%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ALG065+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 : n002.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 0.02s 0.45s
% Output : CNFRefutation 0.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 14
% Syntax : Number of formulae : 209 ( 85 unt; 7 def)
% Number of atoms : 1264 (1192 equ)
% Maximal formula atoms : 250 ( 6 avg)
% Number of connectives : 1487 ( 432 ~; 674 |; 372 &)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 101 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 8 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,
( e3 = op(e2,e4)
& e1 = op(e4,e2)
& e0 = op(op(e4,e2),op(e4,e2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,conjecture,
~ ( ( ( 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 ) )
& ( op(e4,e4) = e4
| op(e4,e4) != e4 )
& ( op(e4,e3) = e4
| op(e4,e4) != e3 )
& ( op(e4,e2) = e4
| op(e4,e4) != e2 )
& ( op(e4,e1) = e4
| op(e4,e4) != e1 )
& ( op(e4,e0) = e4
| op(e4,e4) != e0 )
& ( op(e3,e4) = e3
| op(e3,e3) != e4 )
& ( op(e3,e3) = e3
| op(e3,e3) != e3 )
& ( op(e3,e2) = e3
| op(e3,e3) != e2 )
& ( op(e3,e1) = e3
| op(e3,e3) != e1 )
& ( op(e3,e0) = e3
| op(e3,e3) != e0 )
& ( op(e2,e4) = e2
| op(e2,e2) != e4 )
& ( op(e2,e3) = e2
| op(e2,e2) != e3 )
& ( op(e2,e2) = e2
| op(e2,e2) != e2 )
& ( op(e2,e1) = e2
| op(e2,e2) != e1 )
& ( op(e2,e0) = e2
| op(e2,e2) != e0 )
& ( op(e1,e4) = e1
| op(e1,e1) != e4 )
& ( op(e1,e3) = e1
| op(e1,e1) != e3 )
& ( op(e1,e2) = e1
| op(e1,e1) != e2 )
& ( op(e1,e1) = e1
| op(e1,e1) != e1 )
& ( op(e1,e0) = e1
| op(e1,e1) != e0 )
& ( op(e0,e4) = e0
| op(e0,e0) != e4 )
& ( op(e0,e3) = e0
| op(e0,e0) != e3 )
& ( op(e0,e2) = e0
| op(e0,e0) != e2 )
& ( op(e0,e1) = e0
| op(e0,e0) != e1 )
& ( op(e0,e0) = e0
| op(e0,e0) != e0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
~ ~ ( ( ( 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 ) )
& ( op(e4,e4) = e4
| op(e4,e4) != e4 )
& ( op(e4,e3) = e4
| op(e4,e4) != e3 )
& ( op(e4,e2) = e4
| op(e4,e4) != e2 )
& ( op(e4,e1) = e4
| op(e4,e4) != e1 )
& ( op(e4,e0) = e4
| op(e4,e4) != e0 )
& ( op(e3,e4) = e3
| op(e3,e3) != e4 )
& ( op(e3,e3) = e3
| op(e3,e3) != e3 )
& ( op(e3,e2) = e3
| op(e3,e3) != e2 )
& ( op(e3,e1) = e3
| op(e3,e3) != e1 )
& ( op(e3,e0) = e3
| op(e3,e3) != e0 )
& ( op(e2,e4) = e2
| op(e2,e2) != e4 )
& ( op(e2,e3) = e2
| op(e2,e2) != e3 )
& ( op(e2,e2) = e2
| op(e2,e2) != e2 )
& ( op(e2,e1) = e2
| op(e2,e2) != e1 )
& ( op(e2,e0) = e2
| op(e2,e2) != e0 )
& ( op(e1,e4) = e1
| op(e1,e1) != e4 )
& ( op(e1,e3) = e1
| op(e1,e1) != e3 )
& ( op(e1,e2) = e1
| op(e1,e1) != e2 )
& ( op(e1,e1) = e1
| op(e1,e1) != e1 )
& ( op(e1,e0) = e1
| op(e1,e1) != e0 )
& ( op(e0,e4) = e0
| op(e0,e0) != e4 )
& ( op(e0,e3) = e0
| op(e0,e0) != e3 )
& ( op(e0,e2) = e0
| op(e0,e0) != e2 )
& ( op(e0,e1) = e0
| op(e0,e0) != e1 )
& ( op(e0,e0) = e0
| op(e0,e0) != e0 ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
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(f25,plain,
( op(e3,e1) = e4
| op(e3,e1) = e3
| op(e3,e1) = e2
| op(e3,e1) = e1
| op(e3,e1) = e0 ),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(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(f27,plain,
( op(e3,e3) = e4
| op(e3,e3) = e3
| op(e3,e3) = e2
| op(e3,e3) = e1
| op(e3,e3) = e0 ),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f35,plain,
op(e0,unit) = e0,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f36,plain,
op(unit,e1) = e1,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f37,plain,
op(e1,unit) = e1,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f38,plain,
op(unit,e2) = e2,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f39,plain,
op(e2,unit) = e2,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f40,plain,
op(unit,e3) = e3,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f41,plain,
