258,plain,
( ~ sQ62_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3257,f202]) ).
fof(f3259,plain,
~ sQ62_spl,
inference(contradiction_clause,[status(thm)],[f3258]) ).
fof(f3261,plain,
( ~ sQ72_spl
| ~ sQ74_spl
| e4 = e2 ),
inference(forward_demodulation,[status(thm)],[f1472,f1466]) ).
fof(f3262,plain,
( ~ sQ72_spl
| ~ sQ74_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3261,f203]) ).
fof(f3263,plain,
( ~ sQ72_spl
| ~ sQ74_spl ),
inference(contradiction_clause,[status(thm)],[f3262]) ).
fof(f3279,plain,
( ~ sQ46_spl
| ~ sQ49_spl
| e4 = e1 ),
inference(forward_demodulation,[status(thm)],[f1392,f1383]) ).
fof(f3280,plain,
( ~ sQ46_spl
| ~ sQ49_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3279,f201]) ).
fof(f3281,plain,
( ~ sQ46_spl
| ~ sQ49_spl ),
inference(contradiction_clause,[status(thm)],[f3280]) ).
fof(f3288,plain,
( ~ sQ110_spl
| ~ sQ114_spl
| e4 = e0 ),
inference(forward_demodulation,[status(thm)],[f1600,f1588]) ).
fof(f3289,plain,
( ~ sQ110_spl
| ~ sQ114_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3288,f198]) ).
fof(f3290,plain,
( ~ sQ110_spl
| ~ sQ114_spl ),
inference(contradiction_clause,[status(thm)],[f3289]) ).
fof(f3308,plain,
( ~ sQ120_spl
| ~ sQ124_spl
| e4 = e0 ),
inference(forward_demodulation,[status(thm)],[f1632,f1620]) ).
fof(f3309,plain,
( ~ sQ120_spl
| ~ sQ124_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3308,f198]) ).
fof(f3310,plain,
( ~ sQ120_spl
| ~ sQ124_spl ),
inference(contradiction_clause,[status(thm)],[f3309]) ).
fof(f3339,plain,
( ~ sQ221_spl
| op(e3,e2) = e2 ),
inference(forward_demodulation,[status(thm)],[f207,f2297]) ).
fof(f3340,plain,
( ~ sQ221_spl
| e1 = e2 ),
inference(forward_demodulation,[status(thm)],[f3081,f3339]) ).
fof(f3341,plain,
( ~ sQ221_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3340,f199]) ).
fof(f3342,plain,
~ sQ221_spl,
inference(contradiction_clause,[status(thm)],[f3341]) ).
fof(f3353,plain,
( ~ sQ87_spl
| e1 = e2 ),
inference(forward_demodulation,[status(thm)],[f3081,f1514]) ).
fof(f3354,plain,
( ~ sQ87_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3353,f199]) ).
fof(f3355,plain,
~ sQ87_spl,
inference(contradiction_clause,[status(thm)],[f3354]) ).
fof(f3366,plain,
( ~ sQ129_spl
| op(e4,e0) = e0 ),
inference(backward_demodulation,[status(thm)],[f1648,f34]) ).
fof(f3367,plain,
( ~ sQ129_spl
| op(e0,e4) = e0 ),
inference(backward_demodulation,[status(thm)],[f1648,f35]) ).
fof(f3368,plain,
( ~ sQ129_spl
| op(e4,e1) = e1 ),
inference(backward_demodulation,[status(thm)],[f1648,f36]) ).
fof(f3369,plain,
( ~ sQ129_spl
| op(e1,e4) = e1 ),
inference(backward_demodulation,[status(thm)],[f1648,f37]) ).
fof(f3370,plain,
( ~ sQ129_spl
| op(e4,e2) = e2 ),
inference(backward_demodulation,[status(thm)],[f1648,f38]) ).
fof(f3371,plain,
( ~ sQ129_spl
| op(e2,e4) = e2 ),
inference(backward_demodulation,[status(thm)],[f1648,f39]) ).
fof(f3372,plain,
( ~ sQ129_spl
| op(e4,e3) = e3 ),
inference(backward_demodulation,[status(thm)],[f1648,f40]) ).
fof(f3373,plain,
( ~ sQ129_spl
| op(e3,e4) = e3 ),
inference(backward_demodulation,[status(thm)],[f1648,f41]) ).
fof(f3374,plain,
( ~ sQ129_spl
| op(e4,e4) = e4 ),
inference(backward_demodulation,[status(thm)],[f1648,f42]) ).
fof(f3376,plain,
( ~ sQ129_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f3367,f1299,f1647]) ).
fof(f3377,plain,
( ~ sQ129_spl
| sQ106_spl ),
inference(split_clause,[status(thm)],[f3368,f1574,f1647]) ).
