%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ALG056+1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 11:47:57 AM UTC 2026
% Result : Theorem 0.14s 0.71s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 62
% Number of leaves : 38
% Syntax : Number of formulae : 401 ( 103 unt; 31 def)
% Number of atoms : 2808 (2386 equ)
% Maximal formula atoms : 250 ( 7 avg)
% Number of connectives : 3318 ( 911 ~;1207 |;1144 &)
% ( 56 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 101 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 33 ( 31 usr; 32 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
( ( op(e4,e4) = e4
| op(e4,e4) = e3
| op(e4,e4) = e2
| op(e4,e4) = e1
| op(e4,e4) = e0 )
& ( op(e4,e3) = e4
| op(e4,e3) = e3
| op(e4,e3) = e2
| op(e4,e3) = e1
| op(e4,e3) = e0 )
& ( op(e4,e2) = e4
| op(e4,e2) = e3
| op(e4,e2) = e2
| op(e4,e2) = e1
| op(e4,e2) = e0 )
& ( op(e4,e1) = e4
| op(e4,e1) = e3
| op(e4,e1) = e2
| op(e4,e1) = e1
| op(e4,e1) = e0 )
& ( op(e4,e0) = e4
| op(e4,e0) = e3
| op(e4,e0) = e2
| op(e4,e0) = e1
| op(e4,e0) = e0 )
& ( op(e3,e4) = e4
| op(e3,e4) = e3
| op(e3,e4) = e2
| op(e3,e4) = e1
| op(e3,e4) = e0 )
& ( op(e3,e3) = e4
| op(e3,e3) = e3
| op(e3,e3) = e2
| op(e3,e3) = e1
| op(e3,e3) = e0 )
& ( op(e3,e2) = e4
| op(e3,e2) = e3
| op(e3,e2) = e2
| op(e3,e2) = e1
| op(e3,e2) = e0 )
& ( op(e3,e1) = e4
| op(e3,e1) = e3
| op(e3,e1) = e2
| op(e3,e1) = e1
| op(e3,e1) = e0 )
& ( op(e3,e0) = e4
| op(e3,e0) = e3
| op(e3,e0) = e2
| op(e3,e0) = e1
| op(e3,e0) = e0 )
& ( op(e2,e4) = e4
| op(e2,e4) = e3
| op(e2,e4) = e2
| op(e2,e4) = e1
| op(e2,e4) = e0 )
& ( op(e2,e3) = e4
| op(e2,e3) = e3
| op(e2,e3) = e2
| op(e2,e3) = e1
| op(e2,e3) = e0 )
& ( op(e2,e2) = e4
| op(e2,e2) = e3
| op(e2,e2) = e2
| op(e2,e2) = e1
| op(e2,e2) = e0 )
& ( op(e2,e1) = e4
| op(e2,e1) = e3
| op(e2,e1) = e2
| op(e2,e1) = e1
| op(e2,e1) = e0 )
& ( op(e2,e0) = e4
| op(e2,e0) = e3
| op(e2,e0) = e2
| op(e2,e0) = e1
| op(e2,e0) = e0 )
& ( op(e1,e4) = e4
| op(e1,e4) = e3
| op(e1,e4) = e2
| op(e1,e4) = e1
| op(e1,e4) = e0 )
& ( op(e1,e3) = e4
| op(e1,e3) = e3
| op(e1,e3) = e2
| op(e1,e3) = e1
| op(e1,e3) = e0 )
& ( op(e1,e2) = e4
| op(e1,e2) = e3
| op(e1,e2) = e2
| op(e1,e2) = e1
| op(e1,e2) = e0 )
& ( op(e1,e1) = e4
| op(e1,e1) = e3
| op(e1,e1) = e2
| op(e1,e1) = e1
| op(e1,e1) = e0 )
& ( op(e1,e0) = e4
| op(e1,e0) = e3
| op(e1,e0) = e2
| op(e1,e0) = e1
| op(e1,e0) = e0 )
& ( op(e0,e4) = e4
| op(e0,e4) = e3
| op(e0,e4) = e2
| op(e0,e4) = e1
| op(e0,e4) = e0 )
& ( op(e0,e3) = e4
| op(e0,e3) = e3
| op(e0,e3) = e2
| op(e0,e3) = e1
| op(e0,e3) = e0 )
& ( op(e0,e2) = e4
| op(e0,e2) = e3
| op(e0,e2) = e2
| op(e0,e2) = e1
| op(e0,e2) = e0 )
& ( op(e0,e1) = e4
| op(e0,e1) = e3
| op(e0,e1) = e2
| op(e0,e1) = e1
| op(e0,e1) = e0 )
& ( op(e0,e0) = e4
| op(e0,e0) = e3
| op(e0,e0) = e2
| op(e0,e0) = e1
| op(e0,e0) = e0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
( ( unit = e4
| unit = e3
| unit = e2
| unit = e1
| unit = e0 )
& op(e4,unit) = e4
& op(unit,e4) = e4
& op(e3,unit) = e3
& op(unit,e3) = e3
& op(e2,unit) = e2
& op(unit,e2) = e2
& op(e1,unit) = e1
& op(unit,e1) = e1
& op(e0,unit) = e0
& op(unit,e0) = e0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
( ( op(e4,e4) = e4
| op(e3,e4) = e4
| op(e2,e4) = e4
| op(e1,e4) = e4
| op(e0,e4) = e4 )
& ( op(e4,e4) = e4
| op(e4,e3) = e4
| op(e4,e2) = e4
| op(e4,e1) = e4
| op(e4,e0) = e4 )
& ( op(e4,e4) = e3
| op(e3,e4) = e3
| op(e2,e4) = e3
| op(e1,e4) = e3
| op(e0,e4) = e3 )
& ( op(e4,e4) = e3
| op(e4,e3) = e3
| op(e4,e2) = e3
| op(e4,e1) = e3
| op(e4,e0) = e3 )
& ( op(e4,e4) = e2
| op(e3,e4) = e2
| op(e2,e4) = e2
| op(e1,e4) = e2
| op(e0,e4) = e2 )
& ( op(e4,e4) = e2
| op(e4,e3) = e2
| op(e4,e2) = e2
| op(e4,e1) = e2
| op(e4,e0) = e2 )
& ( op(e4,e4) = e1
| op(e3,e4) = e1
| op(e2,e4) = e1
| op(e1,e4) = e1
| op(e0,e4) = e1 )
& ( op(e4,e4) = e1
| op(e4,e3) = e1
| op(e4,e2) = e1
| op(e4,e1) = e1
| op(e4,e0) = e1 )
& ( op(e4,e4) = e0
| op(e3,e4) = e0
| op(e2,e4) = e0
| op(e1,e4) = e0
| op(e0,e4) = e0 )
& ( op(e4,e4) = e0
| op(e4,e3) = e0
| op(e4,e2) = e0
| op(e4,e1) = e0
| op(e4,e0) = e0 )
& ( op(e4,e3) = e4
| op(e3,e3) = e4
| op(e2,e3) = e4
| op(e1,e3) = e4
| op(e0,e3) = e4 )
& ( op(e3,e4) = e4
| op(e3,e3) = e4
| op(e3,e2) = e4
| op(e3,e1) = e4
| op(e3,e0) = e4 )
& ( op(e4,e3) = e3
| op(e3,e3) = e3
| op(e2,e3) = e3
| op(e1,e3) = e3
| op(e0,e3) = e3 )
& ( op(e3,e4) = e3
| op(e3,e3) = e3
| op(e3,e2) = e3
| op(e3,e1) = e3
| op(e3,e0) = e3 )
& ( op(e4,e3) = e2
| op(e3,e3) = e2
| op(e2,e3) = e2
| op(e1,e3) = e2
| op(e0,e3) = e2 )
& ( op(e3,e4) = e2
| op(e3,e3) = e2
| op(e3,e2) = e2
| op(e3,e1) = e2
| op(e3,e0) = e2 )
& ( op(e4,e3) = e1
| op(e3,e3) = e1
| op(e2,e3) = e1
| op(e1,e3) = e1
| op(e0,e3) = e1 )
& ( op(e3,e4) = e1
| op(e3,e3) = e1
| op(e3,e2) = e1
| op(e3,e1) = e1
| op(e3,e0) = e1 )
& ( op(e4,e3) = e0
| op(e3,e3) = e0
| op(e2,e3) = e0
| op(e1,e3) = e0
| op(e0,e3) = e0 )
& ( op(e3,e4) = e0
| op(e3,e3) = e0
| op(e3,e2) = e0
| op(e3,e1) = e0
| op(e3,e0) = e0 )
& ( op(e4,e2) = e4
| op(e3,e2) = e4
| op(e2,e2) = e4
| op(e1,e2) = e4
| op(e0,e2) = e4 )
& ( op(e2,e4) = e4
| op(e2,e3) = e4
| op(e2,e2) = e4
| op(e2,e1) = e4
| op(e2,e0) = e4 )
& ( op(e4,e2) = e3
| op(e3,e2) = e3
| op(e2,e2) = e3
| op(e1,e2) = e3
| op(e0,e2) = e3 )
& ( op(e2,e4) = e3
| op(e2,e3) = e3
| op(e2,e2) = e3
| op(e2,e1) = e3
| op(e2,e0) = e3 )
& ( op(e4,e2) = e2
| op(e3,e2) = e2
| op(e2,e2) = e2
| op(e1,e2) = e2
| op(e0,e2) = e2 )
& ( op(e2,e4) = e2
| op(e2,e3) = e2
| op(e2,e2) = e2
| op(e2,e1) = e2
| op(e2,e0) = e2 )
& ( op(e4,e2) = e1
| op(e3,e2) = e1
| op(e2,e2) = e1
| op(e1,e2) = e1
| op(e0,e2) = e1 )
& ( op(e2,e4) = e1
| op(e2,e3) = e1
| op(e2,e2) = e1
| op(e2,e1) = e1
| op(e2,e0) = e1 )
& ( op(e4,e2) = e0
| op(e3,e2) = e0
| op(e2,e2) = e0
| op(e1,e2) = e0
| op(e0,e2) = e0 )
& ( op(e2,e4) = e0
| op(e2,e3) = e0
| op(e2,e2) = e0
| op(e2,e1) = e0
| op(e2,e0) = e0 )
& ( op(e4,e1) = e4
| op(e3,e1) = e4
| op(e2,e1) = e4
| op(e1,e1) = e4
| op(e0,e1) = e4 )
& ( op(e1,e4) = e4
| op(e1,e3) = e4
| op(e1,e2) = e4
| op(e1,e1) = e4
| op(e1,e0) = e4 )
& ( op(e4,e1) = e3
| op(e3,e1) = e3
| op(e2,e1) = e3
| op(e1,e1) = e3
| op(e0,e1) = e3 )
& ( op(e1,e4) = e3
| op(e1,e3) = e3
| op(e1,e2) = e3
| op(e1,e1) = e3
| op(e1,e0) = e3 )
& ( op(e4,e1) = e2
| op(e3,e1) = e2
| op(e2,e1) = e2
| op(e1,e1) = e2
| op(e0,e1) = e2 )
& ( op(e1,e4) = e2
| op(e1,e3) = e2
| op(e1,e2) = e2
| op(e1,e1) = e2
| op(e1,e0) = e2 )
& ( op(e4,e1) = e1
| op(e3,e1) = e1
| op(e2,e1) = e1
| op(e1,e1) = e1
| op(e0,e1) = e1 )
& ( op(e1,e4) = e1
| op(e1,e3) = e1
| op(e1,e2) = e1
| op(e1,e1) = e1
| op(e1,e0) = e1 )
& ( op(e4,e1) = e0
| op(e3,e1) = e0
| op(e2,e1) = e0
| op(e1,e1) = e0
| op(e0,e1) = e0 )
& ( op(e1,e4) = e0
| op(e1,e3) = e0
| op(e1,e2) = e0
| op(e1,e1) = e0
| op(e1,e0) = e0 )
& ( op(e4,e0) = e4
| op(e3,e0) = e4
| op(e2,e0) = e4
| op(e1,e0) = e4
| op(e0,e0) = e4 )
& ( op(e0,e4) = e4
| op(e0,e3) = e4
| op(e0,e2) = e4
| op(e0,e1) = e4
| op(e0,e0) = e4 )
& ( op(e4,e0) = e3
| op(e3,e0) = e3
| op(e2,e0) = e3
| op(e1,e0) = e3
| op(e0,e0) = e3 )
& ( op(e0,e4) = e3
| op(e0,e3) = e3
| op(e0,e2) = e3
| op(e0,e1) = e3
| op(e0,e0) = e3 )
& ( op(e4,e0) = e2
| op(e3,e0) = e2
| op(e2,e0) = e2
| op(e1,e0) = e2
| op(e0,e0) = e2 )
& ( op(e0,e4) = e2
| op(e0,e3) = e2
| op(e0,e2) = e2
| op(e0,e1) = e2
| op(e0,e0) = e2 )
& ( op(e4,e0) = e1
| op(e3,e0) = e1
| op(e2,e0) = e1
| op(e1,e0) = e1
| op(e0,e0) = e1 )
& ( op(e0,e4) = e1
| op(e0,e3) = e1
| op(e0,e2) = e1
| op(e0,e1) = e1
| op(e0,e0) = e1 )
& ( op(e4,e0) = e0
| op(e3,e0) = e0
| op(e2,e0) = e0
| op(e1,e0) = e0
| op(e0,e0) = e0 )
& ( op(e0,e4) = e0
| op(e0,e3) = e0
| op(e0,e2) = e0
| op(e0,e1) = e0
| op(e0,e0) = e0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
( op(e4,e3) != op(e4,e4)
& op(e4,e2) != op(e4,e4)
& op(e4,e2) != op(e4,e3)
& op(e4,e1) != op(e4,e4)
& op(e4,e1) != op(e4,e3)
& op(e4,e1) != op(e4,e2)
& op(e4,e0) != op(e4,e4)
& op(e4,e0) != op(e4,e3)
& op(e4,e0) != op(e4,e2)
& op(e4,e0) != op(e4,e1)
& op(e3,e3) != op(e3,e4)
& op(e3,e2) != op(e3,e4)
& op(e3,e2) != op(e3,e3)
& op(e3,e1) != op(e3,e4)
& op(e3,e1) != op(e3,e3)
& op(e3,e1) != op(e3,e2)
& op(e3,e0) != op(e3,e4)
& op(e3,e0) != op(e3,e3)
& op(e3,e0) != op(e3,e2)
& op(e3,e0) != op(e3,e1)
& op(e2,e3) != op(e2,e4)
& op(e2,e2) != op(e2,e4)
& op(e2,e2) != op(e2,e3)
& op(e2,e1) != op(e2,e4)
& op(e2,e1) != op(e2,e3)
& op(e2,e1) != op(e2,e2)
& op(e2,e0) != op(e2,e4)
& op(e2,e0) != op(e2,e3)
& op(e2,e0) != op(e2,e2)
& op(e2,e0) != op(e2,e1)
& op(e1,e3) != op(e1,e4)
& op(e1,e2) != op(e1,e4)
& op(e1,e2) != op(e1,e3)
& op(e1,e1) != op(e1,e4)
& op(e1,e1) != op(e1,e3)
& op(e1,e1) != op(e1,e2)
& op(e1,e0) != op(e1,e4)
& op(e1,e0) != op(e1,e3)
& op(e1,e0) != op(e1,e2)
& op(e1,e0) != op(e1,e1)
& op(e0,e3) != op(e0,e4)
& op(e0,e2) != op(e0,e4)
& op(e0,e2) != op(e0,e3)
& op(e0,e1) != op(e0,e4)
& op(e0,e1) != op(e0,e3)
& op(e0,e1) != op(e0,e2)
& op(e0,e0) != op(e0,e4)
& op(e0,e0) != op(e0,e3)
& op(e0,e0) != op(e0,e2)
& op(e0,e0) != op(e0,e1)
& op(e3,e4) != op(e4,e4)
& op(e2,e4) != op(e4,e4)
& op(e2,e4) != op(e3,e4)
& op(e1,e4) != op(e4,e4)
& op(e1,e4) != op(e3,e4)
& op(e1,e4) != op(e2,e4)
& op(e0,e4) != op(e4,e4)
& op(e0,e4) != op(e3,e4)
& op(e0,e4) != op(e2,e4)
& op(e0,e4) != op(e1,e4)
& op(e3,e3) != op(e4,e3)
& op(e2,e3) != op(e4,e3)
& op(e2,e3) != op(e3,e3)
& op(e1,e3) != op(e4,e3)
& op(e1,e3) != op(e3,e3)
& op(e1,e3) != op(e2,e3)
& op(e0,e3) != op(e4,e3)
& op(e0,e3) != op(e3,e3)
& op(e0,e3) != op(e2,e3)
& op(e0,e3) != op(e1,e3)
& op(e3,e2) != op(e4,e2)
& op(e2,e2) != op(e4,e2)
& op(e2,e2) != op(e3,e2)
& op(e1,e2) != op(e4,e2)
& op(e1,e2) != op(e3,e2)
& op(e1,e2) != op(e2,e2)
& op(e0,e2) != op(e4,e2)
& op(e0,e2) != op(e3,e2)
& op(e0,e2) != op(e2,e2)
& op(e0,e2) != op(e1,e2)
& op(e3,e1) != op(e4,e1)
& op(e2,e1) != op(e4,e1)
& op(e2,e1) != op(e3,e1)
& op(e1,e1) != op(e4,e1)
& op(e1,e1) != op(e3,e1)
& op(e1,e1) != op(e2,e1)
& op(e0,e1) != op(e4,e1)
& op(e0,e1) != op(e3,e1)
& op(e0,e1) != op(e2,e1)
& op(e0,e1) != op(e1,e1)
& op(e3,e0) != op(e4,e0)
& op(e2,e0) != op(e4,e0)
& op(e2,e0) != op(e3,e0)
& op(e1,e0) != op(e4,e0)
& op(e1,e0) != op(e3,e0)
& op(e1,e0) != op(e2,e0)
& op(e0,e0) != op(e4,e0)
& op(e0,e0) != op(e3,e0)
& op(e0,e0) != op(e2,e0)
& op(e0,e0) != op(e1,e0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