op(e3,unit) = e3,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(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(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(f85,plain,
( op(e4,e4) = e0
| op(e4,e3) = e0
| op(e4,e2) = e0
| op(e4,e1) = e0
| op(e4,e0) = e0 ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f89,plain,
( op(e4,e4) = e2
| op(e4,e3) = e2
| op(e4,e2) = e2
| op(e4,e1) = e2
| op(e4,e0) = e2 ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f105,plain,
op(e0,e1) != op(e1,e1),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f107,plain,
op(e0,e1) != op(e3,e1),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f110,plain,
op(e1,e1) != op(e3,e1),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f111,plain,
op(e1,e1) != op(e4,e1),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f114,plain,
op(e3,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(f122,plain,
op(e2,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(f124,plain,
op(e3,e2) != op(e4,e2),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f142,plain,
op(e2,e4) != op(e3,e4),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f157,plain,
op(e1,e0) != op(e1,e3),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f159,plain,
op(e1,e1) != op(e1,e2),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f166,plain,
op(e2,e0) != op(e2,e2),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f173,plain,
op(e2,e2) != 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(f177,plain,
op(e3,e0) != op(e3,e3),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f179,plain,
op(e3,e1) != op(e3,e2),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f195,plain,
e0 != e1,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f196,plain,
e0 != e2,
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(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(f205,plain,
e0 = op(op(e4,e2),op(e4,e2)),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f206,plain,
e1 = op(e4,e2),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f207,plain,
e3 = op(e2,e4),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f208,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(f209,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(f210,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(f211,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(f212,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(f213,plain,
( ( ( 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 )
& ( op(e4,e4) = e4
| op(e4,e4) != e4 )
& ( op(e4,e3) = e4
| op(e4,e4) != e3 )
& ( op(e4,e2) = e4
| op(e4,e4) != e2 )
& ( op(e4,e1) = e4
| op(e4,e4) != e1 )
& ( op(e4,e0) = e4
| op(e4,e4) != e0 )
& ( op(e3,e4) = e3
| op(e3,e3) != e4 )
& ( op(e3,e3) = e3
| op(e3,e3) != e3 )
& ( op(e3,e2) = e3
| op(e3,e3) != e2 )
& ( op(e3,e1) = e3
| op(e3,e3) != e1 )
& ( op(e3,e0) = e3
| op(e3,e3) != e0 )
& ( op(e2,e4) = e2
| op(e2,e2) != e4 )
& ( op(e2,e3) = e2
| op(e2,e2) != e3 )
& ( op(e2,e2) = e2
| op(e2,e2) != e2 )
& ( op(e2,e1) = e2
| op(e2,e2) != e1 )
& ( op(e2,e0) = e2
| op(e2,e2) != e0 )
& ( op(e1,e4) = e1
| op(e1,e1) != e4 )
& ( op(e1,e3) = e1
| op(e1,e1) != e3 )
& ( op(e1,e2) = e1
| op(e1,e1) != e2 )
& ( op(e1,e1) = e1
| op(e1,e1) != e1 )
& ( op(e1,e0) = e1
| op(e1,e1) != e0 )
& ( op(e0,e4) = e0
| op(e0,e0) != e4 )
& ( op(e0,e3) = e0
| op(e0,e0) != e3 )
& ( op(e0,e2) = e0
| op(e0,e0) != e2 )
& ( op(e0,e1) = e0
| op(e0,e0) != e1 )
& ( op(e0,e0) = e0
| op(e0,e0) != e0 ) ),
inference(formula_renaming,[status(thm)],[f8,f212,f211,f210,f209,f208]) ).
fof(f219,plain,
( op(e1,e0) = e1
| op(e1,e1) != e0 ),
inference(cnf_transformation,[status(thm)],[f213]) ).
fof(f228,plain,
( op(e2,e4) = e2
| op(e2,e2) != e4 ),
inference(cnf_transformation,[status(thm)],[f213]) ).
fof(f230,plain,
( op(e3,e1) = e3
| op(e3,e3) != e1 ),
inference(cnf_transformation,[status(thm)],[f213]) ).
