%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ALG064+1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 11:48:00 AM UTC 2026
% Result : Theorem 0.11s 0.57s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 166
% Syntax : Number of formulae : 748 ( 99 unt; 159 def)
% Number of atoms : 3528 (2357 equ)
% Maximal formula atoms : 250 ( 4 avg)
% Number of connectives : 4434 (1654 ~;1546 |;1052 &)
% ( 182 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 101 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 161 ( 159 usr; 160 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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
( e4 = op(e1,e1)
& e3 = op(op(op(e1,e1),op(e1,e1)),op(op(e1,e1),op(e1,e1)))
& e2 = op(op(e1,e1),op(e1,e1))
& e0 = op(e1,op(op(e1,e1),op(e1,e1))) ),
file('/export/starexec/sandbox/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) ) )
& ( op(e4,e4) = e4
| op(e3,e3) = e4
| op(e2,e2) = e4
| op(e1,e1) = e4
| op(e0,e0) = e4 )
& ( op(e4,e4) = e3
| op(e3,e3) = e3
| op(e2,e2) = e3
| op(e1,e1) = e3
| op(e0,e0) = e3 )
& ( op(e4,e4) = e2
| op(e3,e3) = e2
| op(e2,e2) = e2
| op(e1,e1) = e2
| op(e0,e0) = e2 )
& ( op(e4,e4) = e1
| op(e3,e3) = e1
| op(e2,e2) = e1
| op(e1,e1) = e1
| op(e0,e0) = e1 )
& ( op(e4,e4) = e0
| op(e3,e3) = e0
| op(e2,e2) = e0
| op(e1,e1) = e0
| op(e0,e0) = e0 ) ),
file('/export/starexec/sandbox/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) ) )
& ( op(e4,e4) = e4
| op(e3,e3) = e4
| op(e2,e2) = e4
| op(e1,e1) = e4
| op(e0,e0) = e4 )
& ( op(e4,e4) = e3
| op(e3,e3) = e3
| op(e2,e2) = e3
| op(e1,e1) = e3
| op(e0,e0) = e3 )
& ( op(e4,e4) = e2
| op(e3,e3) = e2
| op(e2,e2) = e2
| op(e1,e1) = e2
| op(e0,e0) = e2 )
& ( op(e4,e4) = e1
| op(e3,e3) = e1
| op(e2,e2) = e1
| op(e1,e1) = e1
| op(e0,e0) = e1 )
& ( op(e4,e4) = e0
| op(e3,e3) = e0
| op(e2,e2) = e0
| op(e1,e1) = e0
| op(e0,e0) = e0 ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f15,plain,
( op(e1,e1) = e4
| op(e1,e1) = e3
| op(e1,e1) = e2
| op(e1,e1) = e1
| op(e1,e1) = e0 ),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f20,plain,
( op(e2,e1) = e4
| op(e2,e1) = e3
| op(e2,e1) = e2
| op(e2,e1) = e1
| op(e2,e1) = e0 ),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f21,plain,
( op(e2,e2) = e4
| op(e2,e2) = e3
| op(e2,e2) = e2
| op(e2,e2) = e1
| op(e2,e2) = e0 ),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f26,plain,
( op(e3,e2) = e4
| op(e3,e2) = e3
| op(e3,e2) = e2
| op(e3,e2) = e1
| op(e3,e2) = e0 ),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f33,plain,
( op(e4,e4) = e4
| op(e4,e4) = e3
| op(e4,e4) = e2
| op(e4,e4) = e1
| op(e4,e4) = e0 ),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f34,plain,
op(unit,e0) = 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(f49,plain,
( op(e0,e4) = e2
| op(e0,e3) = e2
| op(e0,e2) = e2
| op(e0,e1) = e2
| op(e0,e0) = e2 ),
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(f59,plain,
( op(e1,e4) = e2
| op(e1,e3) = e2
| op(e1,e2) = e2
| op(e1,e1) = e2
| op(e1,e0) = e2 ),
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(f68,plain,
( op(e4,e2) = e1
| op(e3,e2) = e1
| op(e2,e2) = e1
| op(e1,e2) = e1
| op(e0,e2) = e1 ),
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(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(f79,plain,
( op(e3,e4) = e2
| op(e3,e3) = e2
| op(e3,e2) = e2
| op(e3,e1) = e2
| op(e3,e0) = e2 ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f86,plain,
( op(e4,e4) = e0
| op(e3,e4) = e0
| op(e2,e4) = e0
| op(e1,e4) = e0
| op(e0,e4) = e0 ),
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(f102,plain,
op(e2,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(f106,plain,
op(e0,e1) != op(e2,e1),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f109,plain,
op(e1,e1) != op(e2,e1),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f111,plain,
op(e1,e1) != op(e4,e1),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f117,plain,
op(e0,e2) != op(e3,e2),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f123,plain,
op(e2,e2) != op(e4,e2),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f136,plain,
op(e0,e4) != op(e2,e4),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f141,plain,
op(e1,e4) != op(e4,e4),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f143,plain,
op(e2,e4) != op(e4,e4),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f144,plain,
op(e3,e4) != op(e4,e4),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f145,plain,
op(e0,e0) != op(e0,e1),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f147,plain,
op(e0,e0) != op(e0,e3),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f151,plain,
op(e0,e1) != op(e0,e4),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f161,plain,
op(e1,e1) != op(e1,e4),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f162,plain,
op(e1,e2) != op(e1,e3),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f163,plain,
op(e1,e2) != op(e1,e4),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f165,plain,
op(e2,e0) != op(e2,e1),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f166,plain,
op(e2,e0) != op(e2,e2),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f169,plain,
op(e2,e1) != op(e2,e2),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f170,plain,
op(e2,e1) != op(e2,e3),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f171,plain,
op(e2,e1) != op(e2,e4),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f176,plain,
op(e3,e0) != op(e3,e2),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f182,plain,
op(e3,e2) != op(e3,e3),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f183,plain,
op(e3,e2) != 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(f191,plain,
op(e4,e1) != 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(e1,op(op(e1,e1),op(e1,e1))),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f206,plain,
e2 = op(op(e1,e1),op(e1,e1)),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f207,plain,
e3 = op(op(op(e1,e1),op(e1,e1)),op(op(e1,e1),op(e1,e1))),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f208,plain,
e4 = op(e1,e1),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f209,definition,
( sP0_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,[sP0_prd])],[]) ).
fof(f210,plain,
( ( ( op(op(e4,e4),e4) != e4
& op(op(e4,e4),e4) = e4
& op(e4,e4) != op(e4,e4) )
| sP0_prd )
& ( op(e4,e4) = e4
| op(e3,e3) = e4
| op(e2,e2) = e4
| op(e1,e1) = e4
| op(e0,e0) = e4 )
& ( op(e4,e4) = e3
| op(e3,e3) = e3
| op(e2,e2) = e3
| op(e1,e1) = e3
| op(e0,e0) = e3 )
& ( op(e4,e4) = e2
| op(e3,e3) = e2
| op(e2,e2) = e2
| op(e1,e1) = e2
| op(e0,e0) = e2 )
& ( op(e4,e4) = e1
| op(e3,e3) = e1
| op(e2,e2) = e1
| op(e1,e1) = e1
| op(e0,e0) = e1 )
& ( op(e4,e4) = e0
| op(e3,e3) = e0
| op(e2,e2) = e0
| op(e1,e1) = e0
| op(e0,e0) = e0 ) ),
inference(formula_renaming,[status(thm)],[f8,f209]) ).
fof(f211,plain,
( op(e4,e4) = e0
| op(e3,e3) = e0
| op(e2,e2) = e0
| op(e1,e1) = e0
| op(e0,e0) = e0 ),
inference(cnf_transformation,[status(thm)],[f210]) ).
fof(f212,plain,
( op(e4,e4) = e1
| op(e3,e3) = e1
| op(e2,e2) = e1
| op(e1,e1) = e1
| op(e0,e0) = e1 ),
inference(cnf_transformation,[status(thm)],[f210]) ).
fof(f217,plain,
( op(op(e4,e4),e4) = e4
| sP0_prd ),
inference(cnf_transformation,[status(thm)],[f210]) ).
fof(f219,definition,
( sP1_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,[sP1_prd])],[]) ).
fof(f220,plain,
( sP0_prd
<=> ( ( op(op(e4,e3),e4) != e3
& op(op(e4,e3),e3) = e4
& op(e3,e4) != op(e4,e3) )
| sP1_prd ) ),
inference(formula_renaming,[status(thm)],[f209,f219]) ).
fof(f221,plain,
( ( ( ( op(op(e4,e3),e4) = e3
| op(op(e4,e3),e3) != e4
| op(e3,e4) = op(e4,e3) )
& ~ sP1_prd )
| sP0_prd )
& ( ( op(op(e4,e3),e4) != e3
& op(op(e4,e3),e3) = e4
& op(e3,e4) != op(e4,e3) )
| sP1_prd
| ~ sP0_prd ) ),
inference(NNF_transformation,[status(thm)],[f220]) ).
fof(f223,plain,
( op(op(e4,e3),e3) = e4
| sP1_prd
| ~ sP0_prd ),
inference(cnf_transformation,[status(thm)],[f221]) ).
fof(f227,definition,
( sP2_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,[sP2_prd])],[]) ).
fof(f228,plain,
( sP1_prd
<=> ( ( op(op(e4,e2),e4) != e2
& op(op(e4,e2),e2) = e4
& op(e2,e4) != op(e4,e2) )
| sP2_prd ) ),
inference(formula_renaming,[status(thm)],[f219,f227]) ).
fof(f229,plain,
( ( ( ( op(op(e4,e2),e4) = e2
| op(op(e4,e2),e2) != e4
| op(e2,e4) = op(e4,e2) )
& ~ sP2_prd )
| sP1_prd )
& ( ( op(op(e4,e2),e4) != e2
& op(op(e4,e2),e2) = e4
& op(e2,e4) != op(e4,e2) )
| sP2_prd
| ~ sP1_prd ) ),
inference(NNF_transformation,[status(thm)],[f228]) ).
fof(f231,plain,
( op(op(e4,e2),e2) = e4
| sP2_prd
| ~ sP1_prd ),
inference(cnf_transformation,[status(thm)],[f229]) ).
fof(f235,definition,
( sP3_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,[sP3_prd])],[]) ).
fof(f236,plain,
( sP2_prd
<=> ( ( op(op(e4,e1),e4) != e1
& op(op(e4,e1),e1) = e4
& op(e1,e4) != op(e4,e1) )
| sP3_prd ) ),
inference(formula_renaming,[status(thm)],[f227,f235]) ).
fof(f237,plain,
( ( ( ( op(op(e4,e1),e4) = e1
| op(op(e4,e1),e1) != e4
| op(e1,e4) = op(e4,e1) )
& ~ sP3_prd )
| sP2_prd )
& ( ( op(op(e4,e1),e4) != e1
& op(op(e4,e1),e1) = e4
& op(e1,e4) != op(e4,e1) )
| sP3_prd
| ~ sP2_prd ) ),
inference(NNF_transformation,[status(thm)],[f236]) ).
fof(f239,plain,
( op(op(e4,e1),e1) = e4
| sP3_prd
| ~ sP2_prd ),
inference(cnf_transformation,[status(thm)],[f237]) ).
fof(f243,definition,
( sP4_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,[sP4_prd])],[]) ).
fof(f244,plain,
( sP3_prd
<=> ( ( op(op(e4,e0),e4) != e0
& op(op(e4,e0),e0) = e4
& op(e0,e4) != op(e4,e0) )
| sP4_prd ) ),
inference(formula_renaming,[status(thm)],[f235,f243]) ).
fof(f245,plain,
( ( ( ( op(op(e4,e0),e4) = e0
| op(op(e4,e0),e0) != e4
| op(e0,e4) = op(e4,e0) )
& ~ sP4_prd )
| sP3_prd )
& ( ( op(op(e4,e0),e4) != e0
& op(op(e4,e0),e0) = e4
& op(e0,e4) != op(e4,e0) )
| sP4_prd
| ~ sP3_prd ) ),
inference(NNF_transformation,[status(thm)],[f244]) ).
fof(f246,plain,
( op(e0,e4) != op(e4,e0)
| sP4_prd
| ~ sP3_prd ),
inference(cnf_transformation,[status(thm)],[f245]) ).
fof(f251,definition,
( sP5_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,[sP5_prd])],[]) ).
fof(f252,plain,
( sP4_prd
<=> ( ( op(op(e3,e4),e3) != e4
& op(op(e3,e4),e4) = e3
& op(e4,e3) != op(e3,e4) )
| sP5_prd ) ),
inference(formula_renaming,[status(thm)],[f243,f251]) ).
fof(f253,plain,
( ( ( ( op(op(e3,e4),e3) = e4
| op(op(e3,e4),e4) != e3
| op(e4,e3) = op(e3,e4) )
& ~ sP5_prd )
| sP4_prd )
& ( ( op(op(e3,e4),e3) != e4
& op(op(e3,e4),e4) = e3
& op(e4,e3) != op(e3,e4) )
| sP5_prd
| ~ sP4_prd ) ),
inference(NNF_transformation,[status(thm)],[f252]) ).
fof(f254,plain,
( op(e4,e3) != op(e3,e4)
| sP5_prd
| ~ sP4_prd ),
inference(cnf_transformation,[status(thm)],[f253]) ).
fof(f259,definition,
( sP6_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,[sP6_prd])],[]) ).
fof(f260,plain,
( sP5_prd
<=> ( ( op(op(e3,e3),e3) != e3
& op(op(e3,e3),e3) = e3
& op(e3,e3) != op(e3,e3) )
| sP6_prd ) ),
inference(formula_renaming,[status(thm)],[f251,f259]) ).
fof(f261,plain,
( ( ( ( op(op(e3,e3),e3) = e3
| op(op(e3,e3),e3) != e3
| op(e3,e3) = op(e3,e3) )
& ~ sP6_prd )
| sP5_prd )
& ( ( op(op(e3,e3),e3) != e3
& op(op(e3,e3),e3) = e3
& op(e3,e3) != op(e3,e3) )
| sP6_prd
| ~ sP5_prd ) ),
inference(NNF_transformation,[status(thm)],[f260]) ).
fof(f263,plain,
( op(op(e3,e3),e3) = e3
| sP6_prd
| ~ sP5_prd ),
inference(cnf_transformation,[status(thm)],[f261]) ).
fof(f264,plain,
( op(op(e3,e3),e3) != e3
| sP6_prd
| ~ sP5_prd ),
inference(cnf_transformation,[status(thm)],[f261]) ).
fof(f267,definition,
( sP7_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,[sP7_prd])],[]) ).
fof(f268,plain,
( sP6_prd
<=> ( ( op(op(e3,e2),e3) != e2
& op(op(e3,e2),e2) = e3
& op(e2,e3) != op(e3,e2) )
| sP7_prd ) ),
inference(formula_renaming,[status(thm)],[f259,f267]) ).