( e3 != e4
& e2 != e4
& e2 != e3
& e1 != e4
& e1 != e3
& e1 != e2
& e0 != e4
& e0 != e3
& e0 != e2
& e0 != e1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
( e4 = op(e2,e2)
& e3 = op(e2,op(e2,e2))
& e1 = op(op(e2,op(e2,e2)),op(e2,e2))
& e0 = op(op(e2,e2),op(e2,e2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,conjecture,
~ ( ( ( op(e4,e4) != e4
& op(e4,e4) = e4
& op(e4,e4) = e4 )
| ( op(e4,e3) != e4
& op(e3,e3) = e4
& op(e4,e4) = e3 )
| ( op(e4,e2) != e4
& op(e2,e2) = e4
& op(e4,e4) = e2 )
| ( op(e4,e1) != e4
& op(e1,e1) = e4
& op(e4,e4) = e1 )
| ( op(e4,e0) != e4
& op(e0,e0) = e4
& op(e4,e4) = e0 )
| ( op(e3,e4) != e3
& op(e4,e4) = e3
& op(e3,e3) = e4 )
| ( op(e3,e3) != e3
& op(e3,e3) = e3
& op(e3,e3) = e3 )
| ( op(e3,e2) != e3
& op(e2,e2) = e3
& op(e3,e3) = e2 )
| ( op(e3,e1) != e3
& op(e1,e1) = e3
& op(e3,e3) = e1 )
| ( op(e3,e0) != e3
& op(e0,e0) = e3
& op(e3,e3) = e0 )
| ( op(e2,e4) != e2
& op(e4,e4) = e2
& op(e2,e2) = e4 )
| ( op(e2,e3) != e2
& op(e3,e3) = e2
& op(e2,e2) = e3 )
| ( op(e2,e2) != e2
& op(e2,e2) = e2
& op(e2,e2) = e2 )
| ( op(e2,e1) != e2
& op(e1,e1) = e2
& op(e2,e2) = e1 )
| ( op(e2,e0) != e2
& op(e0,e0) = e2
& op(e2,e2) = e0 )
| ( op(e1,e4) != e1
& op(e4,e4) = e1
& op(e1,e1) = e4 )
| ( op(e1,e3) != e1
& op(e3,e3) = e1
& op(e1,e1) = e3 )
| ( op(e1,e2) != e1
& op(e2,e2) = e1
& op(e1,e1) = e2 )
| ( op(e1,e1) != e1
& op(e1,e1) = e1
& op(e1,e1) = e1 )
| ( op(e1,e0) != e1
& op(e0,e0) = e1
& op(e1,e1) = e0 )
| ( op(e0,e4) != e0
& op(e4,e4) = e0
& op(e0,e0) = e4 )
| ( op(e0,e3) != e0
& op(e3,e3) = e0
& op(e0,e0) = e3 )
| ( op(e0,e2) != e0
& op(e2,e2) = e0
& op(e0,e0) = e2 )
| ( op(e0,e1) != e0
& op(e1,e1) = e0
& op(e0,e0) = e1 )
| ( op(e0,e0) != e0
& op(e0,e0) = e0
& op(e0,e0) = e0 ) )
& ( ( op(e4,op(e4,e4)) = e4
& op(e4,op(e4,e4)) != e4 )
| ( op(e4,op(e3,e4)) = e3
& op(e3,op(e3,e4)) != e4 )
| ( op(e4,op(e2,e4)) = e2
& op(e2,op(e2,e4)) != e4 )
| ( op(e4,op(e1,e4)) = e1
& op(e1,op(e1,e4)) != e4 )
| ( op(e4,op(e0,e4)) = e0
& op(e0,op(e0,e4)) != e4 ) )
& ( ( op(e3,op(e4,e3)) = e4
& op(e4,op(e4,e3)) != e3 )
| ( op(e3,op(e3,e3)) = e3
& op(e3,op(e3,e3)) != e3 )
| ( op(e3,op(e2,e3)) = e2
& op(e2,op(e2,e3)) != e3 )
| ( op(e3,op(e1,e3)) = e1
& op(e1,op(e1,e3)) != e3 )
| ( op(e3,op(e0,e3)) = e0
& op(e0,op(e0,e3)) != e3 ) )
& ( ( op(e2,op(e4,e2)) = e4
& op(e4,op(e4,e2)) != e2 )
| ( op(e2,op(e3,e2)) = e3
& op(e3,op(e3,e2)) != e2 )
| ( op(e2,op(e2,e2)) = e2
& op(e2,op(e2,e2)) != e2 )
| ( op(e2,op(e1,e2)) = e1
& op(e1,op(e1,e2)) != e2 )
| ( op(e2,op(e0,e2)) = e0
& op(e0,op(e0,e2)) != e2 ) )
& ( ( op(e1,op(e4,e1)) = e4
& op(e4,op(e4,e1)) != e1 )
| ( op(e1,op(e3,e1)) = e3
& op(e3,op(e3,e1)) != e1 )
| ( op(e1,op(e2,e1)) = e2
& op(e2,op(e2,e1)) != e1 )
| ( op(e1,op(e1,e1)) = e1
& op(e1,op(e1,e1)) != e1 )
| ( op(e1,op(e0,e1)) = e0
& op(e0,op(e0,e1)) != e1 ) )
& ( ( op(e0,op(e4,e0)) = e4
& op(e4,op(e4,e0)) != e0 )
| ( op(e0,op(e3,e0)) = e3
& op(e3,op(e3,e0)) != e0 )
| ( op(e0,op(e2,e0)) = e2
& op(e2,op(e2,e0)) != e0 )
| ( op(e0,op(e1,e0)) = e1
& op(e1,op(e1,e0)) != e0 )
| ( op(e0,op(e0,e0)) = e0
& op(e0,op(e0,e0)) != e0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
~ ~ ( ( ( op(e4,e4) != e4
& op(e4,e4) = e4
& op(e4,e4) = e4 )
| ( op(e4,e3) != e4
& op(e3,e3) = e4
& op(e4,e4) = e3 )
| ( op(e4,e2) != e4
& op(e2,e2) = e4
& op(e4,e4) = e2 )
| ( op(e4,e1) != e4
& op(e1,e1) = e4
& op(e4,e4) = e1 )
| ( op(e4,e0) != e4
& op(e0,e0) = e4
& op(e4,e4) = e0 )
| ( op(e3,e4) != e3
& op(e4,e4) = e3
& op(e3,e3) = e4 )
| ( op(e3,e3) != e3
& op(e3,e3) = e3
& op(e3,e3) = e3 )
| ( op(e3,e2) != e3
& op(e2,e2) = e3
& op(e3,e3) = e2 )
| ( op(e3,e1) != e3
& op(e1,e1) = e3
& op(e3,e3) = e1 )
| ( op(e3,e0) != e3
& op(e0,e0) = e3
& op(e3,e3) = e0 )
| ( op(e2,e4) != e2
& op(e4,e4) = e2
& op(e2,e2) = e4 )
| ( op(e2,e3) != e2
& op(e3,e3) = e2
& op(e2,e2) = e3 )
| ( op(e2,e2) != e2
& op(e2,e2) = e2
& op(e2,e2) = e2 )
| ( op(e2,e1) != e2
& op(e1,e1) = e2
& op(e2,e2) = e1 )
| ( op(e2,e0) != e2
& op(e0,e0) = e2
& op(e2,e2) = e0 )
| ( op(e1,e4) != e1
& op(e4,e4) = e1
& op(e1,e1) = e4 )
| ( op(e1,e3) != e1
& op(e3,e3) = e1
& op(e1,e1) = e3 )
| ( op(e1,e2) != e1
& op(e2,e2) = e1
& op(e1,e1) = e2 )
| ( op(e1,e1) != e1
& op(e1,e1) = e1
& op(e1,e1) = e1 )
| ( op(e1,e0) != e1
& op(e0,e0) = e1
& op(e1,e1) = e0 )
| ( op(e0,e4) != e0
& op(e4,e4) = e0
& op(e0,e0) = e4 )
| ( op(e0,e3) != e0
& op(e3,e3) = e0
& op(e0,e0) = e3 )
| ( op(e0,e2) != e0
& op(e2,e2) = e0
& op(e0,e0) = e2 )
| ( op(e0,e1) != e0
& op(e1,e1) = e0
& op(e0,e0) = e1 )
| ( op(e0,e0) != e0
& op(e0,e0) = e0
& op(e0,e0) = e0 ) )
& ( ( op(e4,op(e4,e4)) = e4
& op(e4,op(e4,e4)) != e4 )
| ( op(e4,op(e3,e4)) = e3
& op(e3,op(e3,e4)) != e4 )
| ( op(e4,op(e2,e4)) = e2
& op(e2,op(e2,e4)) != e4 )
| ( op(e4,op(e1,e4)) = e1
& op(e1,op(e1,e4)) != e4 )
| ( op(e4,op(e0,e4)) = e0
& op(e0,op(e0,e4)) != e4 ) )
& ( ( op(e3,op(e4,e3)) = e4
& op(e4,op(e4,e3)) != e3 )
| ( op(e3,op(e3,e3)) = e3
& op(e3,op(e3,e3)) != e3 )
| ( op(e3,op(e2,e3)) = e2
& op(e2,op(e2,e3)) != e3 )
| ( op(e3,op(e1,e3)) = e1
& op(e1,op(e1,e3)) != e3 )
| ( op(e3,op(e0,e3)) = e0
& op(e0,op(e0,e3)) != e3 ) )
& ( ( op(e2,op(e4,e2)) = e4
& op(e4,op(e4,e2)) != e2 )
| ( op(e2,op(e3,e2)) = e3
& op(e3,op(e3,e2)) != e2 )
| ( op(e2,op(e2,e2)) = e2
& op(e2,op(e2,e2)) != e2 )
| ( op(e2,op(e1,e2)) = e1
& op(e1,op(e1,e2)) != e2 )
| ( op(e2,op(e0,e2)) = e0
& op(e0,op(e0,e2)) != e2 ) )
& ( ( op(e1,op(e4,e1)) = e4
& op(e4,op(e4,e1)) != e1 )
| ( op(e1,op(e3,e1)) = e3
& op(e3,op(e3,e1)) != e1 )
| ( op(e1,op(e2,e1)) = e2
& op(e2,op(e2,e1)) != e1 )
| ( op(e1,op(e1,e1)) = e1
& op(e1,op(e1,e1)) != e1 )
| ( op(e1,op(e0,e1)) = e0
& op(e0,op(e0,e1)) != e1 ) )
& ( ( op(e0,op(e4,e0)) = e4
& op(e4,op(e4,e0)) != e0 )
| ( op(e0,op(e3,e0)) = e3
& op(e3,op(e3,e0)) != e0 )
| ( op(e0,op(e2,e0)) = e2
& op(e2,op(e2,e0)) != e0 )
| ( op(e0,op(e1,e0)) = e1
& op(e1,op(e1,e0)) != e0 )
| ( op(e0,op(e0,e0)) = e0
& op(e0,op(e0,e0)) != e0 ) ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
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(f34,plain,
op(unit,e0) = e0,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f35,plain,
op(e0,unit) = e0,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f36,plain,
op(unit,e1) = e1,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(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(f44,plain,
( unit = e4
| unit = e3
| unit = e2
| unit = e1
| unit = e0 ),
inference(cnf_transformation,[status(thm)],[f2]) ).
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(f66,plain,
( op(e4,e2) = e0
| op(e3,e2) = e0
| op(e2,e2) = e0
| op(e1,e2) = e0
| op(e0,e2) = e0 ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f67,plain,
( op(e2,e4) = e1
| op(e2,e3) = e1
| op(e2,e2) = e1
| op(e2,e1) = e1
| op(e2,e0) = e1 ),
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(f83,plain,
( op(e3,e4) = e4
| op(e3,e3) = e4
| op(e3,e2) = e4
| op(e3,e1) = e4
| op(e3,e0) = e4 ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f97,plain,
op(e0,e0) != op(e3,e0),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f117,plain,
op(e0,e2) != op(e3,e2),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f122,plain,
op(e2,e2) != op(e3,e2),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f138,plain,
op(e0,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(f149,plain,
op(e0,e1) != op(e0,e2),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f150,plain,
op(e0,e1) != op(e0,e3),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f155,plain,
op(e1,e0) != op(e1,e1),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f156,plain,
op(e1,e0) != op(e1,e2),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f168,plain,
op(e2,e0) != op(e2,e4),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f174,plain,
op(e2,e3) != op(e2,e4),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f175,plain,
op(e3,e0) != op(e3,e1),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f176,plain,
op(e3,e0) != op(e3,e2),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f181,plain,
op(e3,e1) != op(e3,e4),
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(f193,plain,
op(e4,e2) != op(e4,e4),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f194,plain,
op(e4,e3) != op(e4,e4),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f195,plain,
e0 != e1,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f196,plain,
e0 != e2,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f197,plain,
e0 != e3,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f198,plain,
e0 != e4,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f199,plain,
e1 != e2,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f200,plain,
e1 != e3,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f201,plain,
e1 != e4,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f202,plain,
e2 != e3,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f203,plain,
e2 != e4,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f204,plain,
e3 != e4,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f205,plain,
e0 = op(op(e2,e2),op(e2,e2)),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f206,plain,
e1 = op(op(e2,op(e2,e2)),op(e2,e2)),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f207,plain,
e3 = op(e2,op(e2,e2)),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f208,plain,
e4 = op(e2,e2),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f209,definition,
( sP0_prd
<=> ( ( op(e0,op(e3,e0)) = e3
& op(e3,op(e3,e0)) != e0 )
| ( op(e0,op(e2,e0)) = e2
& op(e2,op(e2,e0)) != e0 )
| ( op(e0,op(e1,e0)) = e1
& op(e1,op(e1,e0)) != e0 )
| ( op(e0,op(e0,e0)) = e0
& op(e0,op(e0,e0)) != e0 ) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f210,definition,
( sP1_prd
<=> ( ( op(e1,op(e3,e1)) = e3
& op(e3,op(e3,e1)) != e1 )
| ( op(e1,op(e2,e1)) = e2
& op(e2,op(e2,e1)) != e1 )
| ( op(e1,op(e1,e1)) = e1
& op(e1,op(e1,e1)) != e1 )
| ( op(e1,op(e0,e1)) = e0
& op(e0,op(e0,e1)) != e1 ) ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f211,definition,
( sP2_prd
<=> ( ( op(e2,op(e3,e2)) = e3
& op(e3,op(e3,e2)) != e2 )
| ( op(e2,op(e2,e2)) = e2
& op(e2,op(e2,e2)) != e2 )
| ( op(e2,op(e1,e2)) = e1
& op(e1,op(e1,e2)) != e2 )
| ( op(e2,op(e0,e2)) = e0
& op(e0,op(e0,e2)) != e2 ) ) ),
introduced(definition,[new_symbols(definition,[sP2_prd])],[]) ).