fof(f231,plain,
( op(e3,e2) = e3
| op(e3,e3) != e2 ),
inference(cnf_transformation,[status(thm)],[f213]) ).
fof(f233,plain,
( op(e3,e4) = e3
| op(e3,e3) != e4 ),
inference(cnf_transformation,[status(thm)],[f213]) ).
fof(f236,plain,
( op(e4,e2) = e4
| op(e4,e4) != e2 ),
inference(cnf_transformation,[status(thm)],[f213]) ).
fof(f239,plain,
( op(e4,op(e4,e0)) != e0
| sP0_prd ),
inference(cnf_transformation,[status(thm)],[f213]) ).
fof(f249,definition,
( sP5_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,[sP5_prd])],[]) ).
fof(f250,plain,
( sP0_prd
<=> ( ( op(e0,op(e3,e0)) = e3
& op(e3,op(e3,e0)) != e0 )
| sP5_prd ) ),
inference(formula_renaming,[status(thm)],[f208,f249]) ).
fof(f251,plain,
( ( ( ( op(e0,op(e3,e0)) != e3
| op(e3,op(e3,e0)) = e0 )
& ~ sP5_prd )
| sP0_prd )
& ( ( op(e0,op(e3,e0)) = e3
& op(e3,op(e3,e0)) != e0 )
| sP5_prd
| ~ sP0_prd ) ),
inference(NNF_transformation,[status(thm)],[f250]) ).
fof(f252,plain,
( op(e3,op(e3,e0)) != e0
| sP5_prd
| ~ sP0_prd ),
inference(cnf_transformation,[status(thm)],[f251]) ).
fof(f284,definition,
( sP10_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,[sP10_prd])],[]) ).
fof(f285,plain,
( sP5_prd
<=> ( ( op(e0,op(e2,e0)) = e2
& op(e2,op(e2,e0)) != e0 )
| sP10_prd ) ),
inference(formula_renaming,[status(thm)],[f249,f284]) ).
fof(f286,plain,
( ( ( ( op(e0,op(e2,e0)) != e2
| op(e2,op(e2,e0)) = e0 )
& ~ sP10_prd )
| sP5_prd )
& ( ( op(e0,op(e2,e0)) = e2
& op(e2,op(e2,e0)) != e0 )
| sP10_prd
| ~ sP5_prd ) ),
inference(NNF_transformation,[status(thm)],[f285]) ).
fof(f287,plain,
( op(e2,op(e2,e0)) != e0
| sP10_prd
| ~ sP5_prd ),
inference(cnf_transformation,[status(thm)],[f286]) ).
fof(f319,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 ) )
| sP10_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 )
| ~ sP10_prd ) ),
inference(NNF_transformation,[status(thm)],[f284]) ).
fof(f320,plain,
( op(e1,op(e1,e0)) != e0
| op(e0,op(e0,e0)) != e0
| ~ sP10_prd ),
inference(cnf_transformation,[status(thm)],[f319]) ).
fof(f322,plain,
( op(e1,op(e1,e0)) != e0
| op(e0,op(e0,e0)) = e0
| ~ sP10_prd ),
inference(cnf_transformation,[status(thm)],[f319]) ).
fof(f497,plain,
( op(e2,e2) = e4
| op(e2,e2) = e3
| op(e2,e2) = e2
| op(e2,e2) = e0 ),
inference(backward_subsumption_resolution,[status(thm)],[f21,f498]) ).
fof(f498,plain,
op(e2,e2) != e1,
inference(forward_demodulation,[status(thm)],[f206,f123]) ).
fof(f499,plain,
( op(e3,e2) = e4
| op(e3,e2) = e3
| op(e3,e2) = e2
| op(e3,e2) = e0 ),
inference(backward_subsumption_resolution,[status(thm)],[f26,f500]) ).
fof(f500,plain,
op(e3,e2) != e1,
inference(forward_demodulation,[status(thm)],[f206,f124]) ).
fof(f511,plain,
( unit = e3
| unit = e2
| unit = e1
| unit = e0
| e3 = op(e2,unit) ),
inference(paramodulation,[status(thm)],[f44,f207]) ).
fof(f523,plain,
( unit = e3
| unit = e2
| unit = e1
| unit = e0
| e3 = e2 ),
inference(forward_demodulation,[status(thm)],[f39,f511]) ).
fof(f524,plain,
( unit = e3
| unit = e2
| unit = e1
| unit = e0 ),
inference(forward_subsumption_resolution,[status(thm)],[f523,f202]) ).
fof(f621,plain,
e3 != op(e3,e4),
inference(forward_demodulation,[status(thm)],[f207,f142]) ).