fof(f3378,plain,
( ~ sQ129_spl
| sQ46_spl ),
inference(split_clause,[status(thm)],[f3369,f1382,f1647]) ).
fof(f3379,plain,
( ~ sQ129_spl
| sQ112_spl ),
inference(split_clause,[status(thm)],[f3370,f1593,f1647]) ).
fof(f3380,plain,
( ~ sQ129_spl
| sQ72_spl ),
inference(split_clause,[status(thm)],[f3371,f1465,f1647]) ).
fof(f3381,plain,
( ~ sQ129_spl
| sQ98_spl ),
inference(split_clause,[status(thm)],[f3373,f1548,f1647]) ).
fof(f3382,plain,
( ~ sQ129_spl
| sQ124_spl ),
inference(split_clause,[status(thm)],[f3374,f1631,f1647]) ).
fof(f3384,plain,
( ~ sQ20_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f2952,f1459,f1299]) ).
fof(f3385,plain,
( sQ86_spl
| e1 != e1 ),
inference(forward_demodulation,[status(thm)],[f3081,f1512]) ).
fof(f3386,plain,
( sQ86_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f3385]) ).
fof(f3387,plain,
sQ86_spl,
inference(contradiction_clause,[status(thm)],[f3386]) ).
fof(f3388,plain,
( ~ sQ92_spl
| e4 = e2 ),
inference(forward_demodulation,[status(thm)],[f3098,f1530]) ).
fof(f3389,plain,
( ~ sQ92_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3388,f203]) ).
fof(f3390,plain,
~ sQ92_spl,
inference(contradiction_clause,[status(thm)],[f3389]) ).
fof(f3394,plain,
( ~ sQ108_spl
| ~ sQ152_spl
| op(e1,e4) = e3 ),
inference(forward_demodulation,[status(thm)],[f1864,f1581]) ).
fof(f3399,plain,
op(e3,e0) != e4,
inference(forward_demodulation,[status(thm)],[f3098,f177]) ).
fof(f3401,plain,
e4 != op(e3,e4),
inference(forward_demodulation,[status(thm)],[f3098,f184]) ).
fof(f3412,plain,
( sQ198_spl
| ~ sQ287_spl
| ~ sQ18_spl
| op(e0,e3) != e3 ),
inference(backward_demodulation,[status(thm)],[f3136,f2153]) ).
fof(f3417,plain,
( sQ198_spl
| ~ sQ287_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f3412,f1292,f2720,f2151]) ).
fof(f3427,plain,
( ~ sQ118_spl
| e3 != op(e4,e4) ),
inference(backward_demodulation,[status(thm)],[f1613,f194]) ).
fof(f3429,plain,
( sQ137_spl
| ~ sQ118_spl
| op(e3,e4) != e3 ),
inference(backward_demodulation,[status(thm)],[f1613,f1783]) ).
fof(f3430,plain,
( ~ sQ118_spl
| ~ sQ123_spl ),
inference(split_clause,[status(thm)],[f3427,f1628,f1612]) ).
fof(f3431,plain,
( sQ137_spl
| ~ sQ118_spl
| ~ sQ98_spl ),
inference(split_clause,[status(thm)],[f3429,f1548,f1612,f1781]) ).
fof(f3434,plain,
( ~ sQ67_spl
| op(e2,e0) != e2 ),
inference(backward_demodulation,[status(thm)],[f1450,f167]) ).
fof(f3451,plain,
( ~ sQ34_spl
| e0 = e4 ),
inference(forward_demodulation,[status(thm)],[f3082,f1344]) ).
fof(f3452,plain,
( ~ sQ34_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3451,f198]) ).
fof(f3453,plain,
~ sQ34_spl,
inference(contradiction_clause,[status(thm)],[f3452]) ).
fof(f3454,plain,
( sQ30_spl
| e0 != e0 ),
inference(forward_demodulation,[status(thm)],[f3082,f1333]) ).
fof(f3455,plain,
( sQ30_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f3454]) ).
fof(f3456,plain,
sQ30_spl,
inference(contradiction_clause,[status(thm)],[f3455]) ).
fof(f3458,plain,
( ~ sQ89_spl
| e1 = e4 ),
inference(forward_demodulation,[status(thm)],[f3081,f1520]) ).
fof(f3459,plain,
( ~ sQ89_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3458,f201]) ).
fof(f3460,plain,
~ sQ89_spl,
inference(contradiction_clause,[status(thm)],[f3459]) ).
fof(f3463,plain,
( ~ sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1296,f3097]) ).
fof(f3464,plain,
~ sQ19_spl,
inference(contradiction_clause,[status(thm)],[f3463]) ).