fof(f212,definition,
( sP3_prd
<=> ( ( op(e3,op(e3,e3)) = e3
& op(e3,op(e3,e3)) != e3 )
| ( op(e3,op(e2,e3)) = e2
& op(e2,op(e2,e3)) != e3 )
| ( op(e3,op(e1,e3)) = e1
& op(e1,op(e1,e3)) != e3 )
| ( op(e3,op(e0,e3)) = e0
& op(e0,op(e0,e3)) != e3 ) ) ),
introduced(definition,[new_symbols(definition,[sP3_prd])],[]) ).
fof(f213,definition,
( sP4_prd
<=> ( ( op(e4,op(e3,e4)) = e3
& op(e3,op(e3,e4)) != e4 )
| ( op(e4,op(e2,e4)) = e2
& op(e2,op(e2,e4)) != e4 )
| ( op(e4,op(e1,e4)) = e1
& op(e1,op(e1,e4)) != e4 )
| ( op(e4,op(e0,e4)) = e0
& op(e0,op(e0,e4)) != e4 ) ) ),
introduced(definition,[new_symbols(definition,[sP4_prd])],[]) ).
fof(f214,definition,
( sP5_prd
<=> ( ( op(e4,e3) != e4
& op(e3,e3) = e4
& op(e4,e4) = e3 )
| ( op(e4,e2) != e4
& op(e2,e2) = e4
& op(e4,e4) = e2 )
| ( op(e4,e1) != e4
& op(e1,e1) = e4
& op(e4,e4) = e1 )
| ( op(e4,e0) != e4
& op(e0,e0) = e4
& op(e4,e4) = e0 )
| ( op(e3,e4) != e3
& op(e4,e4) = e3
& op(e3,e3) = e4 )
| ( op(e3,e3) != e3
& op(e3,e3) = e3
& op(e3,e3) = e3 )
| ( op(e3,e2) != e3
& op(e2,e2) = e3
& op(e3,e3) = e2 )
| ( op(e3,e1) != e3
& op(e1,e1) = e3
& op(e3,e3) = e1 )
| ( op(e3,e0) != e3
& op(e0,e0) = e3
& op(e3,e3) = e0 )
| ( op(e2,e4) != e2
& op(e4,e4) = e2
& op(e2,e2) = e4 )
| ( op(e2,e3) != e2
& op(e3,e3) = e2
& op(e2,e2) = e3 )
| ( op(e2,e2) != e2
& op(e2,e2) = e2
& op(e2,e2) = e2 )
| ( op(e2,e1) != e2
& op(e1,e1) = e2
& op(e2,e2) = e1 )
| ( op(e2,e0) != e2
& op(e0,e0) = e2
& op(e2,e2) = e0 )
| ( op(e1,e4) != e1
& op(e4,e4) = e1
& op(e1,e1) = e4 )
| ( op(e1,e3) != e1
& op(e3,e3) = e1
& op(e1,e1) = e3 )
| ( op(e1,e2) != e1
& op(e2,e2) = e1
& op(e1,e1) = e2 )
| ( op(e1,e1) != e1
& op(e1,e1) = e1
& op(e1,e1) = e1 )
| ( op(e1,e0) != e1
& op(e0,e0) = e1
& op(e1,e1) = e0 )
| ( op(e0,e4) != e0
& op(e4,e4) = e0
& op(e0,e0) = e4 )
| ( op(e0,e3) != e0
& op(e3,e3) = e0
& op(e0,e0) = e3 )
| ( op(e0,e2) != e0
& op(e2,e2) = e0
& op(e0,e0) = e2 )
| ( op(e0,e1) != e0
& op(e1,e1) = e0
& op(e0,e0) = e1 )
| ( op(e0,e0) != e0
& op(e0,e0) = e0
& op(e0,e0) = e0 ) ) ),
introduced(definition,[new_symbols(definition,[sP5_prd])],[]) ).
fof(f215,plain,
( ( ( op(e4,e4) != e4
& op(e4,e4) = e4
& op(e4,e4) = e4 )
| sP5_prd )
& ( ( op(e4,op(e4,e4)) = e4
& op(e4,op(e4,e4)) != e4 )
| sP4_prd )
& ( ( op(e3,op(e4,e3)) = e4
& op(e4,op(e4,e3)) != e3 )
| sP3_prd )
& ( ( op(e2,op(e4,e2)) = e4
& op(e4,op(e4,e2)) != e2 )
| sP2_prd )
& ( ( op(e1,op(e4,e1)) = e4
& op(e4,op(e4,e1)) != e1 )
| sP1_prd )
& ( ( op(e0,op(e4,e0)) = e4
& op(e4,op(e4,e0)) != e0 )
| sP0_prd ) ),
inference(formula_renaming,[status(thm)],[f8,f214,f213,f212,f211,f210,f209]) ).
fof(f217,plain,
( op(e0,op(e4,e0)) = e4
| sP0_prd ),
inference(cnf_transformation,[status(thm)],[f215]) ).
fof(f226,plain,
( op(e4,e4) = e4
| sP5_prd ),
inference(cnf_transformation,[status(thm)],[f215]) ).
fof(f228,plain,
( op(e4,e4) != e4
| sP5_prd ),
inference(cnf_transformation,[status(thm)],[f215]) ).
fof(f229,definition,
( sP6_prd
<=> ( ( op(e0,op(e2,e0)) = e2
& op(e2,op(e2,e0)) != e0 )
| ( op(e0,op(e1,e0)) = e1
& op(e1,op(e1,e0)) != e0 )
| ( op(e0,op(e0,e0)) = e0
& op(e0,op(e0,e0)) != e0 ) ) ),
introduced(definition,[new_symbols(definition,[sP6_prd])],[]) ).
fof(f230,plain,
( sP0_prd
<=> ( ( op(e0,op(e3,e0)) = e3
& op(e3,op(e3,e0)) != e0 )
| sP6_prd ) ),
inference(formula_renaming,[status(thm)],[f209,f229]) ).
fof(f231,plain,
( ( ( ( op(e0,op(e3,e0)) != e3
| op(e3,op(e3,e0)) = e0 )
& ~ sP6_prd )
| sP0_prd )
& ( ( op(e0,op(e3,e0)) = e3
& op(e3,op(e3,e0)) != e0 )
| sP6_prd
| ~ sP0_prd ) ),
inference(NNF_transformation,[status(thm)],[f230]) ).
fof(f232,plain,
( op(e3,op(e3,e0)) != e0
| sP6_prd
| ~ sP0_prd ),
inference(cnf_transformation,[status(thm)],[f231]) ).
fof(f264,definition,
( sP11_prd
<=> ( ( op(e4,e2) != e4
& op(e2,e2) = e4
& op(e4,e4) = e2 )
| ( op(e4,e1) != e4
& op(e1,e1) = e4
& op(e4,e4) = e1 )
| ( op(e4,e0) != e4
& op(e0,e0) = e4
& op(e4,e4) = e0 )
| ( op(e3,e4) != e3
& op(e4,e4) = e3
& op(e3,e3) = e4 )
| ( op(e3,e3) != e3
& op(e3,e3) = e3
& op(e3,e3) = e3 )
| ( op(e3,e2) != e3
& op(e2,e2) = e3
& op(e3,e3) = e2 )
| ( op(e3,e1) != e3
& op(e1,e1) = e3
& op(e3,e3) = e1 )
| ( op(e3,e0) != e3
& op(e0,e0) = e3
& op(e3,e3) = e0 )
| ( op(e2,e4) != e2
& op(e4,e4) = e2
& op(e2,e2) = e4 )
| ( op(e2,e3) != e2
& op(e3,e3) = e2
& op(e2,e2) = e3 )
| ( op(e2,e2) != e2
& op(e2,e2) = e2
& op(e2,e2) = e2 )
| ( op(e2,e1) != e2
& op(e1,e1) = e2
& op(e2,e2) = e1 )
| ( op(e2,e0) != e2
& op(e0,e0) = e2
& op(e2,e2) = e0 )
| ( op(e1,e4) != e1
& op(e4,e4) = e1
& op(e1,e1) = e4 )
| ( op(e1,e3) != e1
& op(e3,e3) = e1
& op(e1,e1) = e3 )
| ( op(e1,e2) != e1
& op(e2,e2) = e1
& op(e1,e1) = e2 )
| ( op(e1,e1) != e1
& op(e1,e1) = e1
& op(e1,e1) = e1 )
| ( op(e1,e0) != e1
& op(e0,e0) = e1
& op(e1,e1) = e0 )
| ( op(e0,e4) != e0
& op(e4,e4) = e0
& op(e0,e0) = e4 )
| ( op(e0,e3) != e0
& op(e3,e3) = e0
& op(e0,e0) = e3 )
| ( op(e0,e2) != e0
& op(e2,e2) = e0
& op(e0,e0) = e2 )
| ( op(e0,e1) != e0
& op(e1,e1) = e0
& op(e0,e0) = e1 )
| ( op(e0,e0) != e0
& op(e0,e0) = e0
& op(e0,e0) = e0 ) ) ),
introduced(definition,[new_symbols(definition,[sP11_prd])],[]) ).
fof(f265,plain,
( sP5_prd
<=> ( ( op(e4,e3) != e4
& op(e3,e3) = e4
& op(e4,e4) = e3 )
| sP11_prd ) ),
inference(formula_renaming,[status(thm)],[f214,f264]) ).
fof(f266,plain,
( ( ( ( op(e4,e3) = e4
| op(e3,e3) != e4
| op(e4,e4) != e3 )
& ~ sP11_prd )
| sP5_prd )
& ( ( op(e4,e3) != e4
& op(e3,e3) = e4
& op(e4,e4) = e3 )
| sP11_prd
| ~ sP5_prd ) ),
inference(NNF_transformation,[status(thm)],[f265]) ).
fof(f267,plain,
( op(e4,e4) = e3
| sP11_prd
| ~ sP5_prd ),
inference(cnf_transformation,[status(thm)],[f266]) ).
fof(f272,definition,
( sP12_prd
<=> ( ( op(e0,op(e1,e0)) = e1
& op(e1,op(e1,e0)) != e0 )
| ( op(e0,op(e0,e0)) = e0
& op(e0,op(e0,e0)) != e0 ) ) ),
introduced(definition,[new_symbols(definition,[sP12_prd])],[]) ).
fof(f273,plain,
( sP6_prd
<=> ( ( op(e0,op(e2,e0)) = e2
& op(e2,op(e2,e0)) != e0 )
| sP12_prd ) ),
inference(formula_renaming,[status(thm)],[f229,f272]) ).
fof(f274,plain,
( ( ( ( op(e0,op(e2,e0)) != e2
| op(e2,op(e2,e0)) = e0 )
& ~ sP12_prd )
| sP6_prd )
& ( ( op(e0,op(e2,e0)) = e2
& op(e2,op(e2,e0)) != e0 )
| sP12_prd
| ~ sP6_prd ) ),
inference(NNF_transformation,[status(thm)],[f273]) ).
fof(f276,plain,
( op(e0,op(e2,e0)) = e2
| sP12_prd
| ~ sP6_prd ),
inference(cnf_transformation,[status(thm)],[f274]) ).
fof(f307,definition,
( sP17_prd
<=> ( ( op(e4,e1) != e4
& op(e1,e1) = e4
& op(e4,e4) = e1 )
| ( op(e4,e0) != e4
& op(e0,e0) = e4
& op(e4,e4) = e0 )
| ( op(e3,e4) != e3
& op(e4,e4) = e3
& op(e3,e3) = e4 )
| ( op(e3,e3) != e3
& op(e3,e3) = e3
& op(e3,e3) = e3 )
| ( op(e3,e2) != e3
& op(e2,e2) = e3
& op(e3,e3) = e2 )
| ( op(e3,e1) != e3
& op(e1,e1) = e3
& op(e3,e3) = e1 )
| ( op(e3,e0) != e3
& op(e0,e0) = e3
& op(e3,e3) = e0 )
| ( op(e2,e4) != e2
& op(e4,e4) = e2
& op(e2,e2) = e4 )
| ( op(e2,e3) != e2
& op(e3,e3) = e2
& op(e2,e2) = e3 )
| ( op(e2,e2) != e2
& op(e2,e2) = e2
& op(e2,e2) = e2 )
| ( op(e2,e1) != e2
& op(e1,e1) = e2
& op(e2,e2) = e1 )
| ( op(e2,e0) != e2
& op(e0,e0) = e2
& op(e2,e2) = e0 )
| ( op(e1,e4) != e1
& op(e4,e4) = e1
& op(e1,e1) = e4 )
| ( op(e1,e3) != e1
& op(e3,e3) = e1
& op(e1,e1) = e3 )
| ( op(e1,e2) != e1
& op(e2,e2) = e1
& op(e1,e1) = e2 )
| ( op(e1,e1) != e1
& op(e1,e1) = e1
& op(e1,e1) = e1 )
| ( op(e1,e0) != e1
& op(e0,e0) = e1
& op(e1,e1) = e0 )
| ( op(e0,e4) != e0
& op(e4,e4) = e0
& op(e0,e0) = e4 )
| ( op(e0,e3) != e0
& op(e3,e3) = e0
& op(e0,e0) = e3 )
| ( op(e0,e2) != e0
& op(e2,e2) = e0
& op(e0,e0) = e2 )
| ( op(e0,e1) != e0
& op(e1,e1) = e0
& op(e0,e0) = e1 )
| ( op(e0,e0) != e0
& op(e0,e0) = e0
& op(e0,e0) = e0 ) ) ),
introduced(definition,[new_symbols(definition,[sP17_prd])],[]) ).
fof(f308,plain,
( sP11_prd
<=> ( ( op(e4,e2) != e4
& op(e2,e2) = e4
& op(e4,e4) = e2 )
| sP17_prd ) ),
inference(formula_renaming,[status(thm)],[f264,f307]) ).
fof(f309,plain,
( ( ( ( op(e4,e2) = e4
| op(e2,e2) != e4
| op(e4,e4) != e2 )
& ~ sP17_prd )
| sP11_prd )
& ( ( op(e4,e2) != e4
& op(e2,e2) = e4
& op(e4,e4) = e2 )
| sP17_prd
| ~ sP11_prd ) ),
inference(NNF_transformation,[status(thm)],[f308]) ).
fof(f310,plain,
( op(e4,e4) = e2
| sP17_prd
| ~ sP11_prd ),
inference(cnf_transformation,[status(thm)],[f309]) ).
fof(f315,plain,
( ( ( ( op(e0,op(e1,e0)) != e1
| op(e1,op(e1,e0)) = e0 )
& ( op(e0,op(e0,e0)) != e0
| op(e0,op(e0,e0)) = e0 ) )
| sP12_prd )
& ( ( op(e0,op(e1,e0)) = e1
& op(e1,op(e1,e0)) != e0 )
| ( op(e0,op(e0,e0)) = e0
& op(e0,op(e0,e0)) != e0 )
| ~ sP12_prd ) ),
inference(NNF_transformation,[status(thm)],[f272]) ).
fof(f316,plain,
( op(e1,op(e1,e0)) != e0
| op(e0,op(e0,e0)) != e0
| ~ sP12_prd ),
inference(cnf_transformation,[status(thm)],[f315]) ).
fof(f318,plain,
( op(e1,op(e1,e0)) != e0
| op(e0,op(e0,e0)) = e0
| ~ sP12_prd ),
inference(cnf_transformation,[status(thm)],[f315]) ).