fof(f647,plain,
( e3 = e2
| op(e2,e2) != e4 ),
inference(forward_demodulation,[status(thm)],[f207,f228]) ).
fof(f648,plain,
op(e2,e2) != e4,
inference(forward_subsumption_resolution,[status(thm)],[f647,f202]) ).
fof(f706,plain,
( op(e3,e3) = e3
| op(e3,e3) = e2
| op(e3,e3) = e1
| op(e3,e3) = e0 ),
inference(backward_subsumption_resolution,[status(thm)],[f27,f707]) ).
fof(f707,plain,
op(e3,e3) != e4,
inference(forward_subsumption_resolution,[status(thm)],[f233,f621]) ).
fof(f734,plain,
( e1 = e0
| op(e3,e2) = e0
| op(e2,e2) = e0
| op(e1,e2) = e0
| op(e0,e2) = e0 ),
inference(forward_demodulation,[status(thm)],[f206,f66]) ).
fof(f735,plain,
( op(e3,e2) = e0
| op(e2,e2) = e0
| op(e1,e2) = e0
| op(e0,e2) = e0 ),
inference(forward_subsumption_resolution,[status(thm)],[f734,f195]) ).
fof(f763,plain,
( e1 = e4
| op(e4,e4) != e2 ),
inference(forward_demodulation,[status(thm)],[f206,f236]) ).
fof(f764,plain,
op(e4,e4) != e2,
inference(forward_subsumption_resolution,[status(thm)],[f763,f201]) ).
fof(f807,plain,
op(e2,e2) != e3,
inference(forward_demodulation,[status(thm)],[f207,f173]) ).
fof(f811,plain,
op(e2,e3) != e3,
inference(forward_demodulation,[status(thm)],[f207,f174]) ).
fof(f963,plain,
e0 = op(e1,op(e4,e2)),
inference(forward_demodulation,[status(thm)],[f206,f205]) ).
fof(f967,plain,
e0 != op(e1,e2),
inference(backward_demodulation,[status(thm)],[f982,f159]) ).
fof(f977,plain,
e0 != op(e4,e1),
inference(backward_demodulation,[status(thm)],[f982,f111]) ).
fof(f978,plain,
e0 != op(e3,e1),
inference(backward_demodulation,[status(thm)],[f982,f110]) ).
fof(f980,plain,
( op(e1,e0) = e1
| e0 != e0 ),
inference(backward_demodulation,[status(thm)],[f982,f219]) ).
fof(f981,plain,
op(e0,e1) != e0,
inference(backward_demodulation,[status(thm)],[f982,f105]) ).
fof(f982,plain,
e0 = op(e1,e1),
inference(forward_demodulation,[status(thm)],[f206,f963]) ).
fof(f987,plain,
op(e1,e0) = e1,
inference(trivial_equality_resolution,[status(thm)],[f980]) ).
fof(f1019,plain,
e1 != op(e1,e3),
inference(backward_demodulation,[status(thm)],[f987,f157]) ).
fof(f1043,plain,
( op(e3,e2) = e0
| op(e2,e2) = e0
| op(e0,e2) = e0 ),
inference(backward_subsumption_resolution,[status(thm)],[f735,f967]) ).
fof(f1055,plain,
( op(e4,e4) = e0
| op(e4,e3) = e0
| e1 = e0
| op(e4,e1) = e0
| op(e4,e0) = e0 ),
inference(forward_demodulation,[status(thm)],[f206,f85]) ).
fof(f1056,plain,
( op(e4,e4) = e0
| op(e4,e3) = e0
| op(e4,e1) = e0
| op(e4,e0) = e0 ),
inference(forward_subsumption_resolution,[status(thm)],[f1055,f195]) ).
fof(f1064,plain,
( op(e4,e4) = e0
| op(e4,e3) = e0
| op(e4,e0) = e0 ),
inference(backward_subsumption_resolution,[status(thm)],[f1056,f977]) ).
fof(f1068,plain,
( op(e3,e1) = e4
| op(e3,e1) = e3
| op(e3,e1) = e2
| op(e3,e1) = e1 ),
inference(backward_subsumption_resolution,[status(thm)],[f25,f978]) ).
fof(f1107,plain,
( op(e4,e4) = e2
| op(e4,e3) = e2
| e1 = e2
| op(e4,e1) = e2
| op(e4,e0) = e2 ),
inference(forward_demodulation,[status(thm)],[f206,f89]) ).
fof(f1108,plain,
( op(e4,e4) = e2
| op(e4,e3) = e2
| op(e4,e1) = e2
| op(e4,e0) = e2 ),
inference(forward_subsumption_resolution,[status(thm)],[f1107,f199]) ).