fof(f3472,plain,
( ~ sQ67_spl
| ~ sQ52_spl ),
inference(split_clause,[status(thm)],[f3434,f1401,f1449]) ).
fof(f3473,plain,
( ~ sQ32_spl
| e0 = e2 ),
inference(forward_demodulation,[status(thm)],[f3082,f1338]) ).
fof(f3474,plain,
( ~ sQ32_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3473,f196]) ).
fof(f3475,plain,
~ sQ32_spl,
inference(contradiction_clause,[status(thm)],[f3474]) ).
fof(f3477,plain,
( ~ sQ111_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1591,f3078]) ).
fof(f3478,plain,
~ sQ111_spl,
inference(contradiction_clause,[status(thm)],[f3477]) ).
fof(f3481,plain,
e0 != op(e1,e3),
inference(forward_demodulation,[status(thm)],[f3082,f160]) ).
fof(f3482,plain,
e0 != op(e1,e2),
inference(forward_demodulation,[status(thm)],[f3082,f159]) ).
fof(f3483,plain,
op(e1,e0) != e0,
inference(forward_demodulation,[status(thm)],[f3082,f155]) ).
fof(f3485,plain,
e0 != op(e3,e1),
inference(forward_demodulation,[status(thm)],[f3082,f110]) ).
fof(f3486,plain,
op(e0,e1) != e0,
inference(forward_demodulation,[status(thm)],[f3082,f105]) ).
fof(f3494,plain,
( ~ sQ98_spl
| op(e3,e1) != e3 ),
inference(backward_demodulation,[status(thm)],[f1549,f181]) ).
fof(f3499,plain,
( ~ sQ98_spl
| op(e0,e4) != e3 ),
inference(backward_demodulation,[status(thm)],[f1549,f137]) ).
fof(f3500,plain,
( sQ168_spl
| ~ sQ98_spl
| op(e3,e4) != e3 ),
inference(backward_demodulation,[status(thm)],[f1549,f1964]) ).
fof(f3501,plain,
( sQ168_spl
| ~ sQ98_spl ),
inference(split_clause,[status(thm)],[f3500,f1548,f1962]) ).
fof(f3512,plain,
( ~ sQ15_spl
| e0 != op(e0,e4) ),
inference(backward_demodulation,[status(thm)],[f1284,f154]) ).
fof(f3514,plain,
( ~ sQ109_spl
| op(e4,e0) != e4 ),
inference(forward_demodulation,[status(thm)],[f1584,f185]) ).
fof(f3521,plain,
( ~ sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1277,f2949]) ).
fof(f3522,plain,
~ sQ13_spl,
inference(contradiction_clause,[status(thm)],[f3521]) ).
fof(f3523,plain,
( ~ sQ33_spl
| e0 = e3 ),
inference(forward_demodulation,[status(thm)],[f3082,f1341]) ).
fof(f3524,plain,
( ~ sQ33_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3523,f197]) ).
fof(f3525,plain,
~ sQ33_spl,
inference(contradiction_clause,[status(thm)],[f3524]) ).
fof(f3527,plain,
( ~ sQ81_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1495,f3077]) ).
fof(f3528,plain,
~ sQ81_spl,
inference(contradiction_clause,[status(thm)],[f3527]) ).
fof(f3532,plain,
( ~ sQ84_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1504,f3093]) ).
fof(f3533,plain,
~ sQ84_spl,
inference(contradiction_clause,[status(thm)],[f3532]) ).
fof(f3535,plain,
( ~ sQ18_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f3141,f1372,f1292]) ).
fof(f3536,plain,
( ~ sQ58_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1421,f3006]) ).
fof(f3537,plain,
~ sQ58_spl,
inference(contradiction_clause,[status(thm)],[f3536]) ).
fof(f3540,plain,
( ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1252,f3486]) ).
fof(f3541,plain,
~ sQ5_spl,
inference(contradiction_clause,[status(thm)],[f3540]) ).
fof(f3542,plain,
( ~ sQ80_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1492,f3485]) ).
fof(f3543,plain,
~ sQ80_spl,
inference(contradiction_clause,[status(thm)],[f3542]) ).
fof(f3545,plain,
( ~ sQ18_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f3137,f1260,f1292]) ).
fof(f3546,plain,
( ~ sQ35_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1348,f3482]) ).
fof(f3547,plain,
~ sQ35_spl,
inference(contradiction_clause,[status(thm)],[f3546]) ).
fof(f3548,plain,
( ~ sQ40_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1364,f3481]) ).
fof(f3549,plain,
~ sQ40_spl,
inference(contradiction_clause,[status(thm)],[f3548]) ).
fof(f3550,plain,
( ~ sQ38_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1357,f2948]) ).