fof(f269,plain,
( ( ( ( op(op(e3,e2),e3) = e2
| op(op(e3,e2),e2) != e3
| op(e2,e3) = op(e3,e2) )
& ~ sP7_prd )
| sP6_prd )
& ( ( op(op(e3,e2),e3) != e2
& op(op(e3,e2),e2) = e3
& op(e2,e3) != op(e3,e2) )
| sP7_prd
| ~ sP6_prd ) ),
inference(NNF_transformation,[status(thm)],[f268]) ).
fof(f270,plain,
( op(e2,e3) != op(e3,e2)
| sP7_prd
| ~ sP6_prd ),
inference(cnf_transformation,[status(thm)],[f269]) ).
fof(f275,definition,
( sP8_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,[sP8_prd])],[]) ).
fof(f276,plain,
( sP7_prd
<=> ( ( op(op(e3,e1),e3) != e1
& op(op(e3,e1),e1) = e3
& op(e1,e3) != op(e3,e1) )
| sP8_prd ) ),
inference(formula_renaming,[status(thm)],[f267,f275]) ).
fof(f277,plain,
( ( ( ( op(op(e3,e1),e3) = e1
| op(op(e3,e1),e1) != e3
| op(e1,e3) = op(e3,e1) )
& ~ sP8_prd )
| sP7_prd )
& ( ( op(op(e3,e1),e3) != e1
& op(op(e3,e1),e1) = e3
& op(e1,e3) != op(e3,e1) )
| sP8_prd
| ~ sP7_prd ) ),
inference(NNF_transformation,[status(thm)],[f276]) ).
fof(f278,plain,
( op(e1,e3) != op(e3,e1)
| sP8_prd
| ~ sP7_prd ),
inference(cnf_transformation,[status(thm)],[f277]) ).
fof(f283,definition,
( sP9_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,[sP9_prd])],[]) ).
fof(f284,plain,
( sP8_prd
<=> ( ( op(op(e3,e0),e3) != e0
& op(op(e3,e0),e0) = e3
& op(e0,e3) != op(e3,e0) )
| sP9_prd ) ),
inference(formula_renaming,[status(thm)],[f275,f283]) ).
fof(f285,plain,
( ( ( ( op(op(e3,e0),e3) = e0
| op(op(e3,e0),e0) != e3
| op(e0,e3) = op(e3,e0) )
& ~ sP9_prd )
| sP8_prd )
& ( ( op(op(e3,e0),e3) != e0
& op(op(e3,e0),e0) = e3
& op(e0,e3) != op(e3,e0) )
| sP9_prd
| ~ sP8_prd ) ),
inference(NNF_transformation,[status(thm)],[f284]) ).
fof(f286,plain,
( op(e0,e3) != op(e3,e0)
| sP9_prd
| ~ sP8_prd ),
inference(cnf_transformation,[status(thm)],[f285]) ).
fof(f291,definition,
( sP10_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,[sP10_prd])],[]) ).
fof(f292,plain,
( sP9_prd
<=> ( ( op(op(e2,e4),e2) != e4
& op(op(e2,e4),e4) = e2
& op(e4,e2) != op(e2,e4) )
| sP10_prd ) ),
inference(formula_renaming,[status(thm)],[f283,f291]) ).
fof(f293,plain,
( ( ( ( op(op(e2,e4),e2) = e4
| op(op(e2,e4),e4) != e2
| op(e4,e2) = op(e2,e4) )
& ~ sP10_prd )
| sP9_prd )
& ( ( op(op(e2,e4),e2) != e4
& op(op(e2,e4),e4) = e2
& op(e4,e2) != op(e2,e4) )
| sP10_prd
| ~ sP9_prd ) ),
inference(NNF_transformation,[status(thm)],[f292]) ).
fof(f294,plain,
( op(e4,e2) != op(e2,e4)
| sP10_prd
| ~ sP9_prd ),
inference(cnf_transformation,[status(thm)],[f293]) ).
fof(f299,definition,
( sP11_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,[sP11_prd])],[]) ).
fof(f300,plain,
( sP10_prd
<=> ( ( op(op(e2,e3),e2) != e3
& op(op(e2,e3),e3) = e2
& op(e3,e2) != op(e2,e3) )
| sP11_prd ) ),
inference(formula_renaming,[status(thm)],[f291,f299]) ).
fof(f301,plain,
( ( ( ( op(op(e2,e3),e2) = e3
| op(op(e2,e3),e3) != e2
| op(e3,e2) = op(e2,e3) )
& ~ sP11_prd )
| sP10_prd )
& ( ( op(op(e2,e3),e2) != e3
& op(op(e2,e3),e3) = e2
& op(e3,e2) != op(e2,e3) )
| sP11_prd
| ~ sP10_prd ) ),
inference(NNF_transformation,[status(thm)],[f300]) ).
fof(f302,plain,
( op(e3,e2) != op(e2,e3)
| sP11_prd
| ~ sP10_prd ),
inference(cnf_transformation,[status(thm)],[f301]) ).
fof(f307,definition,
( sP12_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,[sP12_prd])],[]) ).
fof(f308,plain,
( sP11_prd
<=> ( ( op(op(e2,e2),e2) != e2
& op(op(e2,e2),e2) = e2
& op(e2,e2) != op(e2,e2) )
| sP12_prd ) ),
inference(formula_renaming,[status(thm)],[f299,f307]) ).
fof(f309,plain,
( ( ( ( op(op(e2,e2),e2) = e2
| op(op(e2,e2),e2) != e2
| op(e2,e2) = op(e2,e2) )
& ~ sP12_prd )
| sP11_prd )
& ( ( op(op(e2,e2),e2) != e2
& op(op(e2,e2),e2) = e2
& op(e2,e2) != op(e2,e2) )
| sP12_prd
| ~ sP11_prd ) ),
inference(NNF_transformation,[status(thm)],[f308]) ).
fof(f310,plain,
( op(e2,e2) != op(e2,e2)
| sP12_prd
| ~ sP11_prd ),
inference(cnf_transformation,[status(thm)],[f309]) ).
fof(f315,definition,
( sP13_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,[sP13_prd])],[]) ).
fof(f316,plain,
( sP12_prd
<=> ( ( op(op(e2,e1),e2) != e1
& op(op(e2,e1),e1) = e2
& op(e1,e2) != op(e2,e1) )
| sP13_prd ) ),
inference(formula_renaming,[status(thm)],[f307,f315]) ).
fof(f317,plain,
( ( ( ( op(op(e2,e1),e2) = e1
| op(op(e2,e1),e1) != e2
| op(e1,e2) = op(e2,e1) )
& ~ sP13_prd )
| sP12_prd )
& ( ( op(op(e2,e1),e2) != e1
& op(op(e2,e1),e1) = e2
& op(e1,e2) != op(e2,e1) )
| sP13_prd
| ~ sP12_prd ) ),
inference(NNF_transformation,[status(thm)],[f316]) ).
fof(f318,plain,
( op(e1,e2) != op(e2,e1)
| sP13_prd
| ~ sP12_prd ),
inference(cnf_transformation,[status(thm)],[f317]) ).
fof(f323,definition,
( sP14_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,[sP14_prd])],[]) ).
fof(f324,plain,
( sP13_prd
<=> ( ( op(op(e2,e0),e2) != e0
& op(op(e2,e0),e0) = e2
& op(e0,e2) != op(e2,e0) )
| sP14_prd ) ),
inference(formula_renaming,[status(thm)],[f315,f323]) ).
fof(f325,plain,
( ( ( ( op(op(e2,e0),e2) = e0
| op(op(e2,e0),e0) != e2
| op(e0,e2) = op(e2,e0) )
& ~ sP14_prd )
| sP13_prd )
& ( ( op(op(e2,e0),e2) != e0
& op(op(e2,e0),e0) = e2
& op(e0,e2) != op(e2,e0) )
| sP14_prd
| ~ sP13_prd ) ),
inference(NNF_transformation,[status(thm)],[f324]) ).
fof(f326,plain,
( op(e0,e2) != op(e2,e0)
| sP14_prd
| ~ sP13_prd ),
inference(cnf_transformation,[status(thm)],[f325]) ).
fof(f331,definition,
( sP15_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,[sP15_prd])],[]) ).
fof(f332,plain,
( sP14_prd
<=> ( ( op(op(e1,e4),e1) != e4
& op(op(e1,e4),e4) = e1
& op(e4,e1) != op(e1,e4) )
| sP15_prd ) ),
inference(formula_renaming,[status(thm)],[f323,f331]) ).
fof(f333,plain,
( ( ( ( op(op(e1,e4),e1) = e4
| op(op(e1,e4),e4) != e1
| op(e4,e1) = op(e1,e4) )
& ~ sP15_prd )
| sP14_prd )
& ( ( op(op(e1,e4),e1) != e4
& op(op(e1,e4),e4) = e1
& op(e4,e1) != op(e1,e4) )
| sP15_prd
| ~ sP14_prd ) ),
inference(NNF_transformation,[status(thm)],[f332]) ).
fof(f334,plain,
( op(e4,e1) != op(e1,e4)
| sP15_prd
| ~ sP14_prd ),
inference(cnf_transformation,[status(thm)],[f333]) ).
fof(f339,definition,
( sP16_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,[sP16_prd])],[]) ).
fof(f340,plain,
( sP15_prd
<=> ( ( op(op(e1,e3),e1) != e3
& op(op(e1,e3),e3) = e1
& op(e3,e1) != op(e1,e3) )
| sP16_prd ) ),
inference(formula_renaming,[status(thm)],[f331,f339]) ).
fof(f341,plain,
( ( ( ( op(op(e1,e3),e1) = e3
| op(op(e1,e3),e3) != e1
| op(e3,e1) = op(e1,e3) )
& ~ sP16_prd )
| sP15_prd )
& ( ( op(op(e1,e3),e1) != e3
& op(op(e1,e3),e3) = e1
& op(e3,e1) != op(e1,e3) )
| sP16_prd
| ~ sP15_prd ) ),
inference(NNF_transformation,[status(thm)],[f340]) ).
fof(f342,plain,
( op(e3,e1) != op(e1,e3)
| sP16_prd
| ~ sP15_prd ),
inference(cnf_transformation,[status(thm)],[f341]) ).
fof(f347,definition,
( sP17_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,[sP17_prd])],[]) ).
fof(f348,plain,
( sP16_prd
<=> ( ( op(op(e1,e2),e1) != e2
& op(op(e1,e2),e2) = e1
& op(e2,e1) != op(e1,e2) )
| sP17_prd ) ),
inference(formula_renaming,[status(thm)],[f339,f347]) ).
fof(f349,plain,
( ( ( ( op(op(e1,e2),e1) = e2
| op(op(e1,e2),e2) != e1
| op(e2,e1) = op(e1,e2) )
& ~ sP17_prd )
| sP16_prd )
& ( ( op(op(e1,e2),e1) != e2
& op(op(e1,e2),e2) = e1
& op(e2,e1) != op(e1,e2) )
| sP17_prd
| ~ sP16_prd ) ),
inference(NNF_transformation,[status(thm)],[f348]) ).
fof(f351,plain,
( op(op(e1,e2),e2) = e1
| sP17_prd
| ~ sP16_prd ),
inference(cnf_transformation,[status(thm)],[f349]) ).
fof(f355,definition,
( sP18_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,[sP18_prd])],[]) ).
fof(f356,plain,
( sP17_prd
<=> ( ( op(op(e1,e1),e1) != e1
& op(op(e1,e1),e1) = e1
& op(e1,e1) != op(e1,e1) )
| sP18_prd ) ),
inference(formula_renaming,[status(thm)],[f347,f355]) ).
fof(f357,plain,
( ( ( ( op(op(e1,e1),e1) = e1
| op(op(e1,e1),e1) != e1
| op(e1,e1) = op(e1,e1) )
& ~ sP18_prd )
| sP17_prd )
& ( ( op(op(e1,e1),e1) != e1
& op(op(e1,e1),e1) = e1
& op(e1,e1) != op(e1,e1) )
| sP18_prd
| ~ sP17_prd ) ),
inference(NNF_transformation,[status(thm)],[f356]) ).
fof(f358,plain,
( op(e1,e1) != op(e1,e1)
| sP18_prd
| ~ sP17_prd ),
inference(cnf_transformation,[status(thm)],[f357]) ).
fof(f363,definition,
( sP19_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,[sP19_prd])],[]) ).
fof(f364,plain,
( sP18_prd
<=> ( ( op(op(e1,e0),e1) != e0
& op(op(e1,e0),e0) = e1
& op(e0,e1) != op(e1,e0) )
| sP19_prd ) ),
inference(formula_renaming,[status(thm)],[f355,f363]) ).
fof(f365,plain,
( ( ( ( op(op(e1,e0),e1) = e0
| op(op(e1,e0),e0) != e1
| op(e0,e1) = op(e1,e0) )
& ~ sP19_prd )
| sP18_prd )
& ( ( op(op(e1,e0),e1) != e0
& op(op(e1,e0),e0) = e1
& op(e0,e1) != op(e1,e0) )
| sP19_prd
| ~ sP18_prd ) ),
inference(NNF_transformation,[status(thm)],[f364]) ).
fof(f366,plain,
( op(e0,e1) != op(e1,e0)
| sP19_prd
| ~ sP18_prd ),
inference(cnf_transformation,[status(thm)],[f365]) ).
fof(f371,definition,
( sP20_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,[sP20_prd])],[]) ).
fof(f372,plain,
( sP19_prd
<=> ( ( op(op(e0,e4),e0) != e4
& op(op(e0,e4),e4) = e0
& op(e4,e0) != op(e0,e4) )
| sP20_prd ) ),
inference(formula_renaming,[status(thm)],[f363,f371]) ).
fof(f373,plain,
( ( ( ( op(op(e0,e4),e0) = e4
| op(op(e0,e4),e4) != e0
| op(e4,e0) = op(e0,e4) )
& ~ sP20_prd )
| sP19_prd )
& ( ( op(op(e0,e4),e0) != e4
& op(op(e0,e4),e4) = e0
& op(e4,e0) != op(e0,e4) )
| sP20_prd
| ~ sP19_prd ) ),
inference(NNF_transformation,[status(thm)],[f372]) ).
fof(f374,plain,
( op(e4,e0) != op(e0,e4)
| sP20_prd
| ~ sP19_prd ),
inference(cnf_transformation,[status(thm)],[f373]) ).
fof(f379,definition,
( sP21_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,[sP21_prd])],[]) ).
fof(f380,plain,
( sP20_prd
<=> ( ( op(op(e0,e3),e0) != e3
& op(op(e0,e3),e3) = e0
& op(e3,e0) != op(e0,e3) )
| sP21_prd ) ),
inference(formula_renaming,[status(thm)],[f371,f379]) ).