fof(f1180,plain,
( unit = e2
| unit = e1
| unit = e0
| e1 != op(e1,unit) ),
inference(paramodulation,[status(thm)],[f524,f1019]) ).
fof(f1235,plain,
( unit = e2
| unit = e1
| unit = e0
| e1 != e1 ),
inference(forward_demodulation,[status(thm)],[f37,f1180]) ).
fof(f1236,plain,
( unit = e2
| unit = e1
| unit = e0 ),
inference(trivial_equality_resolution,[status(thm)],[f1235]) ).
fof(f1299,plain,
( unit = e1
| unit = e0
| op(unit,e3) != e3 ),
inference(paramodulation,[status(thm)],[f1236,f811]) ).
fof(f1359,plain,
( unit = e1
| unit = e0
| e3 != e3 ),
inference(forward_demodulation,[status(thm)],[f40,f1299]) ).
fof(f1360,plain,
( unit = e1
| unit = e0 ),
inference(trivial_equality_resolution,[status(thm)],[f1359]) ).
fof(f1414,plain,
( unit = e0
| op(e0,unit) != e0 ),
inference(paramodulation,[status(thm)],[f1360,f981]) ).
fof(f1474,plain,
( unit = e0
| e0 != e0 ),
inference(forward_demodulation,[status(thm)],[f35,f1414]) ).
fof(f1475,plain,
unit = e0,
inference(trivial_equality_resolution,[status(thm)],[f1474]) ).
fof(f1531,plain,
( op(e2,op(e2,e0)) != unit
| sP10_prd
| ~ sP5_prd ),
inference(backward_demodulation,[status(thm)],[f1475,f287]) ).
fof(f1533,plain,
( op(e4,e4) = e2
| op(e4,e3) = e2
| op(e4,e1) = e2
| op(e4,unit) = e2 ),
inference(backward_demodulation,[status(thm)],[f1475,f1108]) ).
fof(f1551,plain,
unit = op(e1,e1),
inference(backward_demodulation,[status(thm)],[f1475,f982]) ).
fof(f1561,plain,
op(e3,unit) != op(e3,e3),
inference(backward_demodulation,[status(thm)],[f1475,f177]) ).
fof(f1562,plain,
op(e3,unit) != op(e3,e2),
inference(backward_demodulation,[status(thm)],[f1475,f176]) ).
fof(f1564,plain,
( op(e3,op(e3,e0)) != unit
| sP5_prd
| ~ sP0_prd ),
inference(backward_demodulation,[status(thm)],[f1475,f252]) ).
fof(f1567,plain,
op(e3,unit) != op(e3,e1),
inference(backward_demodulation,[status(thm)],[f1475,f175]) ).
fof(f1572,plain,
op(e2,unit) != op(e2,e2),
inference(backward_demodulation,[status(thm)],[f1475,f166]) ).
fof(f1599,plain,
op(unit,e2) != op(e3,e2),
inference(backward_demodulation,[status(thm)],[f1475,f117]) ).
fof(f1603,plain,
op(unit,e1) != op(e3,e1),
inference(backward_demodulation,[status(thm)],[f1475,f107]) ).
fof(f1614,plain,
( op(e4,op(e4,e0)) != unit
| sP0_prd ),
inference(backward_demodulation,[status(thm)],[f1475,f239]) ).
fof(f1619,plain,
unit != e4,
inference(backward_demodulation,[status(thm)],[f1475,f198]) ).
fof(f1621,plain,
unit != e2,
inference(backward_demodulation,[status(thm)],[f1475,f196]) ).
fof(f1627,plain,
( op(e2,op(e2,unit)) != unit
| sP10_prd
| ~ sP5_prd ),
inference(forward_demodulation,[status(thm)],[f1475,f1531]) ).
fof(f1628,plain,
( op(e2,e2) != unit
| sP10_prd
| ~ sP5_prd ),
inference(forward_demodulation,[status(thm)],[f39,f1627]) ).
fof(f1631,plain,
( op(e4,e4) = e2
| op(e4,e3) = e2
| op(e4,e1) = e2
| e4 = e2 ),
inference(forward_demodulation,[status(thm)],[f43,f1533]) ).
fof(f1632,plain,
( op(e4,e4) = e2
| op(e4,e3) = e2
| op(e4,e1) = e2 ),
inference(forward_subsumption_resolution,[status(thm)],[f1631,f203]) ).
fof(f1667,plain,
e3 != op(e3,e3),
inference(forward_demodulation,[status(thm)],[f41,f1561]) ).