fof(f350,definition,
( sP18_prd
<=> ( ( op(e4,e0) != e4
& op(e0,e0) = e4
& op(e4,e4) = e0 )
| ( op(e3,e4) != e3
& op(e4,e4) = e3
& op(e3,e3) = e4 )
| ( op(e3,e3) != e3
& op(e3,e3) = e3
& op(e3,e3) = e3 )
| ( op(e3,e2) != e3
& op(e2,e2) = e3
& op(e3,e3) = e2 )
| ( op(e3,e1) != e3
& op(e1,e1) = e3
& op(e3,e3) = e1 )
| ( op(e3,e0) != e3
& op(e0,e0) = e3
& op(e3,e3) = e0 )
| ( op(e2,e4) != e2
& op(e4,e4) = e2
& op(e2,e2) = e4 )
| ( op(e2,e3) != e2
& op(e3,e3) = e2
& op(e2,e2) = e3 )
| ( op(e2,e2) != e2
& op(e2,e2) = e2
& op(e2,e2) = e2 )
| ( op(e2,e1) != e2
& op(e1,e1) = e2
& op(e2,e2) = e1 )
| ( op(e2,e0) != e2
& op(e0,e0) = e2
& op(e2,e2) = e0 )
| ( op(e1,e4) != e1
& op(e4,e4) = e1
& op(e1,e1) = e4 )
| ( op(e1,e3) != e1
& op(e3,e3) = e1
& op(e1,e1) = e3 )
| ( op(e1,e2) != e1
& op(e2,e2) = e1
& op(e1,e1) = e2 )
| ( op(e1,e1) != e1
& op(e1,e1) = e1
& op(e1,e1) = e1 )
| ( op(e1,e0) != e1
& op(e0,e0) = e1
& op(e1,e1) = e0 )
| ( op(e0,e4) != e0
& op(e4,e4) = e0
& op(e0,e0) = e4 )
| ( op(e0,e3) != e0
& op(e3,e3) = e0
& op(e0,e0) = e3 )
| ( op(e0,e2) != e0
& op(e2,e2) = e0
& op(e0,e0) = e2 )
| ( op(e0,e1) != e0
& op(e1,e1) = e0
& op(e0,e0) = e1 )
| ( op(e0,e0) != e0
& op(e0,e0) = e0
& op(e0,e0) = e0 ) ) ),
introduced(definition,[new_symbols(definition,[sP18_prd])],[]) ).
fof(f351,plain,
( sP17_prd
<=> ( ( op(e4,e1) != e4
& op(e1,e1) = e4
& op(e4,e4) = e1 )
| sP18_prd ) ),
inference(formula_renaming,[status(thm)],[f307,f350]) ).
fof(f352,plain,
( ( ( ( op(e4,e1) = e4
| op(e1,e1) != e4
| op(e4,e4) != e1 )
& ~ sP18_prd )
| sP17_prd )
& ( ( op(e4,e1) != e4
& op(e1,e1) = e4
& op(e4,e4) = e1 )
| sP18_prd
| ~ sP17_prd ) ),
inference(NNF_transformation,[status(thm)],[f351]) ).
fof(f353,plain,
( op(e4,e4) = e1
| sP18_prd
| ~ sP17_prd ),
inference(cnf_transformation,[status(thm)],[f352]) ).
fof(f358,definition,
( sP19_prd
<=> ( ( op(e3,e4) != e3
& op(e4,e4) = e3
& op(e3,e3) = e4 )
| ( op(e3,e3) != e3
& op(e3,e3) = e3
& op(e3,e3) = e3 )
| ( op(e3,e2) != e3
& op(e2,e2) = e3
& op(e3,e3) = e2 )
| ( op(e3,e1) != e3
& op(e1,e1) = e3
& op(e3,e3) = e1 )
| ( op(e3,e0) != e3
& op(e0,e0) = e3
& op(e3,e3) = e0 )
| ( op(e2,e4) != e2
& op(e4,e4) = e2
& op(e2,e2) = e4 )
| ( op(e2,e3) != e2
& op(e3,e3) = e2
& op(e2,e2) = e3 )
| ( op(e2,e2) != e2
& op(e2,e2) = e2
& op(e2,e2) = e2 )
| ( op(e2,e1) != e2
& op(e1,e1) = e2
& op(e2,e2) = e1 )
| ( op(e2,e0) != e2
& op(e0,e0) = e2
& op(e2,e2) = e0 )
| ( op(e1,e4) != e1
& op(e4,e4) = e1
& op(e1,e1) = e4 )
| ( op(e1,e3) != e1
& op(e3,e3) = e1
& op(e1,e1) = e3 )
| ( op(e1,e2) != e1
& op(e2,e2) = e1
& op(e1,e1) = e2 )
| ( op(e1,e1) != e1
& op(e1,e1) = e1
& op(e1,e1) = e1 )
| ( op(e1,e0) != e1
& op(e0,e0) = e1
& op(e1,e1) = e0 )
| ( op(e0,e4) != e0
& op(e4,e4) = e0
& op(e0,e0) = e4 )
| ( op(e0,e3) != e0
& op(e3,e3) = e0
& op(e0,e0) = e3 )
| ( op(e0,e2) != e0
& op(e2,e2) = e0
& op(e0,e0) = e2 )
| ( op(e0,e1) != e0
& op(e1,e1) = e0
& op(e0,e0) = e1 )
| ( op(e0,e0) != e0
& op(e0,e0) = e0
& op(e0,e0) = e0 ) ) ),
introduced(definition,[new_symbols(definition,[sP19_prd])],[]) ).
fof(f359,plain,
( sP18_prd
<=> ( ( op(e4,e0) != e4
& op(e0,e0) = e4
& op(e4,e4) = e0 )
| sP19_prd ) ),
inference(formula_renaming,[status(thm)],[f350,f358]) ).
fof(f360,plain,
( ( ( ( op(e4,e0) = e4
| op(e0,e0) != e4
| op(e4,e4) != e0 )
& ~ sP19_prd )
| sP18_prd )
& ( ( op(e4,e0) != e4
& op(e0,e0) = e4
& op(e4,e4) = e0 )
| sP19_prd
| ~ sP18_prd ) ),
inference(NNF_transformation,[status(thm)],[f359]) ).
fof(f362,plain,
( op(e0,e0) = e4
| sP19_prd
| ~ sP18_prd ),
inference(cnf_transformation,[status(thm)],[f360]) ).
fof(f366,definition,
( sP20_prd
<=> ( ( op(e3,e3) != e3
& op(e3,e3) = e3
& op(e3,e3) = e3 )
| ( op(e3,e2) != e3
& op(e2,e2) = e3
& op(e3,e3) = e2 )
| ( op(e3,e1) != e3
& op(e1,e1) = e3
& op(e3,e3) = e1 )
| ( op(e3,e0) != e3
& op(e0,e0) = e3
& op(e3,e3) = e0 )
| ( op(e2,e4) != e2
& op(e4,e4) = e2
& op(e2,e2) = e4 )
| ( op(e2,e3) != e2
& op(e3,e3) = e2
& op(e2,e2) = e3 )
| ( op(e2,e2) != e2
& op(e2,e2) = e2
& op(e2,e2) = e2 )
| ( op(e2,e1) != e2
& op(e1,e1) = e2
& op(e2,e2) = e1 )
| ( op(e2,e0) != e2
& op(e0,e0) = e2
& op(e2,e2) = e0 )
| ( op(e1,e4) != e1
& op(e4,e4) = e1
& op(e1,e1) = e4 )
| ( op(e1,e3) != e1
& op(e3,e3) = e1
& op(e1,e1) = e3 )
| ( op(e1,e2) != e1
& op(e2,e2) = e1
& op(e1,e1) = e2 )
| ( op(e1,e1) != e1
& op(e1,e1) = e1
& op(e1,e1) = e1 )
| ( op(e1,e0) != e1
& op(e0,e0) = e1
& op(e1,e1) = e0 )
| ( op(e0,e4) != e0
& op(e4,e4) = e0
& op(e0,e0) = e4 )
| ( op(e0,e3) != e0
& op(e3,e3) = e0
& op(e0,e0) = e3 )
| ( op(e0,e2) != e0
& op(e2,e2) = e0
& op(e0,e0) = e2 )
| ( op(e0,e1) != e0
& op(e1,e1) = e0
& op(e0,e0) = e1 )
| ( op(e0,e0) != e0
& op(e0,e0) = e0
& op(e0,e0) = e0 ) ) ),
introduced(definition,[new_symbols(definition,[sP20_prd])],[]) ).
fof(f367,plain,
( sP19_prd
<=> ( ( op(e3,e4) != e3
& op(e4,e4) = e3
& op(e3,e3) = e4 )
| sP20_prd ) ),
inference(formula_renaming,[status(thm)],[f358,f366]) ).
fof(f368,plain,
( ( ( ( op(e3,e4) = e3
| op(e4,e4) != e3
| op(e3,e3) != e4 )
& ~ sP20_prd )
| sP19_prd )
& ( ( op(e3,e4) != e3
& op(e4,e4) = e3
& op(e3,e3) = e4 )
| sP20_prd
| ~ sP19_prd ) ),
inference(NNF_transformation,[status(thm)],[f367]) ).
fof(f370,plain,
( op(e4,e4) = e3
| sP20_prd
| ~ sP19_prd ),
inference(cnf_transformation,[status(thm)],[f368]) ).
fof(f372,plain,
( ~ sP20_prd
| sP19_prd ),
inference(cnf_transformation,[status(thm)],[f368]) ).
fof(f374,definition,
( sP21_prd
<=> ( ( op(e3,e2) != e3
& op(e2,e2) = e3
& op(e3,e3) = e2 )
| ( op(e3,e1) != e3
& op(e1,e1) = e3
& op(e3,e3) = e1 )
| ( op(e3,e0) != e3
& op(e0,e0) = e3
& op(e3,e3) = e0 )
| ( op(e2,e4) != e2
& op(e4,e4) = e2
& op(e2,e2) = e4 )
| ( op(e2,e3) != e2
& op(e3,e3) = e2
& op(e2,e2) = e3 )
| ( op(e2,e2) != e2
& op(e2,e2) = e2
& op(e2,e2) = e2 )
| ( op(e2,e1) != e2
& op(e1,e1) = e2
& op(e2,e2) = e1 )
| ( op(e2,e0) != e2
& op(e0,e0) = e2
& op(e2,e2) = e0 )
| ( op(e1,e4) != e1
& op(e4,e4) = e1
& op(e1,e1) = e4 )
| ( op(e1,e3) != e1
& op(e3,e3) = e1
& op(e1,e1) = e3 )
| ( op(e1,e2) != e1
& op(e2,e2) = e1
& op(e1,e1) = e2 )
| ( op(e1,e1) != e1
& op(e1,e1) = e1
& op(e1,e1) = e1 )
| ( op(e1,e0) != e1
& op(e0,e0) = e1
& op(e1,e1) = e0 )
| ( op(e0,e4) != e0
& op(e4,e4) = e0
& op(e0,e0) = e4 )
| ( op(e0,e3) != e0
& op(e3,e3) = e0
& op(e0,e0) = e3 )
| ( op(e0,e2) != e0
& op(e2,e2) = e0
& op(e0,e0) = e2 )
| ( op(e0,e1) != e0
& op(e1,e1) = e0
& op(e0,e0) = e1 )
| ( op(e0,e0) != e0
& op(e0,e0) = e0
& op(e0,e0) = e0 ) ) ),
introduced(definition,[new_symbols(definition,[sP21_prd])],[]) ).
fof(f375,plain,
( sP20_prd
<=> ( ( op(e3,e3) != e3
& op(e3,e3) = e3
& op(e3,e3) = e3 )
| sP21_prd ) ),
inference(formula_renaming,[status(thm)],[f366,f374]) ).
fof(f376,plain,
( ( ( ( op(e3,e3) = e3
| op(e3,e3) != e3
| op(e3,e3) != e3 )
& ~ sP21_prd )
| sP20_prd )
& ( ( op(e3,e3) != e3
& op(e3,e3) = e3
& op(e3,e3) = e3 )
| sP21_prd
| ~ sP20_prd ) ),
inference(NNF_transformation,[status(thm)],[f375]) ).
fof(f377,plain,
( op(e3,e3) = e3
| sP21_prd
| ~ sP20_prd ),
inference(cnf_transformation,[status(thm)],[f376]) ).
fof(f379,plain,
( op(e3,e3) != e3
| sP21_prd
| ~ sP20_prd ),
inference(cnf_transformation,[status(thm)],[f376]) ).
fof(f380,plain,
( ~ sP21_prd
| sP20_prd ),
inference(cnf_transformation,[status(thm)],[f376]) ).
fof(f382,definition,
( sP22_prd
<=> ( ( op(e3,e1) != e3
& op(e1,e1) = e3
& op(e3,e3) = e1 )
| ( op(e3,e0) != e3
& op(e0,e0) = e3
& op(e3,e3) = e0 )
| ( op(e2,e4) != e2
& op(e4,e4) = e2
& op(e2,e2) = e4 )
| ( op(e2,e3) != e2
& op(e3,e3) = e2
& op(e2,e2) = e3 )
| ( op(e2,e2) != e2
& op(e2,e2) = e2
& op(e2,e2) = e2 )
| ( op(e2,e1) != e2
& op(e1,e1) = e2
& op(e2,e2) = e1 )
| ( op(e2,e0) != e2
& op(e0,e0) = e2
& op(e2,e2) = e0 )
| ( op(e1,e4) != e1
& op(e4,e4) = e1
& op(e1,e1) = e4 )
| ( op(e1,e3) != e1
& op(e3,e3) = e1
& op(e1,e1) = e3 )
| ( op(e1,e2) != e1
& op(e2,e2) = e1
& op(e1,e1) = e2 )
| ( op(e1,e1) != e1
& op(e1,e1) = e1
& op(e1,e1) = e1 )
| ( op(e1,e0) != e1
& op(e0,e0) = e1
& op(e1,e1) = e0 )
| ( op(e0,e4) != e0
& op(e4,e4) = e0
& op(e0,e0) = e4 )
| ( op(e0,e3) != e0
& op(e3,e3) = e0
& op(e0,e0) = e3 )
| ( op(e0,e2) != e0
& op(e2,e2) = e0
& op(e0,e0) = e2 )
| ( op(e0,e1) != e0
& op(e1,e1) = e0
& op(e0,e0) = e1 )
| ( op(e0,e0) != e0
& op(e0,e0) = e0
& op(e0,e0) = e0 ) ) ),
introduced(definition,[new_symbols(definition,[sP22_prd])],[]) ).
fof(f383,plain,
( sP21_prd
<=> ( ( op(e3,e2) != e3
& op(e2,e2) = e3
& op(e3,e3) = e2 )
| sP22_prd ) ),
inference(formula_renaming,[status(thm)],[f374,f382]) ).
fof(f384,plain,
( ( ( ( op(e3,e2) = e3
| op(e2,e2) != e3
| op(e3,e3) != e2 )
& ~ sP22_prd )
| sP21_prd )
& ( ( op(e3,e2) != e3
& op(e2,e2) = e3
& op(e3,e3) = e2 )
| sP22_prd
| ~ sP21_prd ) ),
inference(NNF_transformation,[status(thm)],[f383]) ).
fof(f386,plain,
( op(e2,e2) = e3
| sP22_prd
| ~ sP21_prd ),
inference(cnf_transformation,[status(thm)],[f384]) ).
fof(f388,plain,
( ~ sP22_prd
| sP21_prd ),
inference(cnf_transformation,[status(thm)],[f384]) ).
fof(f390,definition,
( sP23_prd
<=> ( ( op(e3,e0) != e3
& op(e0,e0) = e3
& op(e3,e3) = e0 )
| ( op(e2,e4) != e2
& op(e4,e4) = e2
& op(e2,e2) = e4 )
| ( op(e2,e3) != e2
& op(e3,e3) = e2
& op(e2,e2) = e3 )
| ( op(e2,e2) != e2
& op(e2,e2) = e2
& op(e2,e2) = e2 )
| ( op(e2,e1) != e2
& op(e1,e1) = e2
& op(e2,e2) = e1 )
| ( op(e2,e0) != e2
& op(e0,e0) = e2
& op(e2,e2) = e0 )
| ( op(e1,e4) != e1
& op(e4,e4) = e1
& op(e1,e1) = e4 )
| ( op(e1,e3) != e1
& op(e3,e3) = e1
& op(e1,e1) = e3 )
| ( op(e1,e2) != e1
& op(e2,e2) = e1
& op(e1,e1) = e2 )
| ( op(e1,e1) != e1
& op(e1,e1) = e1
& op(e1,e1) = e1 )
| ( op(e1,e0) != e1
& op(e0,e0) = e1
& op(e1,e1) = e0 )
| ( op(e0,e4) != e0
& op(e4,e4) = e0
& op(e0,e0) = e4 )
| ( op(e0,e3) != e0
& op(e3,e3) = e0
& op(e0,e0) = e3 )
| ( op(e0,e2) != e0
& op(e2,e2) = e0
& op(e0,e0) = e2 )
| ( op(e0,e1) != e0
& op(e1,e1) = e0
& op(e0,e0) = e1 )
| ( op(e0,e0) != e0
& op(e0,e0) = e0
& op(e0,e0) = e0 ) ) ),
introduced(definition,[new_symbols(definition,[sP23_prd])],[]) ).