fof(f381,plain,
( ( ( ( op(op(e0,e3),e0) = e3
| op(op(e0,e3),e3) != e0
| op(e3,e0) = op(e0,e3) )
& ~ sP21_prd )
| sP20_prd )
& ( ( op(op(e0,e3),e0) != e3
& op(op(e0,e3),e3) = e0
& op(e3,e0) != op(e0,e3) )
| sP21_prd
| ~ sP20_prd ) ),
inference(NNF_transformation,[status(thm)],[f380]) ).
fof(f383,plain,
( op(op(e0,e3),e3) = e0
| sP21_prd
| ~ sP20_prd ),
inference(cnf_transformation,[status(thm)],[f381]) ).
fof(f387,definition,
( sP22_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,[sP22_prd])],[]) ).
fof(f388,plain,
( sP21_prd
<=> ( ( op(op(e0,e2),e0) != e2
& op(op(e0,e2),e2) = e0
& op(e2,e0) != op(e0,e2) )
| sP22_prd ) ),
inference(formula_renaming,[status(thm)],[f379,f387]) ).
fof(f389,plain,
( ( ( ( op(op(e0,e2),e0) = e2
| op(op(e0,e2),e2) != e0
| op(e2,e0) = op(e0,e2) )
& ~ sP22_prd )
| sP21_prd )
& ( ( op(op(e0,e2),e0) != e2
& op(op(e0,e2),e2) = e0
& op(e2,e0) != op(e0,e2) )
| sP22_prd
| ~ sP21_prd ) ),
inference(NNF_transformation,[status(thm)],[f388]) ).
fof(f391,plain,
( op(op(e0,e2),e2) = e0
| sP22_prd
| ~ sP21_prd ),
inference(cnf_transformation,[status(thm)],[f389]) ).
fof(f395,definition,
( sP23_prd
<=> ( 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(f396,plain,
( sP22_prd
<=> ( ( op(op(e0,e1),e0) != e1
& op(op(e0,e1),e1) = e0
& op(e1,e0) != op(e0,e1) )
| sP23_prd ) ),
inference(formula_renaming,[status(thm)],[f387,f395]) ).
fof(f397,plain,
( ( ( ( op(op(e0,e1),e0) = e1
| op(op(e0,e1),e1) != e0
| op(e1,e0) = op(e0,e1) )
& ~ sP23_prd )
| sP22_prd )
& ( ( op(op(e0,e1),e0) != e1
& op(op(e0,e1),e1) = e0
& op(e1,e0) != op(e0,e1) )
| sP23_prd
| ~ sP22_prd ) ),
inference(NNF_transformation,[status(thm)],[f396]) ).
fof(f398,plain,
( op(e1,e0) != op(e0,e1)
| sP23_prd
| ~ sP22_prd ),
inference(cnf_transformation,[status(thm)],[f397]) ).
fof(f403,plain,
( ( op(op(e0,e0),e0) = e0
| op(op(e0,e0),e0) != e0
| op(e0,e0) = op(e0,e0)
| sP23_prd )
& ( ( op(op(e0,e0),e0) != e0
& op(op(e0,e0),e0) = e0
& op(e0,e0) != op(e0,e0) )
| ~ sP23_prd ) ),
inference(NNF_transformation,[status(thm)],[f395]) ).
fof(f404,plain,
( op(e0,e0) != op(e0,e0)
| ~ sP23_prd ),
inference(cnf_transformation,[status(thm)],[f403]) ).
fof(f408,definition,
( sQ0_spl
<=> op(e0,e0) = e0 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f409,plain,
( ~ sQ0_spl
| op(e0,e0) = e0 ),
inference(component_clause,[status(thm)],[f408]) ).
fof(f411,definition,
( sQ1_spl
<=> op(e0,e0) = e1 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f412,plain,
( ~ sQ1_spl
| op(e0,e0) = e1 ),
inference(component_clause,[status(thm)],[f411]) ).
fof(f414,definition,
( sQ2_spl
<=> op(e0,e0) = e2 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f415,plain,
( ~ sQ2_spl
| op(e0,e0) = e2 ),
inference(component_clause,[status(thm)],[f414]) ).
fof(f417,definition,
( sQ3_spl
<=> op(e0,e0) = e3 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f427,definition,
( sQ6_spl
<=> op(e0,e1) = e1 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f428,plain,
( ~ sQ6_spl
| op(e0,e1) = e1 ),
inference(component_clause,[status(thm)],[f427]) ).
fof(f430,definition,
( sQ7_spl
<=> op(e0,e1) = e2 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f431,plain,
( ~ sQ7_spl
| op(e0,e1) = e2 ),
inference(component_clause,[status(thm)],[f430]) ).
fof(f433,definition,
( sQ8_spl
<=> op(e0,e1) = e3 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f434,plain,
( ~ sQ8_spl
| op(e0,e1) = e3 ),
inference(component_clause,[status(thm)],[f433]) ).
fof(f443,definition,
( sQ11_spl
<=> op(e0,e2) = e1 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f444,plain,
( ~ sQ11_spl
| op(e0,e2) = e1 ),
inference(component_clause,[status(thm)],[f443]) ).
fof(f446,definition,
( sQ12_spl
<=> op(e0,e2) = e2 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f447,plain,
( ~ sQ12_spl
| op(e0,e2) = e2 ),
inference(component_clause,[status(thm)],[f446]) ).
fof(f456,definition,
( sQ15_spl
<=> op(e0,e3) = e0 ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f462,definition,
( sQ17_spl
<=> op(e0,e3) = e2 ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f463,plain,
( ~ sQ17_spl
| op(e0,e3) = e2 ),
inference(component_clause,[status(thm)],[f462]) ).
fof(f465,definition,
( sQ18_spl
<=> op(e0,e3) = e3 ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f466,plain,
( ~ sQ18_spl
| op(e0,e3) = e3 ),
inference(component_clause,[status(thm)],[f465]) ).
fof(f472,definition,
( sQ20_spl
<=> op(e0,e4) = e0 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f473,plain,
( ~ sQ20_spl
| op(e0,e4) = e0 ),
inference(component_clause,[status(thm)],[f472]) ).
fof(f475,definition,
( sQ21_spl
<=> op(e0,e4) = e1 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f478,definition,
( sQ22_spl
<=> op(e0,e4) = e2 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f479,plain,
( ~ sQ22_spl
| op(e0,e4) = e2 ),
inference(component_clause,[status(thm)],[f478]) ).
fof(f484,definition,
( sQ24_spl
<=> op(e0,e4) = e4 ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f485,plain,
( ~ sQ24_spl
| op(e0,e4) = e4 ),
inference(component_clause,[status(thm)],[f484]) ).
fof(f486,plain,
( sQ24_spl
| op(e0,e4) != e4 ),
inference(component_clause,[status(thm)],[f484]) ).
fof(f491,definition,
( sQ26_spl
<=> op(e1,e0) = e1 ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f492,plain,
( ~ sQ26_spl
| op(e1,e0) = e1 ),
inference(component_clause,[status(thm)],[f491]) ).
fof(f494,definition,
( sQ27_spl
<=> op(e1,e0) = e2 ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f495,plain,
( ~ sQ27_spl
| op(e1,e0) = e2 ),
inference(component_clause,[status(thm)],[f494]) ).
fof(f497,definition,
( sQ28_spl
<=> op(e1,e0) = e3 ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f498,plain,
( ~ sQ28_spl
| op(e1,e0) = e3 ),
inference(component_clause,[status(thm)],[f497]) ).
fof(f504,definition,
( sQ30_spl
<=> op(e1,e1) = e0 ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f505,plain,
( ~ sQ30_spl
| op(e1,e1) = e0 ),
inference(component_clause,[status(thm)],[f504]) ).
fof(f507,definition,
( sQ31_spl
<=> op(e1,e1) = e1 ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f508,plain,
( ~ sQ31_spl
| op(e1,e1) = e1 ),
inference(component_clause,[status(thm)],[f507]) ).
fof(f510,definition,
( sQ32_spl
<=> op(e1,e1) = e2 ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f511,plain,
( ~ sQ32_spl
| op(e1,e1) = e2 ),
inference(component_clause,[status(thm)],[f510]) ).
fof(f513,definition,
( sQ33_spl
<=> op(e1,e1) = e3 ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f514,plain,
( ~ sQ33_spl
| op(e1,e1) = e3 ),
inference(component_clause,[status(thm)],[f513]) ).
fof(f516,definition,
( sQ34_spl
<=> op(e1,e1) = e4 ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f519,plain,
( sQ34_spl
| sQ33_spl
| sQ32_spl
| sQ31_spl
| sQ30_spl ),
inference(split_clause,[status(thm)],[f15,f504,f507,f510,f513,f516]) ).
fof(f520,definition,
( sQ35_spl
<=> op(e1,e2) = e0 ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f521,plain,
( ~ sQ35_spl
| op(e1,e2) = e0 ),
inference(component_clause,[status(thm)],[f520]) ).
fof(f522,plain,
( sQ35_spl
| op(e1,e2) != e0 ),
inference(component_clause,[status(thm)],[f520]) ).
fof(f523,definition,
( sQ36_spl
<=> op(e1,e2) = e1 ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f524,plain,
( ~ sQ36_spl
| op(e1,e2) = e1 ),
inference(component_clause,[status(thm)],[f523]) ).
fof(f526,definition,
( sQ37_spl
<=> op(e1,e2) = e2 ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f527,plain,
( ~ sQ37_spl
| op(e1,e2) = e2 ),
inference(component_clause,[status(thm)],[f526]) ).
fof(f529,definition,
( sQ38_spl
<=> op(e1,e2) = e3 ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f530,plain,
( ~ sQ38_spl
| op(e1,e2) = e3 ),
inference(component_clause,[status(thm)],[f529]) ).
fof(f532,definition,
( sQ39_spl
<=> op(e1,e2) = e4 ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f533,plain,
( ~ sQ39_spl
| op(e1,e2) = e4 ),
inference(component_clause,[status(thm)],[f532]) ).
fof(f536,definition,
( sQ40_spl
<=> op(e1,e3) = e0 ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f537,plain,
( ~ sQ40_spl
| op(e1,e3) = e0 ),
inference(component_clause,[status(thm)],[f536]) ).
fof(f539,definition,
( sQ41_spl
<=> op(e1,e3) = e1 ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f540,plain,
( ~ sQ41_spl
| op(e1,e3) = e1 ),
inference(component_clause,[status(thm)],[f539]) ).
fof(f542,definition,
( sQ42_spl
<=> op(e1,e3) = e2 ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f543,plain,
( ~ sQ42_spl
| op(e1,e3) = e2 ),
inference(component_clause,[status(thm)],[f542]) ).
fof(f545,definition,
( sQ43_spl
<=> op(e1,e3) = e3 ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f546,plain,
( ~ sQ43_spl
| op(e1,e3) = e3 ),
inference(component_clause,[status(thm)],[f545]) ).
fof(f552,definition,
( sQ45_spl
<=> op(e1,e4) = e0 ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f553,plain,
( ~ sQ45_spl
| op(e1,e4) = e0 ),
inference(component_clause,[status(thm)],[f552]) ).
fof(f555,definition,
( sQ46_spl
<=> op(e1,e4) = e1 ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f556,plain,
( ~ sQ46_spl
| op(e1,e4) = e1 ),
inference(component_clause,[status(thm)],[f555]) ).
fof(f558,definition,
( sQ47_spl
<=> op(e1,e4) = e2 ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f559,plain,
( ~ sQ47_spl
| op(e1,e4) = e2 ),
inference(component_clause,[status(thm)],[f558]) ).
fof(f561,definition,
( sQ48_spl
<=> op(e1,e4) = e3 ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f562,plain,
( ~ sQ48_spl
| op(e1,e4) = e3 ),
inference(component_clause,[status(thm)],[f561]) ).
fof(f564,definition,
( sQ49_spl
<=> op(e1,e4) = e4 ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f565,plain,
( ~ sQ49_spl
| op(e1,e4) = e4 ),
inference(component_clause,[status(thm)],[f564]) ).
fof(f574,definition,
( sQ52_spl
<=> op(e2,e0) = e2 ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f575,plain,
( ~ sQ52_spl
| op(e2,e0) = e2 ),
inference(component_clause,[status(thm)],[f574]) ).
fof(f577,definition,
( sQ53_spl
<=> op(e2,e0) = e3 ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f578,plain,
( ~ sQ53_spl
| op(e2,e0) = e3 ),
inference(component_clause,[status(thm)],[f577]) ).
fof(f580,definition,
( sQ54_spl
<=> op(e2,e0) = e4 ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f584,definition,
( sQ55_spl
<=> op(e2,e1) = e0 ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f585,plain,
( ~ sQ55_spl
| op(e2,e1) = e0 ),
inference(component_clause,[status(thm)],[f584]) ).
fof(f587,definition,
( sQ56_spl
<=> op(e2,e1) = e1 ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f590,definition,
( sQ57_spl
<=> op(e2,e1) = e2 ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f593,definition,
( sQ58_spl
<=> op(e2,e1) = e3 ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f594,plain,
( ~ sQ58_spl
| op(e2,e1) = e3 ),
inference(component_clause,[status(thm)],[f593]) ).
fof(f596,definition,
( sQ59_spl
<=> op(e2,e1) = e4 ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f597,plain,
( ~ sQ59_spl
| op(e2,e1) = e4 ),
inference(component_clause,[status(thm)],[f596]) ).
fof(f599,plain,
( sQ59_spl
| sQ58_spl
| sQ57_spl
| sQ56_spl
| sQ55_spl ),
inference(split_clause,[status(thm)],[f20,f584,f587,f590,f593,f596]) ).
fof(f600,definition,
( sQ60_spl
<=> op(e2,e2) = e0 ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f601,plain,
( ~ sQ60_spl
| op(e2,e2) = e0 ),
inference(component_clause,[status(thm)],[f600]) ).
fof(f603,definition,
( sQ61_spl
<=> op(e2,e2) = e1 ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f604,plain,
( ~ sQ61_spl
| op(e2,e2) = e1 ),
inference(component_clause,[status(thm)],[f603]) ).
fof(f606,definition,
( sQ62_spl
<=> op(e2,e2) = e2 ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f607,plain,
( ~ sQ62_spl
| op(e2,e2) = e2 ),
inference(component_clause,[status(thm)],[f606]) ).
fof(f609,definition,
( sQ63_spl
<=> op(e2,e2) = e3 ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f612,definition,
( sQ64_spl
<=> op(e2,e2) = e4 ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f613,plain,
( ~ sQ64_spl
| op(e2,e2) = e4 ),
inference(component_clause,[status(thm)],[f612]) ).
fof(f615,plain,
( sQ64_spl
| sQ63_spl
| sQ62_spl
| sQ61_spl
| sQ60_spl ),
inference(split_clause,[status(thm)],[f21,f600,f603,f606,f609,f612]) ).