fof(f1668,plain,
e3 != op(e3,e2),
inference(forward_demodulation,[status(thm)],[f41,f1562]) ).
fof(f1671,plain,
( op(e3,op(e3,unit)) != unit
| sP5_prd
| ~ sP0_prd ),
inference(forward_demodulation,[status(thm)],[f1475,f1564]) ).
fof(f1672,plain,
( op(e3,e3) != unit
| sP5_prd
| ~ sP0_prd ),
inference(forward_demodulation,[status(thm)],[f41,f1671]) ).
fof(f1677,plain,
e3 != op(e3,e1),
inference(forward_demodulation,[status(thm)],[f41,f1567]) ).
fof(f1680,plain,
e2 != op(e2,e2),
inference(forward_demodulation,[status(thm)],[f39,f1572]) ).
fof(f1739,plain,
e2 != op(e3,e2),
inference(forward_demodulation,[status(thm)],[f38,f1599]) ).
fof(f1743,plain,
e1 != op(e3,e1),
inference(forward_demodulation,[status(thm)],[f36,f1603]) ).
fof(f1773,plain,
( op(e4,op(e4,unit)) != unit
| sP0_prd ),
inference(forward_demodulation,[status(thm)],[f1475,f1614]) ).
fof(f1774,plain,
( op(e4,e4) != unit
| sP0_prd ),
inference(forward_demodulation,[status(thm)],[f43,f1773]) ).
fof(f1802,plain,
( op(e1,op(e1,e0)) != e0
| op(unit,op(e0,e0)) != e0
| ~ sP10_prd ),
inference(forward_demodulation,[status(thm)],[f1475,f320]) ).
fof(f1803,plain,
( op(e1,op(e1,e0)) != e0
| op(unit,op(unit,e0)) != e0
| ~ sP10_prd ),
inference(forward_demodulation,[status(thm)],[f1475,f1802]) ).
fof(f1804,plain,
( op(e1,op(e1,e0)) != e0
| op(unit,op(unit,unit)) != e0
| ~ sP10_prd ),
inference(forward_demodulation,[status(thm)],[f1475,f1803]) ).
fof(f1805,plain,
( op(e1,op(e1,e0)) != e0
| op(unit,op(unit,unit)) != unit
| ~ sP10_prd ),
inference(forward_demodulation,[status(thm)],[f1475,f1804]) ).
fof(f1806,plain,
( op(e1,op(e1,unit)) != e0
| op(unit,op(unit,unit)) != unit
| ~ sP10_prd ),
inference(forward_demodulation,[status(thm)],[f1475,f1805]) ).
fof(f1807,plain,
( op(e1,e1) != e0
| op(unit,op(unit,unit)) != unit
| ~ sP10_prd ),
inference(forward_demodulation,[status(thm)],[f37,f1806]) ).
fof(f1808,plain,
( op(e1,e1) != unit
| op(unit,op(unit,unit)) != unit
| ~ sP10_prd ),
inference(forward_demodulation,[status(thm)],[f1475,f1807]) ).
fof(f1816,plain,
( op(e1,op(e1,e0)) != e0
| op(unit,op(e0,e0)) = e0
| ~ sP10_prd ),
inference(forward_demodulation,[status(thm)],[f1475,f322]) ).
fof(f1817,plain,
( op(e1,op(e1,e0)) != e0
| op(unit,op(unit,e0)) = e0
| ~ sP10_prd ),
inference(forward_demodulation,[status(thm)],[f1475,f1816]) ).
fof(f1818,plain,
( op(e1,op(e1,e0)) != e0
| op(unit,op(unit,unit)) = e0
| ~ sP10_prd ),
inference(forward_demodulation,[status(thm)],[f1475,f1817]) ).
fof(f1819,plain,
( op(e1,op(e1,e0)) != e0
| op(unit,op(unit,unit)) = unit
| ~ sP10_prd ),
inference(forward_demodulation,[status(thm)],[f1475,f1818]) ).
fof(f1820,plain,
( op(e1,op(e1,unit)) != e0
| op(unit,op(unit,unit)) = unit
| ~ sP10_prd ),
inference(forward_demodulation,[status(thm)],[f1475,f1819]) ).
fof(f1821,plain,
( op(e1,e1) != e0
| op(unit,op(unit,unit)) = unit
| ~ sP10_prd ),
inference(forward_demodulation,[status(thm)],[f37,f1820]) ).
fof(f1822,plain,
( op(e1,e1) != unit
| op(unit,op(unit,unit)) = unit
| ~ sP10_prd ),
inference(forward_demodulation,[status(thm)],[f1475,f1821]) ).