fof(f3551,plain,
~ sQ38_spl,
inference(contradiction_clause,[status(thm)],[f3550]) ).
fof(f3552,plain,
( ~ sQ53_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1405,f3054]) ).
fof(f3553,plain,
~ sQ53_spl,
inference(contradiction_clause,[status(thm)],[f3552]) ).
fof(f3554,plain,
( ~ sQ20_spl
| ~ sQ95_spl ),
inference(split_clause,[status(thm)],[f2951,f1539,f1299]) ).
fof(f3556,plain,
( ~ sQ15_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f3512,f1299,f1283]) ).
fof(f3557,plain,
( ~ sQ73_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1469,f3017]) ).
fof(f3558,plain,
~ sQ73_spl,
inference(contradiction_clause,[status(thm)],[f3557]) ).
fof(f3559,plain,
e0 != op(e2,e1),
inference(forward_demodulation,[status(thm)],[f3082,f109]) ).
fof(f3564,plain,
( ~ sQ128_spl
| op(e3,e3) = e3 ),
inference(backward_demodulation,[status(thm)],[f1645,f41]) ).
fof(f3572,plain,
( ~ sQ128_spl
| sQ93_spl ),
inference(split_clause,[status(thm)],[f3564,f1532,f1644]) ).
fof(f3577,plain,
( ~ sQ55_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1412,f3559]) ).
fof(f3578,plain,
~ sQ55_spl,
inference(contradiction_clause,[status(thm)],[f3577]) ).
fof(f3579,plain,
( ~ sQ25_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1316,f3483]) ).
fof(f3580,plain,
~ sQ25_spl,
inference(contradiction_clause,[status(thm)],[f3579]) ).
fof(f3587,plain,
( ~ sQ138_spl
| ~ sQ116_spl
| op(e1,e3) = e4 ),
inference(backward_demodulation,[status(thm)],[f1607,f1786]) ).
fof(f3589,plain,
( ~ sQ138_spl
| ~ sQ116_spl
| sQ44_spl ),
inference(split_clause,[status(thm)],[f3587,f1375,f1606,f1785]) ).
fof(f3591,plain,
( ~ sQ98_spl
| ~ sQ83_spl ),
inference(split_clause,[status(thm)],[f3494,f1500,f1548]) ).
fof(f3592,plain,
( ~ sQ82_spl
| op(e2,e1) != e2 ),
inference(backward_demodulation,[status(thm)],[f1498,f112]) ).
fof(f3597,plain,
( ~ sQ82_spl
| ~ sQ57_spl ),
inference(split_clause,[status(thm)],[f3592,f1417,f1497]) ).
fof(f3598,plain,
( ~ sQ54_spl
| e4 != op(e4,e0) ),
inference(backward_demodulation,[status(thm)],[f1408,f103]) ).
fof(f3608,plain,
( ~ sQ54_spl
| ~ sQ104_spl ),
inference(split_clause,[status(thm)],[f3598,f1567,f1407]) ).
fof(f3610,plain,
( ~ sQ82_spl
| op(e3,e0) != e2 ),
inference(forward_demodulation,[status(thm)],[f1498,f175]) ).
fof(f3611,plain,
( sQ190_spl
| ~ sQ82_spl
| op(e1,e3) != e2 ),
inference(forward_demodulation,[status(thm)],[f1498,f2104]) ).
fof(f3621,plain,
( sQ152_spl
| ~ sQ108_spl
| op(e1,e4) != e3 ),
inference(backward_demodulation,[status(thm)],[f1581,f1865]) ).
fof(f3643,plain,
( sQ190_spl
| ~ sQ82_spl
| ~ sQ42_spl ),
inference(split_clause,[status(thm)],[f3611,f1369,f1497,f2102]) ).
fof(f3652,plain,
( ~ sQ113_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1597,f2946]) ).
fof(f3653,plain,
~ sQ113_spl,
inference(contradiction_clause,[status(thm)],[f3652]) ).
fof(f3662,plain,
( ~ sQ79_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1488,f3399]) ).
fof(f3663,plain,
~ sQ79_spl,
inference(contradiction_clause,[status(thm)],[f3662]) ).
fof(f3668,plain,
( ~ sQ14_spl
| e4 != op(e0,e4) ),
inference(backward_demodulation,[status(thm)],[f1280,f153]) ).
fof(f3670,plain,
( ~ sQ14_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f3668,f1311,f1279]) ).
fof(f3671,plain,
( ~ sQ98_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f3499,f1308,f1548]) ).
fof(f3672,plain,
( sQ152_spl
| ~ sQ108_spl
| ~ sQ48_spl ),
inference(split_clause,[status(thm)],[f3621,f1388,f1580,f1863]) ).
fof(f3674,plain,
( ~ sQ44_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1376,f3096]) ).