fof(f391,plain,
( sP22_prd
<=> ( ( op(e3,e1) != e3
& op(e1,e1) = e3
& op(e3,e3) = e1 )
| sP23_prd ) ),
inference(formula_renaming,[status(thm)],[f382,f390]) ).
fof(f392,plain,
( ( ( ( op(e3,e1) = e3
| op(e1,e1) != e3
| op(e3,e3) != e1 )
& ~ sP23_prd )
| sP22_prd )
& ( ( op(e3,e1) != e3
& op(e1,e1) = e3
& op(e3,e3) = e1 )
| sP23_prd
| ~ sP22_prd ) ),
inference(NNF_transformation,[status(thm)],[f391]) ).
fof(f393,plain,
( op(e3,e3) = e1
| sP23_prd
| ~ sP22_prd ),
inference(cnf_transformation,[status(thm)],[f392]) ).
fof(f396,plain,
( ~ sP23_prd
| sP22_prd ),
inference(cnf_transformation,[status(thm)],[f392]) ).
fof(f398,definition,
( sP24_prd
<=> ( ( op(e2,e4) != e2
& op(e4,e4) = e2
& op(e2,e2) = e4 )
| ( op(e2,e3) != e2
& op(e3,e3) = e2
& op(e2,e2) = e3 )
| ( op(e2,e2) != e2
& op(e2,e2) = e2
& op(e2,e2) = e2 )
| ( op(e2,e1) != e2
& op(e1,e1) = e2
& op(e2,e2) = e1 )
| ( op(e2,e0) != e2
& op(e0,e0) = e2
& op(e2,e2) = e0 )
| ( op(e1,e4) != e1
& op(e4,e4) = e1
& op(e1,e1) = e4 )
| ( op(e1,e3) != e1
& op(e3,e3) = e1
& op(e1,e1) = e3 )
| ( op(e1,e2) != e1
& op(e2,e2) = e1
& op(e1,e1) = e2 )
| ( op(e1,e1) != e1
& op(e1,e1) = e1
& op(e1,e1) = e1 )
| ( op(e1,e0) != e1
& op(e0,e0) = e1
& op(e1,e1) = e0 )
| ( op(e0,e4) != e0
& op(e4,e4) = e0
& op(e0,e0) = e4 )
| ( op(e0,e3) != e0
& op(e3,e3) = e0
& op(e0,e0) = e3 )
| ( op(e0,e2) != e0
& op(e2,e2) = e0
& op(e0,e0) = e2 )
| ( op(e0,e1) != e0
& op(e1,e1) = e0
& op(e0,e0) = e1 )
| ( op(e0,e0) != e0
& op(e0,e0) = e0
& op(e0,e0) = e0 ) ) ),
introduced(definition,[new_symbols(definition,[sP24_prd])],[]) ).
fof(f399,plain,
( sP23_prd
<=> ( ( op(e3,e0) != e3
& op(e0,e0) = e3
& op(e3,e3) = e0 )
| sP24_prd ) ),
inference(formula_renaming,[status(thm)],[f390,f398]) ).
fof(f400,plain,
( ( ( ( op(e3,e0) = e3
| op(e0,e0) != e3
| op(e3,e3) != e0 )
& ~ sP24_prd )
| sP23_prd )
& ( ( op(e3,e0) != e3
& op(e0,e0) = e3
& op(e3,e3) = e0 )
| sP24_prd
| ~ sP23_prd ) ),
inference(NNF_transformation,[status(thm)],[f399]) ).
fof(f401,plain,
( op(e3,e3) = e0
| sP24_prd
| ~ sP23_prd ),
inference(cnf_transformation,[status(thm)],[f400]) ).
fof(f404,plain,
( ~ sP24_prd
| sP23_prd ),
inference(cnf_transformation,[status(thm)],[f400]) ).
fof(f406,definition,
( sP25_prd
<=> ( ( op(e2,e3) != e2
& op(e3,e3) = e2
& op(e2,e2) = e3 )
| ( op(e2,e2) != e2
& op(e2,e2) = e2
& op(e2,e2) = e2 )
| ( op(e2,e1) != e2
& op(e1,e1) = e2
& op(e2,e2) = e1 )
| ( op(e2,e0) != e2
& op(e0,e0) = e2
& op(e2,e2) = e0 )
| ( op(e1,e4) != e1
& op(e4,e4) = e1
& op(e1,e1) = e4 )
| ( op(e1,e3) != e1
& op(e3,e3) = e1
& op(e1,e1) = e3 )
| ( op(e1,e2) != e1
& op(e2,e2) = e1
& op(e1,e1) = e2 )
| ( op(e1,e1) != e1
& op(e1,e1) = e1
& op(e1,e1) = e1 )
| ( op(e1,e0) != e1
& op(e0,e0) = e1
& op(e1,e1) = e0 )
| ( op(e0,e4) != e0
& op(e4,e4) = e0
& op(e0,e0) = e4 )
| ( op(e0,e3) != e0
& op(e3,e3) = e0
& op(e0,e0) = e3 )
| ( op(e0,e2) != e0
& op(e2,e2) = e0
& op(e0,e0) = e2 )
| ( op(e0,e1) != e0
& op(e1,e1) = e0
& op(e0,e0) = e1 )
| ( op(e0,e0) != e0
& op(e0,e0) = e0
& op(e0,e0) = e0 ) ) ),
introduced(definition,[new_symbols(definition,[sP25_prd])],[]) ).
fof(f407,plain,
( sP24_prd
<=> ( ( op(e2,e4) != e2
& op(e4,e4) = e2
& op(e2,e2) = e4 )
| sP25_prd ) ),
inference(formula_renaming,[status(thm)],[f398,f406]) ).
fof(f408,plain,
( ( ( ( op(e2,e4) = e2
| op(e4,e4) != e2
| op(e2,e2) != e4 )
& ~ sP25_prd )
| sP24_prd )
& ( ( op(e2,e4) != e2
& op(e4,e4) = e2
& op(e2,e2) = e4 )
| sP25_prd
| ~ sP24_prd ) ),
inference(NNF_transformation,[status(thm)],[f407]) ).
fof(f410,plain,
( op(e4,e4) = e2
| sP25_prd
| ~ sP24_prd ),
inference(cnf_transformation,[status(thm)],[f408]) ).
fof(f412,plain,
( ~ sP25_prd
| sP24_prd ),
inference(cnf_transformation,[status(thm)],[f408]) ).
fof(f414,definition,
( sP26_prd
<=> ( ( op(e2,e2) != e2
& op(e2,e2) = e2
& op(e2,e2) = e2 )
| ( op(e2,e1) != e2
& op(e1,e1) = e2
& op(e2,e2) = e1 )
| ( op(e2,e0) != e2
& op(e0,e0) = e2
& op(e2,e2) = e0 )
| ( op(e1,e4) != e1
& op(e4,e4) = e1
& op(e1,e1) = e4 )
| ( op(e1,e3) != e1
& op(e3,e3) = e1
& op(e1,e1) = e3 )
| ( op(e1,e2) != e1
& op(e2,e2) = e1
& op(e1,e1) = e2 )
| ( op(e1,e1) != e1
& op(e1,e1) = e1
& op(e1,e1) = e1 )
| ( op(e1,e0) != e1
& op(e0,e0) = e1
& op(e1,e1) = e0 )
| ( op(e0,e4) != e0
& op(e4,e4) = e0
& op(e0,e0) = e4 )
| ( op(e0,e3) != e0
& op(e3,e3) = e0
& op(e0,e0) = e3 )
| ( op(e0,e2) != e0
& op(e2,e2) = e0
& op(e0,e0) = e2 )
| ( op(e0,e1) != e0
& op(e1,e1) = e0
& op(e0,e0) = e1 )
| ( op(e0,e0) != e0
& op(e0,e0) = e0
& op(e0,e0) = e0 ) ) ),
introduced(definition,[new_symbols(definition,[sP26_prd])],[]) ).
fof(f415,plain,
( sP25_prd
<=> ( ( op(e2,e3) != e2
& op(e3,e3) = e2
& op(e2,e2) = e3 )
| sP26_prd ) ),
inference(formula_renaming,[status(thm)],[f406,f414]) ).
fof(f416,plain,
( ( ( ( op(e2,e3) = e2
| op(e3,e3) != e2
| op(e2,e2) != e3 )
& ~ sP26_prd )
| sP25_prd )
& ( ( op(e2,e3) != e2
& op(e3,e3) = e2
& op(e2,e2) = e3 )
| sP26_prd
| ~ sP25_prd ) ),
inference(NNF_transformation,[status(thm)],[f415]) ).
fof(f417,plain,
( op(e2,e2) = e3
| sP26_prd
| ~ sP25_prd ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f420,plain,
( ~ sP26_prd
| sP25_prd ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f422,definition,
( sP27_prd
<=> ( ( op(e2,e1) != e2
& op(e1,e1) = e2
& op(e2,e2) = e1 )
| ( op(e2,e0) != e2
& op(e0,e0) = e2
& op(e2,e2) = e0 )
| ( op(e1,e4) != e1
& op(e4,e4) = e1
& op(e1,e1) = e4 )
| ( op(e1,e3) != e1
& op(e3,e3) = e1
& op(e1,e1) = e3 )
| ( op(e1,e2) != e1
& op(e2,e2) = e1
& op(e1,e1) = e2 )
| ( op(e1,e1) != e1
& op(e1,e1) = e1
& op(e1,e1) = e1 )
| ( op(e1,e0) != e1
& op(e0,e0) = e1
& op(e1,e1) = e0 )
| ( op(e0,e4) != e0
& op(e4,e4) = e0
& op(e0,e0) = e4 )
| ( op(e0,e3) != e0
& op(e3,e3) = e0
& op(e0,e0) = e3 )
| ( op(e0,e2) != e0
& op(e2,e2) = e0
& op(e0,e0) = e2 )
| ( op(e0,e1) != e0
& op(e1,e1) = e0
& op(e0,e0) = e1 )
| ( op(e0,e0) != e0
& op(e0,e0) = e0
& op(e0,e0) = e0 ) ) ),
introduced(definition,[new_symbols(definition,[sP27_prd])],[]) ).
fof(f423,plain,
( sP26_prd
<=> ( ( op(e2,e2) != e2
& op(e2,e2) = e2
& op(e2,e2) = e2 )
| sP27_prd ) ),
inference(formula_renaming,[status(thm)],[f414,f422]) ).
fof(f424,plain,
( ( ( ( op(e2,e2) = e2
| op(e2,e2) != e2
| op(e2,e2) != e2 )
& ~ sP27_prd )
| sP26_prd )
& ( ( op(e2,e2) != e2
& op(e2,e2) = e2
& op(e2,e2) = e2 )
| sP27_prd
| ~ sP26_prd ) ),
inference(NNF_transformation,[status(thm)],[f423]) ).
fof(f425,plain,
( op(e2,e2) = e2
| sP27_prd
| ~ sP26_prd ),
inference(cnf_transformation,[status(thm)],[f424]) ).
fof(f428,plain,
( ~ sP27_prd
| sP26_prd ),
inference(cnf_transformation,[status(thm)],[f424]) ).
fof(f430,definition,
( sP28_prd
<=> ( ( op(e2,e0) != e2
& op(e0,e0) = e2
& op(e2,e2) = e0 )
| ( op(e1,e4) != e1
& op(e4,e4) = e1
& op(e1,e1) = e4 )
| ( op(e1,e3) != e1
& op(e3,e3) = e1
& op(e1,e1) = e3 )
| ( op(e1,e2) != e1
& op(e2,e2) = e1
& op(e1,e1) = e2 )
| ( op(e1,e1) != e1
& op(e1,e1) = e1
& op(e1,e1) = e1 )
| ( op(e1,e0) != e1
& op(e0,e0) = e1
& op(e1,e1) = e0 )
| ( op(e0,e4) != e0
& op(e4,e4) = e0
& op(e0,e0) = e4 )
| ( op(e0,e3) != e0
& op(e3,e3) = e0
& op(e0,e0) = e3 )
| ( op(e0,e2) != e0
& op(e2,e2) = e0
& op(e0,e0) = e2 )
| ( op(e0,e1) != e0
& op(e1,e1) = e0
& op(e0,e0) = e1 )
| ( op(e0,e0) != e0
& op(e0,e0) = e0
& op(e0,e0) = e0 ) ) ),
introduced(definition,[new_symbols(definition,[sP28_prd])],[]) ).
fof(f431,plain,
( sP27_prd
<=> ( ( op(e2,e1) != e2
& op(e1,e1) = e2
& op(e2,e2) = e1 )
| sP28_prd ) ),
inference(formula_renaming,[status(thm)],[f422,f430]) ).
fof(f432,plain,
( ( ( ( op(e2,e1) = e2
| op(e1,e1) != e2
| op(e2,e2) != e1 )
& ~ sP28_prd )
| sP27_prd )
& ( ( op(e2,e1) != e2
& op(e1,e1) = e2
& op(e2,e2) = e1 )
| sP28_prd
| ~ sP27_prd ) ),
inference(NNF_transformation,[status(thm)],[f431]) ).
fof(f433,plain,
( op(e2,e2) = e1
| sP28_prd
| ~ sP27_prd ),
inference(cnf_transformation,[status(thm)],[f432]) ).
fof(f436,plain,
( ~ sP28_prd
| sP27_prd ),
inference(cnf_transformation,[status(thm)],[f432]) ).
fof(f438,definition,
( sP29_prd
<=> ( ( op(e1,e4) != e1
& op(e4,e4) = e1
& op(e1,e1) = e4 )
| ( op(e1,e3) != e1
& op(e3,e3) = e1
& op(e1,e1) = e3 )
| ( op(e1,e2) != e1
& op(e2,e2) = e1
& op(e1,e1) = e2 )
| ( op(e1,e1) != e1
& op(e1,e1) = e1
& op(e1,e1) = e1 )
| ( op(e1,e0) != e1
& op(e0,e0) = e1
& op(e1,e1) = e0 )
| ( op(e0,e4) != e0
& op(e4,e4) = e0
& op(e0,e0) = e4 )
| ( op(e0,e3) != e0
& op(e3,e3) = e0
& op(e0,e0) = e3 )
| ( op(e0,e2) != e0
& op(e2,e2) = e0
& op(e0,e0) = e2 )
| ( op(e0,e1) != e0
& op(e1,e1) = e0
& op(e0,e0) = e1 )
| ( op(e0,e0) != e0
& op(e0,e0) = e0
& op(e0,e0) = e0 ) ) ),
introduced(definition,[new_symbols(definition,[sP29_prd])],[]) ).
fof(f439,plain,
( sP28_prd
<=> ( ( op(e2,e0) != e2
& op(e0,e0) = e2
& op(e2,e2) = e0 )
| sP29_prd ) ),
inference(formula_renaming,[status(thm)],[f430,f438]) ).
fof(f440,plain,
( ( ( ( op(e2,e0) = e2
| op(e0,e0) != e2
| op(e2,e2) != e0 )
& ~ sP29_prd )
| sP28_prd )
& ( ( op(e2,e0) != e2
& op(e0,e0) = e2
& op(e2,e2) = e0 )
| sP29_prd
| ~ sP28_prd ) ),
inference(NNF_transformation,[status(thm)],[f439]) ).
fof(f441,plain,
( op(e2,e2) = e0
| sP29_prd
| ~ sP28_prd ),
inference(cnf_transformation,[status(thm)],[f440]) ).
fof(f444,plain,
( ~ sP29_prd
| sP28_prd ),
inference(cnf_transformation,[status(thm)],[f440]) ).