fof(f1823,plain,
( op(e1,e1) != unit
| ~ sP10_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f1822,f1808]) ).
fof(f1860,plain,
( unit != unit
| ~ sP10_prd ),
inference(backward_demodulation,[status(thm)],[f1551,f1823]) ).
fof(f1861,plain,
~ sP10_prd,
inference(trivial_equality_resolution,[status(thm)],[f1860]) ).
fof(f1874,plain,
op(e3,e3) != e2,
inference(backward_subsumption_resolution,[status(thm)],[f231,f1668]) ).
fof(f1881,plain,
op(e3,e3) != e1,
inference(backward_subsumption_resolution,[status(thm)],[f230,f1677]) ).
fof(f1972,plain,
( op(e2,e2) = e4
| op(e2,e2) = e3
| op(e2,e2) = e2
| op(e2,e2) = unit ),
inference(forward_demodulation,[status(thm)],[f1475,f497]) ).
fof(f1973,plain,
( op(e2,e2) = e4
| op(e2,e2) = e3
| op(e2,e2) = unit ),
inference(forward_subsumption_resolution,[status(thm)],[f1972,f1680]) ).
fof(f1979,plain,
( op(e2,e2) = e4
| op(e2,e2) = e3
| unit != op(e3,e2) ),
inference(paramodulation,[status(thm)],[f1973,f122]) ).
fof(f1983,plain,
( op(e2,e2) = e4
| unit != op(e3,e2) ),
inference(forward_subsumption_resolution,[status(thm)],[f1979,f807]) ).
fof(f1995,plain,
( op(e3,e2) = e4
| op(e3,e2) = e3
| op(e3,e2) = e2
| op(e3,e2) = unit ),
inference(forward_demodulation,[status(thm)],[f1475,f499]) ).
fof(f1996,plain,
( op(e3,e2) = e4
| op(e3,e2) = e3
| op(e3,e2) = unit ),
inference(forward_subsumption_resolution,[status(thm)],[f1995,f1739]) ).
fof(f2024,plain,
( op(e3,e3) = e3
| op(e3,e3) = e2
| op(e3,e3) = e1
| op(e3,e3) = unit ),
inference(forward_demodulation,[status(thm)],[f1475,f706]) ).
fof(f2025,plain,
( op(e3,e3) = e3
| op(e3,e3) = e2
| op(e3,e3) = unit ),
inference(forward_subsumption_resolution,[status(thm)],[f2024,f1881]) ).
fof(f2129,plain,
( op(e2,e2) != unit
| ~ sP5_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f1628,f1861]) ).
fof(f2303,plain,
( op(e3,e2) = e0
| op(e2,e2) = e0
| op(unit,e2) = e0 ),
inference(forward_demodulation,[status(thm)],[f1475,f1043]) ).
fof(f2304,plain,
( op(e3,e2) = e0
| op(e2,e2) = e0
| e2 = e0 ),
inference(forward_demodulation,[status(thm)],[f38,f2303]) ).
fof(f2305,plain,
( op(e3,e2) = e0
| op(e2,e2) = e0
| e2 = unit ),
inference(forward_demodulation,[status(thm)],[f1475,f2304]) ).
fof(f2306,plain,
( op(e3,e2) = e0
| op(e2,e2) = unit
| e2 = unit ),
inference(forward_demodulation,[status(thm)],[f1475,f2305]) ).
fof(f2307,plain,
( op(e3,e2) = unit
| op(e2,e2) = unit
| e2 = unit ),
inference(forward_demodulation,[status(thm)],[f1475,f2306]) ).
fof(f2308,plain,
( op(e3,e2) = unit
| op(e2,e2) = unit ),
inference(forward_subsumption_resolution,[status(thm)],[f2307,f1621]) ).
fof(f2324,plain,
( op(e4,e4) = e0
| op(e4,e3) = e0
| op(e4,unit) = e0 ),
inference(forward_demodulation,[status(thm)],[f1475,f1064]) ).
fof(f2325,plain,
( op(e4,e4) = e0
| op(e4,e3) = e0
| e4 = e0 ),
inference(forward_demodulation,[status(thm)],[f43,f2324]) ).
fof(f2326,plain,
( op(e4,e4) = e0
| op(e4,e3) = e0
| e4 = unit ),
inference(forward_demodulation,[status(thm)],[f1475,f2325]) ).
fof(f2327,plain,
( op(e4,e4) = e0
| op(e4,e3) = unit
| e4 = unit ),
inference(forward_demodulation,[status(thm)],[f1475,f2326]) ).