fof(f3675,plain,
~ sQ44_spl,
inference(contradiction_clause,[status(thm)],[f3674]) ).
fof(f3677,plain,
( sQ271_spl
| ~ sQ26_spl
| op(e0,e1) != e1 ),
inference(forward_demodulation,[status(thm)],[f1319,f2622]) ).
fof(f3678,plain,
( ~ sQ77_spl
| ~ sQ82_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1482,f3610]) ).
fof(f3679,plain,
( ~ sQ77_spl
| ~ sQ82_spl ),
inference(contradiction_clause,[status(thm)],[f3678]) ).
fof(f3680,plain,
( ~ sQ82_spl
| e2 != op(e3,e4) ),
inference(forward_demodulation,[status(thm)],[f1498,f181]) ).
fof(f3682,plain,
( ~ sQ125_spl
| e0 != op(e3,e0) ),
inference(backward_demodulation,[status(thm)],[f3684,f97]) ).
fof(f3684,plain,
( ~ sQ125_spl
| op(e0,e0) = e0 ),
inference(forward_demodulation,[status(thm)],[f1636,f34]) ).
fof(f3685,plain,
( ~ sQ125_spl
| ~ sQ75_spl ),
inference(split_clause,[status(thm)],[f3682,f1475,f1635]) ).
fof(f3695,plain,
( ~ sQ6_spl
| sQ271_spl
| ~ sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1255,f3677]) ).
fof(f3696,plain,
( ~ sQ6_spl
| sQ271_spl
| ~ sQ26_spl ),
inference(contradiction_clause,[status(thm)],[f3695]) ).
fof(f3701,plain,
( sQ273_spl
| ~ sQ26_spl
| op(e1,e1) != e0 ),
inference(forward_demodulation,[status(thm)],[f1319,f2630]) ).
fof(f3702,plain,
( sQ273_spl
| ~ sQ26_spl
| e0 != e0 ),
inference(forward_demodulation,[status(thm)],[f3082,f3701]) ).
fof(f3703,plain,
( sQ273_spl
| ~ sQ26_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f3702]) ).
fof(f3704,plain,
( sQ273_spl
| ~ sQ26_spl ),
inference(contradiction_clause,[status(thm)],[f3703]) ).
fof(f3706,plain,
( ~ sQ125_spl
| e0 != op(e0,e2) ),
inference(forward_demodulation,[status(thm)],[f3684,f146]) ).
fof(f3718,plain,
( ~ sQ124_spl
| op(e4,e1) != e4 ),
inference(backward_demodulation,[status(thm)],[f1632,f191]) ).
fof(f3724,plain,
( ~ sQ124_spl
| ~ sQ109_spl ),
inference(split_clause,[status(thm)],[f3718,f1583,f1631]) ).
fof(f3729,plain,
( ~ sQ99_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1552,f3401]) ).
fof(f3730,plain,
~ sQ99_spl,
inference(contradiction_clause,[status(thm)],[f3729]) ).
fof(f3731,plain,
( ~ sQ125_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f3706,f1267,f1635]) ).
fof(f3737,plain,
( ~ sQ69_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1456,f3095]) ).
fof(f3738,plain,
~ sQ69_spl,
inference(contradiction_clause,[status(thm)],[f3737]) ).
fof(f3744,plain,
( ~ sQ82_spl
| e2 != op(e4,e1) ),
inference(forward_demodulation,[status(thm)],[f1498,f114]) ).
fof(f3748,plain,
( ~ sQ125_spl
| op(e4,e0) = e4 ),
inference(forward_demodulation,[status(thm)],[f1636,f43]) ).
fof(f3754,plain,
( ~ sQ125_spl
| e4 != op(e2,e4) ),
inference(backward_demodulation,[status(thm)],[f3755,f136]) ).
fof(f3755,plain,
( ~ sQ125_spl
| op(e0,e4) = e4 ),
inference(forward_demodulation,[status(thm)],[f1636,f42]) ).
fof(f3756,plain,
( ~ sQ125_spl
| ~ sQ74_spl ),
inference(split_clause,[status(thm)],[f3754,f1471,f1635]) ).
fof(f3757,plain,
( sQ104_spl
| ~ sQ125_spl
| e4 != e4 ),
inference(forward_demodulation,[status(thm)],[f3748,f1569]) ).
fof(f3758,plain,
( sQ104_spl
| ~ sQ125_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f3757]) ).
fof(f3759,plain,
( sQ104_spl
| ~ sQ125_spl ),
inference(contradiction_clause,[status(thm)],[f3758]) ).
fof(f3760,plain,
( ~ sQ43_spl
| ~ sQ118_spl ),
inference(split_clause,[status(thm)],[f3168,f1612,f1372]) ).