fof(f616,definition,
( sQ65_spl
<=> op(e2,e3) = e0 ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f617,plain,
( ~ sQ65_spl
| op(e2,e3) = e0 ),
inference(component_clause,[status(thm)],[f616]) ).
fof(f628,definition,
( sQ69_spl
<=> op(e2,e3) = e4 ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f629,plain,
( ~ sQ69_spl
| op(e2,e3) = e4 ),
inference(component_clause,[status(thm)],[f628]) ).
fof(f632,definition,
( sQ70_spl
<=> op(e2,e4) = e0 ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f635,definition,
( sQ71_spl
<=> op(e2,e4) = e1 ),
introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition]) ).
fof(f636,plain,
( ~ sQ71_spl
| op(e2,e4) = e1 ),
inference(component_clause,[status(thm)],[f635]) ).
fof(f644,definition,
( sQ74_spl
<=> op(e2,e4) = e4 ),
introduced(definition,[new_symbols(definition,[sQ74_spl])],[split_symbol_definition]) ).
fof(f645,plain,
( ~ sQ74_spl
| op(e2,e4) = e4 ),
inference(component_clause,[status(thm)],[f644]) ).
fof(f648,definition,
( sQ75_spl
<=> op(e3,e0) = e0 ),
introduced(definition,[new_symbols(definition,[sQ75_spl])],[split_symbol_definition]) ).
fof(f649,plain,
( ~ sQ75_spl
| op(e3,e0) = e0 ),
inference(component_clause,[status(thm)],[f648]) ).
fof(f654,definition,
( sQ77_spl
<=> op(e3,e0) = e2 ),
introduced(definition,[new_symbols(definition,[sQ77_spl])],[split_symbol_definition]) ).
fof(f657,definition,
( sQ78_spl
<=> op(e3,e0) = e3 ),
introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition]) ).
fof(f658,plain,
( ~ sQ78_spl
| op(e3,e0) = e3 ),
inference(component_clause,[status(thm)],[f657]) ).
fof(f670,definition,
( sQ82_spl
<=> op(e3,e1) = e2 ),
introduced(definition,[new_symbols(definition,[sQ82_spl])],[split_symbol_definition]) ).
fof(f671,plain,
( ~ sQ82_spl
| op(e3,e1) = e2 ),
inference(component_clause,[status(thm)],[f670]) ).
fof(f673,definition,
( sQ83_spl
<=> op(e3,e1) = e3 ),
introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition]) ).
fof(f674,plain,
( ~ sQ83_spl
| op(e3,e1) = e3 ),
inference(component_clause,[status(thm)],[f673]) ).
fof(f680,definition,
( sQ85_spl
<=> op(e3,e2) = e0 ),
introduced(definition,[new_symbols(definition,[sQ85_spl])],[split_symbol_definition]) ).
fof(f681,plain,
( ~ sQ85_spl
| op(e3,e2) = e0 ),
inference(component_clause,[status(thm)],[f680]) ).
fof(f683,definition,
( sQ86_spl
<=> op(e3,e2) = e1 ),
introduced(definition,[new_symbols(definition,[sQ86_spl])],[split_symbol_definition]) ).
fof(f686,definition,
( sQ87_spl
<=> op(e3,e2) = e2 ),
introduced(definition,[new_symbols(definition,[sQ87_spl])],[split_symbol_definition]) ).
fof(f689,definition,
( sQ88_spl
<=> op(e3,e2) = e3 ),
introduced(definition,[new_symbols(definition,[sQ88_spl])],[split_symbol_definition]) ).
fof(f690,plain,
( ~ sQ88_spl
| op(e3,e2) = e3 ),
inference(component_clause,[status(thm)],[f689]) ).
fof(f692,definition,
( sQ89_spl
<=> op(e3,e2) = e4 ),
introduced(definition,[new_symbols(definition,[sQ89_spl])],[split_symbol_definition]) ).
fof(f693,plain,
( ~ sQ89_spl
| op(e3,e2) = e4 ),
inference(component_clause,[status(thm)],[f692]) ).
fof(f695,plain,
( sQ89_spl
| sQ88_spl
| sQ87_spl
| sQ86_spl
| sQ85_spl ),
inference(split_clause,[status(thm)],[f26,f680,f683,f686,f689,f692]) ).
fof(f696,definition,
( sQ90_spl
<=> op(e3,e3) = e0 ),
introduced(definition,[new_symbols(definition,[sQ90_spl])],[split_symbol_definition]) ).
fof(f697,plain,
( ~ sQ90_spl
| op(e3,e3) = e0 ),
inference(component_clause,[status(thm)],[f696]) ).
fof(f699,definition,
( sQ91_spl
<=> op(e3,e3) = e1 ),
introduced(definition,[new_symbols(definition,[sQ91_spl])],[split_symbol_definition]) ).
fof(f700,plain,
( ~ sQ91_spl
| op(e3,e3) = e1 ),
inference(component_clause,[status(thm)],[f699]) ).
fof(f702,definition,
( sQ92_spl
<=> op(e3,e3) = e2 ),
introduced(definition,[new_symbols(definition,[sQ92_spl])],[split_symbol_definition]) ).
fof(f703,plain,
( ~ sQ92_spl
| op(e3,e3) = e2 ),
inference(component_clause,[status(thm)],[f702]) ).
fof(f705,definition,
( sQ93_spl
<=> op(e3,e3) = e3 ),
introduced(definition,[new_symbols(definition,[sQ93_spl])],[split_symbol_definition]) ).
fof(f706,plain,
( ~ sQ93_spl
| op(e3,e3) = e3 ),
inference(component_clause,[status(thm)],[f705]) ).
fof(f712,definition,
( sQ95_spl
<=> op(e3,e4) = e0 ),
introduced(definition,[new_symbols(definition,[sQ95_spl])],[split_symbol_definition]) ).
fof(f713,plain,
( ~ sQ95_spl
| op(e3,e4) = e0 ),
inference(component_clause,[status(thm)],[f712]) ).
fof(f715,definition,
( sQ96_spl
<=> op(e3,e4) = e1 ),
introduced(definition,[new_symbols(definition,[sQ96_spl])],[split_symbol_definition]) ).
fof(f718,definition,
( sQ97_spl
<=> op(e3,e4) = e2 ),
introduced(definition,[new_symbols(definition,[sQ97_spl])],[split_symbol_definition]) ).
fof(f719,plain,
( ~ sQ97_spl
| op(e3,e4) = e2 ),
inference(component_clause,[status(thm)],[f718]) ).
fof(f737,definition,
( sQ103_spl
<=> op(e4,e0) = e3 ),
introduced(definition,[new_symbols(definition,[sQ103_spl])],[split_symbol_definition]) ).
fof(f738,plain,
( ~ sQ103_spl
| op(e4,e0) = e3 ),
inference(component_clause,[status(thm)],[f737]) ).
fof(f740,definition,
( sQ104_spl
<=> op(e4,e0) = e4 ),
introduced(definition,[new_symbols(definition,[sQ104_spl])],[split_symbol_definition]) ).
fof(f741,plain,
( ~ sQ104_spl
| op(e4,e0) = e4 ),
inference(component_clause,[status(thm)],[f740]) ).
fof(f742,plain,
( sQ104_spl
| op(e4,e0) != e4 ),
inference(component_clause,[status(thm)],[f740]) ).
fof(f750,definition,
( sQ107_spl
<=> op(e4,e1) = e2 ),
introduced(definition,[new_symbols(definition,[sQ107_spl])],[split_symbol_definition]) ).
fof(f751,plain,
( ~ sQ107_spl
| op(e4,e1) = e2 ),
inference(component_clause,[status(thm)],[f750]) ).
fof(f753,definition,
( sQ108_spl
<=> op(e4,e1) = e3 ),
introduced(definition,[new_symbols(definition,[sQ108_spl])],[split_symbol_definition]) ).
fof(f754,plain,
( ~ sQ108_spl
| op(e4,e1) = e3 ),
inference(component_clause,[status(thm)],[f753]) ).
fof(f763,definition,
( sQ111_spl
<=> op(e4,e2) = e1 ),
introduced(definition,[new_symbols(definition,[sQ111_spl])],[split_symbol_definition]) ).
fof(f764,plain,
( ~ sQ111_spl
| op(e4,e2) = e1 ),
inference(component_clause,[status(thm)],[f763]) ).
fof(f769,definition,
( sQ113_spl
<=> op(e4,e2) = e3 ),
introduced(definition,[new_symbols(definition,[sQ113_spl])],[split_symbol_definition]) ).
fof(f770,plain,
( ~ sQ113_spl
| op(e4,e2) = e3 ),
inference(component_clause,[status(thm)],[f769]) ).
fof(f776,definition,
( sQ115_spl
<=> op(e4,e3) = e0 ),
introduced(definition,[new_symbols(definition,[sQ115_spl])],[split_symbol_definition]) ).
fof(f777,plain,
( ~ sQ115_spl
| op(e4,e3) = e0 ),
inference(component_clause,[status(thm)],[f776]) ).
fof(f792,definition,
( sQ120_spl
<=> op(e4,e4) = e0 ),
introduced(definition,[new_symbols(definition,[sQ120_spl])],[split_symbol_definition]) ).
fof(f793,plain,
( ~ sQ120_spl
| op(e4,e4) = e0 ),
inference(component_clause,[status(thm)],[f792]) ).
fof(f795,definition,
( sQ121_spl
<=> op(e4,e4) = e1 ),
introduced(definition,[new_symbols(definition,[sQ121_spl])],[split_symbol_definition]) ).
fof(f796,plain,
( ~ sQ121_spl
| op(e4,e4) = e1 ),
inference(component_clause,[status(thm)],[f795]) ).
fof(f798,definition,
( sQ122_spl
<=> op(e4,e4) = e2 ),
introduced(definition,[new_symbols(definition,[sQ122_spl])],[split_symbol_definition]) ).
fof(f801,definition,
( sQ123_spl
<=> op(e4,e4) = e3 ),
introduced(definition,[new_symbols(definition,[sQ123_spl])],[split_symbol_definition]) ).
fof(f802,plain,
( ~ sQ123_spl
| op(e4,e4) = e3 ),
inference(component_clause,[status(thm)],[f801]) ).
fof(f804,definition,
( sQ124_spl
<=> op(e4,e4) = e4 ),
introduced(definition,[new_symbols(definition,[sQ124_spl])],[split_symbol_definition]) ).
fof(f805,plain,
( ~ sQ124_spl
| op(e4,e4) = e4 ),
inference(component_clause,[status(thm)],[f804]) ).
fof(f807,plain,
( sQ124_spl
| sQ123_spl
| sQ122_spl
| sQ121_spl
| sQ120_spl ),
inference(split_clause,[status(thm)],[f33,f792,f795,f798,f801,f804]) ).
fof(f808,definition,
( sQ125_spl
<=> unit = e0 ),
introduced(definition,[new_symbols(definition,[sQ125_spl])],[split_symbol_definition]) ).
fof(f809,plain,
( ~ sQ125_spl
| unit = e0 ),
inference(component_clause,[status(thm)],[f808]) ).
fof(f811,definition,
( sQ126_spl
<=> unit = e1 ),
introduced(definition,[new_symbols(definition,[sQ126_spl])],[split_symbol_definition]) ).
fof(f812,plain,
( ~ sQ126_spl
| unit = e1 ),
inference(component_clause,[status(thm)],[f811]) ).
fof(f814,definition,
( sQ127_spl
<=> unit = e2 ),
introduced(definition,[new_symbols(definition,[sQ127_spl])],[split_symbol_definition]) ).
fof(f815,plain,
( ~ sQ127_spl
| unit = e2 ),
inference(component_clause,[status(thm)],[f814]) ).
fof(f817,definition,
( sQ128_spl
<=> unit = e3 ),
introduced(definition,[new_symbols(definition,[sQ128_spl])],[split_symbol_definition]) ).
fof(f818,plain,
( ~ sQ128_spl
| unit = e3 ),
inference(component_clause,[status(thm)],[f817]) ).
fof(f820,definition,
( sQ129_spl
<=> unit = e4 ),
introduced(definition,[new_symbols(definition,[sQ129_spl])],[split_symbol_definition]) ).
fof(f821,plain,
( ~ sQ129_spl
| unit = e4 ),
inference(component_clause,[status(thm)],[f820]) ).
fof(f823,plain,
( sQ129_spl
| sQ128_spl
| sQ127_spl
| sQ126_spl
| sQ125_spl ),
inference(split_clause,[status(thm)],[f44,f808,f811,f814,f817,f820]) ).
fof(f828,plain,
( sQ22_spl
| sQ17_spl
| sQ12_spl
| sQ7_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f49,f414,f430,f446,f462,f478]) ).
fof(f831,plain,
( sQ103_spl
| sQ78_spl
| sQ53_spl
| sQ28_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f52,f417,f497,f577,f657,f737]) ).
fof(f838,plain,
( sQ47_spl
| sQ42_spl
| sQ37_spl
| sQ32_spl
| sQ27_spl ),
inference(split_clause,[status(thm)],[f59,f494,f510,f526,f542,f558]) ).
fof(f840,plain,
( sQ48_spl
| sQ43_spl
| sQ38_spl
| sQ33_spl
| sQ28_spl ),
inference(split_clause,[status(thm)],[f61,f497,f513,f529,f545,f561]) ).
fof(f841,plain,
( sQ108_spl
| sQ83_spl
| sQ58_spl
| sQ33_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f62,f433,f513,f593,f673,f753]) ).
fof(f847,plain,
( sQ111_spl
| sQ86_spl
| sQ61_spl
| sQ36_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f68,f443,f523,f603,f683,f763]) ).
fof(f852,plain,
( sQ74_spl
| sQ69_spl
| sQ64_spl
| sQ59_spl
| sQ54_spl ),
inference(split_clause,[status(thm)],[f73,f580,f596,f612,f628,f644]) ).
fof(f855,plain,
( sQ115_spl
| sQ90_spl
| sQ65_spl
| sQ40_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f76,f456,f536,f616,f696,f776]) ).
fof(f858,plain,
( sQ97_spl
| sQ92_spl
| sQ87_spl
| sQ82_spl
| sQ77_spl ),
inference(split_clause,[status(thm)],[f79,f654,f670,f686,f702,f718]) ).
fof(f865,plain,
( sQ120_spl
| sQ95_spl
| sQ70_spl
| sQ45_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f86,f472,f552,f632,f712,f792]) ).
fof(f867,plain,
( sQ121_spl
| sQ96_spl
| sQ71_spl
| sQ46_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f88,f475,f555,f635,f715,f795]) ).
fof(f874,plain,
( sQ120_spl
| sQ90_spl
| sQ60_spl
| sQ30_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f211,f408,f504,f600,f696,f792]) ).
fof(f875,plain,
( sQ121_spl
| sQ91_spl
| sQ61_spl
| sQ31_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f212,f411,f507,f603,f699,f795]) ).