fof(f2328,plain,
( op(e4,e4) = unit
| op(e4,e3) = unit
| e4 = unit ),
inference(forward_demodulation,[status(thm)],[f1475,f2327]) ).
fof(f2329,plain,
( op(e4,e4) = unit
| op(e4,e3) = unit ),
inference(forward_subsumption_resolution,[status(thm)],[f2328,f1619]) ).
fof(f2351,plain,
( op(e3,e1) = e4
| op(e3,e1) = e3
| op(e3,e1) = e2 ),
inference(forward_subsumption_resolution,[status(thm)],[f1068,f1743]) ).
fof(f2383,plain,
op(e2,e2) = unit,
inference(backward_subsumption_resolution,[status(thm)],[f2308,f2385]) ).
fof(f2384,plain,
( op(e3,e2) = e4
| op(e3,e2) = e3 ),
inference(backward_subsumption_resolution,[status(thm)],[f1996,f2385]) ).
fof(f2385,plain,
unit != op(e3,e2),
inference(forward_subsumption_resolution,[status(thm)],[f1983,f648]) ).
fof(f2386,plain,
op(e3,e2) = e4,
inference(forward_subsumption_resolution,[status(thm)],[f2384,f1668]) ).
fof(f2405,plain,
( unit != unit
| ~ sP5_prd ),
inference(backward_demodulation,[status(thm)],[f2383,f2129]) ).
fof(f2416,plain,
~ sP5_prd,
inference(trivial_equality_resolution,[status(thm)],[f2405]) ).
fof(f2417,plain,
( op(e3,e3) != unit
| ~ sP0_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f1672,f2416]) ).
fof(f2427,plain,
op(e3,e1) != e4,
inference(backward_demodulation,[status(thm)],[f2386,f179]) ).
fof(f2476,plain,
( op(e3,e1) = e3
| op(e3,e1) = e2 ),
inference(backward_subsumption_resolution,[status(thm)],[f2351,f2427]) ).
fof(f2478,plain,
op(e3,e1) = e2,
inference(forward_subsumption_resolution,[status(thm)],[f2476,f1677]) ).
fof(f2495,plain,
e2 != op(e4,e1),
inference(backward_demodulation,[status(thm)],[f2478,f114]) ).
fof(f2506,plain,
( op(e4,e3) = e2
| op(e4,e1) = e2 ),
inference(forward_subsumption_resolution,[status(thm)],[f1632,f764]) ).
fof(f2563,plain,
op(e4,e3) = e2,
inference(backward_subsumption_resolution,[status(thm)],[f2506,f2495]) ).
fof(f2568,plain,
( op(e4,e4) = unit
| e2 = unit ),
inference(backward_demodulation,[status(thm)],[f2563,f2329]) ).
fof(f2579,plain,
op(e4,e4) = unit,
inference(forward_subsumption_resolution,[status(thm)],[f2568,f1621]) ).
fof(f2605,plain,
( unit != unit
| sP0_prd ),
inference(backward_demodulation,[status(thm)],[f2579,f1774]) ).
fof(f2612,plain,
sP0_prd,
inference(trivial_equality_resolution,[status(thm)],[f2605]) ).
fof(f2621,plain,
( op(e3,e3) = e3
| op(e3,e3) = e2 ),
inference(backward_subsumption_resolution,[status(thm)],[f2025,f2622]) ).
fof(f2622,plain,
op(e3,e3) != unit,
inference(forward_subsumption_resolution,[status(thm)],[f2417,f2612]) ).
fof(f2623,plain,
op(e3,e3) = e3,
inference(forward_subsumption_resolution,[status(thm)],[f2621,f1874]) ).
fof(f2624,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f2623,f1667]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG065+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.02/0.36 % Computer : n002.cluster.edu
% 0.02/0.36 % Model : x86_64 x86_64
% 0.02/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.36 % Memory : 8046.5625MB
% 0.02/0.36 % OS : Linux 6.8.0-71-generic
% 0.02/0.36 % CPULimit : 300
% 0.02/0.36 % WCLimit : 300
% 0.02/0.36 % DateTime : Mon Sep 21 12:57:49 UTC 2026
% 0.02/0.36 % CPUTime :
% 0.02/0.38 % Drodi V4.1.1
% 0.02/0.45 % Refutation found
% 0.02/0.45 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.02/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.02/0.47 % Elapsed time: 0.098885 seconds
% 0.02/0.47 % CPU time: 0.454029 seconds
% 0.02/0.47 % Total memory used: 122.986 MB
% 0.02/0.47 % Net memory used: 122.552 MB
%------------------------------------------------------------------------------