fof(f3762,plain,
( ~ sQ101_spl
| ~ sQ125_spl
| e4 = e1 ),
inference(forward_demodulation,[status(thm)],[f3748,f1559]) ).
fof(f3763,plain,
( ~ sQ101_spl
| ~ sQ125_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3762,f201]) ).
fof(f3764,plain,
( ~ sQ101_spl
| ~ sQ125_spl ),
inference(contradiction_clause,[status(thm)],[f3763]) ).
fof(f3765,plain,
( ~ sQ124_spl
| ~ sQ104_spl ),
inference(split_clause,[status(thm)],[f3246,f1567,f1631]) ).
fof(f3775,plain,
( ~ sQ109_spl
| ~ sQ104_spl ),
inference(split_clause,[status(thm)],[f3514,f1567,f1583]) ).
fof(f3777,plain,
( ~ sQ21_spl
| ~ sQ125_spl
| e4 = e1 ),
inference(forward_demodulation,[status(thm)],[f3755,f1303]) ).
fof(f3778,plain,
( ~ sQ21_spl
| ~ sQ125_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3777,f201]) ).
fof(f3779,plain,
( ~ sQ21_spl
| ~ sQ125_spl ),
inference(contradiction_clause,[status(thm)],[f3778]) ).
fof(f3781,plain,
( sQ24_spl
| ~ sQ125_spl
| e4 != e4 ),
inference(forward_demodulation,[status(thm)],[f3755,f1313]) ).
fof(f3782,plain,
( sQ24_spl
| ~ sQ125_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f3781]) ).
fof(f3783,plain,
( sQ24_spl
| ~ sQ125_spl ),
inference(contradiction_clause,[status(thm)],[f3782]) ).
fof(f3786,plain,
( ~ sQ107_spl
| ~ sQ82_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1578,f3744]) ).
fof(f3787,plain,
( ~ sQ107_spl
| ~ sQ82_spl ),
inference(contradiction_clause,[status(thm)],[f3786]) ).
fof(f3792,plain,
( ~ sQ125_spl
| op(e3,e0) = e3 ),
inference(forward_demodulation,[status(thm)],[f1636,f41]) ).
fof(f3793,plain,
( sQ160_spl
| ~ sQ125_spl
| e4 != op(e4,e0) ),
inference(forward_demodulation,[status(thm)],[f3755,f1914]) ).
fof(f3794,plain,
( sQ160_spl
| ~ sQ125_spl
| e4 != e4 ),
inference(forward_demodulation,[status(thm)],[f3748,f3793]) ).
fof(f3795,plain,
( sQ160_spl
| ~ sQ125_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f3794]) ).
fof(f3796,plain,
( sQ160_spl
| ~ sQ125_spl ),
inference(contradiction_clause,[status(thm)],[f3795]) ).
fof(f3820,plain,
( ~ sQ125_spl
| op(e0,e3) = e3 ),
inference(forward_demodulation,[status(thm)],[f1636,f40]) ).
fof(f3821,plain,
( ~ sQ125_spl
| op(e2,e0) = e2 ),
inference(forward_demodulation,[status(thm)],[f1636,f39]) ).
fof(f3822,plain,
( ~ sQ125_spl
| op(e0,e2) = e2 ),
inference(forward_demodulation,[status(thm)],[f1636,f38]) ).
fof(f3830,plain,
( sQ235_spl
| ~ sQ125_spl
| e2 != op(e2,e0) ),
inference(forward_demodulation,[status(thm)],[f3822,f2389]) ).
fof(f3831,plain,
( sQ235_spl
| ~ sQ125_spl
| e2 != e2 ),
inference(forward_demodulation,[status(thm)],[f3821,f3830]) ).
fof(f3832,plain,
( sQ235_spl
| ~ sQ125_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f3831]) ).
fof(f3833,plain,
( sQ235_spl
| ~ sQ125_spl ),
inference(contradiction_clause,[status(thm)],[f3832]) ).
fof(f3834,plain,
( sQ18_spl
| ~ sQ125_spl
| e3 != e3 ),
inference(forward_demodulation,[status(thm)],[f3820,f1294]) ).
fof(f3835,plain,
( sQ18_spl
| ~ sQ125_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f3834]) ).
fof(f3836,plain,
( sQ18_spl
| ~ sQ125_spl ),
inference(contradiction_clause,[status(thm)],[f3835]) ).
fof(f3846,plain,
( sQ287_spl
| ~ sQ125_spl
| op(e3,e0) != e3 ),
inference(forward_demodulation,[status(thm)],[f3820,f2722]) ).
fof(f3847,plain,
( sQ287_spl
| ~ sQ125_spl
| e3 != e3 ),
inference(forward_demodulation,[status(thm)],[f3792,f3846]) ).