fof(f879,definition,
( sQ130_spl
<=> sP0_prd ),
introduced(definition,[new_symbols(definition,[sQ130_spl])],[split_symbol_definition]) ).
fof(f886,definition,
( sQ132_spl
<=> op(op(e4,e4),e4) = e4 ),
introduced(definition,[new_symbols(definition,[sQ132_spl])],[split_symbol_definition]) ).
fof(f887,plain,
( ~ sQ132_spl
| op(op(e4,e4),e4) = e4 ),
inference(component_clause,[status(thm)],[f886]) ).
fof(f889,plain,
( sQ132_spl
| sQ130_spl ),
inference(split_clause,[status(thm)],[f217,f879,f886]) ).
fof(f891,definition,
( sQ133_spl
<=> sP1_prd ),
introduced(definition,[new_symbols(definition,[sQ133_spl])],[split_symbol_definition]) ).
fof(f894,definition,
( sQ134_spl
<=> op(e3,e4) = op(e4,e3) ),
introduced(definition,[new_symbols(definition,[sQ134_spl])],[split_symbol_definition]) ).
fof(f896,plain,
( sQ134_spl
| op(e3,e4) != op(e4,e3) ),
inference(component_clause,[status(thm)],[f894]) ).
fof(f898,definition,
( sQ135_spl
<=> op(op(e4,e3),e3) = e4 ),
introduced(definition,[new_symbols(definition,[sQ135_spl])],[split_symbol_definition]) ).
fof(f899,plain,
( ~ sQ135_spl
| op(op(e4,e3),e3) = e4 ),
inference(component_clause,[status(thm)],[f898]) ).
fof(f901,plain,
( sQ135_spl
| sQ133_spl
| ~ sQ130_spl ),
inference(split_clause,[status(thm)],[f223,f879,f891,f898]) ).
fof(f908,definition,
( sQ137_spl
<=> sP2_prd ),
introduced(definition,[new_symbols(definition,[sQ137_spl])],[split_symbol_definition]) ).
fof(f911,definition,
( sQ138_spl
<=> op(e2,e4) = op(e4,e2) ),
introduced(definition,[new_symbols(definition,[sQ138_spl])],[split_symbol_definition]) ).
fof(f913,plain,
( sQ138_spl
| op(e2,e4) != op(e4,e2) ),
inference(component_clause,[status(thm)],[f911]) ).
fof(f915,definition,
( sQ139_spl
<=> op(op(e4,e2),e2) = e4 ),
introduced(definition,[new_symbols(definition,[sQ139_spl])],[split_symbol_definition]) ).
fof(f916,plain,
( ~ sQ139_spl
| op(op(e4,e2),e2) = e4 ),
inference(component_clause,[status(thm)],[f915]) ).
fof(f918,plain,
( sQ139_spl
| sQ137_spl
| ~ sQ133_spl ),
inference(split_clause,[status(thm)],[f231,f891,f908,f915]) ).
fof(f925,definition,
( sQ141_spl
<=> sP3_prd ),
introduced(definition,[new_symbols(definition,[sQ141_spl])],[split_symbol_definition]) ).
fof(f928,definition,
( sQ142_spl
<=> op(e1,e4) = op(e4,e1) ),
introduced(definition,[new_symbols(definition,[sQ142_spl])],[split_symbol_definition]) ).
fof(f930,plain,
( sQ142_spl
| op(e1,e4) != op(e4,e1) ),
inference(component_clause,[status(thm)],[f928]) ).
fof(f932,definition,
( sQ143_spl
<=> op(op(e4,e1),e1) = e4 ),
introduced(definition,[new_symbols(definition,[sQ143_spl])],[split_symbol_definition]) ).
fof(f933,plain,
( ~ sQ143_spl
| op(op(e4,e1),e1) = e4 ),
inference(component_clause,[status(thm)],[f932]) ).
fof(f935,plain,
( sQ143_spl
| sQ141_spl
| ~ sQ137_spl ),
inference(split_clause,[status(thm)],[f239,f908,f925,f932]) ).
fof(f942,definition,
( sQ145_spl
<=> sP4_prd ),
introduced(definition,[new_symbols(definition,[sQ145_spl])],[split_symbol_definition]) ).
fof(f945,definition,
( sQ146_spl
<=> op(e0,e4) = op(e4,e0) ),
introduced(definition,[new_symbols(definition,[sQ146_spl])],[split_symbol_definition]) ).
fof(f947,plain,
( sQ146_spl
| op(e0,e4) != op(e4,e0) ),
inference(component_clause,[status(thm)],[f945]) ).
fof(f948,plain,
( ~ sQ146_spl
| sQ145_spl
| ~ sQ141_spl ),
inference(split_clause,[status(thm)],[f246,f925,f942,f945]) ).
fof(f959,definition,
( sQ149_spl
<=> sP5_prd ),
introduced(definition,[new_symbols(definition,[sQ149_spl])],[split_symbol_definition]) ).
fof(f962,plain,
( ~ sQ134_spl
| sQ149_spl
| ~ sQ145_spl ),
inference(split_clause,[status(thm)],[f254,f942,f959,f894]) ).
fof(f973,definition,
( sQ152_spl
<=> sP6_prd ),
introduced(definition,[new_symbols(definition,[sQ152_spl])],[split_symbol_definition]) ).
fof(f980,definition,
( sQ154_spl
<=> op(op(e3,e3),e3) = e3 ),
introduced(definition,[new_symbols(definition,[sQ154_spl])],[split_symbol_definition]) ).
fof(f983,plain,
( sQ154_spl
| sQ152_spl
| ~ sQ149_spl ),
inference(split_clause,[status(thm)],[f263,f959,f973,f980]) ).
fof(f984,plain,
( ~ sQ154_spl
| sQ152_spl
| ~ sQ149_spl ),
inference(split_clause,[status(thm)],[f264,f959,f973,f980]) ).
fof(f987,definition,
( sQ155_spl
<=> sP7_prd ),
introduced(definition,[new_symbols(definition,[sQ155_spl])],[split_symbol_definition]) ).
fof(f990,definition,
( sQ156_spl
<=> op(e2,e3) = op(e3,e2) ),
introduced(definition,[new_symbols(definition,[sQ156_spl])],[split_symbol_definition]) ).
fof(f992,plain,
( sQ156_spl
| op(e2,e3) != op(e3,e2) ),
inference(component_clause,[status(thm)],[f990]) ).
fof(f993,plain,
( ~ sQ156_spl
| sQ155_spl
| ~ sQ152_spl ),
inference(split_clause,[status(thm)],[f270,f973,f987,f990]) ).
fof(f1004,definition,
( sQ159_spl
<=> sP8_prd ),
introduced(definition,[new_symbols(definition,[sQ159_spl])],[split_symbol_definition]) ).
fof(f1007,definition,
( sQ160_spl
<=> op(e1,e3) = op(e3,e1) ),
introduced(definition,[new_symbols(definition,[sQ160_spl])],[split_symbol_definition]) ).
fof(f1009,plain,
( sQ160_spl
| op(e1,e3) != op(e3,e1) ),
inference(component_clause,[status(thm)],[f1007]) ).
fof(f1010,plain,
( ~ sQ160_spl
| sQ159_spl
| ~ sQ155_spl ),
inference(split_clause,[status(thm)],[f278,f987,f1004,f1007]) ).
fof(f1021,definition,
( sQ163_spl
<=> sP9_prd ),
introduced(definition,[new_symbols(definition,[sQ163_spl])],[split_symbol_definition]) ).
fof(f1024,definition,
( sQ164_spl
<=> op(e0,e3) = op(e3,e0) ),
introduced(definition,[new_symbols(definition,[sQ164_spl])],[split_symbol_definition]) ).
fof(f1026,plain,
( sQ164_spl
| op(e0,e3) != op(e3,e0) ),
inference(component_clause,[status(thm)],[f1024]) ).
fof(f1027,plain,
( ~ sQ164_spl
| sQ163_spl
| ~ sQ159_spl ),
inference(split_clause,[status(thm)],[f286,f1004,f1021,f1024]) ).
fof(f1038,definition,
( sQ167_spl
<=> sP10_prd ),
introduced(definition,[new_symbols(definition,[sQ167_spl])],[split_symbol_definition]) ).
fof(f1041,plain,
( ~ sQ138_spl
| sQ167_spl
| ~ sQ163_spl ),
inference(split_clause,[status(thm)],[f294,f1021,f1038,f911]) ).
fof(f1052,definition,
( sQ170_spl
<=> sP11_prd ),
introduced(definition,[new_symbols(definition,[sQ170_spl])],[split_symbol_definition]) ).
fof(f1055,plain,
( ~ sQ156_spl
| sQ170_spl
| ~ sQ167_spl ),
inference(split_clause,[status(thm)],[f302,f1038,f1052,f990]) ).
fof(f1066,definition,
( sQ173_spl
<=> sP12_prd ),
introduced(definition,[new_symbols(definition,[sQ173_spl])],[split_symbol_definition]) ).
fof(f1069,definition,
( sQ174_spl
<=> op(e2,e2) = op(e2,e2) ),
introduced(definition,[new_symbols(definition,[sQ174_spl])],[split_symbol_definition]) ).
fof(f1071,plain,
( sQ174_spl
| op(e2,e2) != op(e2,e2) ),
inference(component_clause,[status(thm)],[f1069]) ).
fof(f1072,plain,
( ~ sQ174_spl
| sQ173_spl
| ~ sQ170_spl ),
inference(split_clause,[status(thm)],[f310,f1052,f1066,f1069]) ).
fof(f1080,definition,
( sQ176_spl
<=> sP13_prd ),
introduced(definition,[new_symbols(definition,[sQ176_spl])],[split_symbol_definition]) ).
fof(f1083,definition,
( sQ177_spl
<=> op(e1,e2) = op(e2,e1) ),
introduced(definition,[new_symbols(definition,[sQ177_spl])],[split_symbol_definition]) ).
fof(f1085,plain,
( sQ177_spl
| op(e1,e2) != op(e2,e1) ),
inference(component_clause,[status(thm)],[f1083]) ).
fof(f1086,plain,
( ~ sQ177_spl
| sQ176_spl
| ~ sQ173_spl ),
inference(split_clause,[status(thm)],[f318,f1066,f1080,f1083]) ).
fof(f1097,definition,
( sQ180_spl
<=> sP14_prd ),
introduced(definition,[new_symbols(definition,[sQ180_spl])],[split_symbol_definition]) ).
fof(f1100,definition,
( sQ181_spl
<=> op(e0,e2) = op(e2,e0) ),
introduced(definition,[new_symbols(definition,[sQ181_spl])],[split_symbol_definition]) ).
fof(f1102,plain,
( sQ181_spl
| op(e0,e2) != op(e2,e0) ),
inference(component_clause,[status(thm)],[f1100]) ).
fof(f1103,plain,
( ~ sQ181_spl
| sQ180_spl
| ~ sQ176_spl ),
inference(split_clause,[status(thm)],[f326,f1080,f1097,f1100]) ).
fof(f1114,definition,
( sQ184_spl
<=> sP15_prd ),
introduced(definition,[new_symbols(definition,[sQ184_spl])],[split_symbol_definition]) ).
fof(f1117,plain,
( ~ sQ142_spl
| sQ184_spl
| ~ sQ180_spl ),
inference(split_clause,[status(thm)],[f334,f1097,f1114,f928]) ).
fof(f1128,definition,
( sQ187_spl
<=> sP16_prd ),
introduced(definition,[new_symbols(definition,[sQ187_spl])],[split_symbol_definition]) ).
fof(f1131,plain,
( ~ sQ160_spl
| sQ187_spl
| ~ sQ184_spl ),
inference(split_clause,[status(thm)],[f342,f1114,f1128,f1007]) ).
fof(f1142,definition,
( sQ190_spl
<=> sP17_prd ),
introduced(definition,[new_symbols(definition,[sQ190_spl])],[split_symbol_definition]) ).
fof(f1146,definition,
( sQ191_spl
<=> op(op(e1,e2),e2) = e1 ),
introduced(definition,[new_symbols(definition,[sQ191_spl])],[split_symbol_definition]) ).
fof(f1147,plain,
( ~ sQ191_spl
| op(op(e1,e2),e2) = e1 ),
inference(component_clause,[status(thm)],[f1146]) ).
fof(f1149,plain,
( sQ191_spl
| sQ190_spl
| ~ sQ187_spl ),
inference(split_clause,[status(thm)],[f351,f1128,f1142,f1146]) ).
fof(f1156,definition,
( sQ193_spl
<=> sP18_prd ),
introduced(definition,[new_symbols(definition,[sQ193_spl])],[split_symbol_definition]) ).
fof(f1159,definition,
( sQ194_spl
<=> op(e1,e1) = op(e1,e1) ),
introduced(definition,[new_symbols(definition,[sQ194_spl])],[split_symbol_definition]) ).
fof(f1161,plain,
( sQ194_spl
| op(e1,e1) != op(e1,e1) ),
inference(component_clause,[status(thm)],[f1159]) ).
fof(f1162,plain,
( ~ sQ194_spl
| sQ193_spl
| ~ sQ190_spl ),
inference(split_clause,[status(thm)],[f358,f1142,f1156,f1159]) ).
fof(f1170,definition,
( sQ196_spl
<=> sP19_prd ),
introduced(definition,[new_symbols(definition,[sQ196_spl])],[split_symbol_definition]) ).
fof(f1173,definition,
( sQ197_spl
<=> op(e0,e1) = op(e1,e0) ),
introduced(definition,[new_symbols(definition,[sQ197_spl])],[split_symbol_definition]) ).
fof(f1174,plain,
( ~ sQ197_spl
| op(e0,e1) = op(e1,e0) ),
inference(component_clause,[status(thm)],[f1173]) ).
fof(f1175,plain,
( sQ197_spl
| op(e0,e1) != op(e1,e0) ),
inference(component_clause,[status(thm)],[f1173]) ).
fof(f1176,plain,
( ~ sQ197_spl
| sQ196_spl
| ~ sQ193_spl ),
inference(split_clause,[status(thm)],[f366,f1156,f1170,f1173]) ).
fof(f1187,definition,
( sQ200_spl
<=> sP20_prd ),
introduced(definition,[new_symbols(definition,[sQ200_spl])],[split_symbol_definition]) ).
fof(f1190,plain,
( ~ sQ146_spl
| sQ200_spl
| ~ sQ196_spl ),
inference(split_clause,[status(thm)],[f374,f1170,f1187,f945]) ).
fof(f1201,definition,
( sQ203_spl
<=> sP21_prd ),
introduced(definition,[new_symbols(definition,[sQ203_spl])],[split_symbol_definition]) ).
fof(f1205,definition,
( sQ204_spl
<=> op(op(e0,e3),e3) = e0 ),
introduced(definition,[new_symbols(definition,[sQ204_spl])],[split_symbol_definition]) ).