fof(f446,definition,
( sP30_prd
<=> ( ( op(e1,e3) != e1
& op(e3,e3) = e1
& op(e1,e1) = e3 )
| ( op(e1,e2) != e1
& op(e2,e2) = e1
& op(e1,e1) = e2 )
| ( op(e1,e1) != e1
& op(e1,e1) = e1
& op(e1,e1) = e1 )
| ( op(e1,e0) != e1
& op(e0,e0) = e1
& op(e1,e1) = e0 )
| ( op(e0,e4) != e0
& op(e4,e4) = e0
& op(e0,e0) = e4 )
| ( op(e0,e3) != e0
& op(e3,e3) = e0
& op(e0,e0) = e3 )
| ( op(e0,e2) != e0
& op(e2,e2) = e0
& op(e0,e0) = e2 )
| ( op(e0,e1) != e0
& op(e1,e1) = e0
& op(e0,e0) = e1 )
| ( op(e0,e0) != e0
& op(e0,e0) = e0
& op(e0,e0) = e0 ) ) ),
introduced(definition,[new_symbols(definition,[sP30_prd])],[]) ).
fof(f447,plain,
( sP29_prd
<=> ( ( op(e1,e4) != e1
& op(e4,e4) = e1
& op(e1,e1) = e4 )
| sP30_prd ) ),
inference(formula_renaming,[status(thm)],[f438,f446]) ).
fof(f448,plain,
( ( ( ( op(e1,e4) = e1
| op(e4,e4) != e1
| op(e1,e1) != e4 )
& ~ sP30_prd )
| sP29_prd )
& ( ( op(e1,e4) != e1
& op(e4,e4) = e1
& op(e1,e1) = e4 )
| sP30_prd
| ~ sP29_prd ) ),
inference(NNF_transformation,[status(thm)],[f447]) ).
fof(f450,plain,
( op(e4,e4) = e1
| sP30_prd
| ~ sP29_prd ),
inference(cnf_transformation,[status(thm)],[f448]) ).
fof(f452,plain,
( ~ sP30_prd
| sP29_prd ),
inference(cnf_transformation,[status(thm)],[f448]) ).
fof(f454,definition,
( sP31_prd
<=> ( ( op(e1,e2) != e1
& op(e2,e2) = e1
& op(e1,e1) = e2 )
| ( op(e1,e1) != e1
& op(e1,e1) = e1
& op(e1,e1) = e1 )
| ( op(e1,e0) != e1
& op(e0,e0) = e1
& op(e1,e1) = e0 )
| ( op(e0,e4) != e0
& op(e4,e4) = e0
& op(e0,e0) = e4 )
| ( op(e0,e3) != e0
& op(e3,e3) = e0
& op(e0,e0) = e3 )
| ( op(e0,e2) != e0
& op(e2,e2) = e0
& op(e0,e0) = e2 )
| ( op(e0,e1) != e0
& op(e1,e1) = e0
& op(e0,e0) = e1 )
| ( op(e0,e0) != e0
& op(e0,e0) = e0
& op(e0,e0) = e0 ) ) ),
introduced(definition,[new_symbols(definition,[sP31_prd])],[]) ).
fof(f455,plain,
( sP30_prd
<=> ( ( op(e1,e3) != e1
& op(e3,e3) = e1
& op(e1,e1) = e3 )
| sP31_prd ) ),
inference(formula_renaming,[status(thm)],[f446,f454]) ).
fof(f456,plain,
( ( ( ( op(e1,e3) = e1
| op(e3,e3) != e1
| op(e1,e1) != e3 )
& ~ sP31_prd )
| sP30_prd )
& ( ( op(e1,e3) != e1
& op(e3,e3) = e1
& op(e1,e1) = e3 )
| sP31_prd
| ~ sP30_prd ) ),
inference(NNF_transformation,[status(thm)],[f455]) ).
fof(f458,plain,
( op(e3,e3) = e1
| sP31_prd
| ~ sP30_prd ),
inference(cnf_transformation,[status(thm)],[f456]) ).
fof(f460,plain,
( ~ sP31_prd
| sP30_prd ),
inference(cnf_transformation,[status(thm)],[f456]) ).
fof(f462,definition,
( sP32_prd
<=> ( ( op(e1,e1) != e1
& op(e1,e1) = e1
& op(e1,e1) = e1 )
| ( op(e1,e0) != e1
& op(e0,e0) = e1
& op(e1,e1) = e0 )
| ( op(e0,e4) != e0
& op(e4,e4) = e0
& op(e0,e0) = e4 )
| ( op(e0,e3) != e0
& op(e3,e3) = e0
& op(e0,e0) = e3 )
| ( op(e0,e2) != e0
& op(e2,e2) = e0
& op(e0,e0) = e2 )
| ( op(e0,e1) != e0
& op(e1,e1) = e0
& op(e0,e0) = e1 )
| ( op(e0,e0) != e0
& op(e0,e0) = e0
& op(e0,e0) = e0 ) ) ),
introduced(definition,[new_symbols(definition,[sP32_prd])],[]) ).
fof(f463,plain,
( sP31_prd
<=> ( ( op(e1,e2) != e1
& op(e2,e2) = e1
& op(e1,e1) = e2 )
| sP32_prd ) ),
inference(formula_renaming,[status(thm)],[f454,f462]) ).
fof(f464,plain,
( ( ( ( op(e1,e2) = e1
| op(e2,e2) != e1
| op(e1,e1) != e2 )
& ~ sP32_prd )
| sP31_prd )
& ( ( op(e1,e2) != e1
& op(e2,e2) = e1
& op(e1,e1) = e2 )
| sP32_prd
| ~ sP31_prd ) ),
inference(NNF_transformation,[status(thm)],[f463]) ).
fof(f466,plain,
( op(e2,e2) = e1
| sP32_prd
| ~ sP31_prd ),
inference(cnf_transformation,[status(thm)],[f464]) ).
fof(f468,plain,
( ~ sP32_prd
| sP31_prd ),
inference(cnf_transformation,[status(thm)],[f464]) ).
fof(f470,definition,
( sP33_prd
<=> ( ( op(e1,e0) != e1
& op(e0,e0) = e1
& op(e1,e1) = e0 )
| ( op(e0,e4) != e0
& op(e4,e4) = e0
& op(e0,e0) = e4 )
| ( op(e0,e3) != e0
& op(e3,e3) = e0
& op(e0,e0) = e3 )
| ( op(e0,e2) != e0
& op(e2,e2) = e0
& op(e0,e0) = e2 )
| ( op(e0,e1) != e0
& op(e1,e1) = e0
& op(e0,e0) = e1 )
| ( op(e0,e0) != e0
& op(e0,e0) = e0
& op(e0,e0) = e0 ) ) ),
introduced(definition,[new_symbols(definition,[sP33_prd])],[]) ).
fof(f471,plain,
( sP32_prd
<=> ( ( op(e1,e1) != e1
& op(e1,e1) = e1
& op(e1,e1) = e1 )
| sP33_prd ) ),
inference(formula_renaming,[status(thm)],[f462,f470]) ).
fof(f472,plain,
( ( ( ( op(e1,e1) = e1
| op(e1,e1) != e1
| op(e1,e1) != e1 )
& ~ sP33_prd )
| sP32_prd )
& ( ( op(e1,e1) != e1
& op(e1,e1) = e1
& op(e1,e1) = e1 )
| sP33_prd
| ~ sP32_prd ) ),
inference(NNF_transformation,[status(thm)],[f471]) ).
fof(f473,plain,
( op(e1,e1) = e1
| sP33_prd
| ~ sP32_prd ),
inference(cnf_transformation,[status(thm)],[f472]) ).
fof(f475,plain,
( op(e1,e1) != e1
| sP33_prd
| ~ sP32_prd ),
inference(cnf_transformation,[status(thm)],[f472]) ).
fof(f476,plain,
( ~ sP33_prd
| sP32_prd ),
inference(cnf_transformation,[status(thm)],[f472]) ).
fof(f478,definition,
( sP34_prd
<=> ( ( op(e0,e4) != e0
& op(e4,e4) = e0
& op(e0,e0) = e4 )
| ( op(e0,e3) != e0
& op(e3,e3) = e0
& op(e0,e0) = e3 )
| ( op(e0,e2) != e0
& op(e2,e2) = e0
& op(e0,e0) = e2 )
| ( op(e0,e1) != e0
& op(e1,e1) = e0
& op(e0,e0) = e1 )
| ( op(e0,e0) != e0
& op(e0,e0) = e0
& op(e0,e0) = e0 ) ) ),
introduced(definition,[new_symbols(definition,[sP34_prd])],[]) ).
fof(f479,plain,
( sP33_prd
<=> ( ( op(e1,e0) != e1
& op(e0,e0) = e1
& op(e1,e1) = e0 )
| sP34_prd ) ),
inference(formula_renaming,[status(thm)],[f470,f478]) ).
fof(f480,plain,
( ( ( ( op(e1,e0) = e1
| op(e0,e0) != e1
| op(e1,e1) != e0 )
& ~ sP34_prd )
| sP33_prd )
& ( ( op(e1,e0) != e1
& op(e0,e0) = e1
& op(e1,e1) = e0 )
| sP34_prd
| ~ sP33_prd ) ),
inference(NNF_transformation,[status(thm)],[f479]) ).
fof(f481,plain,
( op(e1,e1) = e0
| sP34_prd
| ~ sP33_prd ),
inference(cnf_transformation,[status(thm)],[f480]) ).
fof(f482,plain,
( op(e0,e0) = e1
| sP34_prd
| ~ sP33_prd ),
inference(cnf_transformation,[status(thm)],[f480]) ).
fof(f484,plain,
( ~ sP34_prd
| sP33_prd ),
inference(cnf_transformation,[status(thm)],[f480]) ).
fof(f486,definition,
( sP35_prd
<=> ( ( op(e0,e3) != e0
& op(e3,e3) = e0
& op(e0,e0) = e3 )
| ( op(e0,e2) != e0
& op(e2,e2) = e0
& op(e0,e0) = e2 )
| ( op(e0,e1) != e0
& op(e1,e1) = e0
& op(e0,e0) = e1 )
| ( op(e0,e0) != e0
& op(e0,e0) = e0
& op(e0,e0) = e0 ) ) ),
introduced(definition,[new_symbols(definition,[sP35_prd])],[]) ).
fof(f487,plain,
( sP34_prd
<=> ( ( op(e0,e4) != e0
& op(e4,e4) = e0
& op(e0,e0) = e4 )
| sP35_prd ) ),
inference(formula_renaming,[status(thm)],[f478,f486]) ).
fof(f488,plain,
( ( ( ( op(e0,e4) = e0
| op(e4,e4) != e0
| op(e0,e0) != e4 )
& ~ sP35_prd )
| sP34_prd )
& ( ( op(e0,e4) != e0
& op(e4,e4) = e0
& op(e0,e0) = e4 )
| sP35_prd
| ~ sP34_prd ) ),
inference(NNF_transformation,[status(thm)],[f487]) ).
fof(f489,plain,
( op(e0,e0) = e4
| sP35_prd
| ~ sP34_prd ),
inference(cnf_transformation,[status(thm)],[f488]) ).
fof(f493,plain,
( op(e0,e4) = e0
| op(e4,e4) != e0
| op(e0,e0) != e4
| sP34_prd ),
inference(cnf_transformation,[status(thm)],[f488]) ).
fof(f494,definition,
( sP36_prd
<=> ( ( op(e0,e2) != e0
& op(e2,e2) = e0
& op(e0,e0) = e2 )
| ( op(e0,e1) != e0
& op(e1,e1) = e0
& op(e0,e0) = e1 )
| ( op(e0,e0) != e0
& op(e0,e0) = e0
& op(e0,e0) = e0 ) ) ),
introduced(definition,[new_symbols(definition,[sP36_prd])],[]) ).
fof(f495,plain,
( sP35_prd
<=> ( ( op(e0,e3) != e0
& op(e3,e3) = e0
& op(e0,e0) = e3 )
| sP36_prd ) ),
inference(formula_renaming,[status(thm)],[f486,f494]) ).
fof(f496,plain,
( ( ( ( op(e0,e3) = e0
| op(e3,e3) != e0
| op(e0,e0) != e3 )
& ~ sP36_prd )
| sP35_prd )
& ( ( op(e0,e3) != e0
& op(e3,e3) = e0
& op(e0,e0) = e3 )
| sP36_prd
| ~ sP35_prd ) ),
inference(NNF_transformation,[status(thm)],[f495]) ).
fof(f498,plain,
( op(e3,e3) = e0
| sP36_prd
| ~ sP35_prd ),
inference(cnf_transformation,[status(thm)],[f496]) ).
fof(f502,definition,
( sP37_prd
<=> ( ( op(e0,e1) != e0
& op(e1,e1) = e0
& op(e0,e0) = e1 )
| ( op(e0,e0) != e0
& op(e0,e0) = e0
& op(e0,e0) = e0 ) ) ),
introduced(definition,[new_symbols(definition,[sP37_prd])],[]) ).
fof(f503,plain,
( sP36_prd
<=> ( ( op(e0,e2) != e0
& op(e2,e2) = e0
& op(e0,e0) = e2 )
| sP37_prd ) ),
inference(formula_renaming,[status(thm)],[f494,f502]) ).
fof(f504,plain,
( ( ( ( op(e0,e2) = e0
| op(e2,e2) != e0
| op(e0,e0) != e2 )
& ~ sP37_prd )
| sP36_prd )
& ( ( op(e0,e2) != e0
& op(e2,e2) = e0
& op(e0,e0) = e2 )
| sP37_prd
| ~ sP36_prd ) ),
inference(NNF_transformation,[status(thm)],[f503]) ).
fof(f506,plain,
( op(e2,e2) = e0
| sP37_prd
| ~ sP36_prd ),
inference(cnf_transformation,[status(thm)],[f504]) ).
fof(f510,definition,
( sP38_prd
<=> ( op(e0,e0) != e0
& op(e0,e0) = e0
& op(e0,e0) = e0 ) ),
introduced(definition,[new_symbols(definition,[sP38_prd])],[]) ).
fof(f511,plain,
( sP37_prd
<=> ( ( op(e0,e1) != e0
& op(e1,e1) = e0
& op(e0,e0) = e1 )
| sP38_prd ) ),
inference(formula_renaming,[status(thm)],[f502,f510]) ).
fof(f512,plain,
( ( ( ( op(e0,e1) = e0
| op(e1,e1) != e0
| op(e0,e0) != e1 )
& ~ sP38_prd )
| sP37_prd )
& ( ( op(e0,e1) != e0
& op(e1,e1) = e0
& op(e0,e0) = e1 )
| sP38_prd
| ~ sP37_prd ) ),
inference(NNF_transformation,[status(thm)],[f511]) ).
fof(f513,plain,
( op(e0,e0) = e1
| sP38_prd
| ~ sP37_prd ),
inference(cnf_transformation,[status(thm)],[f512]) ).
fof(f515,plain,
( op(e0,e1) != e0
| sP38_prd
| ~ sP37_prd ),
inference(cnf_transformation,[status(thm)],[f512]) ).
fof(f518,plain,
( ( op(e0,e0) = e0
| op(e0,e0) != e0
| op(e0,e0) != e0
| sP38_prd )
& ( ( op(e0,e0) != e0
& op(e0,e0) = e0
& op(e0,e0) = e0 )
| ~ sP38_prd ) ),
inference(NNF_transformation,[status(thm)],[f510]) ).
fof(f519,plain,
( op(e0,e0) = e0
| ~ sP38_prd ),
inference(cnf_transformation,[status(thm)],[f518]) ).
fof(f521,plain,
( op(e0,e0) != e0
| ~ sP38_prd ),
inference(cnf_transformation,[status(thm)],[f518]) ).
fof(f604,plain,
sP5_prd,
inference(forward_subsumption_resolution,[status(thm)],[f228,f226]) ).
fof(f613,plain,
~ sP38_prd,
inference(forward_subsumption_resolution,[status(thm)],[f521,f519]) ).
fof(f626,plain,
( op(e4,e4) = e3
| sP11_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f267,f604]) ).
fof(f734,plain,
( op(e3,e2) = e3
| op(e3,e2) = e2
| op(e3,e2) = e1
| op(e3,e2) = e0 ),
inference(backward_subsumption_resolution,[status(thm)],[f26,f735]) ).
fof(f735,plain,
e4 != op(e3,e2),
inference(forward_demodulation,[status(thm)],[f208,f122]) ).
fof(f861,plain,
( op(e4,e2) = e0
| op(e3,e2) = e0
| e4 = e0
| op(e1,e2) = e0
| op(e0,e2) = e0 ),
inference(forward_demodulation,[status(thm)],[f208,f66]) ).