fof(f3848,plain,
( sQ287_spl
| ~ sQ125_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f3847]) ).
fof(f3849,plain,
( sQ287_spl
| ~ sQ125_spl ),
inference(contradiction_clause,[status(thm)],[f3848]) ).
fof(f3911,plain,
( sQ227_spl
| ~ sQ39_spl
| e4 != op(e2,e1) ),
inference(backward_demodulation,[status(thm)],[f1360,f2340]) ).
fof(f3917,plain,
( sQ227_spl
| ~ sQ39_spl
| ~ sQ59_spl ),
inference(split_clause,[status(thm)],[f3911,f1423,f1359,f2338]) ).
fof(f4029,plain,
( ~ sQ168_spl
| ~ sQ95_spl
| op(e0,e4) = e3 ),
inference(forward_demodulation,[status(thm)],[f1540,f1963]) ).
fof(f4030,plain,
( ~ sQ168_spl
| ~ sQ95_spl
| ~ sQ125_spl
| e4 = e3 ),
inference(forward_demodulation,[status(thm)],[f3755,f4029]) ).
fof(f4031,plain,
( ~ sQ168_spl
| ~ sQ95_spl
| ~ sQ125_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4030,f204]) ).
fof(f4032,plain,
( ~ sQ168_spl
| ~ sQ95_spl
| ~ sQ125_spl ),
inference(contradiction_clause,[status(thm)],[f4031]) ).
fof(f4039,plain,
( ~ sQ145_spl
| ~ sQ110_spl
| op(e0,e2) = e4 ),
inference(forward_demodulation,[status(thm)],[f1588,f1823]) ).
fof(f4040,plain,
( ~ sQ145_spl
| ~ sQ110_spl
| ~ sQ125_spl
| e2 = e4 ),
inference(forward_demodulation,[status(thm)],[f3822,f4039]) ).
fof(f4041,plain,
( ~ sQ145_spl
| ~ sQ110_spl
| ~ sQ125_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4040,f203]) ).
fof(f4042,plain,
( ~ sQ145_spl
| ~ sQ110_spl
| ~ sQ125_spl ),
inference(contradiction_clause,[status(thm)],[f4041]) ).
fof(f4043,plain,
( ~ sQ72_spl
| ~ sQ71_spl
| e1 = e2 ),
inference(forward_demodulation,[status(thm)],[f1463,f1466]) ).
fof(f4044,plain,
( ~ sQ72_spl
| ~ sQ71_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4043,f199]) ).
fof(f4045,plain,
( ~ sQ72_spl
| ~ sQ71_spl ),
inference(contradiction_clause,[status(thm)],[f4044]) ).
fof(f4048,plain,
( ~ sQ183_spl
| op(e1,e2) = e3 ),
inference(forward_demodulation,[status(thm)],[f3081,f2058]) ).
fof(f4049,plain,
( ~ sQ183_spl
| ~ sQ39_spl
| e4 = e3 ),
inference(forward_demodulation,[status(thm)],[f1360,f4048]) ).
fof(f4050,plain,
( ~ sQ183_spl
| ~ sQ39_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4049,f204]) ).
fof(f4051,plain,
( ~ sQ183_spl
| ~ sQ39_spl ),
inference(contradiction_clause,[status(thm)],[f4050]) ).
fof(f4056,plain,
( ~ sQ206_spl
| ~ sQ71_spl
| op(e1,e4) = e2 ),
inference(forward_demodulation,[status(thm)],[f1463,f2202]) ).
fof(f4057,plain,
( ~ sQ206_spl
| ~ sQ71_spl
| ~ sQ108_spl
| ~ sQ152_spl
| e3 = e2 ),
inference(forward_demodulation,[status(thm)],[f3394,f4056]) ).
fof(f4058,plain,
( ~ sQ206_spl
| ~ sQ71_spl
| ~ sQ108_spl
| ~ sQ152_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4057,f202]) ).
fof(f4059,plain,
( ~ sQ206_spl
| ~ sQ71_spl
| ~ sQ108_spl
| ~ sQ152_spl ),
inference(contradiction_clause,[status(thm)],[f4058]) ).
fof(f4060,plain,
( ~ sQ213_spl
| ~ sQ65_spl
| op(e0,e3) = e2 ),
inference(forward_demodulation,[status(thm)],[f1444,f2248]) ).
fof(f4061,plain,
( ~ sQ213_spl
| ~ sQ65_spl
| ~ sQ125_spl
| e3 = e2 ),
inference(forward_demodulation,[status(thm)],[f3820,f4060]) ).
fof(f4062,plain,
( ~ sQ213_spl
| ~ sQ65_spl
| ~ sQ125_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4061,f202]) ).