fof(f1206,plain,
( ~ sQ204_spl
| op(op(e0,e3),e3) = e0 ),
inference(component_clause,[status(thm)],[f1205]) ).
fof(f1208,plain,
( sQ204_spl
| sQ203_spl
| ~ sQ200_spl ),
inference(split_clause,[status(thm)],[f383,f1187,f1201,f1205]) ).
fof(f1215,definition,
( sQ206_spl
<=> sP22_prd ),
introduced(definition,[new_symbols(definition,[sQ206_spl])],[split_symbol_definition]) ).
fof(f1219,definition,
( sQ207_spl
<=> op(op(e0,e2),e2) = e0 ),
introduced(definition,[new_symbols(definition,[sQ207_spl])],[split_symbol_definition]) ).
fof(f1220,plain,
( ~ sQ207_spl
| op(op(e0,e2),e2) = e0 ),
inference(component_clause,[status(thm)],[f1219]) ).
fof(f1222,plain,
( sQ207_spl
| sQ206_spl
| ~ sQ203_spl ),
inference(split_clause,[status(thm)],[f391,f1201,f1215,f1219]) ).
fof(f1229,definition,
( sQ209_spl
<=> sP23_prd ),
introduced(definition,[new_symbols(definition,[sQ209_spl])],[split_symbol_definition]) ).
fof(f1232,plain,
( ~ sQ197_spl
| sQ209_spl
| ~ sQ206_spl ),
inference(split_clause,[status(thm)],[f398,f1215,f1229,f1173]) ).
fof(f1243,definition,
( sQ212_spl
<=> op(e0,e0) = op(e0,e0) ),
introduced(definition,[new_symbols(definition,[sQ212_spl])],[split_symbol_definition]) ).
fof(f1245,plain,
( sQ212_spl
| op(e0,e0) != op(e0,e0) ),
inference(component_clause,[status(thm)],[f1243]) ).
fof(f1246,plain,
( ~ sQ212_spl
| ~ sQ209_spl ),
inference(split_clause,[status(thm)],[f404,f1229,f1243]) ).
fof(f1253,plain,
e0 = op(e1,e2),
inference(backward_demodulation,[status(thm)],[f206,f205]) ).
fof(f1254,plain,
e3 = op(e2,op(op(e1,e1),op(e1,e1))),
inference(forward_demodulation,[status(thm)],[f206,f207]) ).
fof(f1257,plain,
op(e2,e1) != e3,
inference(backward_demodulation,[status(thm)],[f1263,f169]) ).
fof(f1258,plain,
op(e2,e0) != e3,
inference(backward_demodulation,[status(thm)],[f1263,f166]) ).
fof(f1259,plain,
e3 != op(e4,e2),
inference(backward_demodulation,[status(thm)],[f1263,f123]) ).
fof(f1263,plain,
e3 = op(e2,e2),
inference(forward_demodulation,[status(thm)],[f206,f1254]) ).
fof(f1264,plain,
e2 = op(op(e1,e1),e4),
inference(backward_demodulation,[status(thm)],[f208,f206]) ).
fof(f1265,plain,
e4 != op(e1,e4),
inference(backward_demodulation,[status(thm)],[f208,f161]) ).
fof(f1269,plain,
e4 != op(e4,e1),
inference(backward_demodulation,[status(thm)],[f208,f111]) ).
fof(f1271,plain,
e4 != op(e2,e1),
inference(backward_demodulation,[status(thm)],[f208,f109]) ).
fof(f1289,plain,
( ~ sQ64_spl
| e3 = e4 ),
inference(forward_demodulation,[status(thm)],[f1263,f613]) ).
fof(f1290,plain,
( ~ sQ64_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1289,f204]) ).
fof(f1291,plain,
~ sQ64_spl,
inference(contradiction_clause,[status(thm)],[f1290]) ).
fof(f1306,plain,
( ~ sQ33_spl
| e4 = e3 ),
inference(forward_demodulation,[status(thm)],[f208,f514]) ).
fof(f1307,plain,
( ~ sQ33_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1306,f204]) ).
fof(f1308,plain,
~ sQ33_spl,
inference(contradiction_clause,[status(thm)],[f1307]) ).
fof(f1312,plain,
( ~ sQ62_spl
| e3 = e2 ),
inference(forward_demodulation,[status(thm)],[f1263,f607]) ).
fof(f1313,plain,
( ~ sQ62_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1312,f202]) ).
fof(f1314,plain,
~ sQ62_spl,
inference(contradiction_clause,[status(thm)],[f1313]) ).
fof(f1315,plain,
( ~ sQ32_spl
| e4 = e2 ),
inference(forward_demodulation,[status(thm)],[f208,f511]) ).
fof(f1316,plain,
( ~ sQ32_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1315,f203]) ).
fof(f1317,plain,
~ sQ32_spl,
inference(contradiction_clause,[status(thm)],[f1316]) ).
fof(f1321,plain,
( ~ sQ91_spl
| ~ sQ92_spl
| e2 = e1 ),
inference(forward_demodulation,[status(thm)],[f703,f700]) ).
fof(f1322,plain,
( ~ sQ91_spl
| ~ sQ92_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1321,f199]) ).
fof(f1323,plain,
( ~ sQ91_spl
| ~ sQ92_spl ),
inference(contradiction_clause,[status(thm)],[f1322]) ).
fof(f1324,plain,
( ~ sQ61_spl
| e3 = e1 ),
inference(forward_demodulation,[status(thm)],[f1263,f604]) ).
fof(f1325,plain,
( ~ sQ61_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1324,f200]) ).
fof(f1326,plain,
~ sQ61_spl,
inference(contradiction_clause,[status(thm)],[f1325]) ).
fof(f1327,plain,
( ~ sQ31_spl
| e4 = e1 ),
inference(forward_demodulation,[status(thm)],[f208,f508]) ).
fof(f1328,plain,
( ~ sQ31_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1327,f201]) ).
fof(f1329,plain,
~ sQ31_spl,
inference(contradiction_clause,[status(thm)],[f1328]) ).
fof(f1333,plain,
( ~ sQ60_spl
| e3 = e0 ),
inference(forward_demodulation,[status(thm)],[f1263,f601]) ).
fof(f1334,plain,
( ~ sQ60_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1333,f197]) ).
fof(f1335,plain,
~ sQ60_spl,
inference(contradiction_clause,[status(thm)],[f1334]) ).
fof(f1336,plain,
( ~ sQ30_spl
| e4 = e0 ),
inference(forward_demodulation,[status(thm)],[f208,f505]) ).
fof(f1337,plain,
( ~ sQ30_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1336,f198]) ).
fof(f1338,plain,
~ sQ30_spl,
inference(contradiction_clause,[status(thm)],[f1337]) ).
fof(f1349,plain,
( ~ sQ74_spl
| op(e0,e4) != e4 ),
inference(backward_demodulation,[status(thm)],[f645,f136]) ).
fof(f1373,plain,
( ~ sQ104_spl
| op(e2,e0) != e4 ),
inference(backward_demodulation,[status(thm)],[f741,f103]) ).
fof(f1396,plain,
( ~ sQ103_spl
| ~ sQ104_spl
| e4 = e3 ),
inference(forward_demodulation,[status(thm)],[f741,f738]) ).
fof(f1397,plain,
( ~ sQ103_spl
| ~ sQ104_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1396,f204]) ).
fof(f1398,plain,
( ~ sQ103_spl
| ~ sQ104_spl ),
inference(contradiction_clause,[status(thm)],[f1397]) ).
fof(f1462,plain,
( ~ sQ41_spl
| ~ sQ42_spl
| e2 = e1 ),
inference(forward_demodulation,[status(thm)],[f543,f540]) ).
fof(f1463,plain,
( ~ sQ41_spl
| ~ sQ42_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1462,f199]) ).
fof(f1464,plain,
( ~ sQ41_spl
| ~ sQ42_spl ),
inference(contradiction_clause,[status(thm)],[f1463]) ).
fof(f1498,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| e2 = e1 ),
inference(forward_demodulation,[status(thm)],[f447,f444]) ).
fof(f1499,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1498,f199]) ).
fof(f1500,plain,
( ~ sQ11_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f1499]) ).
fof(f1513,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| e2 = e1 ),
inference(forward_demodulation,[status(thm)],[f431,f428]) ).
fof(f1514,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1513,f199]) ).
fof(f1515,plain,
( ~ sQ6_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f1514]) ).
fof(f1516,plain,
( ~ sQ26_spl
| ~ sQ27_spl
| e2 = e1 ),
inference(forward_demodulation,[status(thm)],[f495,f492]) ).
fof(f1517,plain,
( ~ sQ26_spl
| ~ sQ27_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1516,f199]) ).
fof(f1518,plain,
( ~ sQ26_spl
| ~ sQ27_spl ),
inference(contradiction_clause,[status(thm)],[f1517]) ).
fof(f1519,plain,
( sQ194_spl
| e4 != op(e1,e1) ),
inference(forward_demodulation,[status(thm)],[f208,f1161]) ).
fof(f1520,plain,
( sQ194_spl
| e4 != e4 ),
inference(forward_demodulation,[status(thm)],[f208,f1519]) ).
fof(f1521,plain,
( sQ194_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1520]) ).
fof(f1522,plain,
sQ194_spl,
inference(contradiction_clause,[status(thm)],[f1521]) ).
fof(f1523,plain,
( sQ174_spl
| e3 != op(e2,e2) ),
inference(forward_demodulation,[status(thm)],[f1263,f1071]) ).
fof(f1524,plain,
( sQ174_spl
| e3 != e3 ),
inference(forward_demodulation,[status(thm)],[f1263,f1523]) ).
fof(f1525,plain,
( sQ174_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1524]) ).
fof(f1526,plain,
sQ174_spl,
inference(contradiction_clause,[status(thm)],[f1525]) ).
fof(f1535,plain,
( sQ212_spl
| ~ sQ0_spl
| e0 != op(e0,e0) ),
inference(forward_demodulation,[status(thm)],[f409,f1245]) ).
fof(f1536,plain,
( sQ212_spl
| ~ sQ0_spl
| e0 != e0 ),
inference(forward_demodulation,[status(thm)],[f409,f1535]) ).
fof(f1537,plain,
( sQ212_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1536]) ).
fof(f1538,plain,
( sQ212_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f1537]) ).
fof(f1543,plain,
( ~ sQ129_spl
| op(e2,e4) = e2 ),
inference(backward_demodulation,[status(thm)],[f821,f39]) ).
fof(f1558,plain,
e2 = op(e4,e4),
inference(forward_demodulation,[status(thm)],[f208,f1264]) ).
fof(f1598,plain,
( ~ sQ75_spl
| op(e0,e0) != e0 ),
inference(forward_demodulation,[status(thm)],[f649,f97]) ).
fof(f1613,plain,
( ~ sQ85_spl
| e0 != op(e3,e4) ),
inference(forward_demodulation,[status(thm)],[f681,f183]) ).
fof(f1614,plain,
( ~ sQ85_spl
| ~ sQ95_spl
| e0 != e0 ),
inference(forward_demodulation,[status(thm)],[f713,f1613]) ).
fof(f1615,plain,
( ~ sQ85_spl
| ~ sQ95_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1614]) ).
fof(f1616,plain,
( ~ sQ85_spl
| ~ sQ95_spl ),
inference(contradiction_clause,[status(thm)],[f1615]) ).
fof(f1642,plain,
( ~ sQ124_spl
| e2 = e4 ),
inference(forward_demodulation,[status(thm)],[f1558,f805]) ).
fof(f1643,plain,
( ~ sQ124_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1642,f203]) ).
fof(f1644,plain,
~ sQ124_spl,
inference(contradiction_clause,[status(thm)],[f1643]) ).
fof(f1687,plain,
( ~ sQ55_spl
| e0 != op(e2,e3) ),
inference(forward_demodulation,[status(thm)],[f585,f170]) ).
fof(f1688,plain,
( ~ sQ55_spl
| ~ sQ65_spl
| e0 != e0 ),
inference(forward_demodulation,[status(thm)],[f617,f1687]) ).
fof(f1689,plain,
( ~ sQ55_spl
| ~ sQ65_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1688]) ).
fof(f1690,plain,
( ~ sQ55_spl
| ~ sQ65_spl ),
inference(contradiction_clause,[status(thm)],[f1689]) ).
fof(f1694,plain,
( ~ sQ35_spl
| e0 != op(e1,e3) ),
inference(forward_demodulation,[status(thm)],[f521,f162]) ).
fof(f1695,plain,
( ~ sQ35_spl
| ~ sQ40_spl
| e0 != e0 ),
inference(forward_demodulation,[status(thm)],[f537,f1694]) ).
fof(f1696,plain,
( ~ sQ35_spl
| ~ sQ40_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1695]) ).
fof(f1697,plain,
( ~ sQ35_spl
| ~ sQ40_spl ),
inference(contradiction_clause,[status(thm)],[f1696]) ).
fof(f1757,plain,
( sQ197_spl
| ~ sQ6_spl
| e1 != op(e1,e0) ),
inference(forward_demodulation,[status(thm)],[f428,f1175]) ).
fof(f1758,plain,
( sQ197_spl
| ~ sQ6_spl
| ~ sQ26_spl
| e1 != e1 ),
inference(forward_demodulation,[status(thm)],[f492,f1757]) ).
fof(f1759,plain,
( sQ197_spl
| ~ sQ6_spl
| ~ sQ26_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1758]) ).
fof(f1760,plain,
( sQ197_spl
| ~ sQ6_spl
| ~ sQ26_spl ),
inference(contradiction_clause,[status(thm)],[f1759]) ).
fof(f1762,plain,
( ~ sQ125_spl
| op(e4,e0) = e4 ),
inference(forward_demodulation,[status(thm)],[f809,f43]) ).
fof(f1763,plain,
( ~ sQ125_spl
| sQ104_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1762,f742]) ).
fof(f1764,plain,
( ~ sQ125_spl
| sQ104_spl ),
inference(contradiction_clause,[status(thm)],[f1763]) ).
fof(f1765,plain,
( ~ sQ125_spl
| op(e0,e4) = e4 ),
inference(forward_demodulation,[status(thm)],[f809,f42]) ).
fof(f1766,plain,
( ~ sQ125_spl
| sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1765,f486]) ).
fof(f1767,plain,
( ~ sQ125_spl
| sQ24_spl ),
inference(contradiction_clause,[status(thm)],[f1766]) ).
fof(f1774,plain,
op(e2,e4) != e2,
inference(forward_demodulation,[status(thm)],[f1558,f143]) ).
fof(f1780,plain,
op(e1,e4) != e2,
inference(forward_demodulation,[status(thm)],[f1558,f141]) ).
fof(f1781,plain,
( ~ sQ123_spl
| e2 = e3 ),
inference(forward_demodulation,[status(thm)],[f1558,f802]) ).