fof(f862,plain,
( op(e4,e2) = e0
| op(e3,e2) = e0
| op(e1,e2) = e0
| op(e0,e2) = e0 ),
inference(forward_subsumption_resolution,[status(thm)],[f861,f198]) ).
fof(f865,plain,
( op(e2,e4) = e1
| op(e2,e3) = e1
| e4 = e1
| op(e2,e1) = e1
| op(e2,e0) = e1 ),
inference(forward_demodulation,[status(thm)],[f208,f67]) ).
fof(f866,plain,
( op(e2,e4) = e1
| op(e2,e3) = e1
| op(e2,e1) = e1
| op(e2,e0) = e1 ),
inference(forward_subsumption_resolution,[status(thm)],[f865,f201]) ).
fof(f1039,plain,
( op(e3,e4) = e4
| op(e3,e3) = e4
| op(e3,e1) = e4
| op(e3,e0) = e4 ),
inference(forward_subsumption_resolution,[status(thm)],[f83,f735]) ).
fof(f1050,plain,
( sP21_prd
| ~ sP20_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f379,f377]) ).
fof(f1130,plain,
( e4 = e3
| sP22_prd
| ~ sP21_prd ),
inference(forward_demodulation,[status(thm)],[f208,f386]) ).
fof(f1131,plain,
( sP22_prd
| ~ sP21_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f1130,f204]) ).
fof(f1249,plain,
op(e2,e3) != e3,
inference(backward_demodulation,[status(thm)],[f1261,f174]) ).
fof(f1252,plain,
op(e2,e0) != e3,
inference(backward_demodulation,[status(thm)],[f1261,f168]) ).
fof(f1255,plain,
( e3 = e1
| op(e2,e3) = e1
| op(e2,e1) = e1
| op(e2,e0) = e1 ),
inference(backward_demodulation,[status(thm)],[f1261,f866]) ).
fof(f1261,plain,
e3 = op(e2,e4),
inference(forward_demodulation,[status(thm)],[f208,f207]) ).
fof(f1262,plain,
( unit = e3
| unit = e2
| unit = e1
| unit = e0
| e3 = op(e2,unit) ),
inference(paramodulation,[status(thm)],[f44,f1261]) ).
fof(f1267,plain,
( op(e2,e3) = e1
| op(e2,e1) = e1
| op(e2,e0) = e1 ),
inference(forward_subsumption_resolution,[status(thm)],[f1255,f200]) ).
fof(f1269,plain,
( unit = e3
| unit = e2
| unit = e1
| unit = e0
| e3 = e2 ),
inference(forward_demodulation,[status(thm)],[f39,f1262]) ).
fof(f1270,plain,
( unit = e3
| unit = e2
| unit = e1
| unit = e0 ),
inference(forward_subsumption_resolution,[status(thm)],[f1269,f202]) ).
fof(f1274,plain,
( op(e4,e0) = e3
| op(e3,e0) = e3
| op(e1,e0) = e3
| op(e0,e0) = e3 ),
inference(backward_subsumption_resolution,[status(thm)],[f52,f1252]) ).
fof(f1286,plain,
e0 = op(e4,op(e2,e2)),
inference(forward_demodulation,[status(thm)],[f208,f205]) ).
fof(f1290,plain,
op(e4,e3) != e0,
inference(backward_demodulation,[status(thm)],[f1306,f194]) ).
fof(f1291,plain,
op(e4,e2) != e0,
inference(backward_demodulation,[status(thm)],[f1306,f193]) ).
fof(f1297,plain,
( e0 = e3
| sP20_prd
| ~ sP19_prd ),
inference(backward_demodulation,[status(thm)],[f1306,f370]) ).
fof(f1300,plain,
op(e0,e4) != e0,
inference(backward_demodulation,[status(thm)],[f1306,f138]) ).
fof(f1302,plain,
( e0 = e1
| sP18_prd
| ~ sP17_prd ),
inference(backward_demodulation,[status(thm)],[f1306,f353]) ).
fof(f1303,plain,
( e0 = e2
| sP17_prd
| ~ sP11_prd ),
inference(backward_demodulation,[status(thm)],[f1306,f310]) ).
fof(f1304,plain,
( e0 = e3
| sP11_prd ),
inference(backward_demodulation,[status(thm)],[f1306,f626]) ).
fof(f1306,plain,
e0 = op(e4,e4),
inference(forward_demodulation,[status(thm)],[f208,f1286]) ).
fof(f1314,plain,
( sP20_prd
| ~ sP19_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f1297,f197]) ).
fof(f1315,plain,
( sP18_prd
| ~ sP17_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f1302,f195]) ).
fof(f1316,plain,
( sP17_prd
| ~ sP11_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f1303,f196]) ).
fof(f1317,plain,
sP11_prd,
inference(forward_subsumption_resolution,[status(thm)],[f1304,f197]) ).
fof(f1323,plain,
sP18_prd,
inference(backward_subsumption_resolution,[status(thm)],[f1315,f1324]) ).
fof(f1324,plain,
sP17_prd,
inference(forward_subsumption_resolution,[status(thm)],[f1316,f1317]) ).
fof(f1326,plain,
( op(e0,e0) = e4
| sP19_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f362,f1323]) ).
fof(f1328,plain,
e1 = op(op(e2,e4),op(e2,e2)),
inference(forward_demodulation,[status(thm)],[f208,f206]) ).
fof(f1329,plain,
e1 = op(e3,op(e2,e2)),
inference(forward_demodulation,[status(thm)],[f1261,f1328]) ).
fof(f1330,plain,
op(e3,e3) != e1,
inference(backward_demodulation,[status(thm)],[f1342,f184]) ).
fof(f1331,plain,
op(e3,e2) != e1,
inference(backward_demodulation,[status(thm)],[f1342,f183]) ).
fof(f1332,plain,
op(e3,e1) != e1,
inference(backward_demodulation,[status(thm)],[f1342,f181]) ).
fof(f1334,plain,
( e1 = e4
| op(e3,e3) = e4
| op(e3,e1) = e4
| op(e3,e0) = e4 ),
inference(backward_demodulation,[status(thm)],[f1342,f1039]) ).
fof(f1336,plain,
( e1 = e2
| op(e3,e3) = e2
| op(e3,e2) = e2
| op(e3,e1) = e2
| op(e3,e0) = e2 ),
inference(backward_demodulation,[status(thm)],[f1342,f79]) ).
fof(f1342,plain,
e1 = op(e3,e4),
inference(forward_demodulation,[status(thm)],[f208,f1329]) ).
fof(f1344,plain,
( op(e3,e3) = e4
| op(e3,e1) = e4
| op(e3,e0) = e4 ),
inference(forward_subsumption_resolution,[status(thm)],[f1334,f201]) ).
fof(f1346,plain,
( op(e3,e3) = e2
| op(e3,e2) = e2
| op(e3,e1) = e2
| op(e3,e0) = e2 ),
inference(forward_subsumption_resolution,[status(thm)],[f1336,f199]) ).
fof(f1364,plain,
( op(e3,e3) = e0
| op(e2,e3) = e0
| op(e1,e3) = e0
| op(e0,e3) = e0 ),
inference(backward_subsumption_resolution,[status(thm)],[f76,f1290]) ).
fof(f1371,plain,
( op(e3,e2) = e0
| op(e1,e2) = e0
| op(e0,e2) = e0 ),
inference(backward_subsumption_resolution,[status(thm)],[f862,f1291]) ).
fof(f1405,plain,
( sP23_prd
| ~ sP22_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f393,f1330]) ).
fof(f1431,plain,
( e0 = e2
| sP25_prd
| ~ sP24_prd ),
inference(forward_demodulation,[status(thm)],[f1306,f410]) ).
fof(f1432,plain,
( sP25_prd
| ~ sP24_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f1431,f196]) ).
fof(f1436,plain,
( e4 = e3
| sP26_prd
| ~ sP25_prd ),
inference(forward_demodulation,[status(thm)],[f208,f417]) ).
fof(f1437,plain,
( sP26_prd
| ~ sP25_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f1436,f204]) ).
fof(f1445,plain,
( e4 = e2
| sP27_prd
| ~ sP26_prd ),
inference(forward_demodulation,[status(thm)],[f208,f425]) ).
fof(f1446,plain,
( sP27_prd
| ~ sP26_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f1445,f203]) ).
fof(f1450,plain,
( e4 = e1
| sP28_prd
| ~ sP27_prd ),
inference(forward_demodulation,[status(thm)],[f208,f433]) ).
fof(f1451,plain,
( sP28_prd
| ~ sP27_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f1450,f201]) ).
fof(f1456,plain,
( e4 = e0
| sP29_prd
| ~ sP28_prd ),
inference(forward_demodulation,[status(thm)],[f208,f441]) ).
fof(f1457,plain,
( sP29_prd
| ~ sP28_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f1456,f198]) ).
fof(f1461,plain,
( e0 = e1
| sP30_prd
| ~ sP29_prd ),
inference(forward_demodulation,[status(thm)],[f1306,f450]) ).
fof(f1462,plain,
( sP30_prd
| ~ sP29_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f1461,f195]) ).
fof(f1470,plain,
( sP31_prd
| ~ sP30_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f458,f1330]) ).
fof(f1473,plain,
( e4 = e1
| sP32_prd
| ~ sP31_prd ),
inference(forward_demodulation,[status(thm)],[f208,f466]) ).
fof(f1474,plain,
( sP32_prd
| ~ sP31_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f1473,f201]) ).
fof(f1484,plain,
( op(e1,op(e1,e0)) != e0
| ~ sP12_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f318,f316]) ).
fof(f1485,plain,
( op(e0,op(e2,e0)) = e2
| ~ sP6_prd
| op(e1,op(e1,e0)) != e0 ),
inference(resolution,[status(thm)],[f1484,f276]) ).
fof(f1487,plain,
( sP33_prd
| ~ sP32_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f475,f473]) ).
fof(f1510,plain,
( e4 = e0
| sP37_prd
| ~ sP36_prd ),
inference(forward_demodulation,[status(thm)],[f208,f506]) ).
fof(f1511,plain,
( sP37_prd
| ~ sP36_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f1510,f198]) ).
fof(f1516,plain,
( op(e0,e0) = e1
| ~ sP37_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f513,f613]) ).
fof(f1517,plain,
( ~ sP36_prd
| op(e0,e0) = e1 ),
inference(resolution,[status(thm)],[f1516,f1511]) ).
fof(f1530,plain,
( op(e0,e1) != e0
| ~ sP37_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f515,f613]) ).
fof(f1531,plain,
( ~ sP36_prd
| op(e0,e1) != e0 ),
inference(resolution,[status(thm)],[f1530,f1511]) ).
fof(f1533,plain,
( op(e3,e3) = e0
| ~ sP35_prd
| op(e0,e1) != e0 ),
inference(resolution,[status(thm)],[f1531,f498]) ).
fof(f1536,plain,
( unit = e2
| unit = e1
| unit = e0
| op(unit,e1) != e1 ),
inference(paramodulation,[status(thm)],[f1270,f1332]) ).
fof(f1578,plain,
( unit = e2
| unit = e1
| unit = e0
| e1 != e1 ),
inference(forward_demodulation,[status(thm)],[f36,f1536]) ).
fof(f1579,plain,
( unit = e2
| unit = e1
| unit = e0 ),
inference(trivial_equality_resolution,[status(thm)],[f1578]) ).
fof(f1627,plain,
( unit = e1
| unit = e0
| op(unit,e3) != e3 ),
inference(paramodulation,[status(thm)],[f1579,f1249]) ).
fof(f1671,plain,
( unit = e1
| unit = e0
| e3 != e3 ),
inference(forward_demodulation,[status(thm)],[f40,f1627]) ).
fof(f1672,plain,
( unit = e1
| unit = e0 ),
inference(trivial_equality_resolution,[status(thm)],[f1671]) ).
fof(f1725,plain,
( unit = e1
| op(e3,unit) != op(e3,e2) ),
inference(paramodulation,[status(thm)],[f1672,f176]) ).
fof(f1743,plain,
( unit = e1
| op(e0,e0) != op(unit,e1) ),
inference(paramodulation,[status(thm)],[f1672,f145]) ).
fof(f1748,plain,
( unit = e1
| op(unit,e2) != op(e3,e2) ),
inference(paramodulation,[status(thm)],[f1672,f117]) ).
fof(f1787,plain,
( unit = e1
| e3 != op(e3,e2) ),
inference(forward_demodulation,[status(thm)],[f41,f1725]) ).
fof(f1805,plain,
( unit = e1
| op(e0,e0) != e1 ),
inference(forward_demodulation,[status(thm)],[f36,f1743]) ).
fof(f1810,plain,
( unit = e1
| e2 != op(e3,e2) ),
inference(forward_demodulation,[status(thm)],[f38,f1748]) ).
fof(f1987,plain,
( op(e0,e4) = e0
| e0 != e0
| op(e0,e0) != e4
| sP34_prd ),
inference(forward_demodulation,[status(thm)],[f1306,f493]) ).
fof(f1988,plain,
( op(e0,e4) = e0
| op(e0,e0) != e4
| sP34_prd ),
inference(trivial_equality_resolution,[status(thm)],[f1987]) ).
fof(f1989,plain,
( op(e0,e0) != e4
| sP34_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f1988,f1300]) ).
fof(f1990,plain,
( sP33_prd
| op(e0,e0) != e4 ),
inference(resolution,[status(thm)],[f1989,f484]) ).
fof(f2002,plain,
( sP32_prd
| op(e0,e0) != e4 ),
inference(resolution,[status(thm)],[f1990,f476]) ).
fof(f2003,plain,
( sP31_prd
| op(e0,e0) != e4 ),
inference(resolution,[status(thm)],[f2002,f468]) ).
fof(f2008,plain,
( sP30_prd
| op(e0,e0) != e4 ),
inference(resolution,[status(thm)],[f2003,f460]) ).
fof(f2009,plain,
( sP29_prd
| op(e0,e0) != e4 ),
inference(resolution,[status(thm)],[f2008,f452]) ).
fof(f2010,plain,
( sP28_prd
| op(e0,e0) != e4 ),
inference(resolution,[status(thm)],[f2009,f444]) ).
fof(f2011,plain,
( sP27_prd
| op(e0,e0) != e4 ),
inference(resolution,[status(thm)],[f2010,f436]) ).
fof(f2028,plain,
( sP26_prd
| op(e0,e0) != e4 ),
inference(resolution,[status(thm)],[f2011,f428]) ).
fof(f2029,plain,
( sP25_prd
| op(e0,e0) != e4 ),
inference(resolution,[status(thm)],[f2028,f420]) ).
fof(f2030,plain,
( sP24_prd
| op(e0,e0) != e4 ),
inference(resolution,[status(thm)],[f2029,f412]) ).
fof(f2031,plain,
( sP23_prd
| op(e0,e0) != e4 ),
inference(resolution,[status(thm)],[f2030,f404]) ).
fof(f2032,plain,
( sP22_prd
| op(e0,e0) != e4 ),
inference(resolution,[status(thm)],[f2031,f396]) ).
fof(f2033,plain,
( sP21_prd
| op(e0,e0) != e4 ),
inference(resolution,[status(thm)],[f2032,f388]) ).
fof(f2046,plain,
( op(e3,e2) = e3
| op(e3,e2) = e2
| op(e3,e2) = e0 ),
inference(forward_subsumption_resolution,[status(thm)],[f734,f1331]) ).
fof(f2047,plain,
( unit = e1
| op(e3,e2) = e2
| op(e3,e2) = e0 ),
inference(resolution,[status(thm)],[f2046,f1787]) ).
fof(f2058,plain,
( unit = e1
| op(e3,e2) = e0 ),
inference(forward_subsumption_resolution,[status(thm)],[f2047,f1810]) ).
fof(f2070,plain,
( sP20_prd
| op(e0,e0) != e4 ),
inference(resolution,[status(thm)],[f2033,f380]) ).
fof(f2071,plain,
( sP19_prd
| op(e0,e0) != e4 ),
inference(resolution,[status(thm)],[f2070,f372]) ).
fof(f2072,plain,
sP19_prd,
inference(forward_subsumption_resolution,[status(thm)],[f2071,f1326]) ).
fof(f2073,plain,
sP20_prd,
inference(backward_subsumption_resolution,[status(thm)],[f1314,f2072]) ).