fof(f4063,plain,
( ~ sQ213_spl
| ~ sQ65_spl
| ~ sQ125_spl ),
inference(contradiction_clause,[status(thm)],[f4062]) ).
fof(f4080,plain,
( ~ sQ82_spl
| ~ sQ97_spl ),
inference(split_clause,[status(thm)],[f3680,f1545,f1497]) ).
fof(f4098,plain,
( ~ sQ126_spl
| op(e0,e1) = e0 ),
inference(backward_demodulation,[status(thm)],[f1639,f35]) ).
fof(f4102,plain,
( ~ sQ126_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f4098,f1251,f1638]) ).
fof(f4103,plain,
( ~ sQ129_spl
| sQ100_spl ),
inference(split_clause,[status(thm)],[f3366,f1555,f1647]) ).
fof(f4104,plain,
( ~ sQ129_spl
| sQ118_spl ),
inference(split_clause,[status(thm)],[f3372,f1612,f1647]) ).
fof(f4113,plain,
( ~ sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1271,f3080]) ).
fof(f4114,plain,
~ sQ11_spl,
inference(contradiction_clause,[status(thm)],[f4113]) ).
fof(f4168,plain,
( ~ sQ103_spl
| e3 != op(e4,e3) ),
inference(backward_demodulation,[status(thm)],[f1565,f187]) ).
fof(f4169,plain,
( ~ sQ103_spl
| ~ sQ118_spl ),
inference(split_clause,[status(thm)],[f4168,f1612,f1564]) ).
fof(f4170,plain,
$false,
inference(sat_refutation,[status(thm)],[f1282,f1378,f1458,f1506,f1538,f1650,f1653,f1654,f1658,f1667,f1668,f1672,f1679,f1680,f1681,f1682,f1693,f1694,f1740,f1741,f1760,f1772,f1784,f1788,f1801,f1810,f1825,f1838,f1839,f1847,f1855,f1866,f1880,f1888,f1889,f1896,f1904,f1915,f1929,f1930,f1937,f1945,f1953,f1965,f1975,f1983,f1991,f1999,f2010,f2021,f2029,f2037,f2045,f2060,f2070,f2078,f2079,f2086,f2094,f2105,f2119,f2127,f2135,f2143,f2154,f2168,f2176,f2177,f2184,f2192,f2204,f2214,f2222,f2230,f2238,f2250,f2260,f2268,f2269,f2276,f2277,f2284,f2295,f2306,f2314,f2322,f2330,f2331,f2341,f2355,f2363,f2364,f2371,f2379,f2390,f2404,f2405,f2412,f2420,f2428,f2436,f2450,f2458,f2467,f2474,f2482,f2496,f2504,f2505,f2520,f2528,f2542,f2550,f2551,f2566,f2577,f2588,f2596,f2597,f2612,f2623,f2637,f2645,f2661,f2662,f2669,f2683,f2691,f2707,f2723,f2730,f2731,f2737,f2753,f2761,f2783,f2799,f2807,f2829,f2842,f2853,f2871,f2892,f2909,f2911,f2913,f2915,f2917,f2929,f2956,f2964,f3000,f3048,f3052,f3053,f3065,f3104,f3121,f3124,f3127,f3163,f3166,f3189,f3198,f3205,f3209,f3213,f3216,f3222,f3240,f3250,f3259,f3263,f3281,f3290,f3310,f3342,f3355,f3376,f3377,f3378,f3379,f3380,f3381,f3382,f3384,f3387,f3390,f3417,f3430,f3431,f3453,f3456,f3460,f3464,f3472,f3475,f3478,f3501,f3522,f3525,f3528,f3533,f3535,f3537,f3541,f3543,f3545,f3547,f3549,f3551,f3553,f3554,f3556,f3558,f3572,f3578,f3580,f3589,f3591,f3597,f3608,f3643,f3653,f3663,f3670,f3671,f3672,f3675,f3679,f3685,f3696,f3704,f3724,f3730,f3731,f3738,f3756,f3759,f3760,f3764,f3765,f3775,f3779,f3783,f3787,f3796,f3833,f3836,f3849,f3917,f4032,f4042,f4045,f4051,f4059,f4063,f4080,f4102,f4103,f4104,f4114,f4169]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG059+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n009.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 12:54:58 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.13/0.40 % Drodi V4.1.1
% 0.85/0.69 % Refutation found
% 0.85/0.69 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.85/0.69 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.22/0.71 % Elapsed time: 0.343153 seconds
% 0.22/0.71 % CPU time: 2.074791 seconds
% 0.22/0.71 % Total memory used: 159.639 MB
% 0.22/0.71 % Net memory used: 158.440 MB
%------------------------------------------------------------------------------