fof(f1782,plain,
( ~ sQ123_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1781,f202]) ).
fof(f1783,plain,
~ sQ123_spl,
inference(contradiction_clause,[status(thm)],[f1782]) ).
fof(f1792,plain,
op(e4,e1) != e2,
inference(forward_demodulation,[status(thm)],[f1558,f191]) ).
fof(f1799,plain,
e0 != op(e1,e4),
inference(backward_demodulation,[status(thm)],[f1253,f163]) ).
fof(f1804,plain,
( sQ35_spl
| e0 != e0 ),
inference(forward_demodulation,[status(thm)],[f1253,f522]) ).
fof(f1805,plain,
( sQ35_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1804]) ).
fof(f1806,plain,
sQ35_spl,
inference(contradiction_clause,[status(thm)],[f1805]) ).
fof(f1838,plain,
( ~ sQ37_spl
| e0 = e2 ),
inference(forward_demodulation,[status(thm)],[f1253,f527]) ).
fof(f1839,plain,
( ~ sQ37_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1838,f196]) ).
fof(f1840,plain,
~ sQ37_spl,
inference(contradiction_clause,[status(thm)],[f1839]) ).
fof(f1846,plain,
( ~ sQ6_spl
| e1 != op(e0,e4) ),
inference(forward_demodulation,[status(thm)],[f428,f151]) ).
fof(f1847,plain,
( ~ sQ1_spl
| e1 != op(e0,e1) ),
inference(forward_demodulation,[status(thm)],[f412,f145]) ).
fof(f1848,plain,
( ~ sQ1_spl
| ~ sQ6_spl
| e1 != e1 ),
inference(forward_demodulation,[status(thm)],[f428,f1847]) ).
fof(f1849,plain,
( ~ sQ1_spl
| ~ sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1848]) ).
fof(f1850,plain,
( ~ sQ1_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f1849]) ).
fof(f1902,plain,
( ~ sQ126_spl
| op(e4,e1) = e4 ),
inference(backward_demodulation,[status(thm)],[f812,f43]) ).
fof(f1915,plain,
op(e3,e4) != e2,
inference(forward_demodulation,[status(thm)],[f1558,f144]) ).
fof(f1927,plain,
( ~ sQ49_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f565,f1265]) ).
fof(f1928,plain,
~ sQ49_spl,
inference(contradiction_clause,[status(thm)],[f1927]) ).
fof(f1954,plain,
( ~ sQ120_spl
| e2 = e0 ),
inference(forward_demodulation,[status(thm)],[f1558,f793]) ).
fof(f1955,plain,
( ~ sQ120_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1954,f196]) ).
fof(f1956,plain,
~ sQ120_spl,
inference(contradiction_clause,[status(thm)],[f1955]) ).
fof(f1973,plain,
( ~ sQ36_spl
| e0 = e1 ),
inference(forward_demodulation,[status(thm)],[f1253,f524]) ).
fof(f1974,plain,
( ~ sQ36_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1973,f195]) ).
fof(f1975,plain,
~ sQ36_spl,
inference(contradiction_clause,[status(thm)],[f1974]) ).
fof(f1984,plain,
( ~ sQ126_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1902,f1269]) ).
fof(f1985,plain,
~ sQ126_spl,
inference(contradiction_clause,[status(thm)],[f1984]) ).
fof(f1995,plain,
( ~ sQ58_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f594,f1257]) ).
fof(f1996,plain,
~ sQ58_spl,
inference(contradiction_clause,[status(thm)],[f1995]) ).
fof(f1998,plain,
( ~ sQ42_spl
| ~ sQ43_spl
| e3 = e2 ),
inference(forward_demodulation,[status(thm)],[f546,f543]) ).
fof(f1999,plain,
( ~ sQ42_spl
| ~ sQ43_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1998,f202]) ).
fof(f2000,plain,
( ~ sQ42_spl
| ~ sQ43_spl ),
inference(contradiction_clause,[status(thm)],[f1999]) ).
fof(f2005,plain,
( ~ sQ38_spl
| e0 = e3 ),
inference(forward_demodulation,[status(thm)],[f1253,f530]) ).
fof(f2006,plain,
( ~ sQ38_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2005,f197]) ).
fof(f2007,plain,
~ sQ38_spl,
inference(contradiction_clause,[status(thm)],[f2006]) ).
fof(f2028,plain,
( ~ sQ121_spl
| e2 = e1 ),
inference(forward_demodulation,[status(thm)],[f1558,f796]) ).
fof(f2029,plain,
( ~ sQ121_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2028,f199]) ).
fof(f2030,plain,
~ sQ121_spl,
inference(contradiction_clause,[status(thm)],[f2029]) ).
fof(f2053,plain,
( ~ sQ132_spl
| op(e2,e4) = e4 ),
inference(forward_demodulation,[status(thm)],[f1558,f887]) ).
fof(f2086,plain,
( ~ sQ191_spl
| op(e0,e2) = e1 ),
inference(forward_demodulation,[status(thm)],[f1253,f1147]) ).
fof(f2132,plain,
( ~ sQ128_spl
| op(e3,e0) = e0 ),
inference(forward_demodulation,[status(thm)],[f818,f34]) ).
fof(f2146,plain,
( ~ sQ128_spl
| op(e1,e3) = e1 ),
inference(forward_demodulation,[status(thm)],[f818,f37]) ).
fof(f2149,plain,
( ~ sQ128_spl
| op(e3,e3) = e3 ),
inference(forward_demodulation,[status(thm)],[f818,f40]) ).
fof(f2158,plain,
( ~ sQ0_spl
| e0 != op(e0,e3) ),
inference(forward_demodulation,[status(thm)],[f409,f147]) ).
fof(f2225,plain,
( ~ sQ91_spl
| e1 != op(e3,e4) ),
inference(backward_demodulation,[status(thm)],[f700,f184]) ).
fof(f2236,plain,
( ~ sQ78_spl
| e3 != op(e3,e2) ),
inference(forward_demodulation,[status(thm)],[f658,f176]) ).
fof(f2237,plain,
( ~ sQ91_spl
| op(e3,e2) != e1 ),
inference(forward_demodulation,[status(thm)],[f700,f182]) ).
fof(f2241,plain,
( ~ sQ88_spl
| ~ sQ78_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f690,f2236]) ).
fof(f2242,plain,
( ~ sQ88_spl
| ~ sQ78_spl ),
inference(contradiction_clause,[status(thm)],[f2241]) ).
fof(f2285,plain,
( ~ sQ127_spl
| op(e2,e2) = e2 ),
inference(forward_demodulation,[status(thm)],[f815,f39]) ).
fof(f2286,plain,
( ~ sQ127_spl
| e3 = e2 ),
inference(forward_demodulation,[status(thm)],[f1263,f2285]) ).
fof(f2287,plain,
( ~ sQ127_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2286,f202]) ).
fof(f2288,plain,
~ sQ127_spl,
inference(contradiction_clause,[status(thm)],[f2287]) ).
fof(f2293,plain,
( ~ sQ129_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1543,f1774]) ).
fof(f2294,plain,
~ sQ129_spl,
inference(contradiction_clause,[status(thm)],[f2293]) ).
fof(f2296,plain,
( ~ sQ74_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f1349,f484,f644]) ).
fof(f2301,plain,
( ~ sQ90_spl
| ~ sQ91_spl
| e1 = e0 ),
inference(forward_demodulation,[status(thm)],[f700,f697]) ).
fof(f2302,plain,
( ~ sQ90_spl
| ~ sQ91_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2301,f195]) ).
fof(f2303,plain,
( ~ sQ90_spl
| ~ sQ91_spl ),
inference(contradiction_clause,[status(thm)],[f2302]) ).
fof(f2315,plain,
( ~ sQ55_spl
| e0 != op(e2,e4) ),
inference(backward_demodulation,[status(thm)],[f585,f171]) ).
fof(f2324,plain,
( ~ sQ26_spl
| ~ sQ28_spl
| e3 = e1 ),
inference(forward_demodulation,[status(thm)],[f498,f492]) ).
fof(f2325,plain,
( ~ sQ26_spl
| ~ sQ28_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2324,f200]) ).
fof(f2326,plain,
( ~ sQ26_spl
| ~ sQ28_spl ),
inference(contradiction_clause,[status(thm)],[f2325]) ).
fof(f2329,plain,
( ~ sQ104_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f1373,f580,f740]) ).
fof(f2363,plain,
( ~ sQ45_spl
| e0 != e0 ),
inference(forward_demodulation,[status(thm)],[f553,f1799]) ).
fof(f2364,plain,
( ~ sQ45_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f2363]) ).
fof(f2365,plain,
~ sQ45_spl,
inference(contradiction_clause,[status(thm)],[f2364]) ).
fof(f2374,plain,
( ~ sQ125_spl
| op(e3,e0) = e3 ),
inference(backward_demodulation,[status(thm)],[f809,f41]) ).
fof(f2375,plain,
( ~ sQ125_spl
| op(e0,e3) = e3 ),
inference(backward_demodulation,[status(thm)],[f809,f40]) ).
fof(f2376,plain,
( ~ sQ125_spl
| op(e2,e0) = e2 ),
inference(backward_demodulation,[status(thm)],[f809,f39]) ).
fof(f2377,plain,
( ~ sQ125_spl
| op(e4,e0) = e4 ),
inference(backward_demodulation,[status(thm)],[f809,f43]) ).
fof(f2381,plain,
( ~ sQ125_spl
| op(e0,e1) = e1 ),
inference(backward_demodulation,[status(thm)],[f809,f36]) ).
fof(f2382,plain,
( ~ sQ125_spl
| op(e1,e0) = e1 ),
inference(backward_demodulation,[status(thm)],[f809,f37]) ).
fof(f2439,plain,
( sQ177_spl
| e0 != op(e2,e1) ),
inference(forward_demodulation,[status(thm)],[f1253,f1085]) ).
fof(f2470,plain,
( ~ sQ52_spl
| e2 != op(e3,e0) ),
inference(forward_demodulation,[status(thm)],[f575,f102]) ).
fof(f2497,plain,
( ~ sQ47_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f559,f1780]) ).
fof(f2498,plain,
~ sQ47_spl,
inference(contradiction_clause,[status(thm)],[f2497]) ).
fof(f2511,plain,
( ~ sQ18_spl
| ~ sQ17_spl
| e2 = e3 ),
inference(forward_demodulation,[status(thm)],[f463,f466]) ).
fof(f2512,plain,
( ~ sQ18_spl
| ~ sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2511,f202]) ).
fof(f2513,plain,
( ~ sQ18_spl
| ~ sQ17_spl ),
inference(contradiction_clause,[status(thm)],[f2512]) ).
fof(f2523,plain,
( ~ sQ55_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f2315,f632,f584]) ).
fof(f2524,plain,
( ~ sQ55_spl
| sQ177_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f585,f2439]) ).
fof(f2525,plain,
( ~ sQ55_spl
| sQ177_spl ),
inference(contradiction_clause,[status(thm)],[f2524]) ).
fof(f2536,plain,
( ~ sQ39_spl
| e0 = e4 ),
inference(forward_demodulation,[status(thm)],[f1253,f533]) ).
fof(f2537,plain,
( ~ sQ39_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2536,f198]) ).
fof(f2538,plain,
~ sQ39_spl,
inference(contradiction_clause,[status(thm)],[f2537]) ).
fof(f2553,plain,
( sQ142_spl
| ~ sQ48_spl
| e3 != op(e4,e1) ),
inference(backward_demodulation,[status(thm)],[f562,f930]) ).
fof(f2607,plain,
( ~ sQ93_spl
| ~ sQ90_spl
| e0 = e3 ),
inference(forward_demodulation,[status(thm)],[f697,f706]) ).
fof(f2608,plain,
( ~ sQ93_spl
| ~ sQ90_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2607,f197]) ).
fof(f2609,plain,
( ~ sQ93_spl
| ~ sQ90_spl ),
inference(contradiction_clause,[status(thm)],[f2608]) ).
fof(f2628,plain,
( ~ sQ128_spl
| sQ93_spl ),
inference(split_clause,[status(thm)],[f2149,f705,f817]) ).
fof(f2631,plain,
( ~ sQ128_spl
| sQ41_spl ),
inference(split_clause,[status(thm)],[f2146,f539,f817]) ).
fof(f2634,plain,
( ~ sQ128_spl
| sQ75_spl ),
inference(split_clause,[status(thm)],[f2132,f648,f817]) ).
fof(f2640,plain,
( ~ sQ132_spl
| sQ74_spl ),
inference(split_clause,[status(thm)],[f2053,f644,f886]) ).
fof(f2659,plain,
( ~ sQ46_spl
| ~ sQ48_spl
| e3 = e1 ),
inference(forward_demodulation,[status(thm)],[f562,f556]) ).
fof(f2660,plain,
( ~ sQ46_spl
| ~ sQ48_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2659,f200]) ).
fof(f2661,plain,
( ~ sQ46_spl
| ~ sQ48_spl ),
inference(contradiction_clause,[status(thm)],[f2660]) ).
fof(f2679,plain,
( ~ sQ53_spl
| e3 != e3 ),
inference(forward_demodulation,[status(thm)],[f578,f1258]) ).
fof(f2680,plain,
( ~ sQ53_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f2679]) ).
fof(f2681,plain,
~ sQ53_spl,
inference(contradiction_clause,[status(thm)],[f2680]) ).
fof(f2705,plain,
( ~ sQ22_spl
| ~ sQ24_spl
| e4 = e2 ),
inference(forward_demodulation,[status(thm)],[f485,f479]) ).
fof(f2706,plain,
( ~ sQ22_spl
| ~ sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2705,f203]) ).
fof(f2707,plain,
( ~ sQ22_spl
| ~ sQ24_spl ),
inference(contradiction_clause,[status(thm)],[f2706]) ).
fof(f2711,plain,
( ~ sQ125_spl
| op(e0,e0) != e3 ),
inference(backward_demodulation,[status(thm)],[f2374,f97]) ).
fof(f2715,plain,
( ~ sQ125_spl
| sQ18_spl ),
inference(split_clause,[status(thm)],[f2375,f465,f808]) ).
fof(f2716,plain,
( ~ sQ125_spl
| sQ52_spl ),
inference(split_clause,[status(thm)],[f2376,f574,f808]) ).
fof(f2727,plain,
( ~ sQ125_spl
| ~ sQ8_spl
| e3 = e1 ),
inference(forward_demodulation,[status(thm)],[f434,f2381]) ).
fof(f2728,plain,
( ~ sQ125_spl
| ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2727,f200]) ).
fof(f2729,plain,
( ~ sQ125_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f2728]) ).
fof(f2730,plain,
( ~ sQ125_spl
| sQ26_spl ),
inference(split_clause,[status(thm)],[f2382,f491,f808]) ).