fof(f2074,plain,
sP21_prd,
inference(backward_subsumption_resolution,[status(thm)],[f1050,f2073]) ).
fof(f2075,plain,
sP22_prd,
inference(backward_subsumption_resolution,[status(thm)],[f1131,f2074]) ).
fof(f2076,plain,
sP23_prd,
inference(backward_subsumption_resolution,[status(thm)],[f1405,f2075]) ).
fof(f2099,plain,
( op(e3,e3) = e0
| sP24_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f401,f2076]) ).
fof(f2131,plain,
( op(e3,e2) = e0
| op(unit,e0) != op(e1,e2) ),
inference(paramodulation,[status(thm)],[f2058,f156]) ).
fof(f2136,plain,
( op(e3,e2) = e0
| op(e0,unit) != op(e0,e2) ),
inference(paramodulation,[status(thm)],[f2058,f149]) ).
fof(f2210,plain,
( op(e3,e2) = e0
| e0 != op(e1,e2) ),
inference(forward_demodulation,[status(thm)],[f34,f2131]) ).
fof(f2215,plain,
( op(e3,e2) = e0
| e0 != op(e0,e2) ),
inference(forward_demodulation,[status(thm)],[f35,f2136]) ).
fof(f2745,plain,
op(e3,e2) = e0,
inference(backward_subsumption_resolution,[status(thm)],[f2210,f2746]) ).
fof(f2746,plain,
( op(e3,e2) = e0
| op(e1,e2) = e0 ),
inference(forward_subsumption_resolution,[status(thm)],[f1371,f2215]) ).
fof(f2795,plain,
( op(e3,e3) = e2
| e0 = e2
| op(e3,e1) = e2
| op(e3,e0) = e2 ),
inference(backward_demodulation,[status(thm)],[f2745,f1346]) ).
fof(f2823,plain,
e0 != op(e3,e3),
inference(backward_demodulation,[status(thm)],[f2745,f182]) ).
fof(f2832,plain,
( op(e3,e3) = e2
| op(e3,e1) = e2
| op(e3,e0) = e2 ),
inference(forward_subsumption_resolution,[status(thm)],[f2795,f196]) ).
fof(f2839,plain,
( op(e2,e3) = e0
| op(e1,e3) = e0
| op(e0,e3) = e0 ),
inference(backward_subsumption_resolution,[status(thm)],[f1364,f2823]) ).
fof(f2840,plain,
sP24_prd,
inference(backward_subsumption_resolution,[status(thm)],[f2099,f2823]) ).
fof(f2841,plain,
( ~ sP35_prd
| op(e0,e1) != e0 ),
inference(backward_subsumption_resolution,[status(thm)],[f1533,f2823]) ).
fof(f2844,plain,
( sP36_prd
| ~ sP35_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f498,f2823]) ).
fof(f2847,plain,
sP25_prd,
inference(backward_subsumption_resolution,[status(thm)],[f1432,f2840]) ).
fof(f2848,plain,
sP26_prd,
inference(backward_subsumption_resolution,[status(thm)],[f1437,f2847]) ).
fof(f2884,plain,
sP27_prd,
inference(backward_subsumption_resolution,[status(thm)],[f1446,f2848]) ).
fof(f2885,plain,
sP28_prd,
inference(backward_subsumption_resolution,[status(thm)],[f1451,f2884]) ).
fof(f2886,plain,
sP29_prd,
inference(backward_subsumption_resolution,[status(thm)],[f1457,f2885]) ).
fof(f2887,plain,
sP30_prd,
inference(backward_subsumption_resolution,[status(thm)],[f1462,f2886]) ).
fof(f2888,plain,
sP31_prd,
inference(backward_subsumption_resolution,[status(thm)],[f1470,f2887]) ).
fof(f2889,plain,
sP32_prd,
inference(backward_subsumption_resolution,[status(thm)],[f1474,f2888]) ).
fof(f2913,plain,
sP33_prd,
inference(backward_subsumption_resolution,[status(thm)],[f1487,f2889]) ).
fof(f2915,plain,
( op(e0,e0) = e1
| sP34_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f482,f2913]) ).
fof(f2916,plain,
( op(e1,e1) = e0
| sP34_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f481,f2913]) ).
fof(f2917,plain,
( op(e0,e0) = e4
| ~ sP34_prd
| sP36_prd ),
inference(resolution,[status(thm)],[f2844,f489]) ).
fof(f2995,plain,
( op(e0,e0) = e1
| op(e0,e0) = e4
| ~ sP34_prd ),
inference(resolution,[status(thm)],[f2917,f1517]) ).
fof(f2998,plain,
( op(e0,e0) = e1
| op(e0,e0) = e4 ),
inference(forward_subsumption_resolution,[status(thm)],[f2995,f2915]) ).
fof(f3147,plain,
( unit = e1
| op(e0,e0) = e1
| op(unit,e0) = e4 ),
inference(paramodulation,[status(thm)],[f1672,f2998]) ).
fof(f3158,plain,
( unit = e1
| op(e0,e0) = e1
| e0 = e4 ),
inference(forward_demodulation,[status(thm)],[f34,f3147]) ).
fof(f3159,plain,
( unit = e1
| op(e0,e0) = e1 ),
inference(forward_subsumption_resolution,[status(thm)],[f3158,f198]) ).
fof(f3165,plain,
( op(e3,e3) = e2
| op(e3,unit) = e2
| op(e3,e0) = e2 ),
inference(backward_demodulation,[status(thm)],[f3361,f2832]) ).
fof(f3177,plain,
( op(e1,unit) = e0
| sP34_prd ),
inference(backward_demodulation,[status(thm)],[f3361,f2916]) ).
fof(f3182,plain,
( ~ sP35_prd
| op(e0,unit) != e0 ),
inference(backward_demodulation,[status(thm)],[f3361,f2841]) ).
fof(f3198,plain,
( op(e3,e3) = e4
| op(e3,unit) = e4
| op(e3,e0) = e4 ),
inference(backward_demodulation,[status(thm)],[f3361,f1344]) ).
fof(f3208,plain,
( op(e4,e0) = e3
| op(e3,e0) = e3
| op(unit,e0) = e3
| op(e0,e0) = e3 ),
inference(backward_demodulation,[status(thm)],[f3361,f1274]) ).
fof(f3212,plain,
( op(e2,e3) = unit
| op(e2,e1) = e1
| op(e2,e0) = e1 ),
inference(backward_demodulation,[status(thm)],[f3361,f1267]) ).
fof(f3214,plain,
( op(e0,op(e2,e0)) = e2
| ~ sP6_prd
| op(e1,op(unit,e0)) != e0 ),
inference(backward_demodulation,[status(thm)],[f3361,f1485]) ).
fof(f3301,plain,
op(e3,e0) != op(e3,unit),
inference(backward_demodulation,[status(thm)],[f3361,f175]) ).
fof(f3316,plain,
op(e1,e0) != op(e1,unit),
inference(backward_demodulation,[status(thm)],[f3361,f155]) ).
fof(f3318,plain,
op(e0,unit) != op(e0,e3),
inference(backward_demodulation,[status(thm)],[f3361,f150]) ).
fof(f3358,plain,
unit != e2,
inference(backward_demodulation,[status(thm)],[f3361,f199]) ).
fof(f3360,plain,
e0 != unit,
inference(backward_demodulation,[status(thm)],[f3361,f195]) ).
fof(f3361,plain,
unit = e1,
inference(forward_subsumption_resolution,[status(thm)],[f3159,f1805]) ).
fof(f3364,plain,
( op(e3,e3) = e2
| e3 = e2
| op(e3,e0) = e2 ),
inference(forward_demodulation,[status(thm)],[f41,f3165]) ).
fof(f3365,plain,
( op(e3,e3) = e2
| op(e3,e0) = e2 ),
inference(forward_subsumption_resolution,[status(thm)],[f3364,f202]) ).
fof(f3402,plain,
( op(unit,unit) = e0
| sP34_prd ),
inference(forward_demodulation,[status(thm)],[f3361,f3177]) ).
fof(f3406,plain,
( ~ sP35_prd
| e0 != e0 ),
inference(forward_demodulation,[status(thm)],[f35,f3182]) ).
fof(f3407,plain,
~ sP35_prd,
inference(trivial_equality_resolution,[status(thm)],[f3406]) ).
fof(f3458,plain,
( op(e3,e3) = e4
| e3 = e4
| op(e3,e0) = e4 ),
inference(forward_demodulation,[status(thm)],[f41,f3198]) ).
fof(f3459,plain,
( op(e3,e3) = e4
| op(e3,e0) = e4 ),
inference(forward_subsumption_resolution,[status(thm)],[f3458,f204]) ).
fof(f3481,plain,
( op(e4,e0) = e3
| op(e3,e0) = e3
| e0 = e3
| op(e0,e0) = e3 ),
inference(forward_demodulation,[status(thm)],[f34,f3208]) ).
fof(f3482,plain,
( op(e4,e0) = e3
| op(e3,e0) = e3
| op(e0,e0) = e3 ),
inference(forward_subsumption_resolution,[status(thm)],[f3481,f197]) ).
fof(f3490,plain,
( op(e2,e3) = unit
| op(e2,e1) = e1
| op(e2,e0) = unit ),
inference(forward_demodulation,[status(thm)],[f3361,f3212]) ).
fof(f3491,plain,
( op(e2,e3) = unit
| op(e2,unit) = e1
| op(e2,e0) = unit ),
inference(forward_demodulation,[status(thm)],[f3361,f3490]) ).
fof(f3492,plain,
( op(e2,e3) = unit
| e2 = e1
| op(e2,e0) = unit ),
inference(forward_demodulation,[status(thm)],[f39,f3491]) ).
fof(f3493,plain,
( op(e2,e3) = unit
| e2 = unit
| op(e2,e0) = unit ),
inference(forward_demodulation,[status(thm)],[f3361,f3492]) ).
fof(f3498,plain,
( op(e0,op(e2,e0)) = e2
| ~ sP6_prd
| op(unit,op(unit,e0)) != e0 ),
inference(forward_demodulation,[status(thm)],[f3361,f3214]) ).
fof(f3499,plain,
( op(e0,op(e2,e0)) = e2
| ~ sP6_prd
| op(unit,e0) != e0 ),
inference(forward_demodulation,[status(thm)],[f34,f3498]) ).
fof(f3500,plain,
( op(e0,op(e2,e0)) = e2
| ~ sP6_prd
| e0 != e0 ),
inference(forward_demodulation,[status(thm)],[f34,f3499]) ).
fof(f3501,plain,
( op(e0,op(e2,e0)) = e2
| ~ sP6_prd ),
inference(trivial_equality_resolution,[status(thm)],[f3500]) ).
fof(f3644,plain,
op(e3,e0) != e3,
inference(forward_demodulation,[status(thm)],[f41,f3301]) ).
fof(f3679,plain,
op(unit,e0) != op(e1,unit),
inference(forward_demodulation,[status(thm)],[f3361,f3316]) ).
fof(f3680,plain,
e0 != op(e1,unit),
inference(forward_demodulation,[status(thm)],[f34,f3679]) ).
fof(f3681,plain,
e0 != op(unit,unit),
inference(forward_demodulation,[status(thm)],[f3361,f3680]) ).
fof(f3683,plain,
e0 != op(e0,e3),
inference(forward_demodulation,[status(thm)],[f35,f3318]) ).
fof(f3779,plain,
( op(e0,e0) = e4
| ~ sP34_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f489,f3407]) ).
fof(f3785,plain,
( op(e2,e3) = e0
| op(unit,e3) = e0
| op(e0,e3) = e0 ),
inference(forward_demodulation,[status(thm)],[f3361,f2839]) ).
fof(f3786,plain,
( op(e2,e3) = e0
| e3 = e0
| op(e0,e3) = e0 ),
inference(forward_demodulation,[status(thm)],[f40,f3785]) ).
fof(f3787,plain,
( op(e2,e3) = e0
| op(e0,e3) = e0 ),
inference(forward_subsumption_resolution,[status(thm)],[f3786,f197]) ).
fof(f3843,plain,
sP34_prd,
inference(backward_subsumption_resolution,[status(thm)],[f3402,f3681]) ).
fof(f3846,plain,
op(e2,e3) = e0,
inference(backward_subsumption_resolution,[status(thm)],[f3787,f3683]) ).
fof(f3965,plain,
( op(e4,e0) = e3
| op(e0,e0) = e3 ),
inference(forward_subsumption_resolution,[status(thm)],[f3482,f3644]) ).
fof(f3980,plain,
( e0 = unit
| e2 = unit
| op(e2,e0) = unit ),
inference(forward_demodulation,[status(thm)],[f3846,f3493]) ).
fof(f3981,plain,
( e0 = unit
| op(e2,e0) = unit ),
inference(forward_subsumption_resolution,[status(thm)],[f3980,f3358]) ).
fof(f4017,plain,
( op(e4,e0) = e3
| e4 = e3 ),
inference(backward_demodulation,[status(thm)],[f4026,f3965]) ).
fof(f4021,plain,
e4 != op(e0,e3),
inference(backward_demodulation,[status(thm)],[f4026,f147]) ).
fof(f4024,plain,
e4 != op(e3,e0),
inference(backward_demodulation,[status(thm)],[f4026,f97]) ).
fof(f4026,plain,
op(e0,e0) = e4,
inference(forward_subsumption_resolution,[status(thm)],[f3779,f3843]) ).
fof(f4028,plain,
op(e4,e0) = e3,
inference(forward_subsumption_resolution,[status(thm)],[f4017,f204]) ).
fof(f4040,plain,
( op(e0,e3) = e4
| sP0_prd ),
inference(backward_demodulation,[status(thm)],[f4028,f217]) ).
fof(f4068,plain,
op(e3,e3) = e4,
inference(backward_subsumption_resolution,[status(thm)],[f3459,f4024]) ).
fof(f4094,plain,
( e4 = e2
| op(e3,e0) = e2 ),
inference(backward_demodulation,[status(thm)],[f4068,f3365]) ).
fof(f4098,plain,
op(e3,e0) = e2,
inference(forward_subsumption_resolution,[status(thm)],[f4094,f203]) ).
fof(f4112,plain,
( op(e3,e2) != e0
| sP6_prd
| ~ sP0_prd ),
inference(backward_demodulation,[status(thm)],[f4098,f232]) ).
fof(f4115,plain,
( e0 != e0
| sP6_prd
| ~ sP0_prd ),
inference(forward_demodulation,[status(thm)],[f2745,f4112]) ).
fof(f4116,plain,
( sP6_prd
| ~ sP0_prd ),
inference(trivial_equality_resolution,[status(thm)],[f4115]) ).
fof(f4124,plain,
sP6_prd,
inference(backward_subsumption_resolution,[status(thm)],[f4116,f4125]) ).
fof(f4125,plain,
sP0_prd,
inference(forward_subsumption_resolution,[status(thm)],[f4040,f4021]) ).
fof(f4141,plain,
op(e0,op(e2,e0)) = e2,
inference(forward_subsumption_resolution,[status(thm)],[f3501,f4124]) ).
fof(f4143,plain,
( e0 = unit
| op(e0,unit) = e2 ),
inference(paramodulation,[status(thm)],[f3981,f4141]) ).
fof(f4146,plain,
( e0 = unit
| e0 = e2 ),
inference(forward_demodulation,[status(thm)],[f35,f4143]) ).
fof(f4147,plain,
e0 = unit,
inference(forward_subsumption_resolution,[status(thm)],[f4146,f196]) ).
fof(f4148,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f4147,f3360]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG056+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.57 % Computer : n004.cluster.edu
% 0.09/0.57 % Model : x86_64 x86_64
% 0.09/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.57 % Memory : 8046.5625MB
% 0.09/0.57 % OS : Linux 6.8.0-71-generic
% 0.09/0.57 % CPULimit : 300
% 0.09/0.57 % WCLimit : 300
% 0.09/0.57 % DateTime : Mon Sep 21 12:54:37 UTC 2026
% 0.14/0.57 % CPUTime :
% 0.14/0.60 % Drodi V4.1.1
% 0.14/0.71 % Refutation found
% 0.14/0.71 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.71 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.75 % Elapsed time: 0.159904 seconds
% 0.14/0.75 % CPU time: 0.985929 seconds
% 0.14/0.75 % Total memory used: 133.816 MB
% 0.14/0.75 % Net memory used: 132.758 MB
%------------------------------------------------------------------------------