fof(f2737,plain,
( ~ sQ125_spl
| op(e0,e3) = e3 ),
inference(backward_demodulation,[status(thm)],[f809,f40]) ).
fof(f2738,plain,
( ~ sQ125_spl
| op(e2,e0) = e2 ),
inference(backward_demodulation,[status(thm)],[f809,f39]) ).
fof(f2744,plain,
( ~ sQ125_spl
| op(e1,e0) = e1 ),
inference(backward_demodulation,[status(thm)],[f809,f37]) ).
fof(f2767,plain,
( ~ sQ59_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f597,f1271]) ).
fof(f2768,plain,
~ sQ59_spl,
inference(contradiction_clause,[status(thm)],[f2767]) ).
fof(f2792,plain,
( ~ sQ83_spl
| ~ sQ82_spl
| e2 = e3 ),
inference(forward_demodulation,[status(thm)],[f671,f674]) ).
fof(f2793,plain,
( ~ sQ83_spl
| ~ sQ82_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2792,f202]) ).
fof(f2794,plain,
( ~ sQ83_spl
| ~ sQ82_spl ),
inference(contradiction_clause,[status(thm)],[f2793]) ).
fof(f2797,plain,
( ~ sQ125_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f2711,f417,f808]) ).
fof(f2815,plain,
( ~ sQ52_spl
| ~ sQ77_spl ),
inference(split_clause,[status(thm)],[f2470,f654,f574]) ).
fof(f2818,plain,
( ~ sQ20_spl
| ~ sQ24_spl
| e4 = e0 ),
inference(forward_demodulation,[status(thm)],[f485,f473]) ).
fof(f2819,plain,
( ~ sQ20_spl
| ~ sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2818,f198]) ).
fof(f2820,plain,
( ~ sQ20_spl
| ~ sQ24_spl ),
inference(contradiction_clause,[status(thm)],[f2819]) ).
fof(f2831,plain,
( ~ sQ125_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f2381,f427,f808]) ).
fof(f2864,plain,
( ~ sQ197_spl
| ~ sQ125_spl
| op(e0,e1) = e1 ),
inference(forward_demodulation,[status(thm)],[f2744,f1174]) ).
fof(f2879,plain,
( ~ sQ113_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f770,f1259]) ).
fof(f2880,plain,
~ sQ113_spl,
inference(contradiction_clause,[status(thm)],[f2879]) ).
fof(f2887,plain,
( ~ sQ75_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f1598,f408,f648]) ).
fof(f2896,plain,
( ~ sQ0_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f2158,f456,f408]) ).
fof(f2933,plain,
( ~ sQ12_spl
| e2 != op(e3,e2) ),
inference(forward_demodulation,[status(thm)],[f447,f117]) ).
fof(f2985,plain,
( ~ sQ125_spl
| op(e0,e2) = e2 ),
inference(backward_demodulation,[status(thm)],[f809,f38]) ).
fof(f3009,plain,
( ~ sQ197_spl
| ~ sQ125_spl
| e1 != op(e2,e1) ),
inference(backward_demodulation,[status(thm)],[f2864,f106]) ).
fof(f3016,plain,
( ~ sQ125_spl
| e2 != op(e2,e1) ),
inference(backward_demodulation,[status(thm)],[f2738,f165]) ).
fof(f3066,plain,
( ~ sQ107_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f751,f1792]) ).
fof(f3067,plain,
~ sQ107_spl,
inference(contradiction_clause,[status(thm)],[f3066]) ).
fof(f3068,plain,
( sQ142_spl
| ~ sQ48_spl
| ~ sQ108_spl ),
inference(split_clause,[status(thm)],[f2553,f753,f561,f928]) ).
fof(f3070,plain,
( ~ sQ2_spl
| ~ sQ0_spl
| e0 = e2 ),
inference(forward_demodulation,[status(thm)],[f409,f415]) ).
fof(f3071,plain,
( ~ sQ2_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3070,f196]) ).
fof(f3072,plain,
( ~ sQ2_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f3071]) ).
fof(f3095,plain,
( ~ sQ6_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f1846,f475,f427]) ).
fof(f3109,plain,
( sQ160_spl
| ~ sQ42_spl
| e2 != op(e3,e1) ),
inference(forward_demodulation,[status(thm)],[f543,f1009]) ).
fof(f3110,plain,
( sQ160_spl
| ~ sQ42_spl
| ~ sQ82_spl
| e2 != e2 ),
inference(forward_demodulation,[status(thm)],[f671,f3109]) ).
fof(f3111,plain,
( sQ160_spl
| ~ sQ42_spl
| ~ sQ82_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f3110]) ).
fof(f3112,plain,
( sQ160_spl
| ~ sQ42_spl
| ~ sQ82_spl ),
inference(contradiction_clause,[status(thm)],[f3111]) ).
fof(f3139,plain,
( ~ sQ91_spl
| ~ sQ96_spl ),
inference(split_clause,[status(thm)],[f2225,f715,f699]) ).
fof(f3164,plain,
( ~ sQ207_spl
| ~ sQ125_spl
| op(e2,e2) = e0 ),
inference(backward_demodulation,[status(thm)],[f2985,f1220]) ).
fof(f3169,plain,
( ~ sQ197_spl
| ~ sQ125_spl
| ~ sQ56_spl ),
inference(split_clause,[status(thm)],[f3009,f587,f808,f1173]) ).
fof(f3269,plain,
( ~ sQ207_spl
| ~ sQ125_spl
| sQ60_spl ),
inference(split_clause,[status(thm)],[f3164,f600,f808,f1219]) ).
fof(f3282,plain,
( ~ sQ91_spl
| ~ sQ86_spl ),
inference(split_clause,[status(thm)],[f2237,f683,f699]) ).
fof(f3302,plain,
( sQ164_spl
| ~ sQ125_spl
| e3 != op(e3,e0) ),
inference(forward_demodulation,[status(thm)],[f2737,f1026]) ).
fof(f3303,plain,
( sQ164_spl
| ~ sQ125_spl
| e3 != e3 ),
inference(forward_demodulation,[status(thm)],[f2374,f3302]) ).
fof(f3304,plain,
( sQ164_spl
| ~ sQ125_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f3303]) ).
fof(f3305,plain,
( sQ164_spl
| ~ sQ125_spl ),
inference(contradiction_clause,[status(thm)],[f3304]) ).
fof(f3316,plain,
( sQ134_spl
| ~ sQ95_spl
| e0 != op(e4,e3) ),
inference(forward_demodulation,[status(thm)],[f713,f896]) ).
fof(f3317,plain,
( sQ134_spl
| ~ sQ95_spl
| ~ sQ115_spl
| e0 != e0 ),
inference(forward_demodulation,[status(thm)],[f777,f3316]) ).
fof(f3318,plain,
( sQ134_spl
| ~ sQ95_spl
| ~ sQ115_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f3317]) ).
fof(f3319,plain,
( sQ134_spl
| ~ sQ95_spl
| ~ sQ115_spl ),
inference(contradiction_clause,[status(thm)],[f3318]) ).
fof(f3320,plain,
( ~ sQ135_spl
| ~ sQ115_spl
| op(e0,e3) = e4 ),
inference(forward_demodulation,[status(thm)],[f777,f899]) ).
fof(f3321,plain,
( ~ sQ135_spl
| ~ sQ115_spl
| ~ sQ125_spl
| e3 = e4 ),
inference(forward_demodulation,[status(thm)],[f2737,f3320]) ).
fof(f3322,plain,
( ~ sQ135_spl
| ~ sQ115_spl
| ~ sQ125_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3321,f204]) ).
fof(f3323,plain,
( ~ sQ135_spl
| ~ sQ115_spl
| ~ sQ125_spl ),
inference(contradiction_clause,[status(thm)],[f3322]) ).
fof(f3343,plain,
( ~ sQ125_spl
| ~ sQ57_spl ),
inference(split_clause,[status(thm)],[f3016,f590,f808]) ).
fof(f3355,plain,
( ~ sQ97_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f719,f1915]) ).
fof(f3356,plain,
~ sQ97_spl,
inference(contradiction_clause,[status(thm)],[f3355]) ).
fof(f3363,plain,
( ~ sQ191_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f2086,f443,f1146]) ).
fof(f3393,plain,
( sQ138_spl
| ~ sQ71_spl
| e1 != op(e4,e2) ),
inference(forward_demodulation,[status(thm)],[f636,f913]) ).
fof(f3394,plain,
( sQ138_spl
| ~ sQ71_spl
| ~ sQ111_spl
| e1 != e1 ),
inference(forward_demodulation,[status(thm)],[f764,f3393]) ).
fof(f3395,plain,
( sQ138_spl
| ~ sQ71_spl
| ~ sQ111_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f3394]) ).
fof(f3396,plain,
( sQ138_spl
| ~ sQ71_spl
| ~ sQ111_spl ),
inference(contradiction_clause,[status(thm)],[f3395]) ).
fof(f3397,plain,
( ~ sQ139_spl
| ~ sQ111_spl
| op(e1,e2) = e4 ),
inference(forward_demodulation,[status(thm)],[f764,f916]) ).
fof(f3398,plain,
( ~ sQ139_spl
| ~ sQ111_spl
| e0 = e4 ),
inference(forward_demodulation,[status(thm)],[f1253,f3397]) ).
fof(f3399,plain,
( ~ sQ139_spl
| ~ sQ111_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3398,f198]) ).
fof(f3400,plain,
( ~ sQ139_spl
| ~ sQ111_spl ),
inference(contradiction_clause,[status(thm)],[f3399]) ).
fof(f3414,plain,
( ~ sQ204_spl
| ~ sQ125_spl
| op(e3,e3) = e0 ),
inference(forward_demodulation,[status(thm)],[f2737,f1206]) ).
fof(f3415,plain,
( ~ sQ204_spl
| ~ sQ125_spl
| ~ sQ91_spl
| e1 = e0 ),
inference(forward_demodulation,[status(thm)],[f700,f3414]) ).
fof(f3416,plain,
( ~ sQ204_spl
| ~ sQ125_spl
| ~ sQ91_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3415,f195]) ).
fof(f3417,plain,
( ~ sQ204_spl
| ~ sQ125_spl
| ~ sQ91_spl ),
inference(contradiction_clause,[status(thm)],[f3416]) ).
fof(f3445,plain,
( ~ sQ143_spl
| ~ sQ108_spl
| op(e3,e1) = e4 ),
inference(forward_demodulation,[status(thm)],[f754,f933]) ).
fof(f3446,plain,
( ~ sQ143_spl
| ~ sQ108_spl
| ~ sQ82_spl
| e2 = e4 ),
inference(forward_demodulation,[status(thm)],[f671,f3445]) ).
fof(f3447,plain,
( ~ sQ143_spl
| ~ sQ108_spl
| ~ sQ82_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3446,f203]) ).
fof(f3448,plain,
( ~ sQ143_spl
| ~ sQ108_spl
| ~ sQ82_spl ),
inference(contradiction_clause,[status(thm)],[f3447]) ).
fof(f3486,plain,
( sQ146_spl
| ~ sQ24_spl
| e4 != op(e4,e0) ),
inference(forward_demodulation,[status(thm)],[f485,f947]) ).
fof(f3487,plain,
( sQ146_spl
| ~ sQ24_spl
| ~ sQ125_spl
| e4 != e4 ),
inference(forward_demodulation,[status(thm)],[f2377,f3486]) ).
fof(f3488,plain,
( sQ146_spl
| ~ sQ24_spl
| ~ sQ125_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f3487]) ).
fof(f3489,plain,
( sQ146_spl
| ~ sQ24_spl
| ~ sQ125_spl ),
inference(contradiction_clause,[status(thm)],[f3488]) ).
fof(f3515,plain,
( sQ156_spl
| ~ sQ69_spl
| e4 != op(e3,e2) ),
inference(forward_demodulation,[status(thm)],[f629,f992]) ).
fof(f3516,plain,
( sQ156_spl
| ~ sQ69_spl
| ~ sQ89_spl
| e4 != e4 ),
inference(forward_demodulation,[status(thm)],[f693,f3515]) ).
fof(f3517,plain,
( sQ156_spl
| ~ sQ69_spl
| ~ sQ89_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f3516]) ).
fof(f3518,plain,
( sQ156_spl
| ~ sQ69_spl
| ~ sQ89_spl ),
inference(contradiction_clause,[status(thm)],[f3517]) ).
fof(f3526,plain,
( ~ sQ12_spl
| ~ sQ87_spl ),
inference(split_clause,[status(thm)],[f2933,f686,f446]) ).
fof(f3537,plain,
( sQ181_spl
| ~ sQ125_spl
| e2 != op(e2,e0) ),
inference(forward_demodulation,[status(thm)],[f2985,f1102]) ).
fof(f3538,plain,
( sQ181_spl
| ~ sQ125_spl
| e2 != e2 ),
inference(forward_demodulation,[status(thm)],[f2738,f3537]) ).
fof(f3539,plain,
( sQ181_spl
| ~ sQ125_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f3538]) ).
fof(f3540,plain,
( sQ181_spl
| ~ sQ125_spl ),
inference(contradiction_clause,[status(thm)],[f3539]) ).
fof(f3541,plain,
$false,
inference(sat_refutation,[status(thm)],[f519,f599,f615,f695,f807,f823,f828,f831,f838,f840,f841,f847,f852,f855,f858,f865,f867,f874,f875,f889,f901,f918,f935,f948,f962,f983,f984,f993,f1010,f1027,f1041,f1055,f1072,f1086,f1103,f1117,f1131,f1149,f1162,f1176,f1190,f1208,f1222,f1232,f1246,f1291,f1308,f1314,f1317,f1323,f1326,f1329,f1335,f1338,f1398,f1464,f1500,f1515,f1518,f1522,f1526,f1538,f1616,f1644,f1690,f1697,f1760,f1764,f1767,f1783,f1806,f1840,f1850,f1928,f1956,f1975,f1985,f1996,f2000,f2007,f2030,f2242,f2288,f2294,f2296,f2303,f2326,f2329,f2365,f2498,f2513,f2523,f2525,f2538,f2609,f2628,f2631,f2634,f2640,f2661,f2681,f2707,f2715,f2716,f2729,f2730,f2768,f2794,f2797,f2815,f2820,f2831,f2880,f2887,f2896,f3067,f3068,f3072,f3095,f3112,f3139,f3169,f3269,f3282,f3305,f3319,f3323,f3343,f3356,f3363,f3396,f3400,f3417,f3448,f3489,f3518,f3526,f3540]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG064+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n016.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 12:59:55 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.39 % Drodi V4.1.1
% 0.11/0.57 % Refutation found
% 0.11/0.57 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.57 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.59 % Elapsed time: 0.218706 seconds
% 0.11/0.59 % CPU time: 1.313073 seconds
% 0.11/0.59 % Total memory used: 137.315 MB
% 0.11/0.59 % Net memory used: 136.601 MB
%------------------------------------------------------------